Clathrate formation in the Ba-Pd-Ge system: Phase equilibria, crystal structure, and physical properties

Abstract

Phase relations at subsolidus temperatures as well as at $T=800\phantom{\rule{0.2em}{0ex}}\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$, crystallographic data, electrical and thermal transport measurements, and heat capacity data are reported for several compositions within the clathrate type-I solid solution: ${\mathrm{Ba}}_{8}{\mathrm{Pd}}_{x}{\mathrm{Ge}}_{46\ensuremath{-}x\ensuremath{-}y}{◻}_{y}$ (◻ is a vacancy). The solid solution derives from binary clathrate ${\mathrm{Ba}}_{8}{\mathrm{Ge}}_{43}{◻}_{3}$ with a solubility limit of 3.8 Pd atoms per formula unit at $T=800\phantom{\rule{0.2em}{0ex}}\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$. Structural investigations throughout the homogeneity region confirm cubic primitive symmetry consistent with the space group type $Pm\overline{3}n$ and lattice parameters ranging from $a=1.0657(2)\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ for ${\mathrm{Ba}}_{8}{\mathrm{Ge}}_{43}{◻}_{3}$ to $a=1.077\phantom{\rule{0.2em}{0ex}}41(2)\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ for ${\mathrm{Ba}}_{8}{\mathrm{Pd}}_{3.8}{\mathrm{Ge}}_{42.2}{◻}_{0.0}$. The primary field of clathrate crystallization has been elucidated from micrography and differential thermal analyses. Both heat capacity and inelastic neutron diffraction define a low-lying, almost localized, phonon branch. Studies of transport properties evidence electrons as the majority charge carriers for most of the homogeneity region; however, at the Pd-rich limit, holes dominate the electronic transport. The crossover between both regimes provides appropriate conditions for attractively high Seebeck values. The lattice contribution dominates the overall thermal conductivity.