Close-packed layer spacing as a practical guideline for structure symmetry manipulation of IV-VI/I-V-VI2 thermoelectrics

The crystal-structure symmetry in real space can be inherited in the reciprocal space, making high-symmetry materials the top candidates for thermoelectrics due to their potential for significant electronic band degeneracy. A practical indicator that can quantitatively describe structural changes would help facilitate the advanced thermoelectric material design. In face-centered cubic structures, the spatial environment of the same crystallographic plane family is isotropic, such that the distances between the close-packed layers can be derived from the atomic distances within the layers. Inspired by this, the relationship between inter- and intra-layer geometric information can be used to compare crystal structures with their desired cubic symmetry. The close-packed layer spacing was found to be a practical guideline of crystal structure symmetry in IV-VI chalcogenides and I-V-VI₂ ternary semiconductors, both of which are historically important thermoelectrics. The continuous structural evolution toward high symmetry can be described by the layer spacing when temperature or/and composition change, which is demonstrated by a series of pristine and alloyed thermoelectric materials in this work. The layer-spacing-based guideline provides a quantitative pathway for manipulating crystal structures to improve the electrical and thermal properties of thermoelectric materials.