Although the theory of lattice dynamics was established six decades ago, its accurate implementation for polar solids using the direct (or supercell, small displacement, frozen phonon) approach within the framework of density-function-theory-based first-principles calculations had been a challenge until recently. It arises from the fact that the vibration-induced polarization breaks the lattice periodicity, whereas periodic boundary conditions are required by typical first-principles calculations, leading to an artificial macroscopic electric field. The article reviews a mixed-space approach to treating the interactions between lattice vibration and polarization, its applications to accurately predicting the phonon and associated thermal properties, and its implementations in a number of existing phonon codes.
The present review focuses on the theory of lattice dynamics for polar solids. Here a polar solid implies an insulator or a semiconductor composed of cations with positive charges and anions with negative charges. As a matter of fact, the majorities of modern functional materials are made of polar solids, such as the topological crystalline insulator group-IV tellurides,29 the ferroelectrics and multiferroics,30 and materials for solar cells.31 The accurate descriptions of phonon properties have key roles for the understandings and developments of these materials.
The present paper is organized as follows: 'Basic lattice dynamics of polar solids' describes the basics of lattice dynamics and the fundamentals of the mixed-space approach. 'Helmholtz energy and quasiharmonic approximation' outlines the first-principles thermodynamics based on the phonon theory; More discussions of the mixed-space approach are given in 'The mixed-space approach'. 'Computational procedure' summarizes the common procedures in phonon calculations; 'Phonon software packages have implemented the mixed-space approach' briefs the implementation of the mixed-space approach in several software packages. Extensive applications of the mixed-space approach are summarized in 'Recent calculations using the mixed-space approach'. 'Other phonon software packages' briefs a list of other phonon codes implemented differently from the mixed-space approach for polar solids. 'Software packages for both electronic and phonon calculations' introduces a few widely in use first-principles codes for both electronic and phonon calculations. Finally, the last section is the 'Summary'.
Using the mixed-space approach, phonon and associated properties have been studied for a variety of polar (and non-polar) solids. Most of these calculations are based on the direct approach using the output data from first-principles codes such as VASP11,12 as input. Examples are firstly shown for several energy conversion and storage materials. 2b1af7f3a8