Electronic Property and Negative Thermal Expansion Behavior of Si_136-Ge (x = 8, 32, 40, 104) Clathrate Solid Solution...

We present the electronic and vibrational studies on Si_136-Ge (x = 8, 32, 40, 104) alloys, using the local density approximation (LDA) scheme. We find that a "nearly-direct" band gap exists in the band structure of Si₁₀₄Ge₃₂ and Si₉₆Ge₄₀, when compared with the similarly reported results obtained using a different computational code. The calculated electronic density of state (EDOS) profiles for the valence band remain nearly identical and independent of the Ge concentration (x = 32, 40, 104) even though some variation is found in the lower conduction band (tail part) as composition x is tuned from 8 (or 40) to 104. The negative thermal expansion (NTE) phenomenon is explored using quasi-harmonic approximation (QHA), which takes the volume dependence of the vibrational mode frequencies into consideration, while neglecting the temperature effect on phonon anharmonicity. Determined macroscopic Grüneisen parameter trends show negative values in the low temperature regime (1 K < T < 115 K), indicating the NTE behavior found in Si₁₂₈Ge₈ is analogous to the experimental result for Si₁₃₆. Meanwhile, calculations for the ratio of the vibrational entropy change to the volume change at several characteristic temperatures reconfirm the existence of NTE in Si₁₂₈Ge₈ and Si₁₀₄Ge₃₂.