Unravelling the Creep Behavior of Equiatomic CoCrFeMnNi High-Entropy Alloy Foam: A Molecular Dynamics Study

Unravelling the Creep Behavior of Equiatomic CoCrFeMnNi High-Entropy Alloy Foam: A Molecular Dynamics Study | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Unravelling the Creep Behavior of Equiatomic CoCrFeMnNi High-Entropy Alloy Foam: A Molecular Dynamics Study Ezekiel Edward Nettey-Oppong, Emmanuel Essel Mensah, Stephen Takyi Taylor, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6344719/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 20 Aug, 2025 Read the published version in Multiscale and Multidisciplinary Modeling, Experiments and Design → Version 1 posted 13 You are reading this latest preprint version Abstract High-entropy alloys (HEAs) are a class of materials distinguished by their unique multi-element compositions, offering exceptional mechanical properties such as high strength and thermal stability. Recently, HEA foams have been fabricated, offering several additional advantages over traditional solid HEAs. These include reduced density, which enhances their suitability for lightweight structural applications, and enhanced energy absorption. In this study, molecular dynamics simulations were used to investigate the creep deformation mechanisms of equiatomic CoCrFeMnNi HEA foam under varying conditions, including temperatures of 1300 K, 1600 K, and 1900 K, pressures ranging from 5 to 8 GPa, and porosities from 0–30%. The results demonstrated that an increase in temperature led to higher strain values, particularly in models with porosities below 15%. Structural analysis reveals a reduction in the face-centered cubic (FCC) phase with increasing temperature, accompanied by an increase in amorphous structures and Shockley partial dislocation activity. Dislocation networks became more complex with increasing porosity, with the high dislocation densities observed at high porosities and temperature. Further mean square deviation (MSD) and radial distribution function (RDF) techniques helped elucidate the atomic-scale changes in the HEA structure, showing the significant interplay between temperature, pressure, and porosity on material stability. This study provides valuable insights into the creep behavior and dislocation dynamics of HEA foams, contributing to the optimization of these materials for high-performance applications in extreme environments. High entropy alloys Metal foams Creep Molecular dynamics simulation Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 1. Introduction High entropy alloys (HEAs) represent a novel class of alloys that are distinguished by their unique compositional and structural characteristics [ 1 ]. Unlike traditional alloys that are primarily composed of a single principal element with small amounts of alloying elements, HEAs are composed of five or more principal elements in equal or near-equal atomic proportions [ 1 , 2 ]. This high degree of compositional complexity results in a significantly higher configurational entropy compared to conventional alloys [ 3 ]. The increased entropy stabilizes a single-phase solid solution structure, often a simple face-centered cubic (FCC) or body-centered cubic (BCC) lattice, which can lead to enhanced mechanical properties and improved resistance to deformation[ 4 – 6 ]. High entropy alloys exhibit a broad range of mechanical properties, including high strength, hardness, and excellent wear resistance where materials are exposed to extreme conditions [ 7 , 8 ]. These exceptional properties of HEAs make them ideal for demanding applications in industries. HEAs are increasingly used in the production of exhaust nozzles and gas turbine casings in gas turbine engines, where high thermal stability and resistance to wear and corrosion are crucial [ 9 , 10 ]. Additionally, HEAs are being investigated for use in nuclear reactors, where their ability to withstand high radiation doses and extreme temperatures offers significant advantages[ 7 – 12 ]. The development of HEAs has opened new avenues for material design and innovation. Research into HEAs is ongoing to understand their fundamental behaviors, such as phase stability, thermal conductivity, and diffusion characteristics[ 13 , 14 ]. Additionally, advanced characterization techniques and computational methods, including molecular dynamics simulations, are increasingly employed to explore and predict the properties of HEAs under various conditions. Ongoing research aim to optimize HEA compositions and processing methods, further expanding their potential applications and enhancing their performance in various engineering domains. Although the mechanical and thermal properties of HEAs have received much attention, little is known of their behavior under creep conditions. Creep, a time-dependent deformation phenomenon that occurs when materials are subjected to prolonged loading at elevated temperatures, is a crucial mechanical feature that has a substantial impact on the integrity and durability of materials under high stress and thermal conditions [ 15 , 16 ]. Under such conditions, materials experience deformation behavior that reduces their lifespan, decreases thermal stability and results in material softening. The importance of creep is seen in a variety of applications, from gas turbine blades to parts of power plants, necessitating a thorough understanding of the phenomena to ensure that materials can resist lengthy exposure to high temperatures and mechanical pressures [ 17 – 19 ]. Jo et al [ 20 ] studied the high-temperature tensile and creep properties of CrMnFeCoNi and CrFeCoNi high-entropy alloys between 500–725°C to assess their structural integrity. While both alloys exhibited similar tensile behavior, CrFeCoNi demonstrated significantly longer creep rupture life, lower minimum creep rate, and higher creep activation energy. The improved performance was due to greater lattice distortion, enhancing solid solution strengthening. However, grain boundary weakening was experienced due to sigma phase formation during creep, leading to reduced elongation in long-term conditions. The study by Liu et al [ 21 ] examined the creep behavior of HfNbTaTiZr high-entropy alloy with large grain size, tested at 1100–1250°C and stress levels of 5–30 MPa in a vacuum. Creep was governed by the solute drag mechanism, with stress exponents of 2.5–2.8 and activation energies of 273 ± 15 kJ mol⁻¹. TEM analysis showed that dislocations dominated plastic deformation, leading to grain boundary bulging and migration. The creep rate was controlled by the diffusivity of Ta, which has the lowest diffusion coefficient and restricts dislocation movement. These findings offer guidance for designing refractory HEAs with enhanced creep resistance. Wang et al [ 22 ] developed and characterized a novel HEA, Ti 30 Al 25 Zr 25 Nb 20 , with a single body-centered cubic (BCC) structure. The Young's modulus and nano-hardness were found to be 158.2 ± 5.2 GPa and 8.9 ± 0.2 GPa, respectively. Creep behavior was investigated at 20°C using nano-indentation across various loading rates and peak loads. Results revealed that creep displacement increased with loading rates and peak loads, while the creep strain rate sensitivity index initially decreased before increasing again. This behavior was attributed to dislocation activation volume and hysteresis diffusion effects. Compared to other metallic materials, Ti 30 Al 25 Zr 25 Nb 20 HEA demonstrated a high dislocation activation volume and a low creep strain rate sensitivity index, reflecting its excellent creep resistance. The development of advanced computational tools, such as molecular dynamics (MD) simulations, has significantly enhanced the ability of researchers to investigate the complex atomic-level mechanisms governing material behavior [ 23 – 25 ]. This technological advancement facilitates a thorough examination of fundamental processes involved in creep deformation within intricate alloys, offering valuable insights that complement experimental research. By utilizing empirical interatomic potentials to model atom-to-atom interactions, MD simulations enable the replication of material responses under various temperature and stress conditions [ 26 , 27 ]. This approach allows for the detailed analysis of phenomena such as grain boundary interactions and dislocation mobility [ 28 ], which are critical to understanding creep behavior. Moreover, MD simulations provide a platform for exploring experimental variables that are difficult to manipulate in practical settings, such as temperature gradients and strain rates. As a result, these simulations offer a comprehensive understanding of how imperfections, impurities, and microstructural features influence creep deformation and the mechanical properties of materials. Zhao et al [ 29 ] employed molecular dynamics simulations to explore how temperature, pressure, and grain size affect the high-temperature creep properties of nanocrystalline TiAl alloy. It was shown that increasing temperature and stress significantly enhance the steady-state creep rate and accelerate the rapid creep stage, with smaller grain size further promoting the creep process due to larger proportion of grain boundaries. The creep mechanisms varied with stress levels: dislocation motion dominated at high-stress conditions, while diffusion creep was more prevalent at low-stress conditions. During the rapid creep stage, grain boundary and lattice diffusion were the primary mechanisms driving deformation. Li et al [ 30 ] investigated the dynamic mechanical properties of FeNiCoCrCu high-entropy alloy under tension and compression using molecular dynamics simulations. The findings revealed that at low strain rates, the alloy does not exhibit plastic deformation, but at higher strain rates e 11 s − 1 , it underwent distinct stages of elastic deformation, yielding, and plastic deformation, with increased yield strength. High tensile strain rates lead to stacking faults that enhanced material strength by preventing slip, while Frank dislocations initiated plastic deformation and dislocation interactions stabilize this process. For high strain rate compression, stress relaxation was driven by stacking fault formation, and strain hardening is achieved through twinning and dislocation interactions. In this study, we undertake Molecular Dynamics simulations to conduct an in-depth exploration of the atomistic mechanisms governing the creep deformation observed in foam structures composed of the equiatomic CoCrFeMnNi alloy. Furthermore, an examination of the influence exerted by pressure and porosity on the response of the alloy to creep is studied. The primary objective of this work is to provide a thorough understanding of alloy stability, mechanical properties, and suitability for demanding applications. 2. Computational Method 2.1 HEA Modeling Understanding the atomic-level mechanical behavior of HEAs is crucial for developing advanced materials with superior properties. Molecular dynamics simulation is a powerful tool for this purpose, allowing researchers to investigate the fundamental interactions that govern material performance. In this study, we conducted molecular dynamics simulations using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) [ 31 ]. The simulation was carried out on a cubic lattice structure representing an alloy composed of 20% Cobalt (Co), 20% Chromium (Cr), 20% Iron (Fe), 20% Manganese (Mn), and 20% Nickel (Ni). Figure 1 presents the modeled FCC CoCrFeMnNi equiatomic high-entropy alloy structure, illustrating the spatial arrangement and distribution of individual elements in the system. In this equiatomic HEA, each element is equally distributed, contributing to the stability and mechanical properties of the alloy. The cubic cell length of the structure measured 108 Å, ensuring that the system size is sufficiently large to model the atomic interactions and structural behavior of the alloy under varying conditions. The simulation box was initialized in three dimensions with periodic boundary conditions in all directions. The FCC lattice structure was selected, with a lattice constant of 3.6 Å, and the simulation box had dimensions of 30 lattice units in each direction. Atoms were created within this box, with the respective element fractions assigned randomly. The atomic masses for Co, Cr, Fe, Mn, and Ni were set according to their standard values. The simulations were performed on 7 models based on cubic lattice structures with varying porosities(0%, 5%, 10%, 15%, 20%, 25%, and 30%). 2.2 HEA Foam Modeling To model nanoporous HEA structures, spherical pores were introduced at random locations within the simulation cell, as shown in Fig. 1 (b). The template used for generating pores involved a 3D model where spheres were randomly inserted, and the resulting coordinates dictated the pore locations in the foam structures. These voids were introduced to simulate porosities, a critical feature in modeling foam structures. Some voids are located within the bulk of the material, while others are positioned on the surface. The presence of surface voids is of particular importance since pores significantly influence the mechanical properties and deformation mechanisms of the HEA foam under applied loads. The controlled distribution of voids allows for a systematic study of how porosity levels affect the overall behavior of the alloy during creep simulations. The method aimed to replicate the regular spherical pore geometry observed in experimental HEA foams. In Fig. 1 (c), the resulting HEA foam structure is depicted after void incorporation. The foam-like structure, with defined pore sites, represents a porous material that can be evaluated for mechanical performance, including strength, ductility, and resistance to deformation under high temperature and pressure conditions. This visual representation of the HEA foam highlights the potential for tailoring porosity to enhance the material's properties for specific applications. Unlike conventional methods for creating metal foam structures, this approach eliminated isolated atoms in the voids, improving the accuracy of modeling multi-component systems. Further details of our HEA model and simulation can be found in our previous studies [ 28 ]. Briefly, the conventional approach to constructing foam structures relies on utilizing the physical properties of atoms to create spatial filters that generate pore sites [ 32 , 33 ]. This method, however, isolates atoms in the resulting voids and faces significant challenges when applied to multi-component systems, such as high-entropy. In traditional metal foam modeling, a sacrificial crystal structure is heated above its melting point to form a spatial filter, where atoms with temperatures exceeding a set threshold are removed until a desired fill factor is reached. Subsequently, isolated atoms and clusters are removed using a cluster detection method [ 34 ]. The spatial filter is then applied to the nonporous crystalline metal to eliminate excess atoms. This technique is unsuitable for HEAs, which consist of several elements. During heating, equilibrium fluctuations cause certain elements to experience greater temperature variations than others, leading to uneven atom removal when a cut-off temperature is applied. As a result, the spatial filter would preferentially eliminate specific elements, altering the alloy's molar ratio and producing a foam structure with a different composition than the original. Furthermore, spatial filters prevent the modeling of foam structures with precise pore locations, and even though using a single-element crystal structure can mitigate molar ratio changes, atom removal remains random. Consequently, the conventional method is inadequate for modeling HEA foams making it difficult to assess the impact of porosity on mechanical properties. 2.3 Interatomic Potential and Melting Temperature Evaluation The recently developed pair potential by Gröger et al.[ 35 ] for random FCC CoCrFeMnNi high-entropy alloys was employed to model interatomic interactions. To assess the accuracy of this potential, a liquid-to-solid quench simulation was performed under an isothermal-isobaric (NPT) ensemble, where the system was heated to 1200 K and rapidly quenched to 70 K. Figure 2 provides a comprehensive analysis of the atomic structure and thermodynamic properties of the CoCrFeMnNi equiatomic high-entropy alloy (HEA) system, using Common Neighbor Analysis (CNA) and potential energy-temperature relationship. Figure 2 a depicts the results of the CNA of the final structure after the quenching process, which confirms that all atoms in the system have retained their face-centered cubic (FCC) configuration. The ability to maintain a 100% FCC atom arrangement throughout the simulation highlights the structural stability of the HEA, even after thermal treatment. This result validates the accuracy and reliability of the chosen interatomic potential for modeling the CoCrFeMnNi system. The retention of the FCC structure after quenching is important, as the crystal structure can significantly impact the mechanical properties. Moreover, it indicates that no phase transformations occurred during the quenching process, ensuring that the material maintains its equiatomic distribution and structural integrity. Figure 2 b shows the relationship between potential energy and temperature, with a pronounced shift in potential energy observed around 2000 K. This distinct change serves as an indicator of the melting point of the material. As the temperature increases, the system undergoes a gradual increase in potential energy until a critical point is reached, where the energy rises sharply, suggesting the onset of the phase transition from solid to liquid. The temperature at which this significant change occurs provides an estimate of the melting point of the CoCrFeMnNi HEA. This information is crucial for understanding the thermal stability and processing limits of the material. Determining the melting point enables precise control over processes such as casting, forming, and heat treatments, while also providing critical insights into the behavior of HEA under extreme conditions. This information is particularly important for establishing the appropriate cutoff temperature for the creep study, ensuring accurate simulation of the material's high-temperature performance. The clear correlation between temperature and potential energy further demonstrates the thermodynamic behavior of the alloy, offering essential information about its phase stability and transition mechanisms. 2.4 Creep Simulation Details For the creep simulations, the modeled structures underwent energy minimization and equilibration at different temperatures using the Velocity-Verlet integration scheme and a timestep of 0.005 ps, with the Nose-Hoover barostat ensuring constant pressure throughout the process. To prepare the systems, the potential energy for each system was minimized using the steepest descent method. This step relaxed the system, allowing for energy convergence and eliminating any residual stress. The system was equilibrated at 300 K using the Nose-Hoover thermostat to maintain a stable temperature. A constant pressure and temperature ensemble (NPT) was used, ensuring isotropic conditions. This equilibration phase ran for 100 ps, after which spherical voids were introduced to create porosities corresponding to the different models. To simulate creep behavior, the temperature and pressure conditions were varied across a range of values. Temperatures of 1300 K, 1600 K, and 1900 K were employed, while the pressure was varied at 5 GPa, 6 GPa, 7 GPa, and 8 GPa. The system underwent equilibration at each temperature and pressure combination to ensure stability before creep deformation simulations were initiated. Notably, the variation in porosity was determined by calculating the radius of each void through numerical methods to achieve the desired percent porosity, using the mathematical expression: $$\:\%P=\frac{{V}_{P}}{{V}_{T}}\times\:100\%$$ 1 where %P represents the percent porosity, V P is the pore volume, and V T is the total volume. The creep simulations involved applying compressive stress along the x-axis under constant temperature and pressure conditions, while maintaining stress-free boundaries in the y and z directions. Strain was calculated continuously by monitoring changes in the box length in the x-direction, and the simulation results were recorded over 300 ps. Strain, temperature, pressure, and other key parameters were output at regular intervals, and atomistic configurations were recorded for further analysis. The output from the simulation included data on temperature, potential energy, pressure, and strain, recorded at intervals throughout the simulation. These results were used to analyze the strain-time relationship during the creep process. Additionally, atomistic configurations were recorded at regular intervals for visualization and further analysis. The strain was calculated using the following formula in the direction of the applied sustained stress. $$\:E=\:\frac{l-\text{l}\text{o}}{lo}$$ 2 where, l is the instantaneous length of the cubic sample under applied stress and l o is the undeformed length of the cubic sample. Diffusive properties of the modeled HEA systems were measured using mean square displacement (MSD) defined as: MSD = \(\:⟨\frac{1}{N}\sum\:_{i=0}^{N}{(ri\left(t\right)-ri\left(0\right))}^{2}⟩\) (3) where, N is the particle number, t is time, and r is the distance a specific particle travels over time at different constant temperatures. The Radial Distribution Function (RDF or g(r)), also referred to as the pair correlation function, describes the variation in particle density with respect to distance from a reference particle within a system. It offers valuable information about the local structure of a material by examining how atoms or molecules are spatially arranged relative to each other. The RDF or g(r) can be expressed as: $$\:g\left(r\right)=\:\frac{⟨p\left(r\right)⟩}{{p}_{bulk}}$$ 4 where \(\:⟨p\left(r\right)⟩\) is the local density at a distance r from the reference atom, and \(\:{p}_{bulk}\) is the average bulk density of the atoms. Visualization and analysis were done using OVITO [ 36 ]. The dislocation extraction algorithm (DXA) was used to extract the dislocation planes of the foam structure. To effectively investigate creep deformation in CoCrFeMnNi HEA foam, it is essential to precisely determine its response within the relevant ranges of these parameters. To achieve this, we subject the HEA sample to different temperature, pressure and porosity conditions. By conducting these simulations, we can accurately determine the critical thresholds at which the CoCrFeMnNi HEA foam displays significant creep deformation. This knowledge is pivotal for designing and conducting experiments focused on creep behavior under different temperature, pressure and porosity settings, ensuring that appropriate conditions are selected to comprehensively explore the mechanical properties of the alloy and its response to pressure and porosity-induced deformation. 3. Results and Discussion 3.1 Creep Deformation Behavior The study of the creep deformation behavior of CoCrFeMnNi high-entropy alloy foams revealed consistent trends across all tested models, highlighting a linear relationship between strain and time. This linearity signifies a steady rate of deformation under applied conditions, irrespective of the temperature or porosity variations. Such behavior is critical for materials used for long-term applications under sustained loads, as it allows for more accurate predictions of material performance over extended periods. The steady nature of the deformation rate, particularly in the linear phase, suggests that the HEA foams exhibit predictable mechanical properties, which are essential for reliable material design and engineering applications under high-temperature or high-stress environments [ 37 ]. At a constant pressure of 7 GPa, the strain against time plots as shown in Fig. 3 for the various porosities and temperatures show that deformation behavior remains generally consistent, with strain increasing continuously over time. Figure 3 a-g illustrates the creep deformation behavior of the CoCrFeMnNi HEA foam under constant pressure (7 GPa) and varying temperatures (1300 K, 1600 K, and 1900 K) for different porosities (0–30%). The strain against time plots highlight a linear increase in strain across all porosity levels, with higher temperatures generally leading to greater strain, especially at lower porosities. Additionally, simulation snapshots as shown in Fig. 3 h, depict the structural evolution of the bulk HEA foam (0% porosity) during the deformation process, showing the transition from a fully FCC configuration before deformation to a partially FCC state during deformation, and finally, a completely amorphous structure after deformation. This structural transition demonstrates the shift in mechanical properties of the material as creep progresses. The linear trend across all temperature and porosity variations reinforces the robustness of the material under varying thermal conditions, making it suitable for high-temperature creep applications. These results indicate that the CoCrFeMnNi HEA foam possesses a high tolerance for creep deformation, which is essential for structural components that must withstand prolonged thermal exposure. 3.2 Effect of Porosity on Creep Deformation Behavior Porosity was found to significantly influence the strain behavior in the HEA foam. As outlined in Table 1 , strain values consistently increased with higher porosity levels over the simulation period of 300 ps. At 1300 K, the bulk HEA—0% porosity—exhibited a final strain of 0.239, while the system with 30% porosity displayed a significantly higher strain of 0.456. This trend suggests that porosity acts as a facilitator for deformation by creating stress concentrators within the HEA foam structure. The higher porosity led to localized areas of intense strain, where deformation is more likely to initiate and propagate. As a result, materials with greater porosity experience intense deformation due to the amplification of local stress around these voids. Furthermore, as porosity increases, the capacity of the HEA foam to sustain mechanical loading diminishes, leading to higher overall strain values. This behavior is particularly relevant for applications requiring materials with specific mechanical properties, as controlling the porosity can directly influence the performance of the foam under load. In higher-porosity HEA foams, the interaction of stress concentrators and voids drives significant deformation, potentially leading to early material failure if subjected to long term mechanical loads [ 38 ]. Table 1 Final strain values under creep deformation for the modeled CoCrFeMnNi HEA foams at different porosities and temperatures. Porosity (%) 1300 K 1600 K 1900 K 0 0.239 0.299 0.304 5 0.285 0.321 0.318 10 0.320 0.334 0.326 15 0.356 0.358 0.333 20 0.388 0.377 0.342 25 0.421 0.398 0.362 30 0.456 0.421 0.382 3.3 Effect of Temperature on Creep Deformation Behavior Temperature variations also played a significant role in the strain behavior of the HEA foam, particularly at lower porosity levels. As shown in Table 1 , an increase in temperature from 1300 K to 1900 K led to higher strain values in the models with porosities below 15%. At 0% porosity, the final strain at 1300 K was 0.239, compared to 0.304 at 1900 K. This increase in strain with rising temperature is consistent with the softening of the foam as atomic mobility increases, allowing for easier dislocation movement and enhanced plastic deformation. The temperature-dependent strain behavior in low-porosity HEA foams suggests that the HEA becomes more susceptible to creep deformation as the temperature rises, a critical factor for materials operating in high-thermal environments. Interestingly, this temperature-dependent trend is reversed for HEA foams with porosities of 15% and above. In these higher-porosity models, increasing the temperature from 1300 K to 1900 K led to a reduction in strain. At 30% porosity, the strain decreased from 0.456 at 1300 K to 0.382 at 1900 K. This unexpected behavior may be attributed to the increased size of voids and defects in the HEA foam’s structure at higher porosity levels. These defects can impede dislocation movement, counteracting the usual effect of increased atomic mobility at elevated temperatures [ 39 ]. As a result, despite the higher thermal energy available at 1900 K, the structural defects limit the ability of the HEA foam to deform, leading to a decrease in overall strain. This observation points to a shift in the deformation mechanism of the material, where the foam transitions from ductile to more brittle-like behavior as both temperature and porosity increase [ 40 ]. The interaction between microstructural defects and thermal effects plays a pivotal role in determining the mechanical response of the HEA foam under these conditions. 3.4 Mean Square Displacement (MSD) Analysis The mean square displacement (MSD) provides a quantitative measure of atomic mobility within the CoCrFeMnNi HEA foam [ 41 ]. As temperature increases, MSD values rise significantly, indicating that higher thermal energy leads to greater atomic displacement from their initial lattice positions. At 1300 K, the atomic motion remains relatively constrained, resulting in lower MSD values across all porosity levels. As outlined in Table 2 , the bulk material with 0% porosity exhibited an MSD of 64.134 Ų at 1300 K, reflecting limited atomic mobility. In contrast, at 1900 K, the MSD for the same material increased to 730.188 Ų, demonstrating a significant rise in atomic vibrations as temperature climbs. The effect of temperature on MSD becomes more pronounced with increased porosity. Table 2 MSD values for CoCrFeMnNi HEA foam at different porosity levels and temperatures. Porosity (%) 1300 K 1600 K 1900 K 0 64.134 403.503 730.188 5 141.594 700.935 1048.321 10 223.872 940.897 1339.780 15 375.566 1002.116 1602.523 20 443.619 937.7177 1647.554 25 584.580 1215.419 1804.552 30 652.888 1167.987 1726.400 The introduction of voids within the foam allows for greater freedom of atomic movement, which is reflected in the MSD values. At 5% porosity, the MSD at 1300 K was 141.594 Ų, which increased to 1048.321 Ų at 1900 K. Similarly, for 30% porosity, the MSD values rose from 652.888 Ų at 1300 K to 1726.400 Ų at 1900 K. This trend clearly demonstrates the combined influence of temperature and porosity on atomic mobility: as the material becomes more porous, the MSD increases further, highlighting the reduction in structural integrity and creep resistance. The relationship between MSD and porosity is evident across all temperature ranges. In the bulk HEA (0% porosity), atoms are tightly packed, and their movements are constrained by neighboring atoms, leading to lower MSD values. However, as porosity increases, the atomic arrangement becomes more irregular, with voids allowing for greater freedom of movement. This behavior is further illustrated in Fig. 4 , which shows the MSD analysis of the CoCrFeMnNi HEA foam under constant pressure (7 GPa) at varying temperatures of 1300 K, 1600 K, and 1900 K for different porosity levels. The strain against time plots shown in Fig. 4 a-g, for each porosity level clearly depict the increase in strain with rising temperature and porosity. Additionally, Fig. 4 h depicts the simulation snapshots of the HEA foam with 5% porosity before, during, and after deformation provide a visual representation of the atomic arrangement. Similar to the bulk material before deformation, the atoms maintain a fully FCC configuration, while during deformation, the FCC structure partially collapses. After deformation, the structure becomes fully amorphous, indicating the severe impact of atomic mobility on the material's structural integrity. At 30% porosity, the MSD values are significantly higher at each temperature, with the largest deviation from the lattice structure occurring at 1900 K. This increase in atomic displacement at higher porosities is a direct consequence of the reduced atomic density, which allows for greater mobility and increases the susceptibility of the foam to deformation. The combined effect of elevated temperatures and increased porosity results in a pronounced rise in MSD values, which correlates with a decrease in the material's creep resistance. As atoms move more freely, particularly under high-temperature conditions, the material becomes more prone to sustained deformation under mechanical loading. The reduction in atomic coordination and bonding due to the presence of voids, coupled with increased thermal vibrations, weakens the structural framework of the HEA foam, leading to a reduction in its resistance to creep. 3.5 Radial Distribution Function (RDF) Analysis The radial distribution function (RDF) is a vital tool for understanding the atomic arrangement within the CoCrFeMnNi high-entropy alloy (HEA), particularly in relation to the effects of temperature and porosity. RDF measures the probability of finding atoms at specific interatomic distances, providing key insights into the structural coherence of the material [ 42 ]. temperature increases, the RDF analysis reveals a significant reduction in the height of the peaks, indicating a decrease in the structural order of the HEA. Figure 5 a-g illustrates the changes in the radial distribution function (RDF) of CoCrFeMnNi HEA foam under varying temperature and porosity conditions. Simulation snapshots depicted in Fig. 5 h of the HEA foam (15% porosity) reveal the transition from a fully FCC atomic arrangement before deformation to an amorphous structure after deformation, with stacking faults observed. At lower temperatures, such as 1300 K, the RDF peaks are more pronounced, signifying that the atomic arrangement remains relatively well-ordered. However, as the temperature rises to 1600 K and 1900 K, the peaks gradually decrease in height, reflecting the increased thermal vibrations that cause atoms to deviate from their equilibrium positions. This decrease in peak height is a direct result of the enhanced atomic mobility due to higher thermal energy, which causes the atoms to vibrate more vigorously, increasing the interatomic distances and reducing the likelihood of finding atoms at specific distances. At 1300 K, the RDF peaks indicate a higher probability of finding atoms at characteristic distances due to the coherent structure of the material. As the temperature rises to 1900 K, the peak heights diminish, indicating that thermal motion has expanded the lattice and weakened atomic bonds. The expansion of the HEA at elevated temperatures results in the increased separation of atoms, reducing the likelihood of atomic interactions at regular intervals [ 43 ]. This reduction in atomic coherence is a critical factor contributing to the degradation of mechanical properties, including reduced creep resistance and elastic modulus, as the material becomes more susceptible to sustained deformation under thermal and mechanical stress. In addition to the influence of temperature, porosity also plays a critical role in altering the atomic arrangement within the HEA. As porosity increases from 0–30%, the voids introduced into the structure lead to a significant reduction in RDF peak heights, particularly at higher temperatures. In the bulk CoCrFeMnNi HEA with no porosity, the RDF peaks are sharper and higher, indicating a well-ordered atomic lattice where atoms are tightly packed. As porosity increases, the presence of voids disrupts the regular atomic arrangement, leading to a broader distribution of interatomic distances and a decrease in RDF peak heights. At 30% porosity, the RDF peaks are significantly lower and broader compared to the material with 0% porosity. This behavior is attributable to the increased average interatomic distances caused by the voids in the structure. The introduction of voids reduces the number of neighboring atoms, leading to greater atomic disorder. As a result, the likelihood of finding atoms at expected distances diminishes, reflecting a weakening of the atomic bonding network. This structural disorganization is exacerbated by the concurrent effects of elevated temperature, which further weakens atomic bonds and reduces the mechanical integrity of the foam. The combined effects of increasing temperature and porosity result in a marked reduction in the RDF peak heights, indicating a significant loss of structural coherence in the HEA. The voids created by porosity, combined with the thermal expansion of the lattice at elevated temperatures, reduce the bonding energy between atoms, making the material more susceptible to deformation under sustained stress. This is particularly evident at higher porosity levels (30%) and elevated temperatures (1900 K), where the atomic arrangement becomes increasingly disordered. The reduction in RDF peak heights, coupled with a broader distribution of interatomic distances, reflects the gradual degradation of the atomic structure, leading to weakened mechanical properties such as reduced creep resistance. 3.6 Effect of Pressure on Creep Deformation Behavior The creep behavior of the modeled CoCrFeMnNi high-entropy alloy (HEA) foams was evaluated at a constant temperature of 1900 K across varying pressures of 5 GPa, 6 GPa, 7 GPa, and 8 GPa and porosity levels. Figure 6 illustrates the impact of varying pressure on creep deformation in CoCrFeMnNi HEA at a constant temperature of 1900 K, across different porosity levels. The strain vs. time plots Fig. 6 a-g reveal a clear increase in strain as pressure rises from 5 GPa to 8 GPa, with higher porosity materials consistently showing more significant deformation. Snapshot Fig. 6 h captures the structural changes in the 30% porosity HEA foam during the creep process, progressing from a fully FCC configuration before deformation to a partially FCC structure during deformation, and finally to an amorphous state, indicating stacking faults and the onset of dislocation-driven mechanisms. This highlights the combined effects of pressure and porosity on accelerating creep deformation. The findings indicate a clear relationship between increasing pressure and strain, as well as the amplifying effect of porosity on the susceptibility of the material to deformation. As shown in Table 3 , at 5 GPa and 0% porosity, the strain value is 0.256. As pressure increases to 6 GPa, the strain increases to 0.281, and further rises to 0.304 and 0.326 at 7 GPa and 8 GPa, respectively. This trend of increasing strain with pressure is consistent across all porosity levels, highlighting that higher pressures significantly accelerate creep deformation. At 30% porosity, the strain value under 5 GPa is 0.312, increasing to 0.348 at 6 GPa, 0.382 at 7 GPa, and peaking at 0.415 under 8 GPa. This shows that the foam becomes increasingly susceptible to deformation as both pressure and porosity rise. The influence of porosity is particularly evident when comparing different porosity levels at a constant pressure. Under 7 GPa, the strain value for 0% porosity is 0.304, while for 30% porosity, it is significantly higher at 0.382, reflecting the pronounced effect of porosity on the deformation behavior of the foam. As porosity increases, the introduction of voids into the HEA disrupts the atomic lattice and weakens atomic bonding, making the material more prone to deformation. This effect is exacerbated at higher pressures, where the presence of voids amplifies the material's response to external forces, as shown by the consistently increasing strain values across porosity levels and pressures. Table 3 Strain values for CoCrFeMnNi HEA under varying pressures (5 GPa, 6 GPa, 7 GPa, and 8 GPa) at a constant temperature of 1900 K, across different porosity levels (0–30%). Porosity (%) 5 GPa 6 GPa 7 GPa 8GPa 0 0.256 0.281 0.304 0.326 5 0.267 0.292 0.318 0.341 10 0.270 0.299 0.326 0.352 15 0.274 0.305 0.333 0.360 20 0.279 0.311 0.342 0.372 25 0.289 0.329 0.362 0.393 30 0.312 0.348 0.382 0.415 Increased pressure enhances atomic mobility and dislocation motion, facilitating creep deformation [ 44 ]. At elevated pressures, such as 8 GPa, the external forces cause atoms to rearrange more easily within the lattice, which leads to greater sustained deformation over time. The introduction of porosity further exacerbates this behavior, as the voids serve as stress concentrators that increase local stress and allow for easier atomic movement. As a result, the strain response is more pronounced in the HEAs with higher porosity, particularly at elevated pressures. Thus, the creep behavior of CoCrFeMnNi HEA at 1900 K is strongly influenced by both pressure and porosity. The strain values progressively increase from 0.256 at 5 GPa to 0.415 at 8 GPa across different porosity levels, with higher porosity materials exhibiting greater susceptibility to deformation. These results demonstrate the critical role of pressure and porosity in determining the long-term mechanical performance and durability of HEAs, especially in high-temperature, high-pressure environments commonly encountered in industrial applications. 3.7 Creep Deformation Mechanism of HEA Foam The creep deformation mechanism in CoCrFeMnNi high-entropy alloy (HEA) foam is heavily influenced by its microstructural evolution, dislocation activity, and porosity. The creep deformation structure and dislocation analysis focused on the effects of variable percent porosity and temperature. The structural analysis revealed the presence of various atomic arrangements, including amorphous, FCC, and HCP phases, with an emphasis on stacking faults. The dislocation analysis identified several types of dislocations characterized by their segment types, specifically the Shockley partial dislocations (1/6 ), Stair-rod dislocations (1/6 ), and Hirth dislocations (1/3 ). It is important to note that the analysis of dislocation propagation was conducted by considering the data collected ten frames after the initial occurrence or initiation of the dislocations. This comprehensive examination provided insights into the relationship between porosity and dislocation behavior under elevated temperature and constant pressure conditions. Figure 7 presents snapshots of the dislocation behavior—nucleation and propagation—observed in HEA foams during creep deformation, highlighting significant changes associated with varying levels of porosity. As porosity increases, the microstructures transition from being predominantly FCC to exhibiting a higher prevalence of amorphous structures. This transformation is accompanied by the promotion of Shockley partial dislocations, which become more prominent at higher porosities. Furthermore, the emergence of Stair-rod and Hirth dislocations indicates the development of more complex dislocation interactions within the material. These observations demonstrate the critical influence of porosity on the deformation mechanisms in HEA foams, illustrating how structural changes can alter the fundamental creep behavior of the material under stress. 3.8 Structure and Dislocation Evolution in Creep Deformation of HEA Foam 3.8.1 Effect of Porosity The analysis of the dislocation behavior in the HEA foam structures under creep conditions revealed a strong dependency on the percent porosity of the material. At 0% porosity, dislocation nucleation and propagation mechanisms were dominated by FCC structures, with 59.9% and 33.6% of the structure composed of FCC lattice in the nucleation and propagation stages, respectively. As porosity increased, a gradual transition occurred, with a significant rise in the contribution of amorphous atomic arrangements. At 5% porosity, the nucleation stage had 27.1% of amorphous structures, and by the propagation stage, this proportion increased to 72.8%. At higher porosity levels, such as 30%, the propagation stage contained up to 62.2% amorphous content. The percentage of HCP (hexagonal close-packed) structures remained low across all porosities, but it was noteworthy that as porosity increased, HCP appeared more frequently in the propagation stages. At 0% porosity, HCP content was entirely absent, but at 10% porosity, it rose to 0.7% in the propagation stage. This trend continued up to 1.4% at 30% porosity. This increase in HCP likely correlated with the formation of stacking faults within the crystal structure, as discussed in relation to Shockley partial dislocations. Dislocation activity, specifically the generation of Shockley partials, played a significant role in the deformation of the HEA foam. At 0% porosity, nucleation produced only one Shockley partial dislocation, but this number grew substantially with increased porosity. At 10% porosity, nucleation resulted in 18 Shockley partials, and propagation generated as many as 31. The maximum number of Shockley dislocations appeared at higher porosities during the propagation stage, where up to 39 segments were observed. This high number of Shockley partials indicated that stacking faults became more prevalent as porosity increased, weakening the crystal structure and promoting deformation. Stair-rod and Hirth dislocations also contributed to the deformation mechanism, though to a lesser extent compared to Shockley partials. At lower porosities, these dislocations were absent or very limited. Thus, no Stair-rod or Hirth dislocations were present at 0% porosity, and only two Stair-rod segments appeared at 5% porosity during nucleation. As porosity increased, Stair-rod and Hirth dislocations became more frequent, peaking at 30% porosity with two Stair-rod and two Hirth dislocations during propagation. The distribution of dislocation types suggested that the presence of porosity not only promoted the formation of partial dislocations but also increased the likelihood of more complex dislocation interactions, such as the formation of Stair-rod and Hirth segments. These dislocations served as indicators of the intense localized stress fields created by the pores, which acted as nucleation sites for dislocations and stacking faults. Subsequently, the creep deformation of HEA foam was strongly influenced by porosity. Increased porosity resulted in a higher proportion of amorphous structures and promoted the generation of Shockley partial dislocations, leading to the formation of stacking faults. The introduction of Stair-rod and Hirth dislocations at higher porosities further suggested the complexity of the dislocation network and highlighted the role of pores as stress concentrators that significantly affected the mechanical properties of the material. These findings align with the broader understanding of how porosity weakens the foam structure, contributing to enhanced creep deformation under stress. 3.8.2 Effect of Temperature The effect of temperature on creep deformation behavior was investigated through a systematic analysis of varying percent porosities at three distinct temperatures: 1300 K, 1600 K, and 1900 K. As the temperature increased, there was a notable shift in the structural composition of the materials. At 0% porosity and 1300 K, the material exhibited a significant 66.9% of its structure as FCC, with no observable HCP or dislocations present. However, with a rise in temperature to 1600 K, the proportion of FCC structures decreased to 48.8%, while 51.2% of the structure transitioned to amorphous atomic arrangements, including the emergence of Shockley partial dislocations, highlighting the increased atomic mobility facilitated by the higher temperature. At 1900 K, the trend continued, with the FCC structure further declining to 33.6% and an increase in Shockley dislocations, indicating enhanced deformation mechanisms due to thermal activation. As the percent porosity increased, similar trends were observed across the various temperatures. At 5% porosity, the FCC content decreased from 67.6% at 1300 K to 44.7% at 1600 K, with a corresponding increase in dislocation activity, as evidenced by the rise in Shockley segments from two to twelve. This behavior remained consistent at 10% porosity, where the Shockley dislocations increased from four at 1300 K to 43 at 1600 K, suggesting that temperature not only affected phase stability but also significantly enhanced dislocation generation and mobility. Moreover, the response of the material to higher temperatures also led to the formation of stair-rod dislocations, particularly at 1600 K, with the highest occurrence noted at 15% porosity, where five stair-rod segments were identified. This indicated that temperature played a crucial role in facilitating complex dislocation interactions and the emergence of secondary dislocation types, thereby contributing to the creep behavior of the materials. At 1900 K, the general trend continued, with the FCC content significantly diminishing across all porosity levels, and the proportion of amorphous structures notably increasing, reinforcing the notion that elevated temperatures contributed to greater disorder in the material's microstructure. The highest number of Shockley dislocations was recorded at 25% porosity (39 segments), emphasizing the strong correlation between temperature, porosity, and dislocation behavior. Figure 8 presents a series of snapshots illustrating the structural changes in HEA foam subjected to varying percent porosities at temperatures of 1300 K, 1600 K, and 1900 K. These images effectively capture the intricate dynamics of defect evolution and dislocation segment formation during the creep deformation process. At each temperature, the snapshots reveal distinct alterations in the microstructure, highlighting how increased thermal energy influences the behavior of the material. At 1300 K, the HEA foam displays a relatively stable configuration with limited dislocation activity, characterized by sparse defect meshes. As the temperature rises to 1600 K, a pronounced transformation occurs: the defect mesh becomes more pronounced, and the density of dislocation segments significantly increases. This observation suggests that the elevated temperature facilitates greater atomic mobility, leading to a higher propensity for dislocation nucleation and propagation. Further increasing the temperature to 1900 K results in even more dramatic structural changes. The snapshots indicate a substantial proliferation of dislocation segments, revealing a complex network of defects that interconnect throughout the foam structure. This evolution reflects the material’s response to the combined effects of increased temperature and varying porosity, highlighting how these factors contribute to enhanced creep behavior. Subsequently, the analysis indicated that increasing temperature significantly influenced the creep deformation behavior of materials by promoting the transformation of crystal structures, enhancing dislocation generation, and facilitating complex interactions among different types of dislocations. These findings demonstrate the critical role of thermal conditions in determining the mechanical properties and performance of materials under stress. 3.9 Dislocation and Failure Mechanism in Creep Deformation of HEA foam In CoCrFeMnNi HEA foam, the dislocation mechanism plays a significant role in its deformation behavior, particularly under sustained stress and high temperatures. As the structure undergoes deformation, atoms are displaced from their equilibrium lattice positions, resulting in the formation of dislocations [ 45 ]. These dislocations lead to rearrangement of the lattice structure, facilitating creep deformation. As the strain in the foam increases, perfect dislocations are initially generated, but under localized stress—especially near pore sites—partial dislocations emerge and propagate through the lattice [ 28 ]. The pores within the HEA foam act as stress concentrators, causing intense localized stress fields that initiate dislocations from these pore regions. This is a critical factor in the dislocation nucleation and propagation process, as pores serve as the primary sites for the generation of partial dislocations. The partial dislocations generated in the HEA foam structure include Shockley partials, Stair-rod partials, and Hirth partials. Among the different types of dislocations observed in the HEA foam, Shockley partial dislocations are the most prevalent across all porosity levels. These dislocations are significant contributors to the overall dislocation density and are directly responsible for the formation of stacking faults in the crystal structure of the material (see Figs. 4 h, 5 h and 6 h). Shockley partial dislocations, characterized by their 1/6 Burgers vector, lead to the formation of intrinsic stacking faults within the face-centered cubic (FCC) lattice of the alloy [ 46 ]. These intrinsic stacking faults disrupt the regular ABCABC stacking sequence of the FCC structure, causing a local transformation into a hexagonal close-packed (HCP) stacking sequence. As deformation continues, the stacking faults propagate and interact, giving rise to extrinsic stacking faults and occasionally resulting in the formation of deformation twins [ 47 ]. This structural reconfiguration introduces additional defects in the lattice, further contributing to creep deformation. With further strain, the stacking faults within the structure intersect, forming vacancy strings that nucleate voids [ 48 ]. These vacancy strings, which are perpendicular to the loading axis, evolve into voids, leading to crack initiation and propagation. Dislocations emitted from these vacancy strings facilitate crack growth, particularly from the pore sites, where stress concentrations are highest. As a result, the pores become the primary sites for crack initiation during creep deformation. The propagation of these cracks from pore to pore significantly compromises the structural integrity of the foam. Furthermore, the presence of pores, acting as defects within the lattice, and the proliferation of dislocations and stacking faults result in a reduced stress-bearing capacity of the HEA foam. As the dislocations continue to propagate and interact with the pores, the material’s strength diminishes, leading to accelerated creep deformation. The combined effects of pore-induced dislocation generation, stacking fault formation, and crack propagation culminate in a substantial decrease in the mechanical strength of the HEA foam under high-temperature, constant pressure conditions. 4. Conclusion High-entropy alloys exhibit exceptional mechanical properties, showcasing significant potential for a wide range of engineering applications. The use of atomistic simulations has proven invaluable in enhancing our understanding of HEAs, allowing for the prediction of their behavior under varying conditions. In this study, we provide a comprehensive analysis of the creep deformation mechanisms in equiatomic CoCrFeMnNi HEA foam through molecular dynamics simulations, emphasizing the intricate interplay between porosity, temperature, and pressure. The results indicate that variations in these parameters significantly influence the microstructural evolution of the HEA foam, altering the mechanical behavior of the material at elevated temperatures and under constant stress. We evaluated the effects of varying percent porosities from 0–30% in increments of 5%, temperatures of 1300 K, 1600 K, and 1900 K, as well as pressures of 5 GPa, 6 GPa, 7 GPa, and 8 GPa on the creep behavior of high-entropy alloy foams. The results demonstrated that increasing temperature led to higher strain values across the models. Additionally, mean square deviation and radial distribution function analyses were conducted to further elucidate the structural behavior. Furthermore, the findings revealed that increasing pressure also contributed to higher strain values in the models. These findings illustrate the significant interplay between temperature, pressure, and porosity in influencing the mechanical properties of high-entropy alloy foams. Specifically, the results demonstrate that increasing temperature enhances atomic mobility, leading to a notable shift in the structural composition from FCC to amorphous arrangements, accompanied by a rise in dislocation activity. The emergence of Shockley dislocations and the formation of stair-rod and Hirth dislocations highlight the complexity of dislocation interactions, which are critical in governing the creep behavior of these materials. Furthermore, the study reveals that increased porosity exacerbates the effects of thermal conditions, further promoting dislocation generation and mobility, thereby reinforcing the HEA foam susceptibility to deformation. The significance of this research lies in its potential to inform the design and optimization of HEA foams for high-performance applications in extreme environments. By elucidating the mechanisms underlying creep deformation and the role of microstructural factors, this study contributes to the broader understanding of how HEA foams can be engineered to meet the demanding requirements of modern engineering applications. Future work could expand upon these findings by exploring additional variables and their interactions, ultimately advancing the development of advanced materials with tailored properties for enhanced mechanical performance. Declarations Funding This research did not receive any specific grant from funding agencies in the public, commercial, or non-profit sectors. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Data Availability Statement The data underlying this study is available in the published article. Code Availability Not applicable Ethics approval Not Applicable CRediT authorship contribution statement Ezekiel Edward Nettey-Oppong: Conceptualization, Writing original draft, Writing - review & editing, Visualization, Formal analysis, Investigation. Emmanuel Essel Mensah: Conceptualization, Writing original draft, Writing - review & editing, Visualization, Formal analysis, Investigation. Stephen Takyi Taylor: Conceptualization, Writing original draft, Writing - review & editing, Investigation. Anthony Kwasi Martey: Conceptualization, Writing original draft, Writing - review & editing, Investigation. Eric Asare: Supervision, Validation, Writing - review & editing. Martinson Addo Nartey: Supervision, Validation, Formal analysis, Investigation, Writing - review & editing. Consent to Participate Not Applicable Consent to Publication Not Applicable References Zhang Q et al (2017) The effects of phase constitution on magnetic and mechanical properties of FeCoNi(CuAl)x(x = 0–1.2) high-entropy alloys. J Alloys Compd 693. 10.1016/j.jallcom.2016.09.271 Qi W et al (2022) Effects of Al and Ti co-doping on the strength-ductility- corrosion resistance of CoCrFeNi-AlTi high-entropy alloys. J Alloys Compd 925. 10.1016/j.jallcom.2022.166751 Troparevsky MC, Morris JR, Daene M, Wang Y, Lupini AR, Stocks GM (2015) Beyond Atomic Sizes and Hume-Rothery Rules: Understanding and Predicting High-Entropy Alloys. 10.1007/s11837-015-1594-2 Gorsse S, Tancret F (2018) Current and emerging practices of CALPHAD toward the development of high entropy alloys and complex concentrated alloys. 10.1557/jmr.2018.152 Lee C et al (2018) Lattice distortion in a strong and ductile refractory high-entropy alloy. Acta Mater 160. 10.1016/j.actamat.2018.08.053 Sharma AS, Yadav S, Biswas K, Basu B (2018) High-entropy alloys and metallic nanocomposites: Processing challenges, microstructure development and property enhancement. 10.1016/j.mser.2018.04.003 Yeh JW et al (2004) Nanostructured high-entropy alloys with multiple principal elements: Novel alloy design concepts and outcomes. Adv Eng Mater 6(5). 10.1002/adem.200300567 Tong C, Chen M, Chen S, Yeh J (2005) Mechanical Performance of the Al ^ sub x ^ CoCrCuFeNi High-Entropy Alloy System w … Library , 36, no. May Liao WB et al (2021) Microstructures and mechanical properties of CoCrFeNiMn high-entropy alloy coatings by detonation spraying. Intermetallics (Barking) 132. 10.1016/j.intermet.2021.107138 Dada M, Popoola P, Mathe N (2023) Recent advances of high entropy alloys for aerospace applications: a review. 10.1108/WJE-01-2021-0040 Moschetti M, Burr P, Obbard E, Kruzic JJ, Hosemann P, Gludovatz B (2022) Design considerations for high entropy alloys in advanced nuclear applications. J Nucl Mater 567. 10.1016/j.jnucmat.2022.153814 Ferreirós PA et al (2023) VNbCrMo refractory high-entropy alloy for nuclear applications. Int J Refract Met Hard Mater 113. 10.1016/j.ijrmhm.2023.106200 Yan X, Zhang Y (2020) Functional properties and promising applications of high entropy alloys. Scr Mater 187. 10.1016/j.scriptamat.2020.06.017 Haché MJR, Cheng C, Zou Y (2020) Nanostructured high-entropy materials. 10.1557/jmr.2020.33 Feng CW, Keong CW, Hsueh YP, Wang YY, Sue HJ (2005) Modeling of long-term creep behavior of structural epoxy adhesives. Int J Adhes Adhes 25(5). 10.1016/j.ijadhadh.2004.11.009 Yang Z et al (2018) Flexural creep tests and long-term mechanical behavior of fiber-reinforced polymeric composite tubes. Compos Struct 193. 10.1016/j.compstruct.2018.03.083 Nagarjuna C et al (2022) Developing harmonic structure in CoCrFeMnNi high entropy alloy to enhance mechanical properties via powder metallurgy approach. J Mater Res Technol 17. 10.1016/j.jmrt.2022.01.098 Youssef KM, Zaddach AJ, Niu C, Irving DL, Koch CC (2014) A novel low-density, high-hardness, high-entropy alloy with close-packed single-phase nanocrystalline structures. Mater Res Lett 3(2). 10.1080/21663831.2014.985855 Moravcik I, Cizek J, de Gouvea L, Cupera J, Guban I, Dlouhy I (2019) Nitrogen interstitial alloying of CoCrFeMnNi high entropy alloy through reactive powder milling. 10.3390/e21040363 Jo MG et al (2022) High temperature tensile and creep properties of CrMnFeCoNi and CrFeCoNi high-entropy alloys. Mater Sci Engineering: A 838. 10.1016/j.msea.2022.142748 Liu CJ et al (2022) Tensile creep behavior of HfNbTaTiZr refractory high entropy alloy at elevated temperatures. Acta Mater 237. 10.1016/j.actamat.2022.118188 Wang D, Tan J, Li CJ, Qin XM, Guo SF (2021) Enhanced creep resistance of Ti30Al25Zr25Nb20 high-entropy alloy at room temperature. J Alloys Compd 885. 10.1016/j.jallcom.2021.161038 Yedla N, Salman SA, Karthik V (2022) Molecular Dynamics Simulations for Nanoscale Insight into the Phase Transformation and Deformation Behavior of Shape-Memory Materials, in Shape Memory Composites Based on Polymers and Metals for 4D Printing: Processes, Applications and Challenges , 10.1007/978-3-030-94114-7_4 Wu WP, Şopu D, Eckert J (2021) Molecular dynamics study of the nanoindentation behavior of cu64zr36/cu amorphous/crystalline nanolaminate composites. Materials 14(11). 10.3390/ma14112756 Zhu Y, Gong Q, Yi M (2024) Molecular Dynamics Investigation of Shock-Induced Deformation Behavior and Failure Mechanism in Metallic Materials. 10.1007/s11831-023-10045-8 Chen J, Li P, Lin EE (2020) A molecular dynamics study on the mechanical properties of Fe-Ni alloy nanowires and their temperature dependence. RSC Adv 10(66). 10.1039/d0ra07831j Zepeda-Ruiz LA et al (2021) Atomistic insights into metal hardening. Nat Mater 20(3). 10.1038/s41563-020-00815-1 Nettey-Oppong EE, Mensah EE, Effah E, Asare E, Nartey MA (2023) Mechanical properties and deformation behavior of equiatomic CoCrFeMnNi high-entropy alloy foam: A molecular dynamics study. Solid State Commun 371. 10.1016/j.ssc.2023.115236 Zhao F, Zhang J, He C, Zhang Y, Gao X, Xie L (2020) Molecular dynamics simulation on creep behavior of nanocrystalline tial alloy. Nanomaterials 10(9). 10.3390/nano10091693 Li Q, Jiang C, Du Y (2023) Molecular dynamics study on dynamic mechanical behaviour of FeCoCrCuNi high entropy alloy. Mater Technol 38(1). 10.1080/10667857.2023.2200660 Thompson AP et al (2022) LAMMPS - a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales. Comput Phys Commun 271. 10.1016/j.cpc.2021.108171 Gunkelmann N, Bringa EM, Rosandi Y (2018) Molecular Dynamics Simulations of Aluminum Foams under Tension: Influence of Oxidation. J Phys Chem C 122(45). 10.1021/acs.jpcc.8b07146 Gunkelmann N, Rosandi Y, Ruestes CJ, Bringa EM, Urbassek HM (2016) Compaction and plasticity in nanofoams induced by shock waves: A molecular dynamics study. Comput Mater Sci 119. 10.1016/j.commatsci.2016.03.035 Stoddard SD (1978) Identifying clusters in computer experiments on systems of particles. J Comput Phys 27(2). 10.1016/0021-9991(78)90011-6 Gröger R, Vitek V, Dlouhý A (2020) Effective pair potential for random fcc CoCrFeMnNi alloys. Model Simul Mat Sci Eng 28(7). 10.1088/1361-651X/ab7f8b Stukowski A (2010) Visualization and analysis of atomistic simulation data with OVITO-the Open Visualization Tool. Model Simul Mat Sci Eng 18(1). 10.1088/0965-0393/18/1/015012 Shang Y, Brechtl J, Pistidda C, Liaw PK (2022) Mechanical behavior of high-entropy alloys: A review, in High-Entropy Materials: Theory, Experiments, and Applications , 10.1007/978-3-030-77641-1_10 Huang SM, Nauman EA, Stanciu LA (2019) Investigation of porosity on mechanical properties, degradation and in-vitro cytotoxicity limit of Fe30Mn using space holder technique. Mater Sci Eng C 99. 10.1016/j.msec.2019.02.055 Wang F et al (2020) Multiplicity of dislocation pathways in a refractory multiprincipal element alloy. Sci (1979) 370(6512). 10.1126/science.aba3722 Deluigi OR, Valencia F, Amigo N, Aquistapace F, Gonzalez RI, Bringa EM (2022) Atomistic simulations of tensile deformation of a nanoporous high-entropy alloy. J Mater Sci 57(42). 10.1007/s10853-022-07862-w Leppert L, Albuquerque RQ, Foster AS, Kümmel S (2013) Interplay of electronic structure and atomic mobility in nanoalloys of au and pt. J Phys Chem C 117(33). 10.1021/jp404341v Terban MW, Billinge SJL (2022) Structural Analysis of Molecular Materials Using the Pair Distribution Function. 10.1021/acs.chemrev.1c00237 Varvenne C, Luque A, Curtin WA (2016) Theory of strengthening in fcc high entropy alloys. Acta Mater 118. 10.1016/j.actamat.2016.07.040 Blum W (2008) Mechanisms of creep deformation in steel. Creep-Resistant Steels. 10.1533/9781845694012.2.365 Hull D, Bacon DJ (2011) Introduction to Dislocations . 10.1016/s1369-7021(11)70217-6 Zhao S, Stocks GM, Zhang Y (2017) Stacking fault energies of face-centered cubic concentrated solid solution alloys. Acta Mater 134. 10.1016/j.actamat.2017.05.001 Lu K, Chauhan A, Litvinov D, Schneider M, Laplanche G, Aktaa J (2023) Cooperative deformation mechanisms in a fatigued CoCrNi multi-principal element alloy: A case of low stacking fault energy. J Mech Phys Solids 180. 10.1016/j.jmps.2023.105419 Guo Y, Paramatmuni C, Avcu E (2023) Void Nucleation and Growth from Heterophases and the Exploitation of New Toughening Mechanisms in Metals. 10.3390/cryst13060860 Additional Declarations No competing interests reported. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6344719","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":442092683,"identity":"c7222335-03d8-41f4-aca0-8e54da59891d","order_by":0,"name":"Ezekiel Edward Nettey-Oppong","email":"","orcid":"","institution":"Yonsssei University","correspondingAuthor":false,"prefix":"","firstName":"Ezekiel","middleName":"Edward","lastName":"Nettey-Oppong","suffix":""},{"id":442092687,"identity":"b3f3e233-b5f5-4624-9862-005552694c57","order_by":1,"name":"Emmanuel Essel Mensah","email":"data:image/png;base64,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","orcid":"","institution":"Egypt-Japan University of Science and Technology","correspondingAuthor":true,"prefix":"","firstName":"Emmanuel","middleName":"Essel","lastName":"Mensah","suffix":""},{"id":442092689,"identity":"1b96eca8-2a66-4e94-85a7-eebc558e3687","order_by":2,"name":"Stephen Takyi Taylor","email":"","orcid":"","institution":"Kwame Nkrumah University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Stephen","middleName":"Takyi","lastName":"Taylor","suffix":""},{"id":442092692,"identity":"fc24cce9-69bf-4ff0-9a69-db61c6456598","order_by":3,"name":"Anthony Kwasi Martey","email":"","orcid":"","institution":"Kwame Nkrumah University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Anthony","middleName":"Kwasi","lastName":"Martey","suffix":""},{"id":442092695,"identity":"53cc9803-a93b-4dca-9d8e-cc6eb530cb1b","order_by":4,"name":"Eric Asare","email":"","orcid":"","institution":"Kwame Nkrumah University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Eric","middleName":"","lastName":"Asare","suffix":""},{"id":442092701,"identity":"1e8e18e7-0e9e-4606-8bec-9b704b982c19","order_by":5,"name":"Martinson Addo Nartey","email":"","orcid":"","institution":"Kwame Nkrumah University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Martinson","middleName":"Addo","lastName":"Nartey","suffix":""}],"badges":[],"createdAt":"2025-03-31 12:23:08","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6344719/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6344719/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s41939-025-01006-8","type":"published","date":"2025-08-20T16:12:52+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":81297903,"identity":"079f93cc-1b24-44de-bbb6-f1e22113fb62","added_by":"auto","created_at":"2025-04-24 13:18:14","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":295816,"visible":true,"origin":"","legend":"\u003cp\u003eThe modeled FCC CoCrFeMnNi equiatomic high-entropy alloy (HEA) structure. The individual elements are represented by different colors: Cobalt (Co) in red, Chromium (Cr) in blue, Iron (Fe) in yellow, Manganese (Mn) in pink, and Nickel (Ni) in green. The structure has a cubic cell length of 108 Å. The middle section shows the incorporation of spherical voids within the bulk and on the surface of the HEA structure to model porosities. On the right, the resulting HEA foam structure is depicted after the introduction of voids, illustrating the porous nature of the material and potential applications in mechanical performance evaluations.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-6344719/v1/8a6a254f64adb30d1fb29997.png"},{"id":81298918,"identity":"2b727d9b-7579-4287-a990-7a874da1d483","added_by":"auto","created_at":"2025-04-24 13:34:14","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":173662,"visible":true,"origin":"","legend":"\u003cp\u003eCommon neighbor and melting temperature analysis. (a) Common Neighbor Analysis (CNA) of the final CoCrFeMnNi HEA structure after quenching, confirming that all atoms retained their face-centered cubic (FCC) configuration. The 100% FCC arrangement verifies the accuracy of the chosen interatomic potential in modeling the HEA system. (b) The relationship between potential energy and temperature, illustrating a significant shift in potential energy around 2000 K, indicative of the melting point. This change marks the phase transition from solid to liquid, highlighting the cut off temperature for creep evaluation.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-6344719/v1/5d0fccb859ad84ae91c412d6.png"},{"id":81298624,"identity":"abb8b85e-1461-4872-a1b5-04623960c810","added_by":"auto","created_at":"2025-04-24 13:26:14","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":242625,"visible":true,"origin":"","legend":"\u003cp\u003eCreep deformation behavior of CoCrFeMnNi HEA foam at a constant pressure of 7 GPa, with varying temperatures of 1300 K, 1600 K, and 1900 K. Strain against time plots for HEA foams with different porosities: (a) 0%, (b) 5%, (c) 10%, (d) 15%, (e) 20%, (f) 25%, and (g) 30%. (h) Simulation snapshots of the bulk HEA foam (0% porosity) before deformation (right), during deformation (middle), and after deformation (left). The atomic arrangement of the bulk structure exhibits a complete FCC configuration initially, transitioning to a partial FCC configuration (33.6%) during deformation and a fully amorphous structure (0% FCC) after deformation.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-6344719/v1/d5040d04587725a94b9e8a61.png"},{"id":81298626,"identity":"9bbb18fa-9bae-4331-8efa-12fd0f5b2289","added_by":"auto","created_at":"2025-04-24 13:26:14","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":234856,"visible":true,"origin":"","legend":"\u003cp\u003eMean Square Displacement (MSD) analysis of the modeled CoCrFeMnNi HEA foams under constant pressure (7 GPa) with varying temperatures of 1300 K, 1600 K, and 1900 K, and different porosity levels. Strain against time plots for (a) 0% porosity, (b) 5%, (c) 10%, (d) 15%, (e) 20%, (f) 25%, and (g) 30%. (h) Simulation snapshots of bulk HEA foam with 5% porosity: before deformation (right) fully FCC configuration of atom arrangement, during deformation (middle) partially FCC configuration (26.9%), and after deformation (left) fully amorphous (0% FCC). Notably, HCP configurations (0.2%) were observed during the creep deformation, indicative of stacking faults.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-6344719/v1/ba5ff9dd9bf4e9dec94c9d02.png"},{"id":81297906,"identity":"813acfcd-b084-4803-8e1d-77da761dc923","added_by":"auto","created_at":"2025-04-24 13:18:14","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":249653,"visible":true,"origin":"","legend":"\u003cp\u003eRadial Distribution Function (RDF) analysis of CoCrFeMnNi HEA foam under constant pressure (7 GPa) with varying temperatures of 1300 K, 1600 K, and 1900 K, and porosity levels. Strain vs. time plots for (a) 0% porosity, (b) 5%, (c) 10%, (d) 15%, (e) 20%, (f) 25%, and (g) 30%. (h) Simulation snapshots of bulk HEA foam with 15% porosity: before deformation (right) fully FCC configuration of atom arrangement, during deformation (middle) partially FCC configuration (26.9%), and after deformation (left) fully amorphous (0% FCC), with more HCP configurations (1.1%) than at 5%, indicating stacking faults.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-6344719/v1/aa388b69b4aa121ffa3fef92.png"},{"id":81299901,"identity":"6b3dc4bf-a708-42cf-bafd-cc4359b0fa0f","added_by":"auto","created_at":"2025-04-24 13:42:14","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":263704,"visible":true,"origin":"","legend":"\u003cp\u003eCreep deformation behavior of CoCrFeMnNi HEA foams at a constant temperature of 1900 K with varying pressures of 5 GPa, 6 GPa, 7 GPa, and 8 GPa. Strain vs. time plots are shown for (a) 0%, (b) 5%, (c) 10%, (d) 15%, (e) 20%, (f) 25%, and (g) 30% porosity. (h) Simulation snapshots depict the bulk HEA foam (30% porosity) before deformation with a fully FCC configuration, during deformation with a partially FCC configuration (33.6%), and after deformation showing a completely amorphous structure (0% FCC) having noticeable HCP configurations with the highest stacking faults (1.4%), compared to structures of 5% and 15% porosity.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-6344719/v1/350fdaa5a85b45f67d58b13e.png"},{"id":81297909,"identity":"c7c4bbb0-8707-48b3-b2fa-5b7b240c88de","added_by":"auto","created_at":"2025-04-24 13:18:14","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":231431,"visible":true,"origin":"","legend":"\u003cp\u003eCreep deformation behavior of CoCrFeMnNi HEA foams of varying percent porosities at a constant pressure of 7 GPa and temperature of 1900 K. Snapshots of the dislocation behavior in HEA foam structures under different porosity levels are depicted for structures before creep deformation, the onset of dislocations (nucleation) and further propagation during creep deformation. As porosity increases, there is a shift from FCC-dominated mechanisms at the nucleation stage to a greater presence of amorphous structures, particularly in the propagation stages of deformation. Shockley partial dislocations become more prominent with higher porosity, contributing to stacking fault formation and material weakening. Additionally, Stair-rod and Hirth dislocations emerge at elevated porosity levels, indicating more complex dislocation interactions driven by the presence of pores. These trends highlight the critical role of porosity in influencing the deformation mechanisms of HEA foams.\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-6344719/v1/e49ebcd09152006b005c5514.png"},{"id":81297910,"identity":"9d1903cd-2e1f-4602-90c3-726ba9425fb5","added_by":"auto","created_at":"2025-04-24 13:18:14","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":268109,"visible":true,"origin":"","legend":"\u003cp\u003eCreep deformation behavior of CoCrFeMnNi HEA foams at a constant pressure of 7 GPa and varying temperatures. Snapshots of the HEA foam changes across temperatures of 1300K, 1600K, and 1900K. At lower temperatures, FCC structures dominate, while higher temperatures lead to increased amorphous content and greater dislocation activity. At 1900K, Shockley partials, Stair-rod, and Hirth dislocations become more frequent, indicating high dislocation density. These trends highlight the critical relationship between temperature, porosity, and microstructural integrity in HEA foams, illustrating the ongoing transformation of the material under creep deformation. The detailed visualization of defect meshes, and dislocation segments demonstrate the mechanisms that govern the creep deformation process.\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-6344719/v1/91a2fd021d61cae8e88b52e8.png"},{"id":89847017,"identity":"9a5eaa0f-56cb-4518-ac3c-2c0646a6142a","added_by":"auto","created_at":"2025-08-25 16:38:28","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2667200,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6344719/v1/15f50159-1c7f-4277-845f-f0c5fd9afd37.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Unravelling the Creep Behavior of Equiatomic CoCrFeMnNi High-Entropy Alloy Foam: A Molecular Dynamics Study","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eHigh entropy alloys (HEAs) represent a novel class of alloys that are distinguished by their unique compositional and structural characteristics [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. Unlike traditional alloys that are primarily composed of a single principal element with small amounts of alloying elements, HEAs are composed of five or more principal elements in equal or near-equal atomic proportions [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. This high degree of compositional complexity results in a significantly higher configurational entropy compared to conventional alloys [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. The increased entropy stabilizes a single-phase solid solution structure, often a simple face-centered cubic (FCC) or body-centered cubic (BCC) lattice, which can lead to enhanced mechanical properties and improved resistance to deformation[\u003cspan additionalcitationids=\"CR5\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. High entropy alloys exhibit a broad range of mechanical properties, including high strength, hardness, and excellent wear resistance where materials are exposed to extreme conditions [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. These exceptional properties of HEAs make them ideal for demanding applications in industries. HEAs are increasingly used in the production of exhaust nozzles and gas turbine casings in gas turbine engines, where high thermal stability and resistance to wear and corrosion are crucial [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. Additionally, HEAs are being investigated for use in nuclear reactors, where their ability to withstand high radiation doses and extreme temperatures offers significant advantages[\u003cspan additionalcitationids=\"CR8 CR9 CR10 CR11\" citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe development of HEAs has opened new avenues for material design and innovation. Research into HEAs is ongoing to understand their fundamental behaviors, such as phase stability, thermal conductivity, and diffusion characteristics[\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. Additionally, advanced characterization techniques and computational methods, including molecular dynamics simulations, are increasingly employed to explore and predict the properties of HEAs under various conditions. Ongoing research aim to optimize HEA compositions and processing methods, further expanding their potential applications and enhancing their performance in various engineering domains. Although the mechanical and thermal properties of HEAs have received much attention, little is known of their behavior under creep conditions. Creep, a time-dependent deformation phenomenon that occurs when materials are subjected to prolonged loading at elevated temperatures, is a crucial mechanical feature that has a substantial impact on the integrity and durability of materials under high stress and thermal conditions [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. Under such conditions, materials experience deformation behavior that reduces their lifespan, decreases thermal stability and results in material softening. The importance of creep is seen in a variety of applications, from gas turbine blades to parts of power plants, necessitating a thorough understanding of the phenomena to ensure that materials can resist lengthy exposure to high temperatures and mechanical pressures [\u003cspan additionalcitationids=\"CR18\" citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eJo et al [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e] studied the high-temperature tensile and creep properties of CrMnFeCoNi and CrFeCoNi high-entropy alloys between 500\u0026ndash;725\u0026deg;C to assess their structural integrity. While both alloys exhibited similar tensile behavior, CrFeCoNi demonstrated significantly longer creep rupture life, lower minimum creep rate, and higher creep activation energy. The improved performance was due to greater lattice distortion, enhancing solid solution strengthening. However, grain boundary weakening was experienced due to sigma phase formation during creep, leading to reduced elongation in long-term conditions. The study by Liu et al [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e] examined the creep behavior of HfNbTaTiZr high-entropy alloy with large grain size, tested at 1100\u0026ndash;1250\u0026deg;C and stress levels of 5\u0026ndash;30 MPa in a vacuum. Creep was governed by the solute drag mechanism, with stress exponents of 2.5\u0026ndash;2.8 and activation energies of 273\u0026thinsp;\u0026plusmn;\u0026thinsp;15 kJ mol⁻\u0026sup1;. TEM analysis showed that dislocations dominated plastic deformation, leading to grain boundary bulging and migration. The creep rate was controlled by the diffusivity of Ta, which has the lowest diffusion coefficient and restricts dislocation movement. These findings offer guidance for designing refractory HEAs with enhanced creep resistance.\u003c/p\u003e \u003cp\u003eWang et al [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e] developed and characterized a novel HEA, Ti\u003csub\u003e30\u003c/sub\u003eAl\u003csub\u003e25\u003c/sub\u003eZr\u003csub\u003e25\u003c/sub\u003eNb\u003csub\u003e20\u003c/sub\u003e, with a single body-centered cubic (BCC) structure. The Young's modulus and nano-hardness were found to be 158.2\u0026thinsp;\u0026plusmn;\u0026thinsp;5.2 GPa and 8.9\u0026thinsp;\u0026plusmn;\u0026thinsp;0.2 GPa, respectively. Creep behavior was investigated at 20\u0026deg;C using nano-indentation across various loading rates and peak loads. Results revealed that creep displacement increased with loading rates and peak loads, while the creep strain rate sensitivity index initially decreased before increasing again. This behavior was attributed to dislocation activation volume and hysteresis diffusion effects. Compared to other metallic materials, Ti\u003csub\u003e30\u003c/sub\u003eAl\u003csub\u003e25\u003c/sub\u003eZr\u003csub\u003e25\u003c/sub\u003eNb\u003csub\u003e20\u003c/sub\u003e HEA demonstrated a high dislocation activation volume and a low creep strain rate sensitivity index, reflecting its excellent creep resistance.\u003c/p\u003e \u003cp\u003eThe development of advanced computational tools, such as molecular dynamics (MD) simulations, has significantly enhanced the ability of researchers to investigate the complex atomic-level mechanisms governing material behavior [\u003cspan additionalcitationids=\"CR24\" citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. This technological advancement facilitates a thorough examination of fundamental processes involved in creep deformation within intricate alloys, offering valuable insights that complement experimental research. By utilizing empirical interatomic potentials to model atom-to-atom interactions, MD simulations enable the replication of material responses under various temperature and stress conditions [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. This approach allows for the detailed analysis of phenomena such as grain boundary interactions and dislocation mobility [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e], which are critical to understanding creep behavior. Moreover, MD simulations provide a platform for exploring experimental variables that are difficult to manipulate in practical settings, such as temperature gradients and strain rates. As a result, these simulations offer a comprehensive understanding of how imperfections, impurities, and microstructural features influence creep deformation and the mechanical properties of materials.\u003c/p\u003e \u003cp\u003eZhao et al [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e] employed molecular dynamics simulations to explore how temperature, pressure, and grain size affect the high-temperature creep properties of nanocrystalline TiAl alloy. It was shown that increasing temperature and stress significantly enhance the steady-state creep rate and accelerate the rapid creep stage, with smaller grain size further promoting the creep process due to larger proportion of grain boundaries. The creep mechanisms varied with stress levels: dislocation motion dominated at high-stress conditions, while diffusion creep was more prevalent at low-stress conditions. During the rapid creep stage, grain boundary and lattice diffusion were the primary mechanisms driving deformation. Li et al [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e] investigated the dynamic mechanical properties of FeNiCoCrCu high-entropy alloy under tension and compression using molecular dynamics simulations. The findings revealed that at low strain rates, the alloy does not exhibit plastic deformation, but at higher strain rates e\u003csup\u003e11\u003c/sup\u003es\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, it underwent distinct stages of elastic deformation, yielding, and plastic deformation, with increased yield strength. High tensile strain rates lead to stacking faults that enhanced material strength by preventing slip, while Frank dislocations initiated plastic deformation and dislocation interactions stabilize this process. For high strain rate compression, stress relaxation was driven by stacking fault formation, and strain hardening is achieved through twinning and dislocation interactions.\u003c/p\u003e \u003cp\u003eIn this study, we undertake Molecular Dynamics simulations to conduct an in-depth exploration of the atomistic mechanisms governing the creep deformation observed in foam structures composed of the equiatomic CoCrFeMnNi alloy. Furthermore, an examination of the influence exerted by pressure and porosity on the response of the alloy to creep is studied. The primary objective of this work is to provide a thorough understanding of alloy stability, mechanical properties, and suitability for demanding applications.\u003c/p\u003e"},{"header":"2. Computational Method","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 HEA Modeling\u003c/h2\u003e \u003cp\u003eUnderstanding the atomic-level mechanical behavior of HEAs is crucial for developing advanced materials with superior properties. Molecular dynamics simulation is a powerful tool for this purpose, allowing researchers to investigate the fundamental interactions that govern material performance. In this study, we conducted molecular dynamics simulations using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe simulation was carried out on a cubic lattice structure representing an alloy composed of 20% Cobalt (Co), 20% Chromium (Cr), 20% Iron (Fe), 20% Manganese (Mn), and 20% Nickel (Ni). Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e presents the modeled FCC CoCrFeMnNi equiatomic high-entropy alloy structure, illustrating the spatial arrangement and distribution of individual elements in the system. In this equiatomic HEA, each element is equally distributed, contributing to the stability and mechanical properties of the alloy. The cubic cell length of the structure measured 108 \u0026Aring;, ensuring that the system size is sufficiently large to model the atomic interactions and structural behavior of the alloy under varying conditions. The simulation box was initialized in three dimensions with periodic boundary conditions in all directions. The FCC lattice structure was selected, with a lattice constant of 3.6 \u0026Aring;, and the simulation box had dimensions of 30 lattice units in each direction. Atoms were created within this box, with the respective element fractions assigned randomly. The atomic masses for Co, Cr, Fe, Mn, and Ni were set according to their standard values. The simulations were performed on 7 models based on cubic lattice structures with varying porosities(0%, 5%, 10%, 15%, 20%, 25%, and 30%).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 HEA Foam Modeling\u003c/h2\u003e \u003cp\u003eTo model nanoporous HEA structures, spherical pores were introduced at random locations within the simulation cell, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e (b). The template used for generating pores involved a 3D model where spheres were randomly inserted, and the resulting coordinates dictated the pore locations in the foam structures. These voids were introduced to simulate porosities, a critical feature in modeling foam structures. Some voids are located within the bulk of the material, while others are positioned on the surface. The presence of surface voids is of particular importance since pores significantly influence the mechanical properties and deformation mechanisms of the HEA foam under applied loads. The controlled distribution of voids allows for a systematic study of how porosity levels affect the overall behavior of the alloy during creep simulations. The method aimed to replicate the regular spherical pore geometry observed in experimental HEA foams. In Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e (c), the resulting HEA foam structure is depicted after void incorporation. The foam-like structure, with defined pore sites, represents a porous material that can be evaluated for mechanical performance, including strength, ductility, and resistance to deformation under high temperature and pressure conditions. This visual representation of the HEA foam highlights the potential for tailoring porosity to enhance the material's properties for specific applications.\u003c/p\u003e \u003cp\u003eUnlike conventional methods for creating metal foam structures, this approach eliminated isolated atoms in the voids, improving the accuracy of modeling multi-component systems. Further details of our HEA model and simulation can be found in our previous studies [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. Briefly, the conventional approach to constructing foam structures relies on utilizing the physical properties of atoms to create spatial filters that generate pore sites [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]. This method, however, isolates atoms in the resulting voids and faces significant challenges when applied to multi-component systems, such as high-entropy. In traditional metal foam modeling, a sacrificial crystal structure is heated above its melting point to form a spatial filter, where atoms with temperatures exceeding a set threshold are removed until a desired fill factor is reached. Subsequently, isolated atoms and clusters are removed using a cluster detection method [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e]. The spatial filter is then applied to the nonporous crystalline metal to eliminate excess atoms.\u003c/p\u003e \u003cp\u003eThis technique is unsuitable for HEAs, which consist of several elements. During heating, equilibrium fluctuations cause certain elements to experience greater temperature variations than others, leading to uneven atom removal when a cut-off temperature is applied. As a result, the spatial filter would preferentially eliminate specific elements, altering the alloy's molar ratio and producing a foam structure with a different composition than the original. Furthermore, spatial filters prevent the modeling of foam structures with precise pore locations, and even though using a single-element crystal structure can mitigate molar ratio changes, atom removal remains random. Consequently, the conventional method is inadequate for modeling HEA foams making it difficult to assess the impact of porosity on mechanical properties.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Interatomic Potential and Melting Temperature Evaluation\u003c/h2\u003e \u003cp\u003eThe recently developed pair potential by Gr\u0026ouml;ger et al.[\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e] for random FCC CoCrFeMnNi high-entropy alloys was employed to model interatomic interactions. To assess the accuracy of this potential, a liquid-to-solid quench simulation was performed under an isothermal-isobaric (NPT) ensemble, where the system was heated to 1200 K and rapidly quenched to 70 K. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e provides a comprehensive analysis of the atomic structure and thermodynamic properties of the CoCrFeMnNi equiatomic high-entropy alloy (HEA) system, using Common Neighbor Analysis (CNA) and potential energy-temperature relationship. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea depicts the results of the CNA of the final structure after the quenching process, which confirms that all atoms in the system have retained their face-centered cubic (FCC) configuration. The ability to maintain a 100% FCC atom arrangement throughout the simulation highlights the structural stability of the HEA, even after thermal treatment. This result validates the accuracy and reliability of the chosen interatomic potential for modeling the CoCrFeMnNi system. The retention of the FCC structure after quenching is important, as the crystal structure can significantly impact the mechanical properties. Moreover, it indicates that no phase transformations occurred during the quenching process, ensuring that the material maintains its equiatomic distribution and structural integrity.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb shows the relationship between potential energy and temperature, with a pronounced shift in potential energy observed around 2000 K. This distinct change serves as an indicator of the melting point of the material. As the temperature increases, the system undergoes a gradual increase in potential energy until a critical point is reached, where the energy rises sharply, suggesting the onset of the phase transition from solid to liquid. The temperature at which this significant change occurs provides an estimate of the melting point of the CoCrFeMnNi HEA. This information is crucial for understanding the thermal stability and processing limits of the material. Determining the melting point enables precise control over processes such as casting, forming, and heat treatments, while also providing critical insights into the behavior of HEA under extreme conditions. This information is particularly important for establishing the appropriate cutoff temperature for the creep study, ensuring accurate simulation of the material's high-temperature performance. The clear correlation between temperature and potential energy further demonstrates the thermodynamic behavior of the alloy, offering essential information about its phase stability and transition mechanisms.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4 Creep Simulation Details\u003c/h2\u003e \u003cp\u003eFor the creep simulations, the modeled structures underwent energy minimization and equilibration at different temperatures using the Velocity-Verlet integration scheme and a timestep of 0.005 ps, with the Nose-Hoover barostat ensuring constant pressure throughout the process. To prepare the systems, the potential energy for each system was minimized using the steepest descent method. This step relaxed the system, allowing for energy convergence and eliminating any residual stress. The system was equilibrated at 300 K using the Nose-Hoover thermostat to maintain a stable temperature. A constant pressure and temperature ensemble (NPT) was used, ensuring isotropic conditions. This equilibration phase ran for 100 ps, after which spherical voids were introduced to create porosities corresponding to the different models. To simulate creep behavior, the temperature and pressure conditions were varied across a range of values. Temperatures of 1300 K, 1600 K, and 1900 K were employed, while the pressure was varied at 5 GPa, 6 GPa, 7 GPa, and 8 GPa. The system underwent equilibration at each temperature and pressure combination to ensure stability before creep deformation simulations were initiated. Notably, the variation in porosity was determined by calculating the radius of each void through numerical methods to achieve the desired percent porosity, using the mathematical expression:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:\\%P=\\frac{{V}_{P}}{{V}_{T}}\\times\\:100\\%$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003e%P\u003c/em\u003e represents the percent porosity, \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003eP\u003c/em\u003e\u003c/sub\u003e is the pore volume, and \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003eT\u003c/em\u003e\u003c/sub\u003e is the total volume. The creep simulations involved applying compressive stress along the x-axis under constant temperature and pressure conditions, while maintaining stress-free boundaries in the y and z directions.\u003c/p\u003e \u003cp\u003eStrain was calculated continuously by monitoring changes in the box length in the x-direction, and the simulation results were recorded over 300 ps. Strain, temperature, pressure, and other key parameters were output at regular intervals, and atomistic configurations were recorded for further analysis. The output from the simulation included data on temperature, potential energy, pressure, and strain, recorded at intervals throughout the simulation. These results were used to analyze the strain-time relationship during the creep process. Additionally, atomistic configurations were recorded at regular intervals for visualization and further analysis. The strain was calculated using the following formula in the direction of the applied sustained stress.\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:E=\\:\\frac{l-\\text{l}\\text{o}}{lo}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere, \u003cem\u003el\u003c/em\u003e is the instantaneous length of the cubic sample under applied stress and \u003cem\u003el\u003c/em\u003e\u003csub\u003e\u003cem\u003eo\u003c/em\u003e\u003c/sub\u003e is the undeformed length of the cubic sample. Diffusive properties of the modeled HEA systems were measured using mean square displacement (MSD) defined as:\u003c/p\u003e \u003cp\u003eMSD = \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\u0026lang;\\frac{1}{N}\\sum\\:_{i=0}^{N}{(ri\\left(t\\right)-ri\\left(0\\right))}^{2}\u0026rang;\\)\u003c/span\u003e\u003c/span\u003e(3)\u003c/p\u003e \u003cp\u003ewhere, \u003cem\u003eN\u003c/em\u003e is the particle number, \u003cem\u003et\u003c/em\u003e is time, and \u003cem\u003er\u003c/em\u003e is the distance a specific particle travels over time at different constant temperatures. The Radial Distribution Function (RDF or g(r)), also referred to as the pair correlation function, describes the variation in particle density with respect to distance from a reference particle within a system. It offers valuable information about the local structure of a material by examining how atoms or molecules are spatially arranged relative to each other. The RDF or g(r) can be expressed as:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:g\\left(r\\right)=\\:\\frac{\u0026lang;p\\left(r\\right)\u0026rang;}{{p}_{bulk}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\u0026lang;p\\left(r\\right)\u0026rang;\\)\u003c/span\u003e\u003c/span\u003e is the local density at a distance \u003cem\u003er\u003c/em\u003e from the reference atom, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{p}_{bulk}\\)\u003c/span\u003e\u003c/span\u003e is the average bulk density of the atoms. Visualization and analysis were done using OVITO [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]. The dislocation extraction algorithm (DXA) was used to extract the dislocation planes of the foam structure. To effectively investigate creep deformation in CoCrFeMnNi HEA foam, it is essential to precisely determine its response within the relevant ranges of these parameters. To achieve this, we subject the HEA sample to different temperature, pressure and porosity conditions. By conducting these simulations, we can accurately determine the critical thresholds at which the CoCrFeMnNi HEA foam displays significant creep deformation. This knowledge is pivotal for designing and conducting experiments focused on creep behavior under different temperature, pressure and porosity settings, ensuring that appropriate conditions are selected to comprehensively explore the mechanical properties of the alloy and its response to pressure and porosity-induced deformation.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Results and Discussion","content":"\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Creep Deformation Behavior\u003c/h2\u003e \u003cp\u003eThe study of the creep deformation behavior of CoCrFeMnNi high-entropy alloy foams revealed consistent trends across all tested models, highlighting a linear relationship between strain and time. This linearity signifies a steady rate of deformation under applied conditions, irrespective of the temperature or porosity variations. Such behavior is critical for materials used for long-term applications under sustained loads, as it allows for more accurate predictions of material performance over extended periods. The steady nature of the deformation rate, particularly in the linear phase, suggests that the HEA foams exhibit predictable mechanical properties, which are essential for reliable material design and engineering applications under high-temperature or high-stress environments [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]. At a constant pressure of 7 GPa, the strain against time plots as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e for the various porosities and temperatures show that deformation behavior remains generally consistent, with strain increasing continuously over time.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea-g illustrates the creep deformation behavior of the CoCrFeMnNi HEA foam under constant pressure (7 GPa) and varying temperatures (1300 K, 1600 K, and 1900 K) for different porosities (0\u0026ndash;30%). The strain against time plots highlight a linear increase in strain across all porosity levels, with higher temperatures generally leading to greater strain, especially at lower porosities. Additionally, simulation snapshots as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eh, depict the structural evolution of the bulk HEA foam (0% porosity) during the deformation process, showing the transition from a fully FCC configuration before deformation to a partially FCC state during deformation, and finally, a completely amorphous structure after deformation. This structural transition demonstrates the shift in mechanical properties of the material as creep progresses. The linear trend across all temperature and porosity variations reinforces the robustness of the material under varying thermal conditions, making it suitable for high-temperature creep applications. These results indicate that the CoCrFeMnNi HEA foam possesses a high tolerance for creep deformation, which is essential for structural components that must withstand prolonged thermal exposure.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Effect of Porosity on Creep Deformation Behavior\u003c/h2\u003e \u003cp\u003ePorosity was found to significantly influence the strain behavior in the HEA foam. As outlined in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, strain values consistently increased with higher porosity levels over the simulation period of 300 ps. At 1300 K, the bulk HEA\u0026mdash;0% porosity\u0026mdash;exhibited a final strain of 0.239, while the system with 30% porosity displayed a significantly higher strain of 0.456. This trend suggests that porosity acts as a facilitator for deformation by creating stress concentrators within the HEA foam structure. The higher porosity led to localized areas of intense strain, where deformation is more likely to initiate and propagate. As a result, materials with greater porosity experience intense deformation due to the amplification of local stress around these voids. Furthermore, as porosity increases, the capacity of the HEA foam to sustain mechanical loading diminishes, leading to higher overall strain values. This behavior is particularly relevant for applications requiring materials with specific mechanical properties, as controlling the porosity can directly influence the performance of the foam under load. In higher-porosity HEA foams, the interaction of stress concentrators and voids drives significant deformation, potentially leading to early material failure if subjected to long term mechanical loads [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eFinal strain values under creep deformation for the modeled CoCrFeMnNi HEA foams at different porosities and temperatures.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePorosity (%)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1300 K\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1600 K\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1900 K\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.239\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.299\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.304\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.285\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.321\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.318\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.320\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.334\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.326\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.356\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.358\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.333\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.388\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.377\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.342\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.421\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.398\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.362\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.456\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.421\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.382\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Effect of Temperature on Creep Deformation Behavior\u003c/h2\u003e \u003cp\u003eTemperature variations also played a significant role in the strain behavior of the HEA foam, particularly at lower porosity levels. As shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, an increase in temperature from 1300 K to 1900 K led to higher strain values in the models with porosities below 15%. At 0% porosity, the final strain at 1300 K was 0.239, compared to 0.304 at 1900 K. This increase in strain with rising temperature is consistent with the softening of the foam as atomic mobility increases, allowing for easier dislocation movement and enhanced plastic deformation. The temperature-dependent strain behavior in low-porosity HEA foams suggests that the HEA becomes more susceptible to creep deformation as the temperature rises, a critical factor for materials operating in high-thermal environments.\u003c/p\u003e \u003cp\u003eInterestingly, this temperature-dependent trend is reversed for HEA foams with porosities of 15% and above. In these higher-porosity models, increasing the temperature from 1300 K to 1900 K led to a reduction in strain. At 30% porosity, the strain decreased from 0.456 at 1300 K to 0.382 at 1900 K. This unexpected behavior may be attributed to the increased size of voids and defects in the HEA foam\u0026rsquo;s structure at higher porosity levels. These defects can impede dislocation movement, counteracting the usual effect of increased atomic mobility at elevated temperatures [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e]. As a result, despite the higher thermal energy available at 1900 K, the structural defects limit the ability of the HEA foam to deform, leading to a decrease in overall strain. This observation points to a shift in the deformation mechanism of the material, where the foam transitions from ductile to more brittle-like behavior as both temperature and porosity increase [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e]. The interaction between microstructural defects and thermal effects plays a pivotal role in determining the mechanical response of the HEA foam under these conditions.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e3.4 Mean Square Displacement (MSD) Analysis\u003c/h2\u003e \u003cp\u003eThe mean square displacement (MSD) provides a quantitative measure of atomic mobility within the CoCrFeMnNi HEA foam [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e]. As temperature increases, MSD values rise significantly, indicating that higher thermal energy leads to greater atomic displacement from their initial lattice positions. At 1300 K, the atomic motion remains relatively constrained, resulting in lower MSD values across all porosity levels. As outlined in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, the bulk material with 0% porosity exhibited an MSD of 64.134 \u0026Aring;\u0026sup2; at 1300 K, reflecting limited atomic mobility. In contrast, at 1900 K, the MSD for the same material increased to 730.188 \u0026Aring;\u0026sup2;, demonstrating a significant rise in atomic vibrations as temperature climbs. The effect of temperature on MSD becomes more pronounced with increased porosity.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eMSD values for CoCrFeMnNi HEA foam at different porosity levels and temperatures.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePorosity (%)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1300 K\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1600 K\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1900 K\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e64.134\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e403.503\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e730.188\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e141.594\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e700.935\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1048.321\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e223.872\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e940.897\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1339.780\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e375.566\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1002.116\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1602.523\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e443.619\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e937.7177\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1647.554\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e584.580\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1215.419\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1804.552\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e652.888\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1167.987\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1726.400\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe introduction of voids within the foam allows for greater freedom of atomic movement, which is reflected in the MSD values. At 5% porosity, the MSD at 1300 K was 141.594 \u0026Aring;\u0026sup2;, which increased to 1048.321 \u0026Aring;\u0026sup2; at 1900 K. Similarly, for 30% porosity, the MSD values rose from 652.888 \u0026Aring;\u0026sup2; at 1300 K to 1726.400 \u0026Aring;\u0026sup2; at 1900 K. This trend clearly demonstrates the combined influence of temperature and porosity on atomic mobility: as the material becomes more porous, the MSD increases further, highlighting the reduction in structural integrity and creep resistance. The relationship between MSD and porosity is evident across all temperature ranges. In the bulk HEA (0% porosity), atoms are tightly packed, and their movements are constrained by neighboring atoms, leading to lower MSD values. However, as porosity increases, the atomic arrangement becomes more irregular, with voids allowing for greater freedom of movement. This behavior is further illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, which shows the MSD analysis of the CoCrFeMnNi HEA foam under constant pressure (7 GPa) at varying temperatures of 1300 K, 1600 K, and 1900 K for different porosity levels. The strain against time plots shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea-g, for each porosity level clearly depict the increase in strain with rising temperature and porosity. Additionally, Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eh depicts the simulation snapshots of the HEA foam with 5% porosity before, during, and after deformation provide a visual representation of the atomic arrangement.\u003c/p\u003e \u003cp\u003eSimilar to the bulk material before deformation, the atoms maintain a fully FCC configuration, while during deformation, the FCC structure partially collapses. After deformation, the structure becomes fully amorphous, indicating the severe impact of atomic mobility on the material's structural integrity. At 30% porosity, the MSD values are significantly higher at each temperature, with the largest deviation from the lattice structure occurring at 1900 K. This increase in atomic displacement at higher porosities is a direct consequence of the reduced atomic density, which allows for greater mobility and increases the susceptibility of the foam to deformation. The combined effect of elevated temperatures and increased porosity results in a pronounced rise in MSD values, which correlates with a decrease in the material's creep resistance. As atoms move more freely, particularly under high-temperature conditions, the material becomes more prone to sustained deformation under mechanical loading. The reduction in atomic coordination and bonding due to the presence of voids, coupled with increased thermal vibrations, weakens the structural framework of the HEA foam, leading to a reduction in its resistance to creep.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e3.5 Radial Distribution Function (RDF) Analysis\u003c/h2\u003e \u003cp\u003eThe radial distribution function (RDF) is a vital tool for understanding the atomic arrangement within the CoCrFeMnNi high-entropy alloy (HEA), particularly in relation to the effects of temperature and porosity. RDF measures the probability of finding atoms at specific interatomic distances, providing key insights into the structural coherence of the material [\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e]. temperature increases, the RDF analysis reveals a significant reduction in the height of the peaks, indicating a decrease in the structural order of the HEA. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea-g illustrates the changes in the radial distribution function (RDF) of CoCrFeMnNi HEA foam under varying temperature and porosity conditions. Simulation snapshots depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eh of the HEA foam (15% porosity) reveal the transition from a fully FCC atomic arrangement before deformation to an amorphous structure after deformation, with stacking faults observed. At lower temperatures, such as 1300 K, the RDF peaks are more pronounced, signifying that the atomic arrangement remains relatively well-ordered. However, as the temperature rises to 1600 K and 1900 K, the peaks gradually decrease in height, reflecting the increased thermal vibrations that cause atoms to deviate from their equilibrium positions. This decrease in peak height is a direct result of the enhanced atomic mobility due to higher thermal energy, which causes the atoms to vibrate more vigorously, increasing the interatomic distances and reducing the likelihood of finding atoms at specific distances.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAt 1300 K, the RDF peaks indicate a higher probability of finding atoms at characteristic distances due to the coherent structure of the material. As the temperature rises to 1900 K, the peak heights diminish, indicating that thermal motion has expanded the lattice and weakened atomic bonds. The expansion of the HEA at elevated temperatures results in the increased separation of atoms, reducing the likelihood of atomic interactions at regular intervals [\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e]. This reduction in atomic coherence is a critical factor contributing to the degradation of mechanical properties, including reduced creep resistance and elastic modulus, as the material becomes more susceptible to sustained deformation under thermal and mechanical stress. In addition to the influence of temperature, porosity also plays a critical role in altering the atomic arrangement within the HEA. As porosity increases from 0\u0026ndash;30%, the voids introduced into the structure lead to a significant reduction in RDF peak heights, particularly at higher temperatures. In the bulk CoCrFeMnNi HEA with no porosity, the RDF peaks are sharper and higher, indicating a well-ordered atomic lattice where atoms are tightly packed. As porosity increases, the presence of voids disrupts the regular atomic arrangement, leading to a broader distribution of interatomic distances and a decrease in RDF peak heights.\u003c/p\u003e \u003cp\u003eAt 30% porosity, the RDF peaks are significantly lower and broader compared to the material with 0% porosity. This behavior is attributable to the increased average interatomic distances caused by the voids in the structure. The introduction of voids reduces the number of neighboring atoms, leading to greater atomic disorder. As a result, the likelihood of finding atoms at expected distances diminishes, reflecting a weakening of the atomic bonding network. This structural disorganization is exacerbated by the concurrent effects of elevated temperature, which further weakens atomic bonds and reduces the mechanical integrity of the foam. The combined effects of increasing temperature and porosity result in a marked reduction in the RDF peak heights, indicating a significant loss of structural coherence in the HEA. The voids created by porosity, combined with the thermal expansion of the lattice at elevated temperatures, reduce the bonding energy between atoms, making the material more susceptible to deformation under sustained stress. This is particularly evident at higher porosity levels (30%) and elevated temperatures (1900 K), where the atomic arrangement becomes increasingly disordered. The reduction in RDF peak heights, coupled with a broader distribution of interatomic distances, reflects the gradual degradation of the atomic structure, leading to weakened mechanical properties such as reduced creep resistance.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e3.6 Effect of Pressure on Creep Deformation Behavior\u003c/h2\u003e \u003cp\u003eThe creep behavior of the modeled CoCrFeMnNi high-entropy alloy (HEA) foams was evaluated at a constant temperature of 1900 K across varying pressures of 5 GPa, 6 GPa, 7 GPa, and 8 GPa and porosity levels. Figure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e illustrates the impact of varying pressure on creep deformation in CoCrFeMnNi HEA at a constant temperature of 1900 K, across different porosity levels. The strain vs. time plots Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ea-g reveal a clear increase in strain as pressure rises from 5 GPa to 8 GPa, with higher porosity materials consistently showing more significant deformation. Snapshot Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eh captures the structural changes in the 30% porosity HEA foam during the creep process, progressing from a fully FCC configuration before deformation to a partially FCC structure during deformation, and finally to an amorphous state, indicating stacking faults and the onset of dislocation-driven mechanisms. This highlights the combined effects of pressure and porosity on accelerating creep deformation. The findings indicate a clear relationship between increasing pressure and strain, as well as the amplifying effect of porosity on the susceptibility of the material to deformation.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAs shown in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, at 5 GPa and 0% porosity, the strain value is 0.256. As pressure increases to 6 GPa, the strain increases to 0.281, and further rises to 0.304 and 0.326 at 7 GPa and 8 GPa, respectively. This trend of increasing strain with pressure is consistent across all porosity levels, highlighting that higher pressures significantly accelerate creep deformation. At 30% porosity, the strain value under 5 GPa is 0.312, increasing to 0.348 at 6 GPa, 0.382 at 7 GPa, and peaking at 0.415 under 8 GPa. This shows that the foam becomes increasingly susceptible to deformation as both pressure and porosity rise. The influence of porosity is particularly evident when comparing different porosity levels at a constant pressure. Under 7 GPa, the strain value for 0% porosity is 0.304, while for 30% porosity, it is significantly higher at 0.382, reflecting the pronounced effect of porosity on the deformation behavior of the foam. As porosity increases, the introduction of voids into the HEA disrupts the atomic lattice and weakens atomic bonding, making the material more prone to deformation. This effect is exacerbated at higher pressures, where the presence of voids amplifies the material's response to external forces, as shown by the consistently increasing strain values across porosity levels and pressures.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eStrain values for CoCrFeMnNi HEA under varying pressures (5 GPa, 6 GPa, 7 GPa, and 8 GPa) at a constant temperature of 1900 K, across different porosity levels (0\u0026ndash;30%).\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePorosity (%)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5 GPa\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e6 GPa\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e7 GPa\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e8GPa\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.256\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.281\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.304\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.326\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.267\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.292\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.318\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.341\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.270\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.299\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.326\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.352\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.274\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.305\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.333\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.360\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.279\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.311\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.342\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.372\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.289\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.329\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.362\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.393\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.312\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.348\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.382\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.415\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eIncreased pressure enhances atomic mobility and dislocation motion, facilitating creep deformation [\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e]. At elevated pressures, such as 8 GPa, the external forces cause atoms to rearrange more easily within the lattice, which leads to greater sustained deformation over time. The introduction of porosity further exacerbates this behavior, as the voids serve as stress concentrators that increase local stress and allow for easier atomic movement. As a result, the strain response is more pronounced in the HEAs with higher porosity, particularly at elevated pressures. Thus, the creep behavior of CoCrFeMnNi HEA at 1900 K is strongly influenced by both pressure and porosity. The strain values progressively increase from 0.256 at 5 GPa to 0.415 at 8 GPa across different porosity levels, with higher porosity materials exhibiting greater susceptibility to deformation. These results demonstrate the critical role of pressure and porosity in determining the long-term mechanical performance and durability of HEAs, especially in high-temperature, high-pressure environments commonly encountered in industrial applications.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e3.7 Creep Deformation Mechanism of HEA Foam\u003c/h2\u003e \u003cp\u003eThe creep deformation mechanism in CoCrFeMnNi high-entropy alloy (HEA) foam is heavily influenced by its microstructural evolution, dislocation activity, and porosity. The creep deformation structure and dislocation analysis focused on the effects of variable percent porosity and temperature. The structural analysis revealed the presence of various atomic arrangements, including amorphous, FCC, and HCP phases, with an emphasis on stacking faults. The dislocation analysis identified several types of dislocations characterized by their segment types, specifically the Shockley partial dislocations (1/6\u0026thinsp;\u0026lt;\u0026thinsp;112\u0026gt;), Stair-rod dislocations (1/6\u0026thinsp;\u0026lt;\u0026thinsp;110\u0026gt;), and Hirth dislocations (1/3\u0026thinsp;\u0026lt;\u0026thinsp;100\u0026gt;). It is important to note that the analysis of dislocation propagation was conducted by considering the data collected ten frames after the initial occurrence or initiation of the dislocations. This comprehensive examination provided insights into the relationship between porosity and dislocation behavior under elevated temperature and constant pressure conditions. Figure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e presents snapshots of the dislocation behavior\u0026mdash;nucleation and propagation\u0026mdash;observed in HEA foams during creep deformation, highlighting significant changes associated with varying levels of porosity. As porosity increases, the microstructures transition from being predominantly FCC to exhibiting a higher prevalence of amorphous structures. This transformation is accompanied by the promotion of Shockley partial dislocations, which become more prominent at higher porosities. Furthermore, the emergence of Stair-rod and Hirth dislocations indicates the development of more complex dislocation interactions within the material. These observations demonstrate the critical influence of porosity on the deformation mechanisms in HEA foams, illustrating how structural changes can alter the fundamental creep behavior of the material under stress.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003e3.8 Structure and Dislocation Evolution in Creep Deformation of HEA Foam\u003c/h2\u003e \u003cdiv id=\"Sec16\" class=\"Section3\"\u003e \u003ch2\u003e3.8.1 Effect of Porosity\u003c/h2\u003e \u003cp\u003eThe analysis of the dislocation behavior in the HEA foam structures under creep conditions revealed a strong dependency on the percent porosity of the material. At 0% porosity, dislocation nucleation and propagation mechanisms were dominated by FCC structures, with 59.9% and 33.6% of the structure composed of FCC lattice in the nucleation and propagation stages, respectively. As porosity increased, a gradual transition occurred, with a significant rise in the contribution of amorphous atomic arrangements. At 5% porosity, the nucleation stage had 27.1% of amorphous structures, and by the propagation stage, this proportion increased to 72.8%. At higher porosity levels, such as 30%, the propagation stage contained up to 62.2% amorphous content. The percentage of HCP (hexagonal close-packed) structures remained low across all porosities, but it was noteworthy that as porosity increased, HCP appeared more frequently in the propagation stages. At 0% porosity, HCP content was entirely absent, but at 10% porosity, it rose to 0.7% in the propagation stage. This trend continued up to 1.4% at 30% porosity. This increase in HCP likely correlated with the formation of stacking faults within the crystal structure, as discussed in relation to Shockley partial dislocations.\u003c/p\u003e \u003cp\u003eDislocation activity, specifically the generation of Shockley partials, played a significant role in the deformation of the HEA foam. At 0% porosity, nucleation produced only one Shockley partial dislocation, but this number grew substantially with increased porosity. At 10% porosity, nucleation resulted in 18 Shockley partials, and propagation generated as many as 31. The maximum number of Shockley dislocations appeared at higher porosities during the propagation stage, where up to 39 segments were observed. This high number of Shockley partials indicated that stacking faults became more prevalent as porosity increased, weakening the crystal structure and promoting deformation. Stair-rod and Hirth dislocations also contributed to the deformation mechanism, though to a lesser extent compared to Shockley partials. At lower porosities, these dislocations were absent or very limited. Thus, no Stair-rod or Hirth dislocations were present at 0% porosity, and only two Stair-rod segments appeared at 5% porosity during nucleation. As porosity increased, Stair-rod and Hirth dislocations became more frequent, peaking at 30% porosity with two Stair-rod and two Hirth dislocations during propagation.\u003c/p\u003e \u003cp\u003eThe distribution of dislocation types suggested that the presence of porosity not only promoted the formation of partial dislocations but also increased the likelihood of more complex dislocation interactions, such as the formation of Stair-rod and Hirth segments. These dislocations served as indicators of the intense localized stress fields created by the pores, which acted as nucleation sites for dislocations and stacking faults. Subsequently, the creep deformation of HEA foam was strongly influenced by porosity. Increased porosity resulted in a higher proportion of amorphous structures and promoted the generation of Shockley partial dislocations, leading to the formation of stacking faults. The introduction of Stair-rod and Hirth dislocations at higher porosities further suggested the complexity of the dislocation network and highlighted the role of pores as stress concentrators that significantly affected the mechanical properties of the material. These findings align with the broader understanding of how porosity weakens the foam structure, contributing to enhanced creep deformation under stress.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec17\" class=\"Section3\"\u003e \u003ch2\u003e3.8.2 Effect of Temperature\u003c/h2\u003e \u003cp\u003eThe effect of temperature on creep deformation behavior was investigated through a systematic analysis of varying percent porosities at three distinct temperatures: 1300 K, 1600 K, and 1900 K. As the temperature increased, there was a notable shift in the structural composition of the materials. At 0% porosity and 1300 K, the material exhibited a significant 66.9% of its structure as FCC, with no observable HCP or dislocations present. However, with a rise in temperature to 1600 K, the proportion of FCC structures decreased to 48.8%, while 51.2% of the structure transitioned to amorphous atomic arrangements, including the emergence of Shockley partial dislocations, highlighting the increased atomic mobility facilitated by the higher temperature. At 1900 K, the trend continued, with the FCC structure further declining to 33.6% and an increase in Shockley dislocations, indicating enhanced deformation mechanisms due to thermal activation. As the percent porosity increased, similar trends were observed across the various temperatures. At 5% porosity, the FCC content decreased from 67.6% at 1300 K to 44.7% at 1600 K, with a corresponding increase in dislocation activity, as evidenced by the rise in Shockley segments from two to twelve. This behavior remained consistent at 10% porosity, where the Shockley dislocations increased from four at 1300 K to 43 at 1600 K, suggesting that temperature not only affected phase stability but also significantly enhanced dislocation generation and mobility.\u003c/p\u003e \u003cp\u003eMoreover, the response of the material to higher temperatures also led to the formation of stair-rod dislocations, particularly at 1600 K, with the highest occurrence noted at 15% porosity, where five stair-rod segments were identified. This indicated that temperature played a crucial role in facilitating complex dislocation interactions and the emergence of secondary dislocation types, thereby contributing to the creep behavior of the materials. At 1900 K, the general trend continued, with the FCC content significantly diminishing across all porosity levels, and the proportion of amorphous structures notably increasing, reinforcing the notion that elevated temperatures contributed to greater disorder in the material's microstructure. The highest number of Shockley dislocations was recorded at 25% porosity (39 segments), emphasizing the strong correlation between temperature, porosity, and dislocation behavior. Figure\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e presents a series of snapshots illustrating the structural changes in HEA foam subjected to varying percent porosities at temperatures of 1300 K, 1600 K, and 1900 K. These images effectively capture the intricate dynamics of defect evolution and dislocation segment formation during the creep deformation process. At each temperature, the snapshots reveal distinct alterations in the microstructure, highlighting how increased thermal energy influences the behavior of the material.\u003c/p\u003e \u003cp\u003eAt 1300 K, the HEA foam displays a relatively stable configuration with limited dislocation activity, characterized by sparse defect meshes. As the temperature rises to 1600 K, a pronounced transformation occurs: the defect mesh becomes more pronounced, and the density of dislocation segments significantly increases. This observation suggests that the elevated temperature facilitates greater atomic mobility, leading to a higher propensity for dislocation nucleation and propagation. Further increasing the temperature to 1900 K results in even more dramatic structural changes. The snapshots indicate a substantial proliferation of dislocation segments, revealing a complex network of defects that interconnect throughout the foam structure. This evolution reflects the material\u0026rsquo;s response to the combined effects of increased temperature and varying porosity, highlighting how these factors contribute to enhanced creep behavior. Subsequently, the analysis indicated that increasing temperature significantly influenced the creep deformation behavior of materials by promoting the transformation of crystal structures, enhancing dislocation generation, and facilitating complex interactions among different types of dislocations. These findings demonstrate the critical role of thermal conditions in determining the mechanical properties and performance of materials under stress.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section2\"\u003e \u003ch2\u003e3.9 Dislocation and Failure Mechanism in Creep Deformation of HEA foam\u003c/h2\u003e \u003cp\u003eIn CoCrFeMnNi HEA foam, the dislocation mechanism plays a significant role in its deformation behavior, particularly under sustained stress and high temperatures. As the structure undergoes deformation, atoms are displaced from their equilibrium lattice positions, resulting in the formation of dislocations [\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e]. These dislocations lead to rearrangement of the lattice structure, facilitating creep deformation. As the strain in the foam increases, perfect dislocations are initially generated, but under localized stress\u0026mdash;especially near pore sites\u0026mdash;partial dislocations emerge and propagate through the lattice [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. The pores within the HEA foam act as stress concentrators, causing intense localized stress fields that initiate dislocations from these pore regions. This is a critical factor in the dislocation nucleation and propagation process, as pores serve as the primary sites for the generation of partial dislocations. The partial dislocations generated in the HEA foam structure include Shockley partials, Stair-rod partials, and Hirth partials. Among the different types of dislocations observed in the HEA foam, Shockley partial dislocations are the most prevalent across all porosity levels. These dislocations are significant contributors to the overall dislocation density and are directly responsible for the formation of stacking faults in the crystal structure of the material (see Figs.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eh, \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eh and \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eh). Shockley partial dislocations, characterized by their 1/6\u0026thinsp;\u0026lt;\u0026thinsp;211\u0026thinsp;\u0026gt;\u0026thinsp;Burgers vector, lead to the formation of intrinsic stacking faults within the face-centered cubic (FCC) lattice of the alloy [\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e]. These intrinsic stacking faults disrupt the regular ABCABC stacking sequence of the FCC structure, causing a local transformation into a hexagonal close-packed (HCP) stacking sequence.\u003c/p\u003e \u003cp\u003eAs deformation continues, the stacking faults propagate and interact, giving rise to extrinsic stacking faults and occasionally resulting in the formation of deformation twins [\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e]. This structural reconfiguration introduces additional defects in the lattice, further contributing to creep deformation. With further strain, the stacking faults within the structure intersect, forming vacancy strings that nucleate voids [\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e]. These vacancy strings, which are perpendicular to the loading axis, evolve into voids, leading to crack initiation and propagation. Dislocations emitted from these vacancy strings facilitate crack growth, particularly from the pore sites, where stress concentrations are highest. As a result, the pores become the primary sites for crack initiation during creep deformation. The propagation of these cracks from pore to pore significantly compromises the structural integrity of the foam. Furthermore, the presence of pores, acting as defects within the lattice, and the proliferation of dislocations and stacking faults result in a reduced stress-bearing capacity of the HEA foam. As the dislocations continue to propagate and interact with the pores, the material\u0026rsquo;s strength diminishes, leading to accelerated creep deformation. The combined effects of pore-induced dislocation generation, stacking fault formation, and crack propagation culminate in a substantial decrease in the mechanical strength of the HEA foam under high-temperature, constant pressure conditions.\u003c/p\u003e \u003c/div\u003e"},{"header":"4. Conclusion","content":"\u003cp\u003eHigh-entropy alloys exhibit exceptional mechanical properties, showcasing significant potential for a wide range of engineering applications. The use of atomistic simulations has proven invaluable in enhancing our understanding of HEAs, allowing for the prediction of their behavior under varying conditions. In this study, we provide a comprehensive analysis of the creep deformation mechanisms in equiatomic CoCrFeMnNi HEA foam through molecular dynamics simulations, emphasizing the intricate interplay between porosity, temperature, and pressure. The results indicate that variations in these parameters significantly influence the microstructural evolution of the HEA foam, altering the mechanical behavior of the material at elevated temperatures and under constant stress. We evaluated the effects of varying percent porosities from 0\u0026ndash;30% in increments of 5%, temperatures of 1300 K, 1600 K, and 1900 K, as well as pressures of 5 GPa, 6 GPa, 7 GPa, and 8 GPa on the creep behavior of high-entropy alloy foams. The results demonstrated that increasing temperature led to higher strain values across the models. Additionally, mean square deviation and radial distribution function analyses were conducted to further elucidate the structural behavior.\u003c/p\u003e \u003cp\u003eFurthermore, the findings revealed that increasing pressure also contributed to higher strain values in the models. These findings illustrate the significant interplay between temperature, pressure, and porosity in influencing the mechanical properties of high-entropy alloy foams. Specifically, the results demonstrate that increasing temperature enhances atomic mobility, leading to a notable shift in the structural composition from FCC to amorphous arrangements, accompanied by a rise in dislocation activity. The emergence of Shockley dislocations and the formation of stair-rod and Hirth dislocations highlight the complexity of dislocation interactions, which are critical in governing the creep behavior of these materials. Furthermore, the study reveals that increased porosity exacerbates the effects of thermal conditions, further promoting dislocation generation and mobility, thereby reinforcing the HEA foam susceptibility to deformation. The significance of this research lies in its potential to inform the design and optimization of HEA foams for high-performance applications in extreme environments. By elucidating the mechanisms underlying creep deformation and the role of microstructural factors, this study contributes to the broader understanding of how HEA foams can be engineered to meet the demanding requirements of modern engineering applications. Future work could expand upon these findings by exploring additional variables and their interactions, ultimately advancing the development of advanced materials with tailored properties for enhanced mechanical performance.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis research did not receive any specific grant from funding agencies in the public, commercial, or non-profit sectors.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDeclaration of competing interest\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData Availability Statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe data underlying this study is available in the published article.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCode Availability\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthics approval\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot Applicable\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCRediT authorship contribution statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eEzekiel Edward Nettey-Oppong: Conceptualization, Writing original draft, Writing - review \u0026amp; editing, Visualization, Formal analysis, Investigation. Emmanuel Essel Mensah: Conceptualization, Writing original draft, Writing - review \u0026amp; editing, Visualization, Formal analysis, Investigation. Stephen Takyi Taylor: Conceptualization, Writing original draft, Writing - review \u0026amp; editing, \u0026nbsp;Investigation. Anthony Kwasi Martey: Conceptualization, Writing original draft, Writing - review \u0026amp; editing, \u0026nbsp;Investigation. Eric Asare: Supervision, Validation, Writing - review \u0026amp; editing. Martinson Addo Nartey: Supervision, Validation, Formal analysis, Investigation, Writing - review \u0026amp; editing.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent to Participate\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot Applicable\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent to Publication\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot Applicable\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eZhang Q et al (2017) The effects of phase constitution on magnetic and mechanical properties of FeCoNi(CuAl)x(x\u0026thinsp;=\u0026thinsp;0\u0026ndash;1.2) high-entropy alloys. J Alloys Compd 693. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.jallcom.2016.09.271\u003c/span\u003e\u003cspan address=\"10.1016/j.jallcom.2016.09.271\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eQi W et al (2022) Effects of Al and Ti co-doping on the strength-ductility- corrosion resistance of CoCrFeNi-AlTi high-entropy alloys. J Alloys Compd 925. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.jallcom.2022.166751\u003c/span\u003e\u003cspan address=\"10.1016/j.jallcom.2022.166751\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTroparevsky MC, Morris JR, Daene M, Wang Y, Lupini AR, Stocks GM (2015) Beyond Atomic Sizes and Hume-Rothery Rules: Understanding and Predicting High-Entropy Alloys. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1007/s11837-015-1594-2\u003c/span\u003e\u003cspan address=\"10.1007/s11837-015-1594-2\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGorsse S, Tancret F (2018) Current and emerging practices of CALPHAD toward the development of high entropy alloys and complex concentrated alloys. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1557/jmr.2018.152\u003c/span\u003e\u003cspan address=\"10.1557/jmr.2018.152\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLee C et al (2018) Lattice distortion in a strong and ductile refractory high-entropy alloy. Acta Mater 160. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.actamat.2018.08.053\u003c/span\u003e\u003cspan address=\"10.1016/j.actamat.2018.08.053\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSharma AS, Yadav S, Biswas K, Basu B (2018) High-entropy alloys and metallic nanocomposites: Processing challenges, microstructure development and property enhancement. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.mser.2018.04.003\u003c/span\u003e\u003cspan address=\"10.1016/j.mser.2018.04.003\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYeh JW et al (2004) Nanostructured high-entropy alloys with multiple principal elements: Novel alloy design concepts and outcomes. Adv Eng Mater 6(5). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1002/adem.200300567\u003c/span\u003e\u003cspan address=\"10.1002/adem.200300567\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTong C, Chen M, Chen S, Yeh J (2005) Mechanical Performance of the Al ^ sub x ^ CoCrCuFeNi High-Entropy Alloy System w \u0026hellip; \u003cem\u003eLibrary\u003c/em\u003e, 36, no. May\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLiao WB et al (2021) Microstructures and mechanical properties of CoCrFeNiMn high-entropy alloy coatings by detonation spraying. Intermetallics (Barking) 132. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.intermet.2021.107138\u003c/span\u003e\u003cspan address=\"10.1016/j.intermet.2021.107138\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDada M, Popoola P, Mathe N (2023) Recent advances of high entropy alloys for aerospace applications: a review. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1108/WJE-01-2021-0040\u003c/span\u003e\u003cspan address=\"10.1108/WJE-01-2021-0040\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMoschetti M, Burr P, Obbard E, Kruzic JJ, Hosemann P, Gludovatz B (2022) Design considerations for high entropy alloys in advanced nuclear applications. J Nucl Mater 567. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.jnucmat.2022.153814\u003c/span\u003e\u003cspan address=\"10.1016/j.jnucmat.2022.153814\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFerreir\u0026oacute;s PA et al (2023) VNbCrMo refractory high-entropy alloy for nuclear applications. Int J Refract Met Hard Mater 113. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.ijrmhm.2023.106200\u003c/span\u003e\u003cspan address=\"10.1016/j.ijrmhm.2023.106200\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYan X, Zhang Y (2020) Functional properties and promising applications of high entropy alloys. Scr Mater 187. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.scriptamat.2020.06.017\u003c/span\u003e\u003cspan address=\"10.1016/j.scriptamat.2020.06.017\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHach\u0026eacute; MJR, Cheng C, Zou Y (2020) Nanostructured high-entropy materials. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1557/jmr.2020.33\u003c/span\u003e\u003cspan address=\"10.1557/jmr.2020.33\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFeng CW, Keong CW, Hsueh YP, Wang YY, Sue HJ (2005) Modeling of long-term creep behavior of structural epoxy adhesives. Int J Adhes Adhes 25(5). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.ijadhadh.2004.11.009\u003c/span\u003e\u003cspan address=\"10.1016/j.ijadhadh.2004.11.009\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYang Z et al (2018) Flexural creep tests and long-term mechanical behavior of fiber-reinforced polymeric composite tubes. Compos Struct 193. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.compstruct.2018.03.083\u003c/span\u003e\u003cspan address=\"10.1016/j.compstruct.2018.03.083\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNagarjuna C et al (2022) Developing harmonic structure in CoCrFeMnNi high entropy alloy to enhance mechanical properties via powder metallurgy approach. J Mater Res Technol 17. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.jmrt.2022.01.098\u003c/span\u003e\u003cspan address=\"10.1016/j.jmrt.2022.01.098\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYoussef KM, Zaddach AJ, Niu C, Irving DL, Koch CC (2014) A novel low-density, high-hardness, high-entropy alloy with close-packed single-phase nanocrystalline structures. Mater Res Lett 3(2). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1080/21663831.2014.985855\u003c/span\u003e\u003cspan address=\"10.1080/21663831.2014.985855\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMoravcik I, Cizek J, de Gouvea L, Cupera J, Guban I, Dlouhy I (2019) Nitrogen interstitial alloying of CoCrFeMnNi high entropy alloy through reactive powder milling. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.3390/e21040363\u003c/span\u003e\u003cspan address=\"10.3390/e21040363\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJo MG et al (2022) High temperature tensile and creep properties of CrMnFeCoNi and CrFeCoNi high-entropy alloys. Mater Sci Engineering: A 838. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.msea.2022.142748\u003c/span\u003e\u003cspan address=\"10.1016/j.msea.2022.142748\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLiu CJ et al (2022) Tensile creep behavior of HfNbTaTiZr refractory high entropy alloy at elevated temperatures. Acta Mater 237. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.actamat.2022.118188\u003c/span\u003e\u003cspan address=\"10.1016/j.actamat.2022.118188\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWang D, Tan J, Li CJ, Qin XM, Guo SF (2021) Enhanced creep resistance of Ti30Al25Zr25Nb20 high-entropy alloy at room temperature. J Alloys Compd 885. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.jallcom.2021.161038\u003c/span\u003e\u003cspan address=\"10.1016/j.jallcom.2021.161038\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYedla N, Salman SA, Karthik V (2022) Molecular Dynamics Simulations for Nanoscale Insight into the Phase Transformation and Deformation Behavior of Shape-Memory Materials, in \u003cem\u003eShape Memory Composites Based on Polymers and Metals for 4D Printing: Processes, Applications and Challenges\u003c/em\u003e, \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1007/978-3-030-94114-7_4\u003c/span\u003e\u003cspan address=\"10.1007/978-3-030-94114-7_4\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWu WP, Şopu D, Eckert J (2021) Molecular dynamics study of the nanoindentation behavior of cu64zr36/cu amorphous/crystalline nanolaminate composites. Materials 14(11). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.3390/ma14112756\u003c/span\u003e\u003cspan address=\"10.3390/ma14112756\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhu Y, Gong Q, Yi M (2024) Molecular Dynamics Investigation of Shock-Induced Deformation Behavior and Failure Mechanism in Metallic Materials. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1007/s11831-023-10045-8\u003c/span\u003e\u003cspan address=\"10.1007/s11831-023-10045-8\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChen J, Li P, Lin EE (2020) A molecular dynamics study on the mechanical properties of Fe-Ni alloy nanowires and their temperature dependence. RSC Adv 10(66). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1039/d0ra07831j\u003c/span\u003e\u003cspan address=\"10.1039/d0ra07831j\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZepeda-Ruiz LA et al (2021) Atomistic insights into metal hardening. Nat Mater 20(3). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1038/s41563-020-00815-1\u003c/span\u003e\u003cspan address=\"10.1038/s41563-020-00815-1\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNettey-Oppong EE, Mensah EE, Effah E, Asare E, Nartey MA (2023) Mechanical properties and deformation behavior of equiatomic CoCrFeMnNi high-entropy alloy foam: A molecular dynamics study. Solid State Commun 371. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.ssc.2023.115236\u003c/span\u003e\u003cspan address=\"10.1016/j.ssc.2023.115236\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhao F, Zhang J, He C, Zhang Y, Gao X, Xie L (2020) Molecular dynamics simulation on creep behavior of nanocrystalline tial alloy. Nanomaterials 10(9). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.3390/nano10091693\u003c/span\u003e\u003cspan address=\"10.3390/nano10091693\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLi Q, Jiang C, Du Y (2023) Molecular dynamics study on dynamic mechanical behaviour of FeCoCrCuNi high entropy alloy. Mater Technol 38(1). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1080/10667857.2023.2200660\u003c/span\u003e\u003cspan address=\"10.1080/10667857.2023.2200660\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eThompson AP et al (2022) LAMMPS - a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales. Comput Phys Commun 271. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.cpc.2021.108171\u003c/span\u003e\u003cspan address=\"10.1016/j.cpc.2021.108171\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGunkelmann N, Bringa EM, Rosandi Y (2018) Molecular Dynamics Simulations of Aluminum Foams under Tension: Influence of Oxidation. J Phys Chem C 122(45). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1021/acs.jpcc.8b07146\u003c/span\u003e\u003cspan address=\"10.1021/acs.jpcc.8b07146\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGunkelmann N, Rosandi Y, Ruestes CJ, Bringa EM, Urbassek HM (2016) Compaction and plasticity in nanofoams induced by shock waves: A molecular dynamics study. Comput Mater Sci 119. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.commatsci.2016.03.035\u003c/span\u003e\u003cspan address=\"10.1016/j.commatsci.2016.03.035\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eStoddard SD (1978) Identifying clusters in computer experiments on systems of particles. J Comput Phys 27(2). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/0021-9991(78)90011-6\u003c/span\u003e\u003cspan address=\"10.1016/0021-9991(78)90011-6\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGr\u0026ouml;ger R, Vitek V, Dlouh\u0026yacute; A (2020) Effective pair potential for random fcc CoCrFeMnNi alloys. Model Simul Mat Sci Eng 28(7). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1088/1361-651X/ab7f8b\u003c/span\u003e\u003cspan address=\"10.1088/1361-651X/ab7f8b\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eStukowski A (2010) Visualization and analysis of atomistic simulation data with OVITO-the Open Visualization Tool. Model Simul Mat Sci Eng 18(1). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1088/0965-0393/18/1/015012\u003c/span\u003e\u003cspan address=\"10.1088/0965-0393/18/1/015012\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eShang Y, Brechtl J, Pistidda C, Liaw PK (2022) Mechanical behavior of high-entropy alloys: A review, in \u003cem\u003eHigh-Entropy Materials: Theory, Experiments, and Applications\u003c/em\u003e, \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1007/978-3-030-77641-1_10\u003c/span\u003e\u003cspan address=\"10.1007/978-3-030-77641-1_10\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHuang SM, Nauman EA, Stanciu LA (2019) Investigation of porosity on mechanical properties, degradation and in-vitro cytotoxicity limit of Fe30Mn using space holder technique. Mater Sci Eng C 99. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.msec.2019.02.055\u003c/span\u003e\u003cspan address=\"10.1016/j.msec.2019.02.055\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWang F et al (2020) Multiplicity of dislocation pathways in a refractory multiprincipal element alloy. Sci (1979) 370(6512). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1126/science.aba3722\u003c/span\u003e\u003cspan address=\"10.1126/science.aba3722\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDeluigi OR, Valencia F, Amigo N, Aquistapace F, Gonzalez RI, Bringa EM (2022) Atomistic simulations of tensile deformation of a nanoporous high-entropy alloy. J Mater Sci 57(42). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1007/s10853-022-07862-w\u003c/span\u003e\u003cspan address=\"10.1007/s10853-022-07862-w\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLeppert L, Albuquerque RQ, Foster AS, K\u0026uuml;mmel S (2013) Interplay of electronic structure and atomic mobility in nanoalloys of au and pt. J Phys Chem C 117(33). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1021/jp404341v\u003c/span\u003e\u003cspan address=\"10.1021/jp404341v\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTerban MW, Billinge SJL (2022) Structural Analysis of Molecular Materials Using the Pair Distribution Function. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1021/acs.chemrev.1c00237\u003c/span\u003e\u003cspan address=\"10.1021/acs.chemrev.1c00237\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eVarvenne C, Luque A, Curtin WA (2016) Theory of strengthening in fcc high entropy alloys. Acta Mater 118. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.actamat.2016.07.040\u003c/span\u003e\u003cspan address=\"10.1016/j.actamat.2016.07.040\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBlum W (2008) Mechanisms of creep deformation in steel. Creep-Resistant Steels. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1533/9781845694012.2.365\u003c/span\u003e\u003cspan address=\"10.1533/9781845694012.2.365\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHull D, Bacon DJ (2011) \u003cem\u003eIntroduction to Dislocations\u003c/em\u003e. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/s1369-7021(11)70217-6\u003c/span\u003e\u003cspan address=\"10.1016/s1369-7021(11)70217-6\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhao S, Stocks GM, Zhang Y (2017) Stacking fault energies of face-centered cubic concentrated solid solution alloys. Acta Mater 134. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.actamat.2017.05.001\u003c/span\u003e\u003cspan address=\"10.1016/j.actamat.2017.05.001\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLu K, Chauhan A, Litvinov D, Schneider M, Laplanche G, Aktaa J (2023) Cooperative deformation mechanisms in a fatigued CoCrNi multi-principal element alloy: A case of low stacking fault energy. J Mech Phys Solids 180. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.jmps.2023.105419\u003c/span\u003e\u003cspan address=\"10.1016/j.jmps.2023.105419\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGuo Y, Paramatmuni C, Avcu E (2023) Void Nucleation and Growth from Heterophases and the Exploitation of New Toughening Mechanisms in Metals. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.3390/cryst13060860\u003c/span\u003e\u003cspan address=\"10.3390/cryst13060860\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"multiscale-and-multidisciplinary-modeling-experiments-and-design","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"mmed","sideBox":"Learn more about [Multiscale and Multidisciplinary Modeling, Experiments and Design](https://link.springer.com/journal/41939)","snPcode":"41939","submissionUrl":"https://submission.nature.com/new-submission/41939/3","title":"Multiscale and Multidisciplinary Modeling, Experiments and Design","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"High entropy alloys, Metal foams, Creep, Molecular dynamics simulation","lastPublishedDoi":"10.21203/rs.3.rs-6344719/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6344719/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eHigh-entropy alloys (HEAs) are a class of materials distinguished by their unique multi-element compositions, offering exceptional mechanical properties such as high strength and thermal stability. Recently, HEA foams have been fabricated, offering several additional advantages over traditional solid HEAs. These include reduced density, which enhances their suitability for lightweight structural applications, and enhanced energy absorption. In this study, molecular dynamics simulations were used to investigate the creep deformation mechanisms of equiatomic CoCrFeMnNi HEA foam under varying conditions, including temperatures of 1300 K, 1600 K, and 1900 K, pressures ranging from 5 to 8 GPa, and porosities from 0\u0026ndash;30%. The results demonstrated that an increase in temperature led to higher strain values, particularly in models with porosities below 15%. Structural analysis reveals a reduction in the face-centered cubic (FCC) phase with increasing temperature, accompanied by an increase in amorphous structures and Shockley partial dislocation activity. Dislocation networks became more complex with increasing porosity, with the high dislocation densities observed at high porosities and temperature. Further mean square deviation (MSD) and radial distribution function (RDF) techniques helped elucidate the atomic-scale changes in the HEA structure, showing the significant interplay between temperature, pressure, and porosity on material stability. This study provides valuable insights into the creep behavior and dislocation dynamics of HEA foams, contributing to the optimization of these materials for high-performance applications in extreme environments.\u003c/p\u003e","manuscriptTitle":"Unravelling the Creep Behavior of Equiatomic CoCrFeMnNi High-Entropy Alloy Foam: A Molecular Dynamics Study","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-04-24 13:18:09","doi":"10.21203/rs.3.rs-6344719/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-06-09T15:27:46+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-06-07T14:47:57+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-05-26T12:47:09+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"156206053036157365326318387129558020914","date":"2025-05-12T09:54:46+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"7773222502882730058485621261838401277","date":"2025-05-10T08:36:01+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"214492556427841439801833807159789269185","date":"2025-05-09T16:06:58+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-05-01T14:14:10+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"197043838763018384586145210654841858976","date":"2025-04-04T09:33:28+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"254264711155286211955231916968458171054","date":"2025-04-03T02:01:48+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-04-02T15:53:33+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-04-02T11:08:54+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-04-02T11:07:42+00:00","index":"","fulltext":""},{"type":"submitted","content":"Multiscale and Multidisciplinary Modeling, Experiments and Design","date":"2025-03-31T12:07:52+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"multiscale-and-multidisciplinary-modeling-experiments-and-design","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"mmed","sideBox":"Learn more about [Multiscale and Multidisciplinary Modeling, Experiments and Design](https://link.springer.com/journal/41939)","snPcode":"41939","submissionUrl":"https://submission.nature.com/new-submission/41939/3","title":"Multiscale and Multidisciplinary Modeling, Experiments and Design","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"71bee668-86a3-4ab6-8a02-03bb44d0ad4d","owner":[],"postedDate":"April 24th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-08-25T16:30:05+00:00","versionOfRecord":{"articleIdentity":"rs-6344719","link":"https://doi.org/10.1007/s41939-025-01006-8","journal":{"identity":"multiscale-and-multidisciplinary-modeling-experiments-and-design","isVorOnly":false,"title":"Multiscale and Multidisciplinary Modeling, Experiments and Design"},"publishedOn":"2025-08-20 16:12:52","publishedOnDateReadable":"August 20th, 2025"},"versionCreatedAt":"2025-04-24 13:18:09","video":"","vorDoi":"10.1007/s41939-025-01006-8","vorDoiUrl":"https://doi.org/10.1007/s41939-025-01006-8","workflowStages":[]},"version":"v1","identity":"rs-6344719","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6344719","identity":"rs-6344719","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}