Abstract
It has been recently demonstrated that the pseudoternary Ba8AlxGayGe46–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 Ba8GaxGe46–x, Ba8GaxSi46–x, Ba8AlxGe46–x, and Ba8AlxSi46–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 Ba8GaxGe46–x and Ba8GaxSi46–x than for Ba8AlxGe46–x and Ba8AlxSi46–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 Ba8AlxGe46–x and Ba8AlxSi46–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.
Highlights
In recent years, the importance of order−disorder transitions in functional materials has received increased attention
A complete understanding of the relationship between the unique crystal structure and the diverse and interesting properties is still lacking.[20−22] It is interesting to determine if order−disorder transitions are a general feature in clathrates and how the characteristics of such transitions depend on chemistry and temperature
The contributions to the heat capacities from the disorder obtained via WL simulations (Figure 1b−e) clearly indicate that all of the pseudobinary clathrates considered in this study (Ba8GaxGe46−x, Ba8AlxGe46−x, Ba8GaxSi46−x, and Ba8AlxSi46−x) exhibit order−disorder transitions
Summary
The importance of order−disorder transitions in functional materials has received increased attention. The comparison between SOFs and heat capacities reveals a plausible explanation for the fact that significantly lower transition temperatures are obtained (both experimentally and computationally) for Ba8GaxGe46−x and Ba8GaxSi46−x compared to Ba8AlxGe46−x and Ba8AlxSi46−x This is consistent with previous studies that have shown Al−Al interactions to be less favorable than Ga−Ga interactions, which is reflected by the larger pair effective cluster interactions (ECIs) for the former.[39] it seems likely that a higher temperature would be required to force the transition to a disordered state, which contains more Al−Al bonds. As there appears to be no singular reason for the observed deviation, it is likely the consequence of a number of different factors, including the underlying DFT calculations (including the treatment of the d-states) and the electronic entropy
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