icet - A Python library for constructing and sampling alloy cluster expansions

Alloy cluster expansions (CEs) provide an accurate and computationally efficient mapping of the potential energy surface of multi-component systems that enables comprehensive sampling of the many-dimensional configuration space. Here, we introduce \textsc{icet}, a flexible, extensible, and computationally efficient software package for the construction and sampling of CEs. \textsc{icet} is largely written in Python for easy integration in comprehensive workflows, including first-principles calculations for the generation of reference data and machine learning libraries for training and validation. The package enables training using a variety of linear regression algorithms with and without regularization, Bayesian regression, feature selection, and cross-validation. It also provides complementary functionality for structure enumeration and mapping as well as data management and analysis. Potential applications are illustrated by two examples, including the computation of the phase diagram of a prototypical metallic alloy and the analysis of chemical ordering in an inorganic semiconductor.Comment: 10 page

Optimization of the Thermoelectric Power Factor: Coupling between Chemical Order and Transport Properties

Many thermoelectric materials are multicomponent systems that exhibit chemical ordering, which can affect both thermodynamic and transport properties. Here, we address the coupling between order and thermoelectric performance in the case of a prototypical inorganic clathrate (Ba8Ga16Ge30) using a combination of density functional and Boltzmann transport theory as well as alloy cluster expansions and Monte Carlo simulations. The calculations describe the experimentally observed site occupancy factors and reproduce experimental data for the transport coefficients. By inverting the cluster expansion, we demonstrate that the power factor can be increased by more than 60% for certain chemical ordering patterns that involve reducing the number of the trivalent species on the 6c Wyckoff site. This enhancement is traced to specific features of the electronic band structure. The approach taken in the present work can be readily adapted to other materials and enables a very general form of band structure engineering. In this fashion, it can guide the computational design of compounds with optimal transport properties

Understanding Chemical Ordering in Intermetallic Clathrates from Atomic Scale Simulations

Intermetallic clathrates exhibit great variability with respect to elemental composition and distribution. While this provides a lot of flexibility for tuning properties, it also poses a challenge with regard to developing a comprehensive understanding of these systems. Here, we employ a combination of alloy cluster expansions and density functional theory calculations to exhaustively sample the compositional space with ab initio accuracy. We apply this methodology to study chemical ordering and related properties in the clathrate systems Ba₈Ga_<i>x</i>Ge_{46–<i>x</i>}, Ba₈Ga_<i>x</i>Si_{46–<i>x</i>}, Ba₈Al_<i>x</i>Ge_{46–<i>x</i>}, and Ba₈Al_<i>x</i>Si_{46–<i>x</i>} as a function of composition and temperature. We achieve very good agreement with the available experimental data for the site occupancy factors (SOFs) even for stoichiometries outside the composition range considered during construction of the cluster expansions. This validation enables us to reconcile the variations in the experimental data and explain nonmonotonic variations of the SOFs. In particular, we provide a rationale for the extreme SOF behavior with varying composition observed in Al-based clathrates. Furthermore, we quantify the effect of chemical ordering on both heat capacity and lattice expansion. Finally, we determine the effect of chemical disorder on the displacements of the guest species (Ba), which enables us to at least partially explain experimental observations of the nuclear density of Ba in different clathrates