Thermal and mechanical properties of the clathrate-II <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Na</mml:mi><mml:mn>24</mml:mn></mml:msub><mml:msub><mml:mi>Si</mml:mi><mml:mn>136</mml:mn></mml:msub></mml:mrow></mml:math>

Thermal expansion, lattice dynamics, heat capacity, compressibility, and pressure stability of the intermetallic clathrate ${\mathrm{Na}}_{24}{\mathrm{Si}}_{136}$ have been investigated by a combination first-principles calculations experimentation. Direct comparison properties with those low-density elemental modification ${\mathrm{Si}}_{136}$ provide insight into effects filling silicon framework cages Na on these properties. Calculations phonon dispersion only yield sensible results if atoms in large structure are displaced from cage centers, but exact nature off-centering is difficult to elucidate conclusively. Pronounced peaks calculated density states for ${\mathrm{Na}}_{24}{\mathrm{Si}}_{136}$, absent ${\mathrm{Si}}_{136}$, reflect presence low-energy vibrational modes associated guest atoms, agreement prior inelastic neutron-scattering experiments reflected marked temperature dependence atom atomic displacement parameters determined single-crystal x-ray diffraction. The bulk modulus weakly influenced Si Na, whereas phase under significantly enhanced. room-temperature linear coefficient thermal expansion (CTE) nearly factor 3 greater compared ${\mathrm{Si}}_{136}$. Negative (NTE), observed below 100 K, noticeably ${\mathrm{Na}}_{24}{\mathrm{Si}}_{136}$. In contrast behavior relatively well described conventional Gr\"uneisen-Debye model range 10--700 K. First-principles quasiharmonic approximation correctly predict an increase high-temperature CTE loading, although less than experiment. also fail capture absence NTE perhaps due anharmonic and/or inadequateness ordered structural model.