First-Principles Study of Order–Disorder Transitions in Pseudobinary Clathrates

Abstract

It has been recently demonstrated that the pseudoternary Ba8Al x Ga y Ge46–x–y clathrate undergoes an order–disorder transition with increasing temperature that can be observed via site occupation factors (SOFs) and manifests itself, e.g., in electrical transport properties. Here, we generalize this result and analyze the characteristics of this order–disorder transition in the pseudobinary clathrates Ba8Ga x Ge46–x , Ba8Ga x Si46–x , Ba8Al x Ge46–x , and Ba8Al x Si46–x . To this end, we employ atomistic simulations that combine alloy cluster expansions trained against density functional theory calculations with Wang–Landau and ensemble Monte Carlo simulations. The simulations show that all four systems studied here display order–disorder transitions for at least some composition range. Based on an extensive literature survey, we also provide evidence for signatures of the transition in earlier experimental studies that to the best of our knowledge have hitherto not been related to such transitions. The predicted transition temperatures are lower for Ba8Ga x Ge46–x and Ba8Ga x Si46–x than for Ba8Al x Ge46–x and Ba8Al x Si46–x , although it appears that the simulations underestimate the transition temperatures for Ga-containing systems compared to the experiment. This nonetheless provides a sensible explanation for why the experimentally determined Al SOFs agree better with the simulated high-temperature disordered configurations, while the Ga SOFs more closely agree with the simulated ground-state configurations. As a result of stronger interactions, the SOFs vary substantially, especially near the stoichiometric 16:30 composition, providing an indication of why it has proved difficult to synthesize Ba8Al x Ge46–x and Ba8Al x Si46–x samples at this ratio. The present study thereby yields detailed atomic-scale insights into the ordering in inorganic clathrates that, given the connection to transport properties established earlier, are not only useful from a fundamental perspective but also relevant for applications.

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“…This is especially true when scattering cross-sections are similar among constituent species. For example, inorganic pseudobinary clathrates are most often reported with mixed occupancy among the framework sites 25,26,64 , and ambiguous chemical ordering is common among materials containing vacancies 23,24,28,29 . Recent studies have demonstrated substantial variation in SOF in pseudobinary inorganic clathrates, according to chemical composition, temperature, and synthesis method 25,26 .…”

Organizing Chaos: Boosting Thermoelectric Properties by Ordering the Clathrate Framework of Ba8Cu16As30

“…Conversely, the other disordered arsenide-based clathrates ( A 8 Zn 18 As 28 ; A = K, Rb, Cs, and Cs 8 Cd 18 As 28 ) may also have ordered polymorphs, analogous to Cs 8 {Zn or Cd} 18 Sb 28 . , Some conventional clathrates with Ge and Sn frameworks exhibit polymorphism with an order/disorder transition of vacancy sites. − Recently, more complex conventional clathrates such as Ba 8 Al x Ga 16– x Ge 30 have shown phase transitions relating to the ordering of the framework atoms . The presence of order–disorder transitions in clathrates may be more ubiquitous than current literature suggests and recent studies have shown that the degree of framework ordering affects the transport properties . Along with its interesting structural chemistry, Ba 8 Cu 16 As 30 shows substantially different transport properties for the ordered ( P 2 1 / c ) and disordered ( Pm 3̅ n ) polymorphs.…”

“…26 The presence of order−disorder transitions in clathrates may be more ubiquitous than current literature suggests and recent studies have shown that the degree of framework ordering affects the transport properties. 27 Along with its interesting structural chemistry, Ba 8 Cu 16 As 30 shows substantially different transport properties for the ordered (P2 1 /c) and disordered (Pm3̅ n) polymorphs. The ordered polymorph shows promise as a p-type thermoelectric material and, overall, Ba 8 Cu 16 As 30 is a potential platform for optimizing the thermoelectric figure-of-merit.…”