Anharmonic Quantum Effects in Cubic Boron Nitride Crystal by Path Integral Monte Carlo Simulations

Abstract

Using path‐integral Monte Carlo (PIMC) simulations in the isothermal‐isobaric ensemble, the authors investigate the quantum effects on structural and thermodynamic properties of cubic boron nitride (c‐BN) at pressures varying from 0 up to 162 GPa. The Albe–Tersoff potential is employed to describe the interatomic interactions. The differences between the obtained lattice parameters of the crystal from the PIMC simulation and their experimental values are less than 0.1%. The quantum effects of the atomic zero‐point motion are significant for temperature lower than 1000 K. At ambient pressure, the quantum contribution to the lattice vibrational energy overcomes the classical one for T≲386 K. This temperature dependent crossover shifts to higher temperature with increasing pressure. The ratio of the kinetic to potential vibrational energy is used to quantify the anharmonicity of the system, indicating that the c‐BN is essentially an anharmonic crystal. Furthermore, the root‐mean‐square displacement (RMSD) analysis shows that the quantum effects become insignificant for temperature higher than 1000 K where different atoms (boron and nitrogen) behave similarly. However, for lower temperatures, the quantum effects arise and the atoms have quite different behaviors resembling those from rare‐gas solids (boron) and covalent materials (nitrogen).

Quantum Effects in Two-Dimensional Silicon Carbide

“…To understand the energy results of PIMD simulations at low T , we note that analysis based on perturbation theory and quasiharmonic approximations point out that the low-T energy shift relative to a harmonic model is basically caused by a change of the kinetic energy [29,30]. This happens, indeed, for perturbed harmonic oscillators at T = 0 (considering perturbations of x 3 or x 4 type), where first-order energy changes are due to shifts in E kin , while E pot stays unmodified respect to the harmonic energy [60].…”

“…This kind of simulations allow us to efficiently quantize the nuclear degrees of freedom, including both thermal and quantum fluctuations at finite temperatures [27,28]. This procedure allows one to carry out quantitative analyses of anharmonic effects in condensed matter [29,30].…”

Quantum effects in structural and elastic properties of graphite: Path-integral simulations

“…[30][31][32][33] This procedure is in principle equivalent to a quantization of the vibrational modes in the solid, with the advantage that anharmonicities are directly included in the path-integral simulation procedures. This kind of methods have been used to study properties of materials as diamond, 34,35 silicon, 36 boron nitride, 37,38 and graphene. 32,33,39 We are not aware of any quantum atomistic simulation of graphite.…”