# Structure of Argon Solid Phases Formed from the Liquid State at Different Isobaric Cooling Rates
## 2 Data and Methods  
### Calculated Data  
Using the molecular dynamics method, three series of computer experiments that simulated the processes of isobaric cooling of argon particle systems initiated in initial states at a temperature of 150 K and pressure values of 0.5 MPa, 1 MPa, 2 MPa, 3 MPa and 4 MPa. Cooling of the systems was carried out to a temperature of 40 K, with such cooling, gaseous argon first condensed, and after liquid argon passed into a solid crystalline or glassy state. Cooling of the systems was carried out at rates of \(10^{8}\), \(10^{9}\), \(10^{10}\), \(10^{11}\) and \(10^{12}\) K/s.  
The simulation was carried out in the NanoSim2020 code [11], in which the numerical solution of the dynamics equations for particle systems was performed using the Verlet velocity form algorithm [12].  
In numerical experiments, systems consisting of 4096 argon particles were used, the interaction of which was described by the Lennard-Jones potential [13]:  
\[\mathrm{U_{ij}}=4\epsilon((\sigma/\mathrm{r_{ij}})^{12}\,-\,(\sigma/\mathrm{r_ {ij}})^{6}), \tag{1}\]  
where \(\epsilon/\mathrm{k_{b}}=121\) K is the depth of the potential well, \(\sigma=3.4\) A is the effective particle size [14]. This form of interaction potential has proven itself well in numerical experiments on the study of glass transition and crystallization of argon [15; 16; 17; 18].  
Periodic boundary conditions were used. The time step at the moment of initialization of the systems was \(10^{-15}\) s. After initialization, the system was brought to an equilibrium state for 10,000 iterations of modeling with the barostat procedure enabled.  
The cooling of the system was modeled by proportionally changing the particle velocities by the \(\mathrm{k_{v}}\) coefficient, which provides the necessary rate of temperature change dT/dt  
\[\mathrm{k_{v}}=(1-(3\mathrm{k_{b}}/2\mathrm{E_{k}})(\mathrm{dT/dt})\mathrm{n_ {mid}}\mathrm{\Delta t})^{1/2}, \tag{2}\]where \(\rm E_{ki}\) is the kinetic energy of the system at the i-th iteration of the simulation, \(\rm n_{mid}=100\) is the number of iterations for subsequent relaxation of the system after the act of temperature change.  
When simulating cooling at a rate of \(10^{11}\) K/s and \(10^{12}\) K/s, the time step was reduced to \(10^{-16}\) s.  
To maintain the set pressure value, a barostat was used, which allows modeling the NPT ensemble described in [2], according to which the linear dimensions of the system and the distances between the particles were adjusted by a factor of \(\mu\)  
\[\mu=(1+(\rm P(V)-P)/(3P(V)+\sum U_{ij}(r_{ij})^{2}/3V), \tag{3}\]  
where P(V) is the pressure at the current volume V, P is the pressure set by the experimental conditions. The barostat procedure was performed cyclically after each act of temperature change until the required pressure was reached.  
During the cooling process, according to the temperature dependence of density (Figure 1), the gas-liquid and liquid-solid transition regions were qualitatively distinguished, at cooling rates above \(10^{11}\) K/s, the temperature dependence of density did not undergo characteristic differences in the transition region from liquid to solid, which is characteristic of the process glass transition. In general, the density dynamics is comparable to the results of numerical experiments of the predecessors [16].  
Upon completion of the cooling procedure, the coordinates of the system particles were stored in text files. These coordinate arrays were used as input data for quantitative structural analysis of argon solid phases formed as a result of computer experiments.