A New Model to Predict Optimum Conditions for Growth of 2D Materials on a Substrate

Abstract

Deposition of atoms or molecules on a solid surface is a flexible way to prepare various novel two-dimensional materials if the growth conditions, such as suitable surface and optimum temperature, could be predicted theoretically. However, prediction challenges modern theory of material design because the free energy criteria can hardly be applied to this issue due to the long-standing problem in statistical physics of the calculations of the free energy. Herein, we present an approach to the problem by the demonstrations of graphene and γ-graphyne on the surface of copper crystal, as well as silicene on a silver substrate. Compared with previous state-of-the-art algorithms for calculations of the free energy, our approach is capable of achieving computational precisions at least 10-times higher, which was confirmed by molecular dynamics simulations, and working at least four orders of magnitude faster, which enables us to obtain free energy based on ab initio calculations of the interaction potential instead of the empirical one. The approach was applied to predict the optimum conditions for silicene growth on different surfaces of solid silver based on density functional theory, and the results are in good agreement with previous experimental observations.

Thermal contributions to the structural phase transitions of crystalline aluminum under ultrahigh pressures

“…As formulated in statistical mechanics, the FE can be readily obtained without empirical parameters as long as the partition function (PF) is solved while unfortunately the exact solution to the PF of condensed matters is a long-standing problem because of the complexity of the high dimensional configurational integral [13,40,41], so that state-of-the-art numerical algorithm for PF can hardly afford a system consisting of more than several hundred particles even using empirical interatomic force field and the determined transition pressures for Al were far from the experimental results [42]. Very recently, we put forward a direct integral approach (DIA) to the PF of condensed state systems with ultrahigh efficiency and precision [43][44][45][46], and has been successfully applied to investigate the phase transitions of vanadium [47], the EOS of copper [43] and the optimum growth condition for 2-D materials [44] combined with density functional theory (DFT). Compared with quasi-harmonic phonon model, DIA was examined to be applicable to much wider realm with much higher precision [46].…”

Solution to the key problem of statistical physics -- calculations of partition function of many-body systems

“…For a solid argon system of 500 atoms described by L-J potential at temperatures ranging from 80K to 300K, we ran a NS algorithm with N c ∼ 10 9 and DIA with N c ∼ 10 4 (real computer time is about 4 hours for NS and about 5 seconds for DIA respectively by using one physical core of the CPU) to calculate internal energy and pressure, which were compared to the MD simulations using the same potential function, demonstrating that the precision of DIA is about 10 times higher [50]. The accuracy of DIA has also been proved by calculating the internal energy of graphene or γ-graphyne materials on Cu substrate using Brener potential function [51], and silicene on Ag substrate using Tersoff potential function [52]. Due to the ultrahigh efficiency, DIA has been successfully applied to predict the optimal conditions for silicene growth on Ag substrate with ab initio calculations [52], which should be the first time to calculate the absolute free energy at finite temperatures up to thousands Kelvins with first-principle laws.…”

“…The accuracy of DIA has also been proved by calculating the internal energy of graphene or γ-graphyne materials on Cu substrate using Brener potential function [51], and silicene on Ag substrate using Tersoff potential function [52]. Due to the ultrahigh efficiency, DIA has been successfully applied to predict the optimal conditions for silicene growth on Ag substrate with ab initio calculations [52], which should be the first time to calculate the absolute free energy at finite temperatures up to thousands Kelvins with first-principle laws.…”

Comparison of Two Efficient Methods for Calculating Partition Functions

“…Very recently, we put forward a direct integral approach (DIA) to calculate the PF of condensed matters [ 26 ] and the high accuracy has been proved by molecular dynamics (MD) simulations of condensed copper using tight-binding potential [ 26 ], graphene and -graphyne materials using Brenner potential [ 27 ]. Based on our reinterpretation of the original sense of the integral, it was shown that DIA works at least four-order faster than NS [ 26 ].…”