# Molecular Dynamics Study on the Crystallization Process of Cubic Cu-Au Alloy
## 1 Introduction  
The quantum description of a large, multi-component physical system is usually complex, and its implementation is frequently impossible even for today's supercomputers. In addition, this quantum description often obscured the physical picture of the phenomena under consideration. Therefore, approximate simulations, based on the probabilistic treatment of the system, with parameters included in the problem after their quantum averaging, are often used, where the involved physical quantities are already treated as random variables or classical stochastic processes, and further numerical simulations are carried out using classical equations. This approach was used initially in the 1950s and then intensively developed in the 1980s, widely used now in the theory of solids, chemistry, and molecular biology. One of these is the so-called Molecular Dynamics (MD) method. This method is the most popular in the microscopic analysis [1]. In the framework of MD simulation, Newtonian equations of motion are used with the initial conditions generated randomly. We would like to emphasize here that our publication analyzing the classical model of ionization for two-electron atoms in intense laser beam, described in [2], can be considered as one of the first precursors of the MD method. This model has been demonstrated in detail in [3]. In this model, we started with a random generation of the initial conditions for positions and momenta of electrons by the Monte Carlo (MC) method by a modified Wigner Distribution in Phase Space. Then, the classical Newtonian equations of electrons were integrated. After that, all quantities related to the problem were averaged with the new distribution function created by new points in the phase space of electrons in the given time, \(t\). It follows that the obtained results were in satisfactory agreement with experimental observations. In practice, a real physical system consists of a large number of elements. Therefore, the MD simulation stays a unique possible tool for microscopic analysis level. In this paper, MD simulation was used. In theframework of MD simulation, some aspects should be carefully considered. First of all, the stability of the calculation code is or is not guaranteed with the choice of both numbers of constituents and the number of performed calculations steps. Furthermore, such problems as sensitive dependence of initial conditions leading to chaos, the accuracy of integration method for large system of nonlinear partial differential equations, etc., should be analyzed [4]. In practice, we use a phenomenological criterion for the validity of obtained results: when they are in good agreement with a large class of experimental results obtained before by numerous authors, they can be accepted as satisfied ones. Finally, the most essential aspect of the MD simulation procedure is the suitable choice of pair interaction between involved constituents. In a recent paper, the potential embedded in the simulation was chosen as Sutton-Chen (SC) type with free boundary conditions. We discuss this choice below. The subject of our recent considerations was the Cu-Au alloy. It is a material comprising of two metals, Cu and Au, with a cubic structure. Cu is a metal with high electrical conductivity and ductility, it can oxidize when it is exposed to the environment, and the reduction process from alcohol to aldehyde [5; 6] is also a catalyst [7; 8]. Au is a metal that is very stable for chemical reactions, has very good oxidation resistance, and is considered a heterogeneous substance [9]. When the size of the Au material is decreased to the nanometer size, the photocatalytic activity increased significantly [10]. Many researchers have studied the mechanism of CO oxidation at lower ambient temperatures [11; 12; 13]. Cu-Au alloys also were used in photocatalytic applications, such as methanol production [14; 15], oxidation reactions [16], and organic compounds [17].