Effect of Friction Depth, Velocity, and Cu Content on the Friction Behavior of AgCu Alloys by Molecular Dynamics Simulation

Effect of Friction Depth, Velocity, and Cu Content on the Friction Behavior of AgCu Alloys by Molecular Dynamics Simulation | 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 Article Effect of Friction Depth, Velocity, and Cu Content on the Friction Behavior of AgCu Alloys by Molecular Dynamics Simulation Yi Wang, Yiyi Qian, Yuwei Ma, Zhuo Wang, Shumin Zhang, Dingding Xiang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6512210/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract The silver-copper (AgCu) alloy is widely used in numerous industries such as electronics and electrical engineering due to its excellent electrical conductivity, thermal conductivity, and workability. However, the friction problems during its service can seriously affect the operational stability and service life of equipment. Therefore, it is of great significance to deeply explore the friction and wear behavior of the AgCu alloy. In this study, the molecular dynamics simulation method was employed to conduct an in-depth investigation of the friction and wear behavior of AgCu alloy with different friction depths, velocities, and Cu contents. The study found that there was a close positive correlation between the friction depth and the average friction force. As the depth increases, the contact area enlarges, and the atomic packing, phase transformation, and dislocations increase, resulting in a roughly linear increase in the average friction force.At friction speeds of 0.5 Å/ps, 1 Å/ps, and 1.5 Å/ps, the average friction force increases with the increase of speed, accompanied by expanded strain localization and reduced twinning with intensified work hardening under dynamic loading.The content of the Cu element has a significant impact on the friction behavior of the alloy. When the content increases, the softening of the alloy leads to a significant linear decrease in the average friction force. At the same time, the plasticity is enhanced, the strain region expands, and the disordered atomic structures increase. The results of this study provide an important theoretical basis for a deep understanding of the friction and wear mechanism of the AgCu alloy and the optimization of its performance. AgCu alloy molecular dynamics Friction Behavior Effect Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 1. Introduction Alloying is a classic strategy for optimizing the comprehensive properties of metallic materials. However, the negative correlation between strength and plasticity restricts its engineering applications. Through multi-component alloy design, the use of synergistic mechanisms such as nano-precipitation strengthening and grain boundary regulation can overcome the strength-plasticity trade-off. Developing high-strength and high-plasticity alloys has become a research hotspot.In recent years, various properties of many binary alloys have been widely studied, including Al-Cu [ 1 – 4 ] , Au-Ag [ 5 ] , Fe-Cu [ 6 ] , Zn-Cu [ 7 ] , Cr-Cu [ 8 ] , Mg-Ag [ 9 ] , and many other binary alloys. AgCu alloys have attracted extensive attention due to their excellent comprehensive properties. Current research focuses on the regulation of mechanical properties by the Ag content [ 10 – 13 ] . Zhao et al. [ 14 ] found that an increase in the Ag content makes the eutectic phase distribute in a fibrous form, improving the tensile strength. Song et al. [ 15 ] revealed that an increase in the strain rate enhances the alloy through promoting Ag precipitation and grain-boundary strengthening. These studies provide a theoretical basis for the development of high-strength and wear-resistant contact materials. Due to various factors, it is difficult for traditional methods to conduct research on AgCu alloys [ 16 ] . However, the above-mentioned problems can be analyzed and solved at the atomic level through molecular dynamics (MD) simulation [ 17 ] . At present, MD simulation has been widely used to study the mechanical properties of nanoscale AgCu alloy. During the simulation and calculation process, there are many factors that can affect the mechanical properties of AgCu binary alloy. Among these numerous factors, the grain size of alloying elements, strain rate, as well as the interfacial state and internal microstructure of the alloy all have a significant impact on the mechanical properties of the alloy [ 18 ] . Research indicates [ 19 ] that grain size and Ag content have a significant regulatory effect on the mechanical properties of AgCu alloys. Molecular dynamics simulations reveal that in nanocrystalline AgCu alloys, the segregation behavior of Ag atoms at grain boundaries leads to a parabolic change trend in the resistance to grain boundary friction. Meanwhile, the dislocation density continuously decreases with the increase of Ag content, indicating that Ag atoms at grain boundaries can effectively weaken the strength within the grains [ 20 ] . The collaborative design of ultrafine-grained structures and optimized Ag content can improve the alloy properties, but there exists a critical grain-refinement size threshold, and a high Ag content will significantly increase the preparation cost [ 21 ] . Studies on dynamic mechanical behavior show that the strain rate, by regulating the coordinated evolution of the dislocation motion mode and the grain-boundary slip mechanism, causes a non-linear attenuation trend in the dislocation nucleation stress and yield stress of AgCu nanocomposites [ 22 ] . The AgCu alloy exhibits a characteristic of a deformation mechanism transition from dislocation-slip-dominated to grain-boundary-friction-dominated at different strain rates [ 23 ] , while a specific atomic structure of the Au-Ag alloy exhibits reversible deformation behavior at low strain rates [ 24 ] . The interface state and microstructure of materials are equally crucial for their properties: The oxidation sensitivity of AgCu nanowires restricts their engineering applications [ 25 ] ., but the introduction of dislocation-cluster interactions can improve the fracture toughness through the dislocation-capture mechanism at the crack tip [ 26 ] . The construction of a bimodal nanotwinned structure can achieve efficient strengthening, and its tensile strength is positively correlated with the twin-spacing [ 27 ] . Although AgCu alloys hold broad prospects due to their excellent mechanical properties, challenges remain in their development. Key aspects include composition design, microstructure regulation, and grain -size control. Theoretical calculations are crucial for optimizing design and enhancing performance. Strengthening theoretical research is essential to further improve properties. Existing literature insufficiently explores performance impacts under different conditions. This study aims to reveal the friction-wear mechanism of AgCu alloys at room temperature at the atomic scale by analyzing stress-strain behavior and dislocation evolution. 2. Model and Simulation The friction model of the AgCu alloy was developed in the molecular dynamics software LAMMPS [ 28 ] . The lattice type of the alloy is face-centered cubic (FCC), with the lattice constant set to 4.086. The size of the model is set to 245.6 Å × 122.58 Å × 122.58 Å (60A×30A×30A), and the total number of atoms is 216,000. The crystal orientations of the alloy along the X,Y, and Z axes are set to [100], [010], and [001] directions respectively. A spherical diamond indenter with a radius of 20 Å and a total of 6,140 atoms is adopted. After constructing the initial model, the Ag-Cu MEAM potential is used to describe the atomic interactions in the AgCu alloy. The interactions between carbon atoms in diamond are described by the Tersoff potential, and the interactions between the AgCu alloy and C atoms are described by the Lennard-Jones (L-J) potential. The specific parameters are shown in the following table. Table 1 L-J Parameters for Interactions between Metal Atoms and Carbon Atoms Interaction-atom pair ε(ev) σ(Å) Ag-C 0.02883 2.998266 Cu-C 0.03541 2.79476 To eliminate the unreasonable structures in the model, the conjugate gradient algorithm was employed to minimize the energy of the model. Subsequently, under the isobaric-isothermal ensemble (NPT) at 300 K, the Ag-Cu alloy model was relaxed for 300 ps to reach an equilibrium state, and the Nosé-Hoover thermostat was used during the relaxation process. The atoms in the ranges of 0–8 Å, 8–16 Å, and 16-122.58 Å in the Z-direction were set as the fixed layer, the thermostat layer, and the Newtonian layer respectively. The atoms in the Newtonian layer can move freely. The fixed layer was placed at the bottom of the model to prevent movement in space. The thermostat layer consisted of atoms adjacent to the fixed layer to maintain a constant system temperature. This simulation was only carried out for the thermostat and Newtonian layers. Periodic boundary conditions were applied in the X and Y directions of the model, while a shrink-wrapped boundary condition was used in the Z-direction. The initial position of the indenter was above the substrate. It was pressed into the substrate at a certain speed along the negative Z-axis direction. After reaching a certain depth, it then rubbed along the positive X-axis direction. The model is shown in Fig. 1 . In order to study the influence of friction speed, friction depth, and Cu content on the friction performance of the AgCu alloy, control experiments were carried out in this paper. The main parameter settings are shown in Table 2 . Table 2 Main Parameter Settings of the Experiment Model scale 245.6 Å × 122.58 Å × 122.58 Å The number of atoms 216000 Time step 1fs Temperature 300K Friction speed 0.5 Å/ps /1 Å/ps /1.5 Å/ps Friction depth 10 Å/15 Å/20 Å Friction displacement 100 Å Content of Cu element 5/10/20% In this study, the visualization of simulation results was achieved by the open-source visualization software tool (OVITO [ 29 ] ). The Common Neighbor Analysis (CNA) was used to identify the crystal structures before and after the friction process; the Dislocation Extraction Algorithm (DXA) was employed to identify various dislocation features; and atomic shear strain analysis was adopted to evaluate the shear-related deformation behavior of all samples during the wear process at the atomic scale. 3. Results and Discussion 3.1 Influence of Friction Depth on Friction Behavior In this part, a diamond indenter with a radius of 20 Å was used. At a temperature of 300 K and an indenter velocity of 1 Å/ps, a pressing-down simulation was first carried out on AgCu10. The friction depths were set to 10 Å, 15 Å, and 20 Å respectively. Then, the diamond indenter rubbed along the positive X-axis direction for 100 Å. 3.1.1 Analysis of Friction Force Figure 2 demonstrates the dynamic strain curves of the friction force and normal force during the pressing-down and friction processes when the friction depth is 15 Å. As shown in Fig. 2 , the period from 0–15 Å is the pressing-down process, during which the magnitude of the force fluctuates around 0. In the friction stage from 15–115 Å, the friction force starts to rise rapidly as the displacement gradually increases, then fluctuates up and down around a certain value and gradually increases, and finally stabilizes and fluctuates around a certain value. The reason for the curve fluctuation is the continuous appearance and disappearance of dislocations during the friction process. According to the change of the friction force, this process can be roughly divided into three parts: the early friction stage (0–15 Å), the friction climbing stage (15–20 Å), and the friction stable stage (20–115 Å). From 0 to 15 Å, the tip of the spherical indenter with a radius of 20 Å initially contacts the alloy surface, and the friction force is rapidly generated and increases slowly. Subsequently, from 15 to 20 Å, the friction stage begins, and the indenter gradually comes into full contact with the surface of the alloy, so the friction force climbs rapidly as the displacement increases. When the displacement is greater than 20 Å, the friction force basically remains fluctuating around a certain value. In the friction simulation study by Wu et al. [ 30 ] , the response curve of the friction force also demonstrates a similar trend. Figure 3 visually demonstrates the dynamic changes in the friction force of the AgCu10 alloy under friction depths of 10 Å, 15 Å, and 20 Å, respectively. It can be clearly observed from the Fig. 3 that there is an extremely close and significant correlation between the friction depth and the average friction force. As the friction depth gradually increases, the average friction force shows an almost linear increase trend. Specifically, when the friction depth is 10 Å, the average friction force reaches a minimum value of 32.52 nN. When the friction depth rises to 20 Å, the average friction force reaches a maximum value of 64.38 nN. During the friction process, work hardening occurs due to the formation of chips and deposits, which has a decisive impact on the increase in friction force [ 31 ] . As the friction depth deepens, the amount of deposits and debris continues to increase, further promoting the rise of friction force. When the friction depth increases, the contact area between the tool and the alloy expands significantly. The expansion of the contact area leads to an increase in the resistance of alloy atoms to the cutting tool. When rubbing along the positive X-axis direction, more dislocations are generated, and the atomic accumulation phenomenon is further intensified. At this time, the cutting tool must apply a greater tangential force to break the original crystal structure of the alloy, ultimately causing a substantial increase in the friction force. 3.1.2 Surface Morphology Analysis Figure 4 shows the atomic surface morphologies when the friction depths are 10 Å, 15 Å and 20 Å respectively. As can be seen from the Fig. 4 , after the diamond indenter finishes pressing down, there is no obvious atomic accumulation around the indenter. During the subsequent friction process, as the friction displacement increases, the atomic accumulation on both sides of the indenter path gradually increases, and the friction track becomes more and more obvious. At the end of the friction, atoms accumulate intensively in front of the indenter's movement, forming a distinct bulge where the atomic accumulation is the most abundant and prominent. With the increase of the friction depth, it is also evident that the atomic accumulation increases. When the friction depth is 15 Å, the atoms already show a tendency to accumulate above the indenter. When the depth is 20 Å, the atomic accumulation above the indenter is particularly obvious. This is because at a greater depth, the indenter will push more atoms. As the depth and friction displacement increase, more and more atoms accumulate. Since the radius of the diamond is 20 Å, the atoms accumulate above the indenter. 3.1.3 Atomic Shear Strain Analysis Figure 5 demonstrates the atomic shear strain diagrams at different depths. Diagrams a, b, and c correspond to friction depths of 10 Å, 15 Å, and 20 Å respectively, while 1, 2, and 3 represent friction displacements of 0 Å, 50 Å, and 100 Å. As can be seen from the Fig. 5 , the deformation region nucleates from the contact area between the indenter and the substrate, distributes near the indenter, and is arranged approximately at a 45° angle. During the friction process, the region with the highest shear strain is consistently concentrated in the area near the indenter. As the friction depth increases, the number of atoms with large atomic shear strain gradually increases. It can also be observed here that atoms accumulate above the indenter. This is because the contact area between the tool and the workpiece increases with the increase of the machining depth, causing more atoms to be directly affected by the scratching process. This phenomenon leads to an increase in the number of atoms subjected to high strain and stress. Therefore, the deformation level of the workpiece rises with the increase of the cutting depth. 3.1.4 Atomic Lattice Evolution Analysis Figure 6 shows the lattice evolution diagrams during the friction process at different depths. As depicted, it can be seen that during the friction process, the vast majority of atoms in the alloy sample remain in the FCC structure, while a small number of atoms near the indenter transform into an amorphous structure, a BCC structure, or an HCP structure. Diagrams (b) and (c) represent the crystal structures when the friction depths are 50 Å and 100 Å respectively. It can be observed that with the increase of the friction depth, the amorphous, BCC, and HCP structures gradually increase and continue to extend deeper into the alloy sample.This exhibits similar characteristics to the evolution of atomic shear strain in the previous Fig. 5 . 3.1.5 Dislocation Evolution Analysis Figure 7 demonstrates the dislocation evolution diagrams during the friction process at different depths. As shown, during the friction process, dislocations and HCP atoms always form near the indenter and continuously appear and disappear as the friction process proceeds. With the increase of the friction depth, more and more dislocations form around the indenter. As shown in Fig. 7 c, this is particularly obvious when the friction depth is 20 Å, with a large number of dislocations and stacking faults forming near the indenter. Among these dislocations, Shockley partial dislocations account for the vast majority and exhibit a gliding phenomenon, constantly emerging near the tool as the scratching tool moves. 3.2 Influence of Friction Speed on Friction Behavior In this part, a diamond indenter with a radius of 20 Å was used. At a temperature of 300 K, the indenter speeds were set to 0.5 Å/ps, 1 Å/ps, and 1.5 Å/ps respectively. First, a pressing-down simulation was carried out on AgCu10 with a friction depth of 15 Å. Then, the diamond indenter rubbed along the positive X-axis direction for 100 Å. 3.2.1 Analysis of Friction Force Figure 8 presents the evolution law of the friction force of the AgCu10 alloy when the friction speeds are 0.5 Å/ps, 1 Å/ps, and 1.5 Å/ps respectively. Experimental data indicate that the average friction force shows a significant upward trend with the increase of the friction speed. The underlying mechanism involves the synergistic effect of thermal softening and work hardening. Analyzing from the microscopic level, the generation of friction force stems from the coupling of intermolecular forces and mechanical interlocking effects on the contact surface. When the friction speed increases, the activity of surface molecules enhances, and the intermolecular interaction energy increases, resulting in an increase in the adhesion force component. At the same time, the local temperature rise caused by high-speed friction promotes material softening, reducing the mechanical interlocking resistance. However, the work-hardening effect compensates for the impact of softening, ultimately resulting in a net increase in the friction force. This non-linear response characteristic provides an important basis for understanding the tribological behavior of alloys under dynamic loads. 3.2.2 Atomic Shear Strain Analysis Figure 9 demonstrates the distribution characteristics of atomic shear strain of the AgCu10 alloy at different friction speeds. The experimental results indicate that the deformation region is always concentrated in the indenter contact area. As the friction process progresses, the large shear-strain region gradually expands. When the friction speed increases from 0.5 Å/ps to 1.5 Å/ps, the proportion of the small-shear-strain region with ε 0.3 first increases and then decreases. At a friction distance of 50 Å, the area of the high-strain region at a speed of 1.5 Å/ps is the smallest, but at this time, the average friction force reaches a maximum value of 68.2 nN. This phenomenon can be attributed to the synergistic effect of multi-scale deformation mechanisms: The local temperature rise caused by high-speed friction promotes the thermally-activated process of dislocation slip, enabling more grain-boundary regions to participate in the deformation, resulting in the expansion of the small-strain region. At the same time, the material's dynamic recovery ability is enhanced under high-speed loading, which inhibits the further development of the high-strain region. 3.2.3 Atomic Lattice Evolution Analysis Figure 10 demonstrates the lattice evolution of AgCu alloy under different sliding velocities. Initially, distinct structural responses are observed: increasing sliding velocity induces higher twinning activity around the indenter. Notably, at the mid-friction stage (50 Å displacement), the 0.5 Å/ps velocity condition exhibits extensive twinning In front of and below the indenter, whereas higher velocities (1.0-1.5 Å/ps) show reduced twinning density. This twinning reduction mechanism can be attributed to the competing effects of dynamic recovery and thermal softening at elevated sliding speeds.The presence of twin boundaries acts as barriers to dislocation nucleation, effectively mitigating plowing-induced plastic deformation. Conversely, reduced twinning leads to increased work hardening through intensified dislocation accumulation. This microstructural trade-off results in a velocity-dependent friction response: higher sliding velocities produce greater frictional forces due to the combined effects of reduced twinning suppression and enhanced work hardening. These observations highlight the critical role of velocity-induced twinning dynamics in governing tribological behavior at the nanoscale. (158 words) 3.3 Influence of Different Cu Element Contents on Friction Behavior In this part, a diamond indenter with a radius of 20 Å was used. At a temperature of 300 K and an indenter speed of 1 Å/ps, a pressing-down simulation was first carried out on AgCu alloys with Cu contents of 5%, 10% and 20% respectively, at a depth of 15 Å. Then, the diamond indenter rubbed along the positive X-axis direction for 100 Å. 3.3.1 Analysis of Friction Force Figure 11 shows the average friction forces during the friction process for alloys with Cu contents of 5%, 10% and 20% respectively. As can be seen from the Fig. 11 , during the friction process, the average friction force is closely related to the Cu element content. When the Cu element content in the AgCu alloy gradually increases, the average friction force of the alloy shows a significant downward trend, presenting an obvious negative-correlation linear relationship. The reason is that with the increase in the number of copper atoms, the lattice parameters and crystal structure of the AgCu alloy are affected to varying degrees. The presence of copper atoms in the alloy is likely to cause distortion of the alloy's crystal structure, thus reducing the overall hardness of the material. During the friction process, compared with materials with higher hardness, the softer Cu is more likely to undergo plastic deformation without strong resistance, thus reducing the overall friction force. 3.3.2 Surface Morphology Analysis Figure 12 shows the friction surface morphology diagrams during the friction process for alloys with Cu contents of 5%, 10% and 20% respectively. It can be seen from the Fig. 12 that after the friction is completed, atoms accumulate on both sides of the friction path, clearly outlining a friction track. Among them, when the Cu content is 5%, this friction path is the most prominent. When the Cu content reaches 10%, in the initial stage of friction, the path is not clear; however, as the friction continues, the number of accumulated atoms gradually increases, the path becomes clearer, and its accumulation height even exceeds that when the Cu content is 5% in the later stage. When the Cu content reaches the maximum value of 20%, the friction path has disappeared, and only a small amount of atoms accumulate at the end position. A similar phenomenon was also observed in the study by Li et al. [ 32 ] . This is mainly because as the Cu element content continues to increase, the internal microstructure of the AgCu alloy changes. The radius of copper atoms is different from that of silver atoms. After more copper atoms are incorporated, the alloy lattice will be distorted, and the lattice constant will change, resulting in a weakening of the overall inter-atomic bonding force of the alloy, which is macroscopically manifested as a gradual decrease in hardness. During the friction process, a lower hardness means that the material has a weaker ability to resist external force deformation, so it is more prone to plastic deformation. When the Cu content is low, the material can still maintain a certain rigidity, and the atomic accumulation shows an obvious friction path; as the Cu content increases, the material is continuously'reshaped' during friction, the atoms are more likely to flow, and the accumulation morphology changes, thus resulting in the different phenomena of the friction path changing with the Cu content as described above. It can be seen that the Cu element content has a non-negligible impact on the friction process and results. 3.3.3 Atomic Shear Strain Analysis Figure 13 shows the atomic shear strain diagrams during the friction process for alloys with Cu contents of 5%, 10% and 20% respectively. Diagrams a, b, and c correspond to Cu contents of 5%, 10%, and 20% respectively, while 1, 2, and 3 represent friction displacements of 0 Å, 50 Å, and 100 Å. As can be seen from the Fig. 13 , with the continuation of friction, the number of atoms exhibiting atomic shear strain increases. When the Cu element content changes, a notable phenomenon is that the number of atoms with a small atomic shear strain increases beneath the indenter. Over time, these atoms accumulate under the indenter, forming a space with small atomic shear stress, and this phenomenon is most obvious when the Cu content reaches 20%. This is because different elements in the alloy have different hardness levels.When the content of Cu in the AgCu alloy rises, the alloy softens, the binding force between atoms weakens, and atoms are more likely to displace and rearrange under force. Macroscopically, this is manifested as an increase in the deformable area of the alloy. During friction, this area provides more room for atomic movement, allowing atoms with small atomic shear strain to accumulate more freely under the indenter, resulting in the formation and expansion of the space with small atomic shear stress, which is particularly significant when the Cu content is 20%. 3.3.4 Atomic Lattice Evolution Analysis Figure 14 shows the lattice evolution diagrams during the friction process for alloys with Cu contents of 5%, 10% and 20% respectively. As depicted, it can be seen that during the friction process, the FCC structure of the AgCu alloy is damaged by the indenter, and the atoms near the indenter transform into an amorphous structure, a BCC structure, or an HCP structure. When the Cu content is 20%, the FCC structure beneath the indenter is damaged most severely. As the friction process proceeds, more atoms transform into an amorphous structure and other structures. During the friction process, with the increase of the copper content, the lattice distortion of the alloy also increases, and the evolution mode of the alloy's crystal structure changes. Due to the differences in atomic size and chemical bonding between copper atoms and silver atoms, when the copper content is high, under the action of friction force, the atoms in the alloy are more likely to rearrange, resulting in more FCC-phase atoms transforming into other phases. 4. Conclusions In this paper, molecular dynamics simulations were utilized to deeply investigate the friction behaviors of AgCu alloys with different depths, friction speeds, and Cu contents. A comprehensive analysis was conducted on the obtained results, including friction forces, surface morphologies, strain distributions, and dislocation evolutions. 1. Effect of depth on friction: The depth is closely related to the average friction force. As the friction depth increases, the average friction force generally shows a linear increase. This is because a greater friction depth increases the contact area between the tool and the alloy, causing more alloy atoms to participate in the friction. Meanwhile, more atoms accumulate on the alloy surface, more FCC-phase atoms inside transform into other phases, and more dislocations are generated. 2. Effect of friction speed on friction: Average friction force increases with sliding velocity (0.5-1.5 Å/ps). Higher velocities enhance adhesion, reduce twinning, and augment work hardening. Localized heating causes thermal softening, partially offset by strain rate strengthening. Net friction increase results from strain rate strengthening outweighing thermal softening, revealing the interplay between mechanical and thermal effects. 3. Effect of Cu content on friction: The copper content exerts a remarkable influence on the friction behavior of the Ag-Cu alloy. As the copper content rises, the average frictional force demonstrates a distinct linear decline. Concurrently, the plowing effect weakens, and the accumulation of surface atoms decreases. The alteration in the elemental proportion gives rise to the softening of the alloy. A higher copper content enhances the alloy's plasticity, broadens the strain region, and increases the number of disordered structures. This indicates that there exists a trade-off between reducing friction and the tendency towards amorphization. Declarations Funding: This research was funded by the National Natural Science Foundation of China [52405176], the Guangdong Province Natural Science Foundation [2023A1515011558], the Ministry of Education Chunhui Plan Project [HZKY20220434], the State Key Laboratory of Solid Lubrication Fund [LSL-2204], the Open Fund of The Key Laboratory for Metallurgical Equipment and Control Technology of Ministry of Education in Wuhan University of Science and Technology [MECOF2024B02], the Fundamental Research Funds for the Central Universities [N2403019], the Tribology Science Fund of the State Key Laboratory of Tribology in Advanced Equipment [SKLTKF24B15]. Author Contribution Y. W.designed and carried out the simulation experiments and wrote the main manuscript text. Y.Q.and Z.W. curated the data and prepared all figures and graphs. Y.M. drafted the initial version of the manuscript and participated in its revision. 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Modelling and simulation in materials science and engineering, 2010,18(1):15012. Wu Y, Tan J, Li X, et al. Molecular dynamics study on friction of high-entropy alloy FeNiCrCoCu[J]. Materials today communications, 2023,37:107107. AlMotasem A T, Bergström J, Gåård A, et al. Atomistic Insights on the Wear/Friction Behavior of Nanocrystalline Ferrite During Nanoscratching as Revealed by Molecular Dynamics[J]. Tribology letters, 2017,65(3):1-13. Li X, Zhang R, Liu Z, et al. Molecular dynamics study on friction of the iron-aluminum alloy[J]. Materials today communications, 2022,33:104402. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 05 Jun, 2025 Reviews received at journal 04 Jun, 2025 Reviewers agreed at journal 29 May, 2025 Reviews received at journal 26 May, 2025 Reviewers agreed at journal 24 May, 2025 Reviewers invited by journal 22 May, 2025 Editor assigned by journal 06 May, 2025 Submission checks completed at journal 06 May, 2025 First submitted to journal 23 Apr, 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-6512210","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":461297467,"identity":"a3865959-3c46-459f-a7d0-08abe2c070b8","order_by":0,"name":"Yi Wang","email":"","orcid":"","institution":"School of Mechanical Engineering and Automation, Northeastern University","correspondingAuthor":false,"prefix":"","firstName":"Yi","middleName":"","lastName":"Wang","suffix":""},{"id":461297468,"identity":"30962b1c-b8a7-498d-bad6-671d469dd539","order_by":1,"name":"Yiyi Qian","email":"","orcid":"","institution":"School of Mechanical Engineering and Automation, Northeastern University","correspondingAuthor":false,"prefix":"","firstName":"Yiyi","middleName":"","lastName":"Qian","suffix":""},{"id":461297469,"identity":"298cdd7d-b47a-4547-ac67-cd92318f60a1","order_by":2,"name":"Yuwei Ma","email":"","orcid":"","institution":"School of Mechanical Engineering and Automation, Northeastern University","correspondingAuthor":false,"prefix":"","firstName":"Yuwei","middleName":"","lastName":"Ma","suffix":""},{"id":461297470,"identity":"13f333ec-0ea3-4fb8-b5ab-c2726bb5b7fb","order_by":3,"name":"Zhuo Wang","email":"","orcid":"","institution":"School of Mechanical Engineering and Automation, Northeastern University","correspondingAuthor":false,"prefix":"","firstName":"Zhuo","middleName":"","lastName":"Wang","suffix":""},{"id":461297471,"identity":"f5d75532-ddb4-4eec-a7de-21aedb01b188","order_by":4,"name":"Shumin Zhang","email":"","orcid":"","institution":"Beijing Key Laboratory of Long-life Technology of Precise Rotation and Transmission Mechanisms, BeijingInstitute of Control Engineering","correspondingAuthor":false,"prefix":"","firstName":"Shumin","middleName":"","lastName":"Zhang","suffix":""},{"id":461297472,"identity":"2d7365b6-d5dd-47eb-ad67-16f86a84ee39","order_by":5,"name":"Dingding Xiang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+ElEQVRIiWNgGAWjYBACg8Mgko1ZjoGBsfEATJAoLcZALQ3EaZFsgGhJBNHEaeFnZ3728EuZdfra9sMNBxh32CQ2sDdvk2CouYNTCxszm7mxzLn03G1nEoFazqQlNvAcK5NgOPYMjxYGM2nJtsO52w6AtLQdTmyQyDGTYGw4jNthzOzfQFrSzc4/BGn5n9gg/wa/FslmHjPJj22HE8xugG0B2iXBg1+LwWGeMmmGc+mG224AbUlsSzZu40krtkg4hkfL+ePbJH+UWcubnU9/+OBjm51sP/vhjTc+1ODWAgLMPDBWAihAYAx8gPEHAQWjYBSMglEwwgEAv/ZYaD2WQIoAAAAASUVORK5CYII=","orcid":"","institution":"School of Mechanical Engineering and Automation, Northeastern University","correspondingAuthor":true,"prefix":"","firstName":"Dingding","middleName":"","lastName":"Xiang","suffix":""}],"badges":[],"createdAt":"2025-04-23 11:38:20","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6512210/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6512210/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":83445353,"identity":"bf43bd15-286d-4997-899d-456d77818064","added_by":"auto","created_at":"2025-05-26 10:58:15","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":207913,"visible":true,"origin":"","legend":"\u003cp\u003eMolecular Dynamics Model of Friction in AgCu Alloy\u003c/p\u003e","description":"","filename":"image1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6512210/v1/6ca66f9c0ec6aec6fc3962ae.jpg"},{"id":83444722,"identity":"ebaf8350-d9fe-49d6-a30a-409c6d513041","added_by":"auto","created_at":"2025-05-26 10:50:15","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":72959,"visible":true,"origin":"","legend":"\u003cp\u003eDynamic strain curves of (a)friction force and (b)normal force\u003c/p\u003e","description":"","filename":"image2.png","url":"https://assets-eu.researchsquare.com/files/rs-6512210/v1/8de295045fc42b5dc47f5afc.png"},{"id":83444723,"identity":"19c46fbb-f682-435e-8809-43626f99639a","added_by":"auto","created_at":"2025-05-26 10:50:15","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":84589,"visible":true,"origin":"","legend":"\u003cp\u003e(a)friction forces and (b)Average friction forces at different depths\u003c/p\u003e","description":"","filename":"image3.png","url":"https://assets-eu.researchsquare.com/files/rs-6512210/v1/bfb2ae9dc59094335d645921.png"},{"id":83445354,"identity":"b76e46f5-cad5-487d-9832-b7a3225458a8","added_by":"auto","created_at":"2025-05-26 10:58:15","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":568505,"visible":true,"origin":"","legend":"\u003cp\u003eSurface morphologies when the friction depths are (a)10 Å, (b)15 Å and (c)20 Å respectively\u003c/p\u003e","description":"","filename":"image4.png","url":"https://assets-eu.researchsquare.com/files/rs-6512210/v1/bca41c052bd0cf493f5fec18.png"},{"id":83445359,"identity":"19342548-a65e-405c-a421-f8fab0223def","added_by":"auto","created_at":"2025-05-26 10:58:17","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":1450805,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution of atomic shear stress at friction distances of 0 Å, 50 Å and 100 Å for different friction depths\u003c/p\u003e","description":"","filename":"image5.png","url":"https://assets-eu.researchsquare.com/files/rs-6512210/v1/3d1000e1cb5eadee3a0b26c4.png"},{"id":83444737,"identity":"f7dfc24c-61ca-4c64-bd6a-cde00a0ba626","added_by":"auto","created_at":"2025-05-26 10:50:16","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":1143686,"visible":true,"origin":"","legend":"\u003cp\u003eAtomic lattice evolution diagrams at friction distances of 0 Å, 50 Å and 100 Å for different friction depths\u003c/p\u003e","description":"","filename":"image6.png","url":"https://assets-eu.researchsquare.com/files/rs-6512210/v1/3d34049e320564db1735a91a.png"},{"id":83444736,"identity":"75be5120-caf3-4cec-aac5-f50e543e3f10","added_by":"auto","created_at":"2025-05-26 10:50:16","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":328091,"visible":true,"origin":"","legend":"\u003cp\u003eDislocation evolution at friction distances of 0 Å, 50 Å and 100 Å for different friction depths.\u003c/p\u003e","description":"","filename":"image7.png","url":"https://assets-eu.researchsquare.com/files/rs-6512210/v1/786ec3d167d91afc73b79120.png"},{"id":83444727,"identity":"c66932b5-631e-4458-8624-4eda0fdb0eae","added_by":"auto","created_at":"2025-05-26 10:50:16","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":87287,"visible":true,"origin":"","legend":"\u003cp\u003e(a)friction forces and (b)Average friction forces when the friction speeds are 0.5 Å/ps, 1 Å/ps, and 1.5 Å/ps respectively.\u003c/p\u003e","description":"","filename":"image8.png","url":"https://assets-eu.researchsquare.com/files/rs-6512210/v1/0d8158a89bf62779390ddfc0.png"},{"id":83445357,"identity":"3217bec0-55e9-4f00-a8b2-6e337aa29b1e","added_by":"auto","created_at":"2025-05-26 10:58:16","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":1251255,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution of atomic shear stress at friction distances of 0 Å, 50 Å and 100 Å for different friction speeds\u003c/p\u003e","description":"","filename":"image9.png","url":"https://assets-eu.researchsquare.com/files/rs-6512210/v1/23ae8915d5329dc7d366609b.png"},{"id":83444731,"identity":"0797d2f2-9308-4e01-8871-c5a20451827d","added_by":"auto","created_at":"2025-05-26 10:50:16","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":1079126,"visible":true,"origin":"","legend":"\u003cp\u003eAtomic lattice evolution diagrams at friction distances of 0 Å, 50 Å, and 100 Å under different friction speeds\u003c/p\u003e","description":"","filename":"image10.png","url":"https://assets-eu.researchsquare.com/files/rs-6512210/v1/117fead559adc5aeb32ee8eb.png"},{"id":83445356,"identity":"0172b787-4cec-4be0-ae35-5d2974f6d8a5","added_by":"auto","created_at":"2025-05-26 10:58:16","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":88311,"visible":true,"origin":"","legend":"\u003cp\u003e(a)friction forces and (b)average friction forces of alloys with Cu of 5%, 10% and 20% respectively\u003c/p\u003e","description":"","filename":"image11.png","url":"https://assets-eu.researchsquare.com/files/rs-6512210/v1/b7d84c253caaac9098a5ca7e.png"},{"id":83444734,"identity":"e699def6-b470-45fd-90d8-914d938ab234","added_by":"auto","created_at":"2025-05-26 10:50:16","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":536488,"visible":true,"origin":"","legend":"\u003cp\u003eFriction surface morphology diagrams of alloys with Cu of (a)5%, (b)10% and (c)20% respectively\u003c/p\u003e","description":"","filename":"image12.png","url":"https://assets-eu.researchsquare.com/files/rs-6512210/v1/150f909db006314575cb610e.png"},{"id":83444735,"identity":"53ff4de0-aab0-4e9a-a823-623407be8100","added_by":"auto","created_at":"2025-05-26 10:50:16","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":1268703,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution of atomic shear stress at friction distances of 0 Å, 50 Å and 100 Å for different Cu contents\u003c/p\u003e","description":"","filename":"image13.png","url":"https://assets-eu.researchsquare.com/files/rs-6512210/v1/812fa23862dcc4d43ca48e54.png"},{"id":83444729,"identity":"4c0a24e1-e8f6-4107-818c-3fc02a5643ba","added_by":"auto","created_at":"2025-05-26 10:50:16","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":1163029,"visible":true,"origin":"","legend":"\u003cp\u003eAtomic lattice evolution diagrams at friction distances of 0 Å, 50 Å and 100 Å for different Cu contents\u003c/p\u003e","description":"","filename":"image14.png","url":"https://assets-eu.researchsquare.com/files/rs-6512210/v1/ca94eb8ac54712cbcf9d416a.png"},{"id":83445576,"identity":"c4468255-afdf-4ba8-be9e-9bba48e92516","added_by":"auto","created_at":"2025-05-26 11:06:18","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":9811843,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6512210/v1/c367ac0e-bc4d-465d-8726-b0677513b7b0.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Effect of Friction Depth, Velocity, and Cu Content on the Friction Behavior of AgCu Alloys by Molecular Dynamics Simulation","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eAlloying is a classic strategy for optimizing the comprehensive properties of metallic materials. However, the negative correlation between strength and plasticity restricts its engineering applications. Through multi-component alloy design, the use of synergistic mechanisms such as nano-precipitation strengthening and grain boundary regulation can overcome the strength-plasticity trade-off. Developing high-strength and high-plasticity alloys has become a research hotspot.In recent years, various properties of many binary alloys have been widely studied, including Al-Cu\u003csup\u003e[\u003cspan additionalcitationids=\"CR2 CR3\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]\u003c/sup\u003e, Au-Ag\u003csup\u003e[\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]\u003c/sup\u003e, Fe-Cu\u003csup\u003e[\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]\u003c/sup\u003e, Zn-Cu\u003csup\u003e[\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]\u003c/sup\u003e, Cr-Cu\u003csup\u003e[\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]\u003c/sup\u003e, Mg-Ag\u003csup\u003e[\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]\u003c/sup\u003e, and many other binary alloys.\u003c/p\u003e \u003cp\u003eAgCu alloys have attracted extensive attention due to their excellent comprehensive properties. Current research focuses on the regulation of mechanical properties by the Ag content\u003csup\u003e[\u003cspan additionalcitationids=\"CR11 CR12\" citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]\u003c/sup\u003e. Zhao et al.\u003csup\u003e[\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]\u003c/sup\u003e found that an increase in the Ag content makes the eutectic phase distribute in a fibrous form, improving the tensile strength. Song et al.\u003csup\u003e[\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]\u003c/sup\u003e revealed that an increase in the strain rate enhances the alloy through promoting Ag precipitation and grain-boundary strengthening. These studies provide a theoretical basis for the development of high-strength and wear-resistant contact materials. Due to various factors, it is difficult for traditional methods to conduct research on AgCu alloys\u003csup\u003e[\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]\u003c/sup\u003e. However, the above-mentioned problems can be analyzed and solved at the atomic level through molecular dynamics (MD) simulation\u003csup\u003e[\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]\u003c/sup\u003e. At present, MD simulation has been widely used to study the mechanical properties of nanoscale AgCu alloy. During the simulation and calculation process, there are many factors that can affect the mechanical properties of AgCu binary alloy. Among these numerous factors, the grain size of alloying elements, strain rate, as well as the interfacial state and internal microstructure of the alloy all have a significant impact on the mechanical properties of the alloy\u003csup\u003e[\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eResearch indicates\u003csup\u003e[\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]\u003c/sup\u003e that grain size and Ag content have a significant regulatory effect on the mechanical properties of AgCu alloys. Molecular dynamics simulations reveal that in nanocrystalline AgCu alloys, the segregation behavior of Ag atoms at grain boundaries leads to a parabolic change trend in the resistance to grain boundary friction. Meanwhile, the dislocation density continuously decreases with the increase of Ag content, indicating that Ag atoms at grain boundaries can effectively weaken the strength within the grains\u003csup\u003e[\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]\u003c/sup\u003e. The collaborative design of ultrafine-grained structures and optimized Ag content can improve the alloy properties, but there exists a critical grain-refinement size threshold, and a high Ag content will significantly increase the preparation cost\u003csup\u003e[\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]\u003c/sup\u003e. Studies on dynamic mechanical behavior show that the strain rate, by regulating the coordinated evolution of the dislocation motion mode and the grain-boundary slip mechanism, causes a non-linear attenuation trend in the dislocation nucleation stress and yield stress of AgCu nanocomposites\u003csup\u003e[\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]\u003c/sup\u003e. The AgCu alloy exhibits a characteristic of a deformation mechanism transition from dislocation-slip-dominated to grain-boundary-friction-dominated at different strain rates\u003csup\u003e[\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]\u003c/sup\u003e, while a specific atomic structure of the Au-Ag alloy exhibits reversible deformation behavior at low strain rates\u003csup\u003e[\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]\u003c/sup\u003e. The interface state and microstructure of materials are equally crucial for their properties: The oxidation sensitivity of AgCu nanowires restricts their engineering applications\u003csup\u003e[\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]\u003c/sup\u003e., but the introduction of dislocation-cluster interactions can improve the fracture toughness through the dislocation-capture mechanism at the crack tip\u003csup\u003e[\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]\u003c/sup\u003e. The construction of a bimodal nanotwinned structure can achieve efficient strengthening, and its tensile strength is positively correlated with the twin-spacing\u003csup\u003e[\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eAlthough AgCu alloys hold broad prospects due to their excellent mechanical properties, challenges remain in their development. Key aspects include composition design, microstructure regulation, and grain -size control. Theoretical calculations are crucial for optimizing design and enhancing performance. Strengthening theoretical research is essential to further improve properties. Existing literature insufficiently explores performance impacts under different conditions. This study aims to reveal the friction-wear mechanism of AgCu alloys at room temperature at the atomic scale by analyzing stress-strain behavior and dislocation evolution.\u003c/p\u003e"},{"header":"2. Model and Simulation","content":"\u003cp\u003eThe friction model of the AgCu alloy was developed in the molecular dynamics software LAMMPS\u003csup\u003e[\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]\u003c/sup\u003e. The lattice type of the alloy is face-centered cubic (FCC), with the lattice constant set to 4.086. The size of the model is set to 245.6 \u0026Aring; \u0026times; 122.58 \u0026Aring; \u0026times; 122.58 \u0026Aring; (60A\u0026times;30A\u0026times;30A), and the total number of atoms is 216,000. The crystal orientations of the alloy along the X,Y, and Z axes are set to [100], [010], and [001] directions respectively. A spherical diamond indenter with a radius of 20 \u0026Aring; and a total of 6,140 atoms is adopted. After constructing the initial model, the Ag-Cu MEAM potential is used to describe the atomic interactions in the AgCu alloy. The interactions between carbon atoms in diamond are described by the Tersoff potential, and the interactions between the AgCu alloy and C atoms are described by the Lennard-Jones (L-J) potential. The specific parameters are shown in the following table.\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\u003eL-J Parameters for Interactions between Metal Atoms and Carbon Atoms\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\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 \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eInteraction-atom pair\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eε(ev)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eσ(\u0026Aring;)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAg-C\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.02883\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.998266\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCu-C\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.03541\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.79476\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\u003eTo eliminate the unreasonable structures in the model, the conjugate gradient algorithm was employed to minimize the energy of the model. Subsequently, under the isobaric-isothermal ensemble (NPT) at 300 K, the Ag-Cu alloy model was relaxed for 300 ps to reach an equilibrium state, and the Nos\u0026eacute;-Hoover thermostat was used during the relaxation process. The atoms in the ranges of 0\u0026ndash;8 \u0026Aring;, 8\u0026ndash;16 \u0026Aring;, and 16-122.58 \u0026Aring; in the Z-direction were set as the fixed layer, the thermostat layer, and the Newtonian layer respectively. The atoms in the Newtonian layer can move freely. The fixed layer was placed at the bottom of the model to prevent movement in space. The thermostat layer consisted of atoms adjacent to the fixed layer to maintain a constant system temperature. This simulation was only carried out for the thermostat and Newtonian layers. Periodic boundary conditions were applied in the X and Y directions of the model, while a shrink-wrapped boundary condition was used in the Z-direction. The initial position of the indenter was above the substrate. It was pressed into the substrate at a certain speed along the negative Z-axis direction. After reaching a certain depth, it then rubbed along the positive X-axis direction. The model is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn order to study the influence of friction speed, friction depth, and Cu content on the friction performance of the AgCu alloy, control experiments were carried out in this paper. The main parameter settings are shown in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\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\u003eMain Parameter Settings of the Experiment\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eModel scale\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e245.6 \u0026Aring; \u0026times; 122.58 \u0026Aring; \u0026times; 122.58 \u0026Aring;\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eThe number of atoms\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e216000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTime step\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1fs\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTemperature\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e300K\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFriction speed\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.5 \u0026Aring;/ps /1 \u0026Aring;/ps /1.5 \u0026Aring;/ps\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFriction depth\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e10 \u0026Aring;/15 \u0026Aring;/20 \u0026Aring;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFriction displacement\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e100 \u0026Aring;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eContent of Cu element\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5/10/20%\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\u003eIn this study, the visualization of simulation results was achieved by the open-source visualization software tool (OVITO\u003csup\u003e[\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]\u003c/sup\u003e). The Common Neighbor Analysis (CNA) was used to identify the crystal structures before and after the friction process; the Dislocation Extraction Algorithm (DXA) was employed to identify various dislocation features; and atomic shear strain analysis was adopted to evaluate the shear-related deformation behavior of all samples during the wear process at the atomic scale.\u003c/p\u003e"},{"header":"3. Results and Discussion","content":"\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Influence of Friction Depth on Friction Behavior\u003c/h2\u003e \u003cp\u003eIn this part, a diamond indenter with a radius of 20 \u0026Aring; was used. At a temperature of 300 K and an indenter velocity of 1 \u0026Aring;/ps, a pressing-down simulation was first carried out on AgCu10. The friction depths were set to 10 \u0026Aring;, 15 \u0026Aring;, and 20 \u0026Aring; respectively. Then, the diamond indenter rubbed along the positive X-axis direction for 100 \u0026Aring;.\u003c/p\u003e \u003cdiv id=\"Sec5\" class=\"Section3\"\u003e \u003ch2\u003e3.1.1 Analysis of Friction Force\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e demonstrates the dynamic strain curves of the friction force and normal force during the pressing-down and friction processes when the friction depth is 15 \u0026Aring;. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, the period from 0\u0026ndash;15 \u0026Aring; is the pressing-down process, during which the magnitude of the force fluctuates around 0. In the friction stage from 15\u0026ndash;115 \u0026Aring;, the friction force starts to rise rapidly as the displacement gradually increases, then fluctuates up and down around a certain value and gradually increases, and finally stabilizes and fluctuates around a certain value. The reason for the curve fluctuation is the continuous appearance and disappearance of dislocations during the friction process. According to the change of the friction force, this process can be roughly divided into three parts: the early friction stage (0\u0026ndash;15 \u0026Aring;), the friction climbing stage (15\u0026ndash;20 \u0026Aring;), and the friction stable stage (20\u0026ndash;115 \u0026Aring;). From 0 to 15 \u0026Aring;, the tip of the spherical indenter with a radius of 20 \u0026Aring; initially contacts the alloy surface, and the friction force is rapidly generated and increases slowly. Subsequently, from 15 to 20 \u0026Aring;, the friction stage begins, and the indenter gradually comes into full contact with the surface of the alloy, so the friction force climbs rapidly as the displacement increases. When the displacement is greater than 20 \u0026Aring;, the friction force basically remains fluctuating around a certain value. In the friction simulation study by Wu et al.\u003csup\u003e[\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]\u003c/sup\u003e, the response curve of the friction force also demonstrates a similar trend.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e visually demonstrates the dynamic changes in the friction force of the AgCu10 alloy under friction depths of 10 \u0026Aring;, 15 \u0026Aring;, and 20 \u0026Aring;, respectively. It can be clearly observed from the Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e that there is an extremely close and significant correlation between the friction depth and the average friction force. As the friction depth gradually increases, the average friction force shows an almost linear increase trend. Specifically, when the friction depth is 10 \u0026Aring;, the average friction force reaches a minimum value of 32.52 nN. When the friction depth rises to 20 \u0026Aring;, the average friction force reaches a maximum value of 64.38 nN. During the friction process, work hardening occurs due to the formation of chips and deposits, which has a decisive impact on the increase in friction force\u003csup\u003e[\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]\u003c/sup\u003e. As the friction depth deepens, the amount of deposits and debris continues to increase, further promoting the rise of friction force. When the friction depth increases, the contact area between the tool and the alloy expands significantly. The expansion of the contact area leads to an increase in the resistance of alloy atoms to the cutting tool. When rubbing along the positive X-axis direction, more dislocations are generated, and the atomic accumulation phenomenon is further intensified. At this time, the cutting tool must apply a greater tangential force to break the original crystal structure of the alloy, ultimately causing a substantial increase in the friction force.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section3\"\u003e \u003ch2\u003e3.1.2 Surface Morphology Analysis\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e shows the atomic surface morphologies when the friction depths are 10 \u0026Aring;, 15 \u0026Aring; and 20 \u0026Aring; respectively. As can be seen from the Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, after the diamond indenter finishes pressing down, there is no obvious atomic accumulation around the indenter. During the subsequent friction process, as the friction displacement increases, the atomic accumulation on both sides of the indenter path gradually increases, and the friction track becomes more and more obvious. At the end of the friction, atoms accumulate intensively in front of the indenter's movement, forming a distinct bulge where the atomic accumulation is the most abundant and prominent. With the increase of the friction depth, it is also evident that the atomic accumulation increases. When the friction depth is 15 \u0026Aring;, the atoms already show a tendency to accumulate above the indenter. When the depth is 20 \u0026Aring;, the atomic accumulation above the indenter is particularly obvious. This is because at a greater depth, the indenter will push more atoms. As the depth and friction displacement increase, more and more atoms accumulate. Since the radius of the diamond is 20 \u0026Aring;, the atoms accumulate above the indenter.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section3\"\u003e \u003ch2\u003e3.1.3 Atomic Shear Strain Analysis\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e demonstrates the atomic shear strain diagrams at different depths. Diagrams a, b, and c correspond to friction depths of 10 \u0026Aring;, 15 \u0026Aring;, and 20 \u0026Aring; respectively, while 1, 2, and 3 represent friction displacements of 0 \u0026Aring;, 50 \u0026Aring;, and 100 \u0026Aring;. As can be seen from the Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, the deformation region nucleates from the contact area between the indenter and the substrate, distributes near the indenter, and is arranged approximately at a 45\u0026deg; angle. During the friction process, the region with the highest shear strain is consistently concentrated in the area near the indenter. As the friction depth increases, the number of atoms with large atomic shear strain gradually increases. It can also be observed here that atoms accumulate above the indenter. This is because the contact area between the tool and the workpiece increases with the increase of the machining depth, causing more atoms to be directly affected by the scratching process. This phenomenon leads to an increase in the number of atoms subjected to high strain and stress. Therefore, the deformation level of the workpiece rises with the increase of the cutting depth.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section3\"\u003e \u003ch2\u003e3.1.4 Atomic Lattice Evolution Analysis\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e shows the lattice evolution diagrams during the friction process at different depths. As depicted, it can be seen that during the friction process, the vast majority of atoms in the alloy sample remain in the FCC structure, while a small number of atoms near the indenter transform into an amorphous structure, a BCC structure, or an HCP structure. Diagrams (b) and (c) represent the crystal structures when the friction depths are 50 \u0026Aring; and 100 \u0026Aring; respectively. It can be observed that with the increase of the friction depth, the amorphous, BCC, and HCP structures gradually increase and continue to extend deeper into the alloy sample.This exhibits similar characteristics to the evolution of atomic shear strain in the previous Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section3\"\u003e \u003ch2\u003e3.1.5 Dislocation Evolution Analysis\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e demonstrates the dislocation evolution diagrams during the friction process at different depths. As shown, during the friction process, dislocations and HCP atoms always form near the indenter and continuously appear and disappear as the friction process proceeds. With the increase of the friction depth, more and more dislocations form around the indenter. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ec, this is particularly obvious when the friction depth is 20 \u0026Aring;, with a large number of dislocations and stacking faults forming near the indenter. Among these dislocations, Shockley partial dislocations account for the vast majority and exhibit a gliding phenomenon, constantly emerging near the tool as the scratching tool moves.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Influence of Friction Speed on Friction Behavior\u003c/h2\u003e \u003cp\u003eIn this part, a diamond indenter with a radius of 20 \u0026Aring; was used. At a temperature of 300 K, the indenter speeds were set to 0.5 \u0026Aring;/ps, 1 \u0026Aring;/ps, and 1.5 \u0026Aring;/ps respectively. First, a pressing-down simulation was carried out on AgCu10 with a friction depth of 15 \u0026Aring;. Then, the diamond indenter rubbed along the positive X-axis direction for 100 \u0026Aring;.\u003c/p\u003e \u003cdiv id=\"Sec11\" class=\"Section3\"\u003e \u003ch2\u003e3.2.1 Analysis of Friction Force\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e presents the evolution law of the friction force of the AgCu10 alloy when the friction speeds are 0.5 \u0026Aring;/ps, 1 \u0026Aring;/ps, and 1.5 \u0026Aring;/ps respectively. Experimental data indicate that the average friction force shows a significant upward trend with the increase of the friction speed. The underlying mechanism involves the synergistic effect of thermal softening and work hardening. Analyzing from the microscopic level, the generation of friction force stems from the coupling of intermolecular forces and mechanical interlocking effects on the contact surface. When the friction speed increases, the activity of surface molecules enhances, and the intermolecular interaction energy increases, resulting in an increase in the adhesion force component. At the same time, the local temperature rise caused by high-speed friction promotes material softening, reducing the mechanical interlocking resistance. However, the work-hardening effect compensates for the impact of softening, ultimately resulting in a net increase in the friction force. This non-linear response characteristic provides an important basis for understanding the tribological behavior of alloys under dynamic loads.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section3\"\u003e \u003ch2\u003e3.2.2 Atomic Shear Strain Analysis\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e demonstrates the distribution characteristics of atomic shear strain of the AgCu10 alloy at different friction speeds. The experimental results indicate that the deformation region is always concentrated in the indenter contact area. As the friction process progresses, the large shear-strain region gradually expands. When the friction speed increases from 0.5 \u0026Aring;/ps to 1.5 \u0026Aring;/ps, the proportion of the small-shear-strain region with ε\u0026thinsp;\u0026lt;\u0026thinsp;0.1 increases significantly, while the area percentage of the high-strain region with ε\u0026thinsp;\u0026gt;\u0026thinsp;0.3 first increases and then decreases. At a friction distance of 50 \u0026Aring;, the area of the high-strain region at a speed of 1.5 \u0026Aring;/ps is the smallest, but at this time, the average friction force reaches a maximum value of 68.2 nN. This phenomenon can be attributed to the synergistic effect of multi-scale deformation mechanisms: The local temperature rise caused by high-speed friction promotes the thermally-activated process of dislocation slip, enabling more grain-boundary regions to participate in the deformation, resulting in the expansion of the small-strain region. At the same time, the material's dynamic recovery ability is enhanced under high-speed loading, which inhibits the further development of the high-strain region.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section3\"\u003e \u003ch2\u003e3.2.3 Atomic Lattice Evolution Analysis\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e demonstrates the lattice evolution of AgCu alloy under different sliding velocities. Initially, distinct structural responses are observed: increasing sliding velocity induces higher twinning activity around the indenter. Notably, at the mid-friction stage (50 \u0026Aring; displacement), the 0.5 \u0026Aring;/ps velocity condition exhibits extensive twinning In front of and below the indenter, whereas higher velocities (1.0-1.5 \u0026Aring;/ps) show reduced twinning density. This twinning reduction mechanism can be attributed to the competing effects of dynamic recovery and thermal softening at elevated sliding speeds.The presence of twin boundaries acts as barriers to dislocation nucleation, effectively mitigating plowing-induced plastic deformation. Conversely, reduced twinning leads to increased work hardening through intensified dislocation accumulation. This microstructural trade-off results in a velocity-dependent friction response: higher sliding velocities produce greater frictional forces due to the combined effects of reduced twinning suppression and enhanced work hardening. These observations highlight the critical role of velocity-induced twinning dynamics in governing tribological behavior at the nanoscale. (158 words)\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Influence of Different Cu Element Contents on Friction Behavior\u003c/h2\u003e \u003cp\u003eIn this part, a diamond indenter with a radius of 20 \u0026Aring; was used. At a temperature of 300 K and an indenter speed of 1 \u0026Aring;/ps, a pressing-down simulation was first carried out on AgCu alloys with Cu contents of 5%, 10% and 20% respectively, at a depth of 15 \u0026Aring;. Then, the diamond indenter rubbed along the positive X-axis direction for 100 \u0026Aring;.\u003c/p\u003e \u003cdiv id=\"Sec15\" class=\"Section3\"\u003e \u003ch2\u003e3.3.1 Analysis of Friction Force\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e shows the average friction forces during the friction process for alloys with Cu contents of 5%, 10% and 20% respectively. As can be seen from the Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e, during the friction process, the average friction force is closely related to the Cu element content. When the Cu element content in the AgCu alloy gradually increases, the average friction force of the alloy shows a significant downward trend, presenting an obvious negative-correlation linear relationship. The reason is that with the increase in the number of copper atoms, the lattice parameters and crystal structure of the AgCu alloy are affected to varying degrees. The presence of copper atoms in the alloy is likely to cause distortion of the alloy's crystal structure, thus reducing the overall hardness of the material. During the friction process, compared with materials with higher hardness, the softer Cu is more likely to undergo plastic deformation without strong resistance, thus reducing the overall friction force.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section3\"\u003e \u003ch2\u003e3.3.2 Surface Morphology Analysis\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e shows the friction surface morphology diagrams during the friction process for alloys with Cu contents of 5%, 10% and 20% respectively. It can be seen from the Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e that after the friction is completed, atoms accumulate on both sides of the friction path, clearly outlining a friction track. Among them, when the Cu content is 5%, this friction path is the most prominent. When the Cu content reaches 10%, in the initial stage of friction, the path is not clear; however, as the friction continues, the number of accumulated atoms gradually increases, the path becomes clearer, and its accumulation height even exceeds that when the Cu content is 5% in the later stage. When the Cu content reaches the maximum value of 20%, the friction path has disappeared, and only a small amount of atoms accumulate at the end position. A similar phenomenon was also observed in the study by Li et al.\u003csup\u003e[\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]\u003c/sup\u003e. This is mainly because as the Cu element content continues to increase, the internal microstructure of the AgCu alloy changes. The radius of copper atoms is different from that of silver atoms. After more copper atoms are incorporated, the alloy lattice will be distorted, and the lattice constant will change, resulting in a weakening of the overall inter-atomic bonding force of the alloy, which is macroscopically manifested as a gradual decrease in hardness. During the friction process, a lower hardness means that the material has a weaker ability to resist external force deformation, so it is more prone to plastic deformation. When the Cu content is low, the material can still maintain a certain rigidity, and the atomic accumulation shows an obvious friction path; as the Cu content increases, the material is continuously'reshaped' during friction, the atoms are more likely to flow, and the accumulation morphology changes, thus resulting in the different phenomena of the friction path changing with the Cu content as described above. It can be seen that the Cu element content has a non-negligible impact on the friction process and results.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec17\" class=\"Section3\"\u003e \u003ch2\u003e3.3.3 Atomic Shear Strain Analysis\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e shows the atomic shear strain diagrams during the friction process for alloys with Cu contents of 5%, 10% and 20% respectively. Diagrams a, b, and c correspond to Cu contents of 5%, 10%, and 20% respectively, while 1, 2, and 3 represent friction displacements of 0 \u0026Aring;, 50 \u0026Aring;, and 100 \u0026Aring;. As can be seen from the Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e, with the continuation of friction, the number of atoms exhibiting atomic shear strain increases. When the Cu element content changes, a notable phenomenon is that the number of atoms with a small atomic shear strain increases beneath the indenter. Over time, these atoms accumulate under the indenter, forming a space with small atomic shear stress, and this phenomenon is most obvious when the Cu content reaches 20%. This is because different elements in the alloy have different hardness levels.When the content of Cu in the AgCu alloy rises, the alloy softens, the binding force between atoms weakens, and atoms are more likely to displace and rearrange under force. Macroscopically, this is manifested as an increase in the deformable area of the alloy. During friction, this area provides more room for atomic movement, allowing atoms with small atomic shear strain to accumulate more freely under the indenter, resulting in the formation and expansion of the space with small atomic shear stress, which is particularly significant when the Cu content is 20%.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section3\"\u003e \u003ch2\u003e3.3.4 Atomic Lattice Evolution Analysis\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003e shows the lattice evolution diagrams during the friction process for alloys with Cu contents of 5%, 10% and 20% respectively. As depicted, it can be seen that during the friction process, the FCC structure of the AgCu alloy is damaged by the indenter, and the atoms near the indenter transform into an amorphous structure, a BCC structure, or an HCP structure. When the Cu content is 20%, the FCC structure beneath the indenter is damaged most severely. As the friction process proceeds, more atoms transform into an amorphous structure and other structures. During the friction process, with the increase of the copper content, the lattice distortion of the alloy also increases, and the evolution mode of the alloy's crystal structure changes. Due to the differences in atomic size and chemical bonding between copper atoms and silver atoms, when the copper content is high, under the action of friction force, the atoms in the alloy are more likely to rearrange, resulting in more FCC-phase atoms transforming into other phases.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"4. Conclusions","content":"\u003cp\u003eIn this paper, molecular dynamics simulations were utilized to deeply investigate the friction behaviors of AgCu alloys with different depths, friction speeds, and Cu contents. A comprehensive analysis was conducted on the obtained results, including friction forces, surface morphologies, strain distributions, and dislocation evolutions.\u003c/p\u003e\n\u003cp\u003e1. Effect of depth on friction: The depth is closely related to the average friction force. As the friction depth increases, the average friction force generally shows a linear increase. This is because a greater friction depth increases the contact area between the tool and the alloy, causing more alloy atoms to participate in the friction. Meanwhile, more atoms accumulate on the alloy surface, more FCC-phase atoms inside transform into other phases, and more dislocations are generated.\u003c/p\u003e\n\u003cp\u003e2. Effect of friction speed on friction: Average friction force increases with sliding velocity (0.5-1.5 \u0026Aring;/ps). Higher velocities enhance adhesion, reduce twinning, and augment work hardening. Localized heating causes thermal softening, partially offset by strain rate strengthening. Net friction increase results from strain rate strengthening outweighing thermal softening, revealing the interplay between mechanical and thermal effects.\u003c/p\u003e\n\u003cp\u003e3. Effect of Cu content on friction: The copper content exerts a remarkable influence on the friction behavior of the Ag-Cu alloy. As the copper content rises, the average frictional force demonstrates a distinct linear decline. Concurrently, the plowing effect weakens, and the accumulation of surface atoms decreases. The alteration in the elemental proportion gives rise to the softening of the alloy. A higher copper content enhances the alloy\u0026apos;s plasticity, broadens the strain region, and increases the number of disordered structures. This indicates that there exists a trade-off between reducing friction and the tendency towards amorphization.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eFunding:\u003c/h2\u003e \u003cp\u003eThis research was funded by the National Natural Science Foundation of China [52405176], the Guangdong Province Natural Science Foundation [2023A1515011558], the Ministry of Education Chunhui Plan Project [HZKY20220434], the State Key Laboratory of Solid Lubrication Fund [LSL-2204], the Open Fund of The Key Laboratory for Metallurgical Equipment and Control Technology of Ministry of Education in Wuhan University of Science and Technology [MECOF2024B02], the Fundamental Research Funds for the Central Universities [N2403019], the Tribology Science Fund of the State Key Laboratory of Tribology in Advanced Equipment [SKLTKF24B15].\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eY. W.designed and carried out the simulation experiments and wrote the main manuscript text. Y.Q.and Z.W. curated the data and prepared all figures and graphs. Y.M. drafted the initial version of the manuscript and participated in its revision. X.D. and S.Z. is the corresponding author and supervised the submission processAll authors reviewed and approved the final manuscript for submission.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eXu M, Zhang H, Yuan T, et al. Microstructural characteristics and cracking mechanism of Al-Cu alloys in wire arc additive manufacturing[J]. Materials characterization, 2023,197:112677.\u003c/li\u003e\n\u003cli\u003eLi J, L\u0026uuml; S, Wu S, et al. Micro-mechanism of simultaneous improvement of strength and ductility of squeeze-cast Al-Cu alloy[J]. Materials science \u0026amp; engineering. 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Materials today communications, 2022,33:104402.\u003c/li\u003e\n\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":"surface-science-and-technology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Surface Science and Technology](https://link.springer.com/journal/44251)","snPcode":"44251","submissionUrl":"https://submission.springernature.com/new-submission/44251/3","title":"Surface Science and Technology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Open","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"AgCu alloy, molecular dynamics, Friction Behavior, Effect","lastPublishedDoi":"10.21203/rs.3.rs-6512210/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6512210/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe silver-copper (AgCu) alloy is widely used in numerous industries such as electronics and electrical engineering due to its excellent electrical conductivity, thermal conductivity, and workability. However, the friction problems during its service can seriously affect the operational stability and service life of equipment. Therefore, it is of great significance to deeply explore the friction and wear behavior of the AgCu alloy. In this study, the molecular dynamics simulation method was employed to conduct an in-depth investigation of the friction and wear behavior of AgCu alloy with different friction depths, velocities, and Cu contents. The study found that there was a close positive correlation between the friction depth and the average friction force. As the depth increases, the contact area enlarges, and the atomic packing, phase transformation, and dislocations increase, resulting in a roughly linear increase in the average friction force.At friction speeds of 0.5 \u0026Aring;/ps, 1 \u0026Aring;/ps, and 1.5 \u0026Aring;/ps, the average friction force increases with the increase of speed, accompanied by expanded strain localization and reduced twinning with intensified work hardening under dynamic loading.The content of the Cu element has a significant impact on the friction behavior of the alloy. When the content increases, the softening of the alloy leads to a significant linear decrease in the average friction force. At the same time, the plasticity is enhanced, the strain region expands, and the disordered atomic structures increase. The results of this study provide an important theoretical basis for a deep understanding of the friction and wear mechanism of the AgCu alloy and the optimization of its performance.\u003c/p\u003e","manuscriptTitle":"Effect of Friction Depth, Velocity, and Cu Content on the Friction Behavior of AgCu Alloys by Molecular Dynamics Simulation","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-05-26 10:50:09","doi":"10.21203/rs.3.rs-6512210/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-06-06T02:15:34+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-06-05T02:38:19+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"268336522080887498301751389550409779070","date":"2025-05-29T08:12:51+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-05-26T08:39:26+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"315168641452998085507689055154558217857","date":"2025-05-24T10:27:59+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-05-22T10:00:24+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-05-07T02:01:09+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-05-07T02:00:04+00:00","index":"","fulltext":""},{"type":"submitted","content":"Surface Science and Technology","date":"2025-04-23T11:30:07+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"surface-science-and-technology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Surface Science and Technology](https://link.springer.com/journal/44251)","snPcode":"44251","submissionUrl":"https://submission.springernature.com/new-submission/44251/3","title":"Surface Science and Technology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Open","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"6269b5ba-2892-45f0-b5bf-c64f2d220ae2","owner":[],"postedDate":"May 26th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2025-07-23T13:53:45+00:00","versionOfRecord":[],"versionCreatedAt":"2025-05-26 10:50:09","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6512210","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6512210","identity":"rs-6512210","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}