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Free, publicly-accessible full text available November 1, 2025
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While anomalous diffusion coefficients with non-Arrhenius-like temperature dependence are observed in a number of metals, a conclusive comprehensive framework of explanation has not been brought forward to date. Here, we use first-principles calculations based on density functional theory to calculate self-diffusion coefficients in the bcc metals Mo and β-Ti by coupling quasiharmonic transition state theory and large-displacement phonon calculations and show that anharmonicity from thermal expansion is the major reason for the anomalous temperature dependence. We use a modified Debye approach to quantify the thermal expansion over the entire temperature range and introduce a method to relax the vacancy structure in a mechanically unstable crystal such as β-Ti. The effect of thermal expansion is found to be crucial for the nonlinear, non-Arrhenius “anomalous” self-diffusion in both bcc systems, with β-Ti showing a 60% larger relative nonlinearity parameter than Mo. Our results point to temperature dependence in the diffusion prefactor from thermal expansion as the major origin of anomalous self-diffusion. The methodology proposed for β-Ti is general and simple enough to be applicable to other mechanically unstable crystals.more » « less
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Abstract During the search for transition metal‐free alkyne hydrogenation catalysts, two new ternary Ca−Ga−Ge phases, Ca2Ga4Ge6(Cmc21, a=4.1600(10) Å, b=23.283(5) Å, c=10.789(3) Å) and Ca3Ga4Ge6(C2/m, a=24.063(2) Å, b=4.1987(4) Å, c=10.9794(9) Å, β=91.409(4)°), were discovered. These compounds are isostructural to the previously established Yb2Ga4Ge6and Yb3Ga4Ge6analogues, and according to Zintl‐Klemm counting rules, consist of anionic [Ga4Ge6]4−and [Ga4Ge6]6−frameworks in which every Ga and Ge atom would have a formal octet with no Ga−Ga or Ga−Ge π‐bonding. These compounds are metallic, based on temperature dependent electrical resistivity and thermopower measurements for Ca3Ga4Ge6, along with density functional theory calculations for both phases. Unlike the highly active 13‐layer trigonal CaGaGe phase, these new compounds exhibit minimal activity in the semi/full alkyne hydrogenation of phenylacetylene, which is consistent with previous observations that the lack of a formal octet for framework atoms is essential for catalysis in these Zintl‐Klemm compounds.more » « less