Understanding Chemical Ordering in Intermetallic Clathrates from Atomic Scale Simulations

Abstract

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 Ba 8 Ga x Ge 46−x , Ba 8 Ga x Si 46−x , Ba 8 Al x Ge 46−x , and Ba 8 Al x Si 46−x 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.

Thermal conductivity in intermetallic clathrates: A first-principles perspective

“…The splitting of the modes can be viewed as a consequence of the facts that (i ) the guest atom is not located at the immediate center of the cage, (ii ) the latter is shaped like a tetrakaidekahedron, and (iii ) the Al and Ga atoms are not necessarily symmetrically distributed between the framework sites. 22 For Ba 8 Al x Si 46−x the phonon modes slightly soften with increasing x; a similar trend albeit even weaker can also be observed for the lower two groups in the case of Ba 8 Ga 16 Ge 30 . This behavior correlates with the increase in the lattice constant, which is larger for Ba 8 Al x Si 46−x than for Ba 8 Ga x Ge 46−x [gray lines in Fig.…”

“…II B), which has been found to yield an excellent description of finite temperature properties for other materials. 46,47 As a first step in assessing the performance of these functionals we determined the temperature dependence 22. In this context it must be noted that it is not always possible to find experimental data for the lattice parameters for the stoichiometric compounds.…”

“…1). [9][10][11] Ba 8 Ga 16 Ge 30 has been investigated extensively both experimentally 5,6,[12][13][14][15][16] and theoretically, 13,[17][18][19][20][21][22][23][24] especially because of its promising thermoelectric properties.…”

Robust cluster expansion of multicomponent systems using structured sparsity

“…Initially, CE was largely applied to binary alloys 2, [13][14][15][16][17][18][19][20][21][22][23][24][25][26] . Thereafter, it has been applied to more complex systems, including ternary to quinary alloys 5,6,12,[27][28][29] , semiconductors 7,30 , battery materials 31,32 , clathrates 33,34 , magnetic alloys [35][36][37] , and nanoscale alloys 3,4,11,[38][39][40][41][42] . In complex systems, the reduced symmetry increases the number of symmetrically distinct clusters, exacerbating the cluster selection problem.…”

“…The first emphasizes using physical insights, such as via specific priors in the Bayesian framework 43 or via selection rules to incorporate smaller clusters before larger ones 44,45 . The second approach espouses using sparsity-driven regularization such as compressed sensing 6,33,34,[46][47][48][49] . Fundamentally, CE is a standard linear regression problem y = Xβ-the response y i is the first-principles energy of the ith structure in the training set {σ}, the coefficient β j is the ECI of the jth cluster, and the component x ij of the design matrix X is the correlation function Φ j (σ i ) of structure i with respect to cluster j.…”