Predicting ground-state configurations and electronic properties of the thermoelectric clathrates Ba$_{8}$Al$_{x}$Si$_{46-x}$ and Sr$_{8}$Al$_{x}$Si$_{46-x}$

TL;DR

This study uses first-principles calculations and a cluster-expansion approach to predict ground states and electronic properties of Ba$_{8}$Al$_{x}$Si$_{46-x}$ and Sr$_{8}$Al$_{x}$Si$_{46-x}$ clathrates, revealing a metal-semiconductor transition at specific compositions.

Contribution

It introduces an efficient iterative cluster-expansion method combined with simulated annealing to predict ground states of complex thermoelectric clathrates.

Findings

Lattice constants increase linearly with Al content, matching experiments.

Configurations with x=16 exhibit a metal-semiconductor transition.

Ground states at x=16 have indirect band gaps of 0.36 eV and 0.30 eV.

Abstract

The structural and electronic properties of the clathrate compounds Ba$_{8}$Al$_{x}$Si$_{46-x}$ and Sr$_{8}$Al$_{x}$Si$_{46-x}$ are studied from first principles, considering an Al content $x$ between 6 and 16. Due to the large number of possible substitutional configurations we make use of a special iterative cluster-expansion approach, to predict ground states and quasi-degenerate structures in a highly efficient way. These are found from a simulated annealing technique where millions of configurations are sampled. For both compounds, we find a linear increase of the lattice constant with the number of Al substituents, confirming experimental observations for Ba$_{8}$Al$_{x}$Si$_{46-x}$. Also the calculated bond distances between high-symmetry sites agree well with experiment for the full compositional range. For $x$ being below 16, all configurations are metallic for both materials. At the charge-balanced composition ($x=16$), the substitutional ordering leads to a metal-semiconductor transition, and the ground states of Ba$_{8}$Al$_{16}$Si$_{30}$ and Sr$_{8}$Al$_{16}$Si$_{30}$ exhibit indirect Kohn-Sham band gaps of 0.36 and 0.30 eV, respectively, while configurations higher in energy are metals. The finding of semiconducting behavior is a promising result in view of exploiting these materials in thermoelectric applications.