First principles calculations are employed to investigate both type I and II silicon clathrates. The phonon and infrared spectra of both types of clathrate are obtained. We find a localized vibrational mode of Si46 whose frequency is 375.0 cm−1, where the vibration in the mode localizes in the hexagonal chain. The heat capacity of both clathrates is the same as that of the diamond phase Si (d-Si). When the temperature is lower than 100 K, the Debye temperatures of the clathrates are higher than that of d-Si; however, the Debye temperatures of both clathrates at high temperature (>100 K) are lower than that of the d-Si. The mean free paths (λ) and thermal conductivities (κ) of the clathrates are larger than those of d-Si at low temperature. The Seebeck coefficients (S) of the clathrates are higher than that of d-Si in the temperature interval 300–1000 K; however, both clathrates exhibit a lower value of σ/τ when compared to the d-Si.

Articles you may be interested inPhonon and thermal transport properties of the misfit-layered oxide thermoelectric Ca3Co4O9 from first principles Appl. Phys. Lett.Lattice thermal conductivity of a silicon nanowire under surface stress A study of the vibrational and thermoelectric properties of silicon type I and II clathratesWe present the results of vibrational and thermal properties for small diameter silicon nanowires ͑Si-NWs͒ from first principles calculations. Phonon spectrums of the Si-NWs are obtained based on the density functional perturbation theory. We found that heat-carrying acoustic branches exhibit "bending," which results from the strong interaction between acoustic and no-zero-frequency flexural modes. The bending of acoustic branches implies that the phonon group velocity ͑V = d / dq͒ of Si-NWs is less than that of corresponding bulk silicon. Therefore, a lower lattice thermal conductivity of Si-NWs can be caused by the bending of acoustic phonon. In comparison with bulk silicon, optical branches of Si-NWs exhibit "blueshift," which is due to the high frequency vibration of silicon atoms at the edge of Si-NWs. From the obtained phonon spectrums, specific heat is calculated. The specific heat of Si-NWs is also lower than that of bulk silicon crystal. The reduction in the specific heat is due to the small magnitude of vibration density of states of low frequency phonons. In the temperature range from 100 to 1000 K, the Debye temperatures are obtained. We found that the Debye temperature of the Si-NWs is much higher than that in the corresponding bulk silicon. Especially, Debye temperature of tetrahedral Si-NW is nearly twice higher than that of bulk silicon. From the temperature dependence of Hamholtz free energy of Si-NWs, we find that the cagelike Si-NWs have higher thermal stability than the tetrahedral Si-NW.