Full optimization of quasiharmonic free energy with an anharmonic lattice model: Application to thermal expansion and pyroelectricity of wurtzite GaN and ZnO

Pyroelectric Effect in Tetragonal Ferroelectrics BaTiO3 and KNbO3 Studied with Density Functional Theory

“…38 We also tested the impact of using a larger number of supercells ( 60), but we observed that the choice of the supercell size and displacement magnitude contributed more to the convergence of the SCPH procedure than the larger displacement force dataset size. Observed fitting errors of the quartic force constants (1.67% for BaTiO 3 and 0.62% for KNbO 3 ) are comparable to previously reported values (for example, 0.77 and 2.19% for GaN and ZnO, respectively 31 ). When calculating the forces on atoms for supercells, a tight SCF convergence criterion (TOLDEE keyword) of 10 −10 au was applied.…”

“…In addition, the inclusion of nonanalytic correction in SCPH led to unphysical behavior of lowest-frequency phonon modes. LO-TO splitting has similarly been omitted in a previous study of pyroelectricity in GaN and ZnO . We have however included LO-TO splitting with nonanalytic correction for the harmonic frequencies obtained at the Γ point with the approach implemented in CRYSTAL − and report them in the Supporting Information (Tables S5 and S6) along with experimental and previously reported theoretical values.…”

“…LO-TO splitting has similarly been omitted in a previous study of pyroelectricity in GaN and ZnO. 31 We have however included LO-TO splitting with nonanalytic correction for the harmonic frequencies obtained at the Γ point with the approach implemented in CRYSTAL 67−69 and report them in the Supporting Information (Tables S5 and S6) along with experimental and previously reported theoretical values. Example ALM (for fitting cubic and quartic force constants) and ANPHON (for SCPH calculations) inputs are given in the Supporting Information.…”

“…It should be stressed that the methodology outlined here does not take into account thermal expansion of the unit cell, unlike, for example, in the work of Tadano et al for GaN and ZnO. 31 In addition, a secondary piezoelectric contribution to the pyroelectric effect has to be taken into account separately (see below). A tertiary pyroelectric effect based on temperature gradients is also known, but obtaining it from atomic-level DFT calculations would be rather complicated, and the tertiary effect is neglected here.…”

A First-Principles Explanation of the Luminescent Line Shape of SrLiAl3N4:Eu2+ Phosphor for Light-Emitting Diode Applications

“…To compute the effect of thermal expansion, the volumetric quasi-harmonic approximation (QHA) is used, neglecting deviatoric thermal stresses and internal forces (v-ZSISA approximation). − The only contributions to the thermal expansion of the crystal are the coupling between phonons and the change in unit cell volume, with cell parameters and internal coordinates relaxed at fixed volumes. We obtain the temperature versus volume curve of the undoped SLA by minimizing the Helmholtz free energy (FE) ,, F false( V , T false) = E false( V false) + F vib false( V , T false) where F vib false( V , T false) = ∑ q ν ℏ ω boldq ν ( V ) 2 + k B T ln false( 1 − normale − ℏ ω boldq ν ( V ) / k normalB T false) Here, E ( V ) is the static DFT energy versus volume curve, with all non-volumetric degrees of freedom relaxed, and F vib ( V , T ) is the vibration energy with the same cell and atomic geometry.…”