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A first-principles lattice dynamical study of type-I, type-II, and type-VIII silicon clathrates

Abstract

The pristine crystalline type-I, type-II, and type-VIII silicon clathrates have been studied using state of the art first-principles calculations based on density functional theory and density functional perturbation theory. We apply quasi-harmonic approximation to study structural stability, the possibility of temperature or pressure-driven phase transitions, along with Grüneisen parameters, coefficients of thermal expansion and thermal conductivities to estimate the degree of phonon anharmonicity for selected silicon clathrates. It is shown that a pressure-driven phase transition between type-I and type-II silicon clathrates may occur, and a temperature-driven phase transition between type-I and type-VIII Si clathrates at high temperature is likely. We further show that the relatively high Grüneisen parameters (1.5, 1.65, and 1.29, respectively for Si46-I, Si136-II, Si46-VIII), the existence of negative regions in the thermal expansion coefficient curves and very low thermal conductivities all indicate that the phonon anharmonicity in these silicon clathrates is high.

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Notes

  1. The Birch-Murnaghan equation of state for the energy E as a function of volume V reads E(V= E 0 + 9/8(BV 0)[(V 0/V)2/3 − 1]2 {1 + [(4 − B′)/2][1 − (V 0/V)2/3]}. E, E 0 , V, V 0, B and B′ are the energy, minimum energy, the volume, volume at the minimum energy, the bulk modulus and its pressure derivative, respectively.

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Acknowledgements

The authors would like to thank the Texas Tech High Performance Computing Center for many hours of computing time.

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Correspondence to Payam Norouzzadeh.

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Norouzzadeh, P., Myles, C.W. A first-principles lattice dynamical study of type-I, type-II, and type-VIII silicon clathrates. J Mater Sci 51, 4538–4548 (2016). https://doi.org/10.1007/s10853-016-9766-1

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  • DOI: https://doi.org/10.1007/s10853-016-9766-1

Keywords

  • Clathrate
  • Debye Temperature
  • Helmholtz Free Energy
  • Lattice Thermal Conductivity
  • Negative Thermal Expansion