AB-INITIO STUDY OF THE ORIGIN OF NEGATIVE THERMAL EXPANSION

Thermal expansion is an important measurable anharmonic property of materials. Within the quasi-harmonic approximation, the anharmonic effects are expressed by the change of the phonon frequencies with volume, i.e. the Grüneisen parameter of the material. Anomalies in the phonon spectrum, manifested by decrease in the phonon frequencies with decreasing volume, can lead to anomalies in the thermal expansion of the material. A detailed quasi-harmonic analysis of the phonon spectrum and Grüneisen parameter in the entire Brillouin zone is performed to study the origin of negative isotropic thermal expansion in diamond silicon at low temperatures. In addition, the anisotropic thermal expansion in hexagonal closed packed titanium is also investigated at low temperatures. It is found that the anomalous softening in silicon, which causes the anomaly in the thermal expansion, appears in the transverse acoustic branches in the whole Brillouin zone but becomes much more significant at its borders. In contrast, the negative anisotropic thermal expansion in titanium is accompanied by an anomalous softening just in the vicinity of the H symmetry point.