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Thermal and mechanical properties of clathrate-II Na24Si136



Matthew Beekman, Antti Karttunen, Winnie Wong-Ng, Mingjian Zhang, Yu-Sheng Chen, Christian Posadas, Andrew Jarymowycz, Ethan Cruise, Wanyue Peng, Alexandra Zevalkink, James A. Kaduk, George S. Nolas


Thermal expansion, lattice dynamics, heat capacity, compressibility, and pressure stability of the intermetallic clathrate Na24Si136 have been investigated by a combination of first principles calculations and experiment. Direct comparison of the properties of Na24Si136 with those of the low-density elemental modification Si136 provide insights into the effects of filling the silicon clathrate framework cages with Na on these properties. Calculations of the phonon dispersion only yield sensible results if the Na atoms in the large cages of the structure are displaced from the cage centers, but the exact nature of off-centering is difficult to elucidate. Pronounced peaks in the calculated phonon density of states for Na24Si136, absent for Si136, reflect the presence of low energy vibrational modes associated with the guest atoms, in agreement with prior inelastic neutron scattering experiments and reflected in marked temperature dependence of the guest atom atomic displacement parameters determined by single crystal X-ray diffraction. The bulk modulus is only weakly influenced by filling the Si framework cages with Na, whereas the phase stability under pressure is significantly enhanced. The room temperature linear coefficient of thermal expansion (CTE) is nearly a factor of 3 greater for Na24Si136 compared to Si136. Negative thermal expansion (NTE), observed in Si136 below 100 K, is noticeably absent in Na24Si136. In contrast to Si136, the thermal expansion behavior in Na24Si136 is relatively well described by the conventional Grüneisen-Debye model in the temperature range 10 to 700 K. First principles calculations in the quasi-harmonic approximation correctly predicts an increase in high temperature CTE with Na loading but fails to capture the absence of NTE, perhaps due to anharmonic effects and/or inadequateness of the ordered structural model.
Physical Review B


Intermetallic clathrate Na24Si136, Thermal expansion, Lattice dynamics, Heat capacity, Compressibility


Beekman, M. , Karttunen, A. , Wong-Ng, W. , Zhang, M. , Chen, Y. , Posadas, C. , Jarymowycz, A. , Cruise, E. , Peng, W. , Zevalkink, A. , Kaduk, J. and Nolas, G. (2022), Thermal and mechanical properties of clathrate-II Na24Si136, Physical Review B, [online],, (Accessed November 29, 2022)
Created June 30, 2022, Updated September 23, 2022