Molecular dynamics study on the structural properties and phase transformation of Cu-Au nanoparticles

The electroreduction of CO2 to carbon-containing products carries considerable significance. Cu-Au alloys have been considered as potential bimetallic catalysts recently. However, the current theoretical study of obtaining Cu-Au alloys that could enhance the catalytic activity is insufficiently thorough. Herein, the structural properties and phase transition rules of Cu-Au nanoparticles are investigated utilizing molecular dynamics. The results indicate that the percentage of disordered atoms in Cu-Au nanoparticles decreases and the melting temperature increases with the growth of particle size. Moreover, the coordination number decreases with increasing radial distance. Cu-Au nanoparticles are coexisting in crystalline and amorphous states during melting. The structural properties of Cu-Au catalysts could be regulated by the phase transition rules, which provided a theoretical basis for the modification of surface activity.


Introduction
The increasing concentration of CO 2 in the atmosphere has caused numerous environmental issues recently, and the electroreduction of CO 2 into high value-added carbon-containing products holds tremendous environmental significance and economic merit [1,2]. In this process, it is crucial to prepare catalysts with excellent performance. The Cu metal is the only metal catalyst that can efficiently reduce CO 2 to polycarbonate products [3,4]. However, the large-scale application of Cu catalyst products is still inevitably constrained. Specifically, Cu metal catalysts present superior catalytic stability, but their high overpotential, low activity, and inhomogeneous selectivity constitute the main obstacles to their application [5][6][7].
To develop high selectivity and favorable stability of Cu-based catalysts, considerable investigations have been conducted around tuning the catalytic properties of Cu-based catalysts. The first idea is surface modification of the monometal, namely, changing the surface morphology of the monometal by different physicochemical techniques to enhance the properties of the catalyst [8,9]. In addition, the metals would exhibit distinctive catalytic activity different from the bulk material as they are reverted to nanometer size [10]; the synthesis of nanoparticles with distinct components enables the exposure of more catalytic sites, and the higher surface energy of the nanoparticles facilitates reducing the hindrance of electron transfer that would lead to lower free energy [11,12]. More than that, there are many valuable investigations. The catalytic rate exponentially depends on the adsorption energy between the active sites and reactants [13]. Adsorption energy is determined by the composition, size and facet of the nanocrystals. Earlier work has shown that the decrease of the icosahedral Cu cluster size and the increase of the truncated octahedral Cu cluster size contribute to the selectivity of CO 2 reduction [14]. By regulating the crystal phase structure of nanomaterial, the relationship between the intrinsic catalytic activity of nanomaterial has been studied [15,16]. Nevertheless, there are still challenges in employing nanoparticles of a single element as catalysts, and the stability of the catalysts is difficult to guarantee during catalytic reactions [17]. Non-mixable metals on the bulk scale could be alloyed on the Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. nanoscale, presenting an opportunity to combine different elements to constitute bimetallic or polymetallic nanoparticles [10]. Some scientists have proposed the solution idea of bimetallic catalysts, which is to improve the properties of Cu catalysts by introducing a new second metal [18][19][20].
So far, bimetallic nanoparticles have served as one of the predominant catalyst forms. Yang's group synthesized two types of Au-Cu structures with ordered and disordered atoms, and found that with the increase of atomic ordering, the nanoparticles formed interphase shell structures that greatly upgraded their catalytic properties [21]. Moreover, Kim et al [22] constructed a Cu-Au alloy and experimentally demonstrated that the d-band of the metal would migrate after alloying of Cu with Au; the catalytic properties are substantially elevated after alloying as discovered when it is used for catalysing CO 2 . It can be seen that the unique structure of the bimetallic catalyst not only hybridizes the atomic orbitals of the metals, but also increases the components to transform the nanoparticle structure and generate synergistic effects between different metals [23,24]. By combining Cu and Au, the Cu-Au alloy nanoparticles not only feature favorable stability and optical tunability, but also characterize high catalytic activity thanks to the synergistic effect between the two components [10]. Cu-Au alloys could decrease the surface binding energy and consequently reduce the free energy of intermediate reactions by modifying the d-band [25]. The phase transition process of Cu-Au alloy core-shell structure involves atomic diffusion behavior. Currently, the studies on the dynamics of the phase transition process of the core-shell structure are scarce since the simulation time is time-consuming and the calculation is heavy. Thus, the effects of many factors such as structure and size on the phase transition behavior are still to be explored, and the microstructural evolution and phase transition mechanisms of nanoparticles have not been very well understood.
Herein, the structural properties and phase transition regulation of Cu-Au nanoparticles are investigated by utilizing the molecular dynamics method supported based on LAMMPS software [26]. Firstly, the influences of the thermodynamic phase transformation on the surface structure are further explored according to the structural properties. In addition, the structure of the Cu-Au nanoparticle surface layer is subdivided into 30 layers using the nanoparticle hierarchical calculation method, and the structural properties of the coordination number and active sites of the Cu-Au nanoparticle surface layer are resolved layer by layer. This research provides support for the construction of a simplified model of first principles, a simulation reference for the regulation of surface structure, and a theoretical basis for the enhancement of the catalytic properties of Cu-Au nanoparticles.

Computational method
In this study, molecular dynamics simulations were carried out for the structural characteristics and phase transition laws of Cu-Au nanoparticles. In some cases, nanoparticles below 1 nm or even single atoms are more active, but the activity of such structures is usually influenced by frontline orbitals and requires matrix support. Additionally, the activity of particles above 10 nm may be related to the surface coordination environment and is not a direct effect of size effects. Therefore, based on LAMMPS software, we simulated 10 configurations with particle sizes in the range of 1-10 nm. The fine structure analysis of nanomaterials could explain the phase transition mechanism and feed back the computational model, which is the basis and guarantee to solve the experimental design and theoretical calculation. The initial model of Cu-Au nanoparticles was established at 10% Au content [27]. The spherical Cu-Au nanoparticles with different sizes might exhibit both atomically ordered and atomically disordered structures, and nanoparticles form the core-shell structure as the degree of atomically ordered increases [21]. The lattice strains and vacancies exist in the surface shell layers, while the internal cores have the similar atomic structure as the bulk material [28,29]. The main potential function applied an embedded atom method (EAM) potential for the binary Cu-Au system developed by Gola [30]. Before simulating the phase transition process, the whole system was placed at 300 K for 50 ps relaxation and thermodynamic equilibrium treatment. In this process, the ensemble is an isothermal isobaric (NPT) ensemble, the thermostat is Nose-Hoover, the barostat is Berendsen, and the time step is 1 fs. After the thermodynamic equilibrium treatment, the NPT ensemble was also used to run for 50 ps, and the temperature of the system was linearly increased from 300 K to 3000 K to simulate the phase transition process, and at the same time, the temperature, potential energy and kinetic energy of the entire system, shell and core were collected. The common neighbor analysis (CNA) crystal structure analysis command was applied to identify the local crystal structure around the atoms, and the calculation command was 'compute cna/atom' [31]. The focus of this work is to study the nanoparticle structure in layers. For example, the Cu-Au nanoparticle structure with a particle radius of 3 nm is divided into 100 layers for research, the surface layer structure is divided into 30 layers (with an interval of 0.01 nm), and the core structure is divided into 70 layers. Statistical changes in coordination number, potential energy, kinetic energy and atomic number of atoms with different layers are calculated. All data are made by taking the average of three calculations.

Results and discussion
3.1. Thermal stability of Cu-Au nanoparticles The melting process of Cu-Au nanoparticles (300 K to 3000 K) is simulated to contribute to the understanding of the thermal stability mechanism of Cu-Au catalysts. The melting process of Cu-Au nanoparticles could be visualized by OVITO post-processing software. OVITO is a scientific visualization and analysis software for atomic and particle simulation data, contributing to a clearer understanding of material phenomena and physical processes. It has emerged as a formidable tool for analyzing, interpreting, and illustrating simulation results in a widening range of computational simulation studies [32]. Figure 1 exhibits the melting structures of Cu-Au nanoparticles with diameters of 3 nm, 6 nm, and 9 nm, respectively. In which, the blue color is the Cu atoms initially located on the surface layer of the nanoparticles, the red color is the Cu atoms in the core, and the yellow color is the Au atoms. We note that the initial state of each model core-shell structure undergoes a transformation as the melting process continues. The existence of more defects such as dangling bonds and vacancies on the surface of Cu-Au nanoparticles results in a lower coordination number and surface melting temperature; consequently, the surface activity is increased so that the atoms in the surface layer gradually diffuse to the interior, and finally a disordered distribution of alloy atoms is obtained [33].
The feature of disordered atoms: short-range order within a few atomic diameters, but disorder beyond this range, similar to a liquid structure. In general, the melting structure is disordered which could be judged according to the Lindemann melting criterion. Furthermore, numerous experiments and theories have confirmed that the surface of nanomaterials also has liquid-like characteristics at room temperature, i.e., disordered characteristics [34]. The percentage of atoms attributed to the Face-centered cubic (Fcc) and disordered states in the Cu-Au alloy model could also reflect the thermal stability of the catalyst. In table 1, the percentage of Fcc in 10 alloy configurations gradually increases with the growth of alloy particle dimension, while that of disordered atoms progressively decreases. This might be explained by the fact that the larger the particle size, the fewer defects such as dangling bonds and vacancies on the surface of Cu-Au nanoparticles, and the surface activity is considered weak at elevated melting temperatures [35,36].
To discuss the effect of morphology on phase transition, figure 2 shows the potential energy (E p )-temperature (T) curves of Cu-Au particles with different morphologies. The morphologies in figure 2(a)-(c) are a spherical nanoparticle with a diameter of 6 nm, a cubic nanoparticle with a side length of 6 nm, and a cylinder with a cross-sectional diameter of 6 nm and a height of 6 nm, respectively. As can be seen from all  figures, the potential energies of nanoparticles increase slowly with temperature, regardless of the morphology; when the temperatures reach the melting points, the potential energies undergo the moderate changes, which are the sign of the thermodynamic first-order phase transition [37,38]. The melting points of the spherical, cubic and cylindrical nanoparticles are 1217 K, 1245 K, and 1278 K, respectively. Among them, the cubic particles have the highest potential energy, while the potential energy of spherical particles shows the least. Moreover, the tendency of the potential energy change near the melting point is most pronounced for cylindrical particles, followed by spherical ones. Our following investigations are dominated by spherical particles. The melting point values of Cu-Au nanoparticles at 2-10 nm diameters are present in figure 3. It can be observed that the melting point of nanoparticles continues to trend upward with increasing particle size. The melting point displays a remarkable variation at particle diameters less than 5 nm; however, the variation of melting point smooths out at particle diameters greater than 5 nm and gradually converges to that of the bulk material. This regularity is in general agreement with the theoretical predictions in the literature based on equation (1) [39].
Where T nano is the melting temperature of Cu-Au nanoparticles, T bulk is the melting temperature of bulk Cu-Au, η is the stacking coefficient, r 0 is the atomic radius, R is the nanoparticle radius, CN, ρ bulk , and ρ nano are the coordination number and density of Cu-Au bulk, and the density of nanoparticles, respectively. We observed that the melting points in figure 3 differ from the previous results in literature [33]. This possible error could be caused by the potential function. Summing up the above analysis, it can be concluded that the smaller the size of Cu-Au nanoparticles, the lower the melting point and the subsequent increase in activity.

Activity of Cu-Au nanoparticle shells
To explore more about the phase transition law of the core and shell layers on Cu-Au nanoparticles, the E p and T variation curves are presented in figure 4. Cooperating with figure 1, the blue atoms represent the Cu atoms in the shell layer, which are amorphous structure; the red atoms indicate the Cu atoms in the core, which are Fcc structure, and the yellow atoms stand for the Au atoms in the core, which are also Fcc structure. The Cu-Au nanoparticles have a particle size of 6 nm. The nanoparticle consists of 2355 Cu atoms in the shell layer along with 6256 Cu atoms and 986 Au atoms in the core. It was observed that the potential energy of nanoparticles exhibits a linear increase with rising temperature at lower temperatures, and then deviates significantly from the linear relationship, whereas the deviation could be attributed to the appearance of surface prefusion [40]. The E p difference of the core is larger than that of the shell, i.e., the region where the potential energy of the core deviates markedly from linearity with the change in temperature is greater. This indicates that the potential heat of melting from the core is stronger than that from the shell, resulting in the shell melting initially during the phase transition and in turn gradually expanding to the interior as the temperature increases [41]. Moreover, it can be seen that the core atomic potential energy is almost equal to the bulk material atomic potential energy, indicating that the surface activity of Cu-Au nanoparticles is related to the shell layer and not much to the core.
The mean square displacement (MSD) is the average value describing the square of the particle displacement and is used to characterize the diffusion of liquid metal particles. A correspondence exists between MSD and physical parameters such as the atomic diffusion coefficient and the Debye temperature [42]. The MSD is calculated by equation (2).
Where r(0) is the coordinate of the structure at the initial moment and r(t) is the coordinate of the structure at moment t. It is shown that there is an upper limit to MSD as the system is in the solid state, a linear relationship between MSD as the system is in the liquid state. Figure 5 shows the MSD variation of the shell and core of Cu-Au nanoparticles with a particle diameters of 6 nm. The temperature is increased from 300 K to 1200 K. Then, the atomic vibrational properties of the shell and core are investigated by using the NPT system for 50 ps of insulation at 1200 K. To ensure the reliability of the data, we first relaxed the simulation system by 50 ps, and then zeroed the data before conducting the subsequent 50 ps data statistics. After that, the MSD of the shell and core regions are calculated at 1200 K. It can be seen that the MSD of both shell and core atoms are linear (purple and orange lines in figure). This indicates that both shell and core atoms melt at a temperature of 1200 K. The temperature is increased to 1100 K employing the same simulation conditions, and it is found that the MSD of the shell layer still has a certain slope (blue line), while the MSD of the core nearly leveled off (green line). It indicates that the shell atoms melt while the core atoms do not melt at a temperature of 1100 K. In addition, the MSD of the shell atoms is significantly larger than that of the core, indicating that the atomic vibration frequency of the shell is higher than that of the core. The Lindemann melting criterion suggests that the MSD of the crystal is proportional to the square of the Debye temperature, and that melting occurs upon meeting a certain critical value [43]. Further, the temperature is increased to 900 K, and there are almost horizontal situations in the MSD of both shell and core atoms (black and red lines). This demonstrates that both shell and core atoms remain in the solid unmelted state at 900 K. In summary, the structural properties of Cu-Au catalysts could be regulated by the phase transition law, which can provide a theoretical basis for the regulation of surface activity.

Study on the fine structure of Cu-Au nanoparticles
Evidence from the above studies suggests that the thermal stability and activity of Cu-Au nanoparticles depend on the shell structure and atomic thermal vibrations, but the shell structure that fulfills satisfactory catalytic properties remains to be explored. The relationship between the coordination number of Cu-Au nanoparticles along the radial direction at different sizes are as shown in figure 6. It can be noticed that the coordination numbers with particle diameters of 4 nm, 6 nm, 8 nm, and 10 nm decrease layer by layer at a distance of 0.36 nm from the surface layer. This result reveals that the surface activity of nanoparticles is caused by the unsaturation of the coordination number of the surface atoms in the surface layer. Therefore, the nanoparticles could be simplified utilizing this model. The surface shell layer is calculated with the first principles to obtain more subtle electronic properties, whereas the internal core is performed using nanothermodynamics or molecular dynamics. It is expected to rationalize the design of high-performance Cu-Au nanocatalysts. Figure 7 depicts the distribution rule of coordination number with radial distance for Cu-Au nanoparticles with a diameter of 6 nm at different temperature conditions. As shown in the figure, the coordination number gets smaller as the temperature rises. The coordination numbers of 300 K, 600 K, 900 K, 1200 K, and 1500 K are about 12, 12, 11, 10 and 8, respectively, for center distances less than 13.49 Å. The coordination numbers are all significantly reduced to 5 or 6 as the center distance is greater than 13.49 Å. The current academic models such as  coordination number theory and coordination number d-band center theory [44], which are based on the variation of coordination number and have a structure comparable to our calculation. Figure 8 shows the radial distribution function of Cu-Au nanoparticles with a diameter of 6 nm at different temperatures. It can be seen from the figure that at 300 K, the second peak in the curve is wider, which is a signal amorphous phase. With the increase of temperature, the peak positions and relative intensity of the first peak of the curve vary for each temperature, and the two small peaks of the second peak gradually turned into 'steamed bread peaks', and the internal 'amorphization' of the particles gradually occur [45]. At 1500 K, the first and second peaks are symmetrical, which is a typical liquid structure.

Conclusions
The reduction of CO 2 to valuable fuels utilizing electrochemistry driven by renewable energy sources is a potentially sustainable route to reduce CO 2 emissions and alleviate dependence on fossil fuels. Cu-Au alloy nanoparticles have recently caught considerable attention in catalysis for their promising stability, optical tenability, and catalytic activity. Nevertheless, the continuous and intuitive acquiring of such bimetallic nanoparticles that could enhance the catalytic activity has not been theoretically studied thoroughly enough. In this paper, the microstructural evolution and phase transition rules of the core-shell structure on Cu-Au alloy  are investigated by molecular dynamics. The study found that Cu-Au particles are divided into surface shell and internal core, and the radial distance of the shell layer is about 0.36 nm. The melting process gradually diffuses from the surface to the interior, where Cu-Au nanoparticles appear to co-exist in crystalline and amorphous states. The smaller the particle size, the lower the melting point, whereby the melting point of Cu-Au nanoparticles with a diameter of 6 nm is 1217 K. Defects as surface overhanging bonds and vacancies increase with decreasing size, and the catalytic activity grows accordingly. In addition, the coordination number is inversely proportional to both radial length and temperature. The results of this effort are expected to establish the foundation for subsequent research on Cu-Au alloy nanosystems.

Data availability statement
The data cannot be made publicly available upon publication because no suitable repository exists for hosting data in this field of study. The data that support the findings of this study are available upon reasonable request from the authors.