Divergent Trends in Surface Atomic Segregation During Rapid Heating of Fe-Ni-Cr-Co-Cu High-Entropy Alloy Nanoparticles: A Molecular Dynamics Study

Divergent Trends in Surface Atomic Segregation During Rapid Heating of Fe-Ni-Cr-Co-Cu High-Entropy Alloy Nanoparticles: 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 Divergent Trends in Surface Atomic Segregation During Rapid Heating of Fe-Ni-Cr-Co-Cu High-Entropy Alloy Nanoparticles: A Molecular Dynamics Study Wenchao Shi, Yapeng Jia This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7277006/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 26 Oct, 2025 Read the published version in Journal of Nanoparticle Research → Version 1 posted 7 You are reading this latest preprint version Abstract As a crucial component in additive manufacturing, understanding the melting process of high-entropy alloy nanoparticles (HEAs-NPs) is indispensable for achieving high-precision and high-performance additive manufacturing components. In this study, molecular dynamics simulations were employed to investigate the different trends in surface atomic preferences during the heating and rapid melting processes of Fe-Ni-Cr-Co-Cu HEAs-NPs under various sizes and melting rates. The results indicate that the surface structure of the NPs remains stable before reaching the melting point; once the melting point is attained, the surface melts rapidly first, followed by the overall melting of the NP. During the heating process, Cu and Cr exhibit surface segregation phenomena before melting, and this trend remains stable, unaffected by NP size and heating rate. After reaching the melting point, Cu segregation at the surface intensifies, while Cr no longer segregates to the surface, and the trend of Fe segregation at the surface decreases as the heating rate increases. Furthermore, we conducted an in-depth analysis of the causes of these different trends in surface atomic preferences during the heating and melting process from the perspectives of average atomic potential energy. Our research reveals the melting characteristics and surface atomic preference trends of Fe-Ni-Cr-Co-Cu HEA-NPs, providing valuable insights for the use of HEA-NPs in additive manufacturing. high entropy alloy nanoparticles melting surface segregation heating rate molecular dynamics Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 1. Introduction The rapid advancement of advanced manufacturing technologies has positioned additive manufacturing (AM) as a revolutionary production method, fundamentally reshaping material processing paradigms. Critically, the emergence of ultrafast laser and electron beam technologies has drawn substantial research attention due to their unparalleled capacity for achieving rapid heating regimes – a pivotal factor in controlling microstructure evolution and defect mitigation during AM processes. High-entropy alloys (HEAs), characterized by their unique compositional design concepts and exceptional properties such as high strength, high hardness, and good corrosion resistance, have garnered widespread attention. In recent years, the integration of HEAs with AM technology has become a focal area of research, attracting extensive academic and industrial interest. [ 1 – 6 ] However, the behavior of HEAs during AM processes, particularly the melting behavior of NPs under high-energy heat sources such as lasers or electron beams, remains incompletely understood. The melting process is a crucial step in material shaping and property formation in AM, directly influencing the microstructure and macroscopic properties of the final components. [ 7 – 10 ] Due to the complex composition of HEA-NPs and the experimental difficulties at high temperatures, traditional experimental methods face numerous challenges in studying their melting processes and microstructure evolution. [ 11 ] In recent years, with the rapid advancement of computer technology, molecular dynamics (MD) simulations have emerged as an effective computational method, playing an increasingly important role in the field of materials science. Studies by Ju et al. using MD to simulate the melting mechanism of Pt–Pd–Rh–Co HEA-NPs and by Liang et al. on the thermal stability of Al-Cu-Fe-Cr-Ni HEA-NPs and bulk alloys have provided new insights into understanding the dynamic behavior and microstructure evolution of HEA-NPs at the nanoscale. [ 4 , 11 , 12 ] Previous studies have not delved deeply into the relationship between the surface atomic preference trends of Fe-Ni-Cr-Co-Cu HEA-NPs during heating and melting processes and the heating rate. By systematically simulating the melting processes of NPs under different heating rates and sizes, we reveal the microscopic mechanisms of high-entropy alloy nanoparticle melting at the atomic scale, providing new perspectives and ideas for finely controlling the melting process of HEA-NPs. 2. Theory and methods The melting process of Fe-Ni-Cr-Co-Cu HEA-NPs was simulated using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) [ 11 ]. The lattice constant was set to 3.55 Å [ 12 ], and the NPs had diameters of 5 nm, 10 nm, and 15 nm, with a 1:1:1:1:1 ratio for each element. As shown in Fig. 1 , the outermost 0.5 nm region of the nanoparticles was designated as the shell region, while the region inside the shell was termed the core region. The Embedded Atom Method (EAM) potential function developed by Farkas et al. [ 12 ] was employed. This potential function has been successfully applied in simulations of Ni-Fe-Cr-Co-Cu high-entropy alloys, achieving good results in simulating various aspects such as thermophysical properties, chemical complexity, alloy design, solidification, and behavior in 3D printing. [ 13 – 16 ] Random atomic substitution was employed to achieve doping in the nanoparticles, with 10,000 models doped for each nanoparticle size. Energy minimization was performed on all models, and the structure with the lowest energy was selected for subsequent simulation steps. The boundary condition used in the simulation was the NVT ensemble. Following the simulation method of Zhu et al., the central 0.5 nm region of the nanoparticle was fixed to prevent movement or rotation during the simulation. [ 17 ] Temperature control was achieved using a Nose-Hoover thermostat. [ 18 ] The simulation steps were as follows: Firstly, the conjugate gradient method was used to minimize the system energy at 0 K. Subsequently, the NVT ensemble was implemented to simulate the microstructural evolution of the system at 300 K. The time step was set to 1 fs, and 100,000 time steps were run to allow the system to reach equilibrium. The melting process of the nanoparticles was simulated using the NVT ensemble at heating rates of 1, 2, 4, 8, and 16 K/ps, heating from 300 K to 2300 K. The heating rate in this study was selected to account for the heating process under extreme non-equilibrium conditions during micro/nanofabrication.[ 6 , 19 ]Surface extraction was performed using OVITO software, and data statistics were conducted using Python. [ 20 ] 3. Results and Discussions 3.1 The melting of HEA-NPs This study simulated the melting process of Fe-Ni-Cr-Co-Cu HEA-NPs under various sizes and heating rates, and statistically analyzed the average atomic potential energy of atoms in the whole, shell, and core regions of the NPs during heating. The melting state was determined by an abrupt change in the potential energy curve, which indicated a significant change in the energy state of the solid system and marked the initiation of melting. [ 17 ] The simulation results showed that despite the differences in size and heating rate of the HEA-NPs, their T-P curves exhibited similar characteristics: an initial linear increase followed by an abrupt change. Figure (d) demonstrates that NPs of different sizes exhibit similar melting behaviors. Taking the 5 nm NP as an example, we investigate the melting process of the HEA-NP. As shown in Figures (a), (b), and (c), during the initial heating stage, the potential energy of atoms in the three regions (Whole, Shell, and Core) increases linearly. When the temperature rises to 1500 K, the slopes of the T-P curves for the Whole and Shell regions increase, but they still maintain a linear trend. As the temperature continues to increase above 1780 K, significant abrupt changes occur in the T-P curves of all three regions, marking the onset of melting for the entire NPs. With further temperature increase, the potential energy curves resume linear growth, indicating that the NPs have completely melted, transitioning from a solid state to a liquid state. Observation of the T-P plots reveals that the growth rate of atomic potential energy accelerates in the Whole and Shell regions at 1500 K, suggesting intensified thermal vibration of surface atoms in the NPs. However, since no abrupt change in the curves is observed, the surface structure of the NPs remains stable. In contrast, Zhu et al. simulated the melting process of pure Cu-NPs and found that surface atoms begin to pre-melt at lower temperatures, resulting in a different growth pattern of the T-P curve for surface atoms compared to the Core and Whole regions, exhibiting a nonlinear increase [ 17 ].In HEA-NPs, the T-P curves of all three regions increase linearly with temperature and ultimately undergo abrupt changes. The melting process of Cu-NPs differs from this. This is attributed to the significant differences in melting points among different elements in alloy NPs. For example, Cu has a melting point of 1300 K, while Ni, Fe, and Cr have melting points above 1800 K. This difference in melting points grants unique melting characteristics to HEA-NPs. Figure 3 displays the temperature-mean squared displacement (T-MSD) curves for different regions (Whole, Core, Shell) of a 5 nm NP at a heating rate of 1 K/ps. The variation in MSD values directly reflects the atomic motion state. As the temperature increases, when it exceeds 1500 K, the MSD values in the Shell and Whole regions gradually rise, while the Core region maintains a lower level. When the temperature reaches above 1780 K, the MSD of all regions undergoes a sharp jump. Notably, the temperatures at which the MSD values of the three regions begin to increase slowly are different, with the Shell region starting at the lowest temperature, indicating that shell atoms gain greater potential energy during the heating process. However, the MSD values of the three curves jump at nearly the same temperature, suggesting that all regions of the NP melt almost simultaneously. From the structural snapshot, it can be clearly observed that during the heating process, some atoms in the NP undergo lattice distortion before others; Meanwhile, the overall structure of NP remains unchanged, indicating that the HEA-NP structure remains stable before reaching the melting point. When the melting point is reached, the atoms located on the surface of the NP first undergo a significant transformation into an amorphous state, and the NP no longer maintains its regular circular shape. Subsequently, some atoms in the core region also transformed into an amorphous state. As the temperature further increases, almost all atoms in NP undergo transformation. Amorphous state indicates that NP has completely melted at this point. The whole process was very fast. The atoms located in the central part are fixed, so there is no structural change throughout the entire process of the atoms in that part. From the potential energy snapshots, it can be further observed that when the temperature is below 1500 K, the overall potential energy of the NP is relatively low, indicating that the structure of the NP is relatively stable at this point. However, when the temperature exceeds 1500 K, the potential energy of some atoms in the NP begins to gradually increase, while the potential energy of most atoms remains at a lower level, and the structure of the NP remains intact. At 1800 K, there are apparent signs of structural breakdown in the NP, with the shell region starting to melt and the overall potential energy of the shell region rising. When the temperature reaches 2000 K, the potential energy of the entire NP increases significantly, and the NP has completely transitioned from a solid state to a liquid state. Notably, due to the central region being fixed, the potential energy in this area does not change significantly during the entire heating process and remains blue. 3.2. Element Segregation Phenomenon Prior to Melting During the Heating Process of HEA-NPs By statistically analyzing the proportion of metal atoms in the shell region of NPs, we found that the distribution of various metal elements on the surface of NPs is not uniform, indicating the occurrence of surface segregation in HEA-NPs. Specifically, before melting, the surface concentrations of Cu and Cr elements in NPs are higher than 20%, and this segregation trend appears regardless of NP size and heating rate. As shown in the figure, the heating process of 5 nm HEA-NPs at a heating rate of 1 K/ps is taken as an example to analyze the segregation phenomenon before melting of the nanoparticles. Segregation is already present at 0 K, with Cu and Cr more likely to aggregate on the surface of the nanoparticles. This result is in good agreement with the experimental findings of Mao et al., who also observed segregation of Cu and Cr on the surface of NPs. [ 22 ] Additionally, simulations revealed that this trend persists until the alloy NPs melt. Across the considered sizes of alloy NPs and heating rates, all NPs exhibited the same segregation phenomenon.The stable surface segregation of NP before melting also reflects the stability of HEA-NP structure during heating process. We statistically analyzed the average atomic potential energy of Fe, Ni, Cr, Co, and Cu in the shell region as a function of temperature. Deppert et al. have pointed out that the surface segregation tendency of binary alloy nanoparticles (NPs) is influenced by the surface and cohesive energies of their constituents. [ 21 ] Since the average atomic potential energy can reflect changes in these two types of energy, we continued to use this metric in our analysis. Figure 6 shows that the average atomic potential energy of Cu is significantly higher than that of the other elements, resulting in the greatest tendency for Cu to segregate to the surface. The potential energy of Cr is also higher than the average of all elements, leading to a surface composition of Cr exceeding 20%, while the proportions of the other elements decrease accordingly. The figure indicates that during heating from 1 K, the temperature-potential energy (T-P) curves of all elements except Cu are nearly linear. The T-P curve of only copper becomes curved after 1000K, while the other curves continue to increase linearly. Therefore, during the heating process, the entire HEA-NP maintains its structural stability, and the segregation pattern of all elements remains unchanged. In summary, due to their higher potential energies, Cu and Cr atoms tend to segregate to the surface of the NP, and this segregation pattern remains stable during heating. 3.3. Element Segregation Phenomenon During the Melting Process of HEA-NPs After reaching the melting point, the HEA-NP rapidly transitions from a solid state to a liquid state. Through statistical analysis of the elemental proportions in the shell region, we observed a significant enhancement in Cu surface segregation during the melting process, while the segregation of Cr diminishes as the temperature rises to the melting stage. Simultaneously, Fe accumulates on the surface of the NP, and its segregation trend is correlated with the heating rate but independent of the NP size. Specifically, during the melting process, slower heating rates result in stronger surface segregation of Cu and Fe. As the heating rate increases, the degree of surface segregation for Cu and Fe decreases. At a heating rate of 16 K/ps, there is no segregation of iron atoms on the NP surface. As shown in Fig. 8 , Figures (a) and (b) respectively depict the proportion of Fe and Cu elements in the shell region of alloy nanoparticles at heating rates of 1, 2, 4, 8, and 16 K/ps. During the melting process, Cu atoms consistently exhibit a strong tendency for surface segregation. Although this segregation trend weakens with increasing heating rate, Cu atoms still occupy a significant proportion of the surface atoms. In contrast, the surface segregation of Fe atoms decreases significantly as the heating rate increases. At 1 K/ps, Fe atoms show a strong segregation tendency, but when the heating rate rises to 16 K/ps, surface segregation of Fe atoms nearly disappears. Additionally, at all heating rates, the segregation tendencies of both Cu and Fe on the surface decrease as the heating rate increases. We comprehensively analyzed the temperature-potential energy diagrams of Fe and Cu in NP. The results indicate that heating rate has a significant impact on the slope of the T-P curves, specifically, faster heating rates result in smaller slope during the melting stage. This implies that elements acquire energy at different rates during heating, thereby significantly influencing their segregation trends. Physical model calculations and MD simulations by Lee and Samsonov, among others, further confirm the close correlation between HEA segregation phenomena and component potential energy. [ 22 – 25 ] Figure 9 visually demonstrates the variations in T-P curve slopes for the same element under different heating rates. In addition, Mao et al. emphasized the crucial role of entropy change in the trend of element segregation. [ 20 ] For the simulation system in our work, the heating rate determines the change in system entropy. By introducing auxiliary lines K1 and K2, we conducted an in-depth analysis of the slope variations in the T-P curves of Fe and Cu. In the diagram, the purple line K1 and the red line K2 exhibit the same slope. The K1 line is tangent to the T-P curve of Fe at a heating rate of 1K/ps, while the K2 line is tangent to the T-P curve of Fe at 16K/ps and the T-P curve of Cr at 1K/ps. Our findings reveal that Fe exhibits a higher T-P curve slope and a strong surface segregation trend at a heating rate of 1K/ps. However, when the heating rate is increased to 16K/ps, the slope decreases significantly, approaching the T-P curve of Cr at 1K/ps, and no surface segregation trend is observed for Fe at this point. Interestingly, despite Cu exhibiting a high segregation trend at all heating rates due to its high energy, its T-P curve slope is relatively low and similar to that of the K2 curve. However, Cu's inherent high potential energy results in a strong segregation tendency across all heating rates, sizes, and throughout the entire heating process. In summary, the segregation trends of elements in HEA-NPs are not only related to their intrinsic energy but also influenced by the slope of the T-P curve during heating, which reflects the rate of system energy increase. This finding provides a novel perspective for effective control of phase deposition issues in additive manufacturing processes based on HEA-NPs. 4. Conclusion We systematically investigated the microstructural evolution and elemental behavior of HEA-NPs during heating and melting, revealing their unique melting mechanisms and surface atomic segregation characteristics. Specifically, Fe-Ni-Cr-Co-Cu HEA-NPs maintained structural stability prior to heating to the melting point, with melting initiating at the surface and rapidly extending throughout the entire NP. During the heating stage, Cu and Cr exhibited stable surface segregation trends. However, upon entering the melting stage, Cr segregation disappeared, and the degree of elemental segregation was significantly influenced by the heating rate: as the heating rate increased, the degree of Cu segregation decreased, but surface segregation persisted; in contrast, Fe showed significant segregation at a heating rate of 1K/ps but almost no segregation at 16K/ps. This unique elemental segregation pattern is closely related to the average atomic potential energy of each component in the HEA-NP and their average atomic potential energy increase rates during heating. Declarations Author Contribution Conceptualization, S.W; methodology, S.W; softwires; validation, S.W.; formal analysis, S.W.; investigation, S.W. ; resources, S.W; data curation, S.W.; writing–original draft preparation, S.W; writing–review and editing, S.W. , Y.P.J; visualization, S.W.; supervision, S.W.; project administration, S.W,Y.P.J; All authors have read and agreed to the published version of the manuscript. Acknowledgments Our work has not received any financial support. References Deluigi O R , Pasianot R C , Valencia F J ,et al.Simulations of primary damage in a High Entropy Alloy: Probing enhanced radiation resistance[J].Acta Materialia, 2021, 213:116951.DOI:10.1016/j.actamat.2021.116951. Plimpton S .Fast Parallel Algorithms for Short-Range Molecular Dynamics[J].Journal of Computational Physics, 1995, 117(1):1-19.DOI:10.1006/jcph.1995.1039. 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Cite Share Download PDF Status: Published Journal Publication published 26 Oct, 2025 Read the published version in Journal of Nanoparticle Research → Version 1 posted Reviewers agreed at journal 05 Aug, 2025 Reviewers agreed at journal 05 Aug, 2025 Reviewers agreed at journal 05 Aug, 2025 Reviewers invited by journal 05 Aug, 2025 Editor assigned by journal 04 Aug, 2025 Submission checks completed at journal 03 Aug, 2025 First submitted to journal 02 Aug, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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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-7277006","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":495952297,"identity":"78046897-8883-4de4-90cf-0866f368a902","order_by":0,"name":"Wenchao Shi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAtUlEQVRIiWNgGAWjYLACxoYDCfzMzAcfkKZFsp0t2YA0LQbnecwEiFJtzn742GPeHXfyjA8zmDEw1NhEE9Ri2ZOWbsx75lmx2WGGtAcMx9JyGwhpMbjBYybN23Y4cdthhuMGjA2HidHC/w2sZXMzY5sEkVp42MBaNjAzsxGp5UyaueFcoJYZh9mYDRKI8svxw88evAVq6e8///HBhxobwlqAgA3BTCBCOZqWUTAKRsEoGAXYAACz4ELyzVWMngAAAABJRU5ErkJggg==","orcid":"","institution":"Guangdong Institute of Arts and Sciences","correspondingAuthor":true,"prefix":"","firstName":"Wenchao","middleName":"","lastName":"Shi","suffix":""},{"id":495952298,"identity":"2555e02e-a119-4a65-bdad-962ee750d55f","order_by":1,"name":"Yapeng Jia","email":"","orcid":"","institution":"the Ministry of Ecology and Environment of the People's Republic of China","correspondingAuthor":false,"prefix":"","firstName":"Yapeng","middleName":"","lastName":"Jia","suffix":""}],"badges":[],"createdAt":"2025-08-02 09:08:23","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7277006/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7277006/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11051-025-06474-0","type":"published","date":"2025-10-26T16:17:08+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":88629092,"identity":"5f35bf98-2307-48c1-8461-04c3b2d0b12a","added_by":"auto","created_at":"2025-08-08 13:26:54","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":491592,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic diagram of NPs and Shell-Core regions, where different colors represent different types of atoms\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-7277006/v1/e8421d34d17ed1cbd09b8345.png"},{"id":88628073,"identity":"96e998b1-ce2b-486e-8590-4eb9993cc23c","added_by":"auto","created_at":"2025-08-08 13:18:54","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":196138,"visible":true,"origin":"","legend":"\u003cp\u003e(a), (b), and (c) present the temperature-potential energy (T-P) plots for the regions of whole, core, and shell within 5 nm NPs, respectively, under different heating rates. Figure (d) displays the T-P curves for NPs with diameters of 5 nm, 10 nm, and 15 nm at a heating rate of 1 K/ps.The T-P curves of different heating rates and diameters NP are represented by different colors.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-7277006/v1/247c82678328c37f87e348cc.png"},{"id":88629297,"identity":"3fe813cf-82f9-4b08-9218-3a37eb702a5d","added_by":"auto","created_at":"2025-08-08 13:34:54","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":72403,"visible":true,"origin":"","legend":"\u003cp\u003eThe T-MSD (temperature-mean squared displacement) curves for different regions within a 5 nm NP at a heating rate of 1 K/ps are presented.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-7277006/v1/ca0c1b7610ca0effefd42196.png"},{"id":88629094,"identity":"396b873a-6ac1-4733-9bd8-142b3490b21a","added_by":"auto","created_at":"2025-08-08 13:26:54","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":275188,"visible":true,"origin":"","legend":"\u003cp\u003e(a), (b), (c), and (d) show structural snapshots of 5 nm NPs with a cross-section\u0026lt;100\u0026gt;at a heating rate of 1 K/ps. Green atoms have a face centered cubic structure. Fig. (a) shows the non melted NP, Fig. (b) and (c) show the NP during the melting process, and Fig. (d) shows the fully melted NP.\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-7277006/v1/e2db168cb64267e471e37c5a.png"},{"id":88628075,"identity":"6eb9c8f9-a4e6-4cc0-9556-797a8b7c8325","added_by":"auto","created_at":"2025-08-08 13:18:54","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":623810,"visible":true,"origin":"","legend":"\u003cp\u003e(a), (b), (c), and (d) show potential energy snapshots of a 5 nm NP with a \u0026lt;100\u0026gt; cross-section at heating rates of 1 K/ps, at temperatures of 450 K, 1650 K, 1800 K, and 2000 K, respectively. The color blue represents lower energy, while red represents higher energy. Due to the central region being set as fixed, the potential energy in this area does not change significantly during the entire heating process.\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-7277006/v1/3bf22f2cb36c14d8c87b3acf.png"},{"id":88630259,"identity":"512464aa-6495-44ac-878a-79fdfbbd5241","added_by":"auto","created_at":"2025-08-08 13:42:54","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":73098,"visible":true,"origin":"","legend":"\u003cp\u003eThe proportion of each element in the shell region of the NP varies with temperature, with Cu and Cr exceeding 20%, while Fe, Ni, and Co are below 20%. During the heating process, the proportions of these elements remain basically stable.\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-7277006/v1/81e6436d2fcb2014d9bcede7.png"},{"id":88628076,"identity":"f9db6a4a-02a6-4d19-993e-4d75dd9dc3a6","added_by":"auto","created_at":"2025-08-08 13:18:54","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":106195,"visible":true,"origin":"","legend":"\u003cp\u003eThe T-P curves of each element in the shell region of the NP, due to the similar average atomic potential energies of Fe and Ni, the red curve (Fe) nearly overlaps with the black curve (Ni).\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-7277006/v1/15d3b55e96610ba543022d5f.png"},{"id":88629302,"identity":"9f0b94ab-b8be-4dbe-a8fc-0bbe0b649061","added_by":"auto","created_at":"2025-08-08 13:34:55","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":96512,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Surface atomic fraction of Fe vs. temperature curve, (b) Surface atomic fraction of Cu vs. temperature curve, with curves of varying colors indicating different heating rates.\u003c/p\u003e","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-7277006/v1/193de7886552a9d085eb0e33.png"},{"id":88628084,"identity":"df4a5eed-8650-4ce4-ac9b-8f3a263d1ce6","added_by":"auto","created_at":"2025-08-08 13:18:54","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":101391,"visible":true,"origin":"","legend":"\u003cp\u003eThe melting of 5nm NPs involves a melting process, which is characterized by the T-P curves of (a) Fe and Cr, and (b) Cu. The T-P curves at different heating rates are represented by different colors. In both (a) and (b), the purple line K1 and the red line K2 have the same slope. The K1 curve is tangent to the T-P curve of Fe at a heating rate of 1K/ps, while the K2 curve is tangent to the T-P curve of Fe at 16K/ps and the T-P curve of Cr at 1/ps.\u003c/p\u003e","description":"","filename":"floatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-7277006/v1/f969e88f0357482d0a1fdb00.png"},{"id":94490759,"identity":"9a5df423-fbae-44b7-89b1-fd1abe321018","added_by":"auto","created_at":"2025-10-27 17:14:49","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2465688,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7277006/v1/663c07e4-e07a-4e40-8a3e-3964bf4aaacf.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Divergent Trends in Surface Atomic Segregation During Rapid Heating of Fe-Ni-Cr-Co-Cu High-Entropy Alloy Nanoparticles: A Molecular Dynamics Study","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe rapid advancement of advanced manufacturing technologies has positioned additive manufacturing (AM) as a revolutionary production method, fundamentally reshaping material processing paradigms. Critically, the emergence of ultrafast laser and electron beam technologies has drawn substantial research attention due to their unparalleled capacity for achieving rapid heating regimes \u0026ndash; a pivotal factor in controlling microstructure evolution and defect mitigation during AM processes. High-entropy alloys (HEAs), characterized by their unique compositional design concepts and exceptional properties such as high strength, high hardness, and good corrosion resistance, have garnered widespread attention. In recent years, the integration of HEAs with AM technology has become a focal area of research, attracting extensive academic and industrial interest. [\u003cspan additionalcitationids=\"CR2 CR3 CR4 CR5\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]\u003c/p\u003e\u003cp\u003eHowever, the behavior of HEAs during AM processes, particularly the melting behavior of NPs under high-energy heat sources such as lasers or electron beams, remains incompletely understood. The melting process is a crucial step in material shaping and property formation in AM, directly influencing the microstructure and macroscopic properties of the final components. [\u003cspan additionalcitationids=\"CR8 CR9\" citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e] Due to the complex composition of HEA-NPs and the experimental difficulties at high temperatures, traditional experimental methods face numerous challenges in studying their melting processes and microstructure evolution. [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e] In recent years, with the rapid advancement of computer technology, molecular dynamics (MD) simulations have emerged as an effective computational method, playing an increasingly important role in the field of materials science. Studies by Ju et al. using MD to simulate the melting mechanism of Pt\u0026ndash;Pd\u0026ndash;Rh\u0026ndash;Co HEA-NPs and by Liang et al. on the thermal stability of Al-Cu-Fe-Cr-Ni HEA-NPs and bulk alloys have provided new insights into understanding the dynamic behavior and microstructure evolution of HEA-NPs at the nanoscale. [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]\u003c/p\u003e\u003cp\u003ePrevious studies have not delved deeply into the relationship between the surface atomic preference trends of Fe-Ni-Cr-Co-Cu HEA-NPs during heating and melting processes and the heating rate. By systematically simulating the melting processes of NPs under different heating rates and sizes, we reveal the microscopic mechanisms of high-entropy alloy nanoparticle melting at the atomic scale, providing new perspectives and ideas for finely controlling the melting process of HEA-NPs.\u003c/p\u003e"},{"header":"2. Theory and methods","content":"\u003cp\u003eThe melting process of Fe-Ni-Cr-Co-Cu HEA-NPs was simulated using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. The lattice constant was set to 3.55 \u0026Aring; [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e], and the NPs had diameters of 5 nm, 10 nm, and 15 nm, with a 1:1:1:1:1 ratio for each element. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, the outermost 0.5 nm region of the nanoparticles was designated as the shell region, while the region inside the shell was termed the core region. The Embedded Atom Method (EAM) potential function developed by Farkas et al. [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e] was employed. This potential function has been successfully applied in simulations of Ni-Fe-Cr-Co-Cu high-entropy alloys, achieving good results in simulating various aspects such as thermophysical properties, chemical complexity, alloy design, solidification, and behavior in 3D printing. [\u003cspan additionalcitationids=\"CR14 CR15\" citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eRandom atomic substitution was employed to achieve doping in the nanoparticles, with 10,000 models doped for each nanoparticle size. Energy minimization was performed on all models, and the structure with the lowest energy was selected for subsequent simulation steps. The boundary condition used in the simulation was the NVT ensemble. Following the simulation method of Zhu et al., the central 0.5 nm region of the nanoparticle was fixed to prevent movement or rotation during the simulation. [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e] Temperature control was achieved using a Nose-Hoover thermostat. [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e] The simulation steps were as follows: Firstly, the conjugate gradient method was used to minimize the system energy at 0 K. Subsequently, the NVT ensemble was implemented to simulate the microstructural evolution of the system at 300 K. The time step was set to 1 fs, and 100,000 time steps were run to allow the system to reach equilibrium. The melting process of the nanoparticles was simulated using the NVT ensemble at heating rates of 1, 2, 4, 8, and 16 K/ps, heating from 300 K to 2300 K. The heating rate in this study was selected to account for the heating process under extreme non-equilibrium conditions during micro/nanofabrication.[\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]Surface extraction was performed using OVITO software, and data statistics were conducted using Python. [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]\u003c/p\u003e"},{"header":"3. Results and Discussions","content":"\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\u003ch2\u003e3.1 The melting of HEA-NPs\u003c/h2\u003e\u003cp\u003eThis study simulated the melting process of Fe-Ni-Cr-Co-Cu HEA-NPs under various sizes and heating rates, and statistically analyzed the average atomic potential energy of atoms in the whole, shell, and core regions of the NPs during heating. The melting state was determined by an abrupt change in the potential energy curve, which indicated a significant change in the energy state of the solid system and marked the initiation of melting. [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e] The simulation results showed that despite the differences in size and heating rate of the HEA-NPs, their T-P curves exhibited similar characteristics: an initial linear increase followed by an abrupt change.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eFigure (d) demonstrates that NPs of different sizes exhibit similar melting behaviors. Taking the 5 nm NP as an example, we investigate the melting process of the HEA-NP. As shown in Figures (a), (b), and (c), during the initial heating stage, the potential energy of atoms in the three regions (Whole, Shell, and Core) increases linearly. When the temperature rises to 1500 K, the slopes of the T-P curves for the Whole and Shell regions increase, but they still maintain a linear trend. As the temperature continues to increase above 1780 K, significant abrupt changes occur in the T-P curves of all three regions, marking the onset of melting for the entire NPs. With further temperature increase, the potential energy curves resume linear growth, indicating that the NPs have completely melted, transitioning from a solid state to a liquid state.\u003c/p\u003e\u003cp\u003eObservation of the T-P plots reveals that the growth rate of atomic potential energy accelerates in the Whole and Shell regions at 1500 K, suggesting intensified thermal vibration of surface atoms in the NPs. However, since no abrupt change in the curves is observed, the surface structure of the NPs remains stable. In contrast, Zhu et al. simulated the melting process of pure Cu-NPs and found that surface atoms begin to pre-melt at lower temperatures, resulting in a different growth pattern of the T-P curve for surface atoms compared to the Core and Whole regions, exhibiting a nonlinear increase [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e].In HEA-NPs, the T-P curves of all three regions increase linearly with temperature and ultimately undergo abrupt changes. The melting process of Cu-NPs differs from this. This is attributed to the significant differences in melting points among different elements in alloy NPs. For example, Cu has a melting point of 1300 K, while Ni, Fe, and Cr have melting points above 1800 K. This difference in melting points grants unique melting characteristics to HEA-NPs.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e displays the temperature-mean squared displacement (T-MSD) curves for different regions (Whole, Core, Shell) of a 5 nm NP at a heating rate of 1 K/ps. The variation in MSD values directly reflects the atomic motion state. As the temperature increases, when it exceeds 1500 K, the MSD values in the Shell and Whole regions gradually rise, while the Core region maintains a lower level. When the temperature reaches above 1780 K, the MSD of all regions undergoes a sharp jump. Notably, the temperatures at which the MSD values of the three regions begin to increase slowly are different, with the Shell region starting at the lowest temperature, indicating that shell atoms gain greater potential energy during the heating process. However, the MSD values of the three curves jump at nearly the same temperature, suggesting that all regions of the NP melt almost simultaneously.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eFrom the structural snapshot, it can be clearly observed that during the heating process, some atoms in the NP undergo lattice distortion before others; Meanwhile, the overall structure of NP remains unchanged, indicating that the HEA-NP structure remains stable before reaching the melting point. When the melting point is reached, the atoms located on the surface of the NP first undergo a significant transformation into an amorphous state, and the NP no longer maintains its regular circular shape. Subsequently, some atoms in the core region also transformed into an amorphous state. As the temperature further increases, almost all atoms in NP undergo transformation. Amorphous state indicates that NP has completely melted at this point. The whole process was very fast. The atoms located in the central part are fixed, so there is no structural change throughout the entire process of the atoms in that part.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eFrom the potential energy snapshots, it can be further observed that when the temperature is below 1500 K, the overall potential energy of the NP is relatively low, indicating that the structure of the NP is relatively stable at this point. However, when the temperature exceeds 1500 K, the potential energy of some atoms in the NP begins to gradually increase, while the potential energy of most atoms remains at a lower level, and the structure of the NP remains intact. At 1800 K, there are apparent signs of structural breakdown in the NP, with the shell region starting to melt and the overall potential energy of the shell region rising. When the temperature reaches 2000 K, the potential energy of the entire NP increases significantly, and the NP has completely transitioned from a solid state to a liquid state. Notably, due to the central region being fixed, the potential energy in this area does not change significantly during the entire heating process and remains blue.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\u003ch2\u003e3.2. Element Segregation Phenomenon Prior to Melting During the Heating Process of HEA-NPs\u003c/h2\u003e\u003cp\u003eBy statistically analyzing the proportion of metal atoms in the shell region of NPs, we found that the distribution of various metal elements on the surface of NPs is not uniform, indicating the occurrence of surface segregation in HEA-NPs. Specifically, before melting, the surface concentrations of Cu and Cr elements in NPs are higher than 20%, and this segregation trend appears regardless of NP size and heating rate.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eAs shown in the figure, the heating process of 5 nm HEA-NPs at a heating rate of 1 K/ps is taken as an example to analyze the segregation phenomenon before melting of the nanoparticles. Segregation is already present at 0 K, with Cu and Cr more likely to aggregate on the surface of the nanoparticles. This result is in good agreement with the experimental findings of Mao et al., who also observed segregation of Cu and Cr on the surface of NPs. [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e] Additionally, simulations revealed that this trend persists until the alloy NPs melt. Across the considered sizes of alloy NPs and heating rates, all NPs exhibited the same segregation phenomenon.The stable surface segregation of NP before melting also reflects the stability of HEA-NP structure during heating process.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eWe statistically analyzed the average atomic potential energy of Fe, Ni, Cr, Co, and Cu in the shell region as a function of temperature. Deppert et al. have pointed out that the surface segregation tendency of binary alloy nanoparticles (NPs) is influenced by the surface and cohesive energies of their constituents. [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e] Since the average atomic potential energy can reflect changes in these two types of energy, we continued to use this metric in our analysis. Figure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e shows that the average atomic potential energy of Cu is significantly higher than that of the other elements, resulting in the greatest tendency for Cu to segregate to the surface. The potential energy of Cr is also higher than the average of all elements, leading to a surface composition of Cr exceeding 20%, while the proportions of the other elements decrease accordingly. The figure indicates that during heating from 1 K, the temperature-potential energy (T-P) curves of all elements except Cu are nearly linear. The T-P curve of only copper becomes curved after 1000K, while the other curves continue to increase linearly. Therefore, during the heating process, the entire HEA-NP maintains its structural stability, and the segregation pattern of all elements remains unchanged. In summary, due to their higher potential energies, Cu and Cr atoms tend to segregate to the surface of the NP, and this segregation pattern remains stable during heating.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\u003ch2\u003e3.3. Element Segregation Phenomenon During the Melting Process of HEA-NPs\u003c/h2\u003e\u003cp\u003eAfter reaching the melting point, the HEA-NP rapidly transitions from a solid state to a liquid state. Through statistical analysis of the elemental proportions in the shell region, we observed a significant enhancement in Cu surface segregation during the melting process, while the segregation of Cr diminishes as the temperature rises to the melting stage. Simultaneously, Fe accumulates on the surface of the NP, and its segregation trend is correlated with the heating rate but independent of the NP size. Specifically, during the melting process, slower heating rates result in stronger surface segregation of Cu and Fe. As the heating rate increases, the degree of surface segregation for Cu and Fe decreases. At a heating rate of 16 K/ps, there is no segregation of iron atoms on the NP surface.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eAs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e, Figures (a) and (b) respectively depict the proportion of Fe and Cu elements in the shell region of alloy nanoparticles at heating rates of 1, 2, 4, 8, and 16 K/ps. During the melting process, Cu atoms consistently exhibit a strong tendency for surface segregation. Although this segregation trend weakens with increasing heating rate, Cu atoms still occupy a significant proportion of the surface atoms. In contrast, the surface segregation of Fe atoms decreases significantly as the heating rate increases. At 1 K/ps, Fe atoms show a strong segregation tendency, but when the heating rate rises to 16 K/ps, surface segregation of Fe atoms nearly disappears. Additionally, at all heating rates, the segregation tendencies of both Cu and Fe on the surface decrease as the heating rate increases.\u003c/p\u003e\u003cp\u003eWe comprehensively analyzed the temperature-potential energy diagrams of Fe and Cu in NP. The results indicate that heating rate has a significant impact on the slope of the T-P curves, specifically, faster heating rates result in smaller slope during the melting stage. This implies that elements acquire energy at different rates during heating, thereby significantly influencing their segregation trends. Physical model calculations and MD simulations by Lee and Samsonov, among others, further confirm the close correlation between HEA segregation phenomena and component potential energy. [\u003cspan class=\"CitationRef\"\u003e22\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e25\u003c/span\u003e]\u003c/p\u003e\n\u003cp\u003eFigure\u0026nbsp;9 visually demonstrates the variations in T-P curve slopes for the same element under different heating rates. In addition, Mao et al. emphasized the crucial role of entropy change in the trend of element segregation. [\u003cspan class=\"CitationRef\"\u003e20\u003c/span\u003e] For the simulation system in our work, the heating rate determines the change in system entropy.\u003c/p\u003e\n\u003cp\u003eBy introducing auxiliary lines K1 and K2, we conducted an in-depth analysis of the slope variations in the T-P curves of Fe and Cu. In the diagram, the purple line K1 and the red line K2 exhibit the same slope. The K1 line is tangent to the T-P curve of Fe at a heating rate of 1K/ps, while the K2 line is tangent to the T-P curve of Fe at 16K/ps and the T-P curve of Cr at 1K/ps. Our findings reveal that Fe exhibits a higher T-P curve slope and a strong surface segregation trend at a heating rate of 1K/ps. However, when the heating rate is increased to 16K/ps, the slope decreases significantly, approaching the T-P curve of Cr at 1K/ps, and no surface segregation trend is observed for Fe at this point.\u003c/p\u003e\n\u003cp\u003eInterestingly, despite Cu exhibiting a high segregation trend at all heating rates due to its high energy, its T-P curve slope is relatively low and similar to that of the K2 curve. However, Cu\u0026apos;s inherent high potential energy results in a strong segregation tendency across all heating rates, sizes, and throughout the entire heating process. In summary, the segregation trends of elements in HEA-NPs are not only related to their intrinsic energy but also influenced by the slope of the T-P curve during heating, which reflects the rate of system energy increase. This finding provides a novel perspective for effective control of phase deposition issues in additive manufacturing processes based on HEA-NPs.\u003c/p\u003e"},{"header":"4. Conclusion","content":"\u003cp\u003eWe systematically investigated the microstructural evolution and elemental behavior of HEA-NPs during heating and melting, revealing their unique melting mechanisms and surface atomic segregation characteristics. Specifically, Fe-Ni-Cr-Co-Cu HEA-NPs maintained structural stability prior to heating to the melting point, with melting initiating at the surface and rapidly extending throughout the entire NP. During the heating stage, Cu and Cr exhibited stable surface segregation trends. However, upon entering the melting stage, Cr segregation disappeared, and the degree of elemental segregation was significantly influenced by the heating rate: as the heating rate increased, the degree of Cu segregation decreased, but surface segregation persisted; in contrast, Fe showed significant segregation at a heating rate of 1K/ps but almost no segregation at 16K/ps. This unique elemental segregation pattern is closely related to the average atomic potential energy of each component in the HEA-NP and their average atomic potential energy increase rates during heating.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eConceptualization, S.W; methodology, S.W; softwires; validation, S.W.; formal analysis, S.W.; investigation, S.W. ; resources, S.W; data curation, S.W.; writing\u0026ndash;original draft preparation, S.W; writing\u0026ndash;review and editing, S.W. , Y.P.J; visualization, S.W.; supervision, S.W.; project administration, S.W,Y.P.J; All authors have read and agreed to the published version of the manuscript.\u003c/p\u003e\u003ch2\u003eAcknowledgments\u003c/h2\u003e\u003cp\u003eOur work has not received any financial support.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eDeluigi O R , Pasianot R C , Valencia F J ,et al.Simulations of primary damage in a High Entropy Alloy: Probing enhanced radiation resistance[J].Acta Materialia, 2021, 213:116951.DOI:10.1016/j.actamat.2021.116951.\u003c/li\u003e\n\u003cli\u003ePlimpton S .Fast Parallel Algorithms for Short-Range Molecular Dynamics[J].Journal of Computational Physics, 1995, 117(1):1-19.DOI:10.1006/jcph.1995.1039.\u003c/li\u003e\n\u003cli\u003eZhang Y , Jiang S , Wang M .Atomistic investigation on superelasticity of NiTi shape memory alloy with complex microstructures based on molecular dynamics simulation[J].International Journal of Plasticity, 2020, 125:27-51.DOI:10.1016/j.ijplas.2019.09.001.\u003c/li\u003e\n\u003cli\u003eJu S P , Lee I J , Chen H Y .Melting mechanism of Pt\u0026ndash;Pd\u0026ndash;Rh\u0026ndash;Co high entropy alloy nanoparticle: An insight from molecular dynamics simulation[J].Journal of Alloys and Compounds, 2020, 858:157681.DOI:10.1016/j.jallcom.2020.157681.\u003c/li\u003e\n\u003cli\u003eAl Z W , Putri R A K , Abukhadra M R ,et al.Recent experimental and theoretical advances in the design and science of high-entropy alloy nanoparticles[J].Nano Energy, 2023:110.\u003c/li\u003e\n\u003cli\u003eYuxiang W , Lingchao K , Yongxiong C ,et al.Femtosecond laser melting NbMoTaW refractory high entropy alloy: A micro-scale thermodynamic simulation[J].Applied Surface Science, 2023, 613:155997-.DOI:10.1016/j.apsusc.2022.155997.\u003c/li\u003e\n\u003cli\u003eJi P , Wang Z , Mu Y ,et al.Microstructural Evolution of (Feconi)85.84al7.07ti7.09 High-Entropy Alloy Fabricated by an Optimized Selective Laser Melting Process[J].SSRN Electronic Journal, 2022.DOI:10.2139/ssrn.4154877.\u003c/li\u003e\n\u003cli\u003eWang H , Zhu Z G , Chen H ,et al.Effect of cyclic rapid thermal loadings on the microstructural evolution of a CrMnFeCoNi high-entropy alloy manufactured by selective laser melting[J].Acta Materialia, 2020, 196:609-625.DOI:10.1016/j.actamat.2020.07.006.\u003c/li\u003e\n\u003cli\u003eChen W , Fu Z , Fang S ,et al.Alloying behavior, microstructure and mechanical properties in a FeNiCrCo0.3Al0.7 high entropy alloy[J].Materials \u0026amp; Design, 2013, 51:854-860.DOI:10.1016/j.matdes.2013.04.061.\u003c/li\u003e\n\u003cli\u003eYuan Y , Wang J J , Wei J ,et al.Cu alloying enables superior strength-ductility combination and high corrosion resistance of FeMnCoCr high entropy alloy[J].Journal of Alloys and Compounds, 2024, 970.DOI:10.1016/j.jallcom.2023.172543.\u003c/li\u003e\n\u003cli\u003eYang H , Shao Z , Lu Q ,et al.Development of reduced-activation and radiation-resistant high-entropy alloys for fusion reactor[J].International Journal of Refractory Metals and Hard Materials, 2024, 121.DOI:10.1016/j.ijrmhm.2024.106674.\u003c/li\u003e\n\u003cli\u003eO.R. 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In this study, molecular dynamics simulations were employed to investigate the different trends in surface atomic preferences during the heating and rapid melting processes of Fe-Ni-Cr-Co-Cu HEAs-NPs under various sizes and melting rates. The results indicate that the surface structure of the NPs remains stable before reaching the melting point; once the melting point is attained, the surface melts rapidly first, followed by the overall melting of the NP. During the heating process, Cu and Cr exhibit surface segregation phenomena before melting, and this trend remains stable, unaffected by NP size and heating rate. After reaching the melting point, Cu segregation at the surface intensifies, while Cr no longer segregates to the surface, and the trend of Fe segregation at the surface decreases as the heating rate increases. Furthermore, we conducted an in-depth analysis of the causes of these different trends in surface atomic preferences during the heating and melting process from the perspectives of average atomic potential energy. Our research reveals the melting characteristics and surface atomic preference trends of Fe-Ni-Cr-Co-Cu HEA-NPs, providing valuable insights for the use of HEA-NPs in additive manufacturing.\u003c/p\u003e","manuscriptTitle":"Divergent Trends in Surface Atomic Segregation During Rapid Heating of Fe-Ni-Cr-Co-Cu High-Entropy Alloy Nanoparticles: A Molecular Dynamics Study","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-08-08 13:18:50","doi":"10.21203/rs.3.rs-7277006/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"217111835560399642180728262491498745718","date":"2025-08-05T10:28:24+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"72926088490892171767175923860419483815","date":"2025-08-05T09:21:59+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"227772499394929821655799160081276038803","date":"2025-08-05T06:19:07+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-08-05T05:55:06+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-08-04T20:34:29+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-08-04T00:30:54+00:00","index":"","fulltext":""},{"type":"submitted","content":"Journal of Nanoparticle Research","date":"2025-08-02T09:04:32+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"journal-of-nanoparticle-research","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"nano","sideBox":"Learn more about [Journal of Nanoparticle Research](http://link.springer.com/journal/11051)","snPcode":"11051","submissionUrl":"https://submission.nature.com/new-submission/11051/3","title":"Journal of Nanoparticle Research","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"1ae15a39-224a-40a9-9ed9-d606d0c5560d","owner":[],"postedDate":"August 8th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-10-27T16:32:52+00:00","versionOfRecord":{"articleIdentity":"rs-7277006","link":"https://doi.org/10.1007/s11051-025-06474-0","journal":{"identity":"journal-of-nanoparticle-research","isVorOnly":false,"title":"Journal of Nanoparticle Research"},"publishedOn":"2025-10-26 16:17:08","publishedOnDateReadable":"October 26th, 2025"},"versionCreatedAt":"2025-08-08 13:18:50","video":"","vorDoi":"10.1007/s11051-025-06474-0","vorDoiUrl":"https://doi.org/10.1007/s11051-025-06474-0","workflowStages":[]},"version":"v1","identity":"rs-7277006","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7277006","identity":"rs-7277006","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}