Electronic property and negative thermal expansion behavior of Si136-xGex (X = 8, 32, 40, 104) clathrate solid solution from first principles

Dong Xue, Charles W. Myles

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We present the electronic and vibrational studies on Si136-xGex (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.

Original languageEnglish
Article number851
Issue number6
StatePublished - Jun 2019


  • Electronic density of states
  • Free energy
  • Macroscopic Grüneisen parameter
  • Phonon anharmonicity
  • Vibrational entropy


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