Ab initio lattice dynamical studies of silicon clathrate frameworks and   their negative thermal expansion
  The thermal and lattice dynamical properties of seven silicon clathrate framework structures are investigated with ab initio density functional methods (frameworks I, II, IV, V, VII, VIII, and H). The negative thermal expansion (NTE) phenomenon is investigated by means of quasiharmonic approximation and applying it to equal time displacement correlation functions. The thermal properties of the studied clathrate frameworks, excluding the VII framework, resemble those of the crystalline silicon diamond structure. The clathrate framework VII was found to have anomalous NTE temperature range up to 300 K and it is suitable for further studies of the mechanisms of NTE. Investigation of the displacement correlation functions revealed that in NTE, the volume derivatives of the mean square displacements and mean square relative displacements of atoms behave similarly to the vibrational entropy volume derivatives and consequently to the coefficients of thermal expansion as a function of temperature. All studied clathrate frameworks, excluding the VII framework, possess a phonon band gap or even two in the case of the framework V. 
Ville J. H\"ark\"onen and Antti J. Karttunen
cond-mat.mtrl-sci