Thermal expansion of clathrate-II Na₂₄Si₁₃₆

Thermal expansion of the intermetallic clathrate Na₂₄Si₁₃₆ has been investigated using temperature dependent X-ray diffraction and first-principles calculations. Direct comparison of the thermal expansion of Na₂₄Si₁₃₆ with the low-density elemental modification Si₁₃₆ provides insight into the effects of filling the silicon clathrate framework cages. The room-temperature linear coefficient of thermal expansion (CTE) is nearly a factor of 3 greater for Na₂₄Si₁₃₆ compared to Si₁₃₆, indicating the guest atoms increase the anharmonicity of the interatomic interactions. Negative thermal expansion (NTE), observed in Si₁₃₆ below 100 K, is 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 of 10–700 K. First-principles calculations in the quasiharmonic approximation correctly predict an increase in high-temperature CTE with Na loading, although the increase is less than observed in experiment. The calculations also fail to capture the absence of NTE in Na₂₄Si₁₃₆, perhaps due to anharmonic effects and/or inadequateness of the ordered structural model used in the calculations.