Thermal expansions in quartz: A geometrical consideration

Abstract

Thermal expansion behaviors in a- and c-axes in quartz are formulated in terms of the rotational motions of the corner-linked rigid SiO₄ units around the <100>_hex and the expansion of the tetrahedral units. Collective transfer motions of atoms between the double-wells of potential energies, observed in a previous molecular dynamics study, are the major component of the rotational motions in the β-phase and at higher temperatures in the α-phase. The thermal expansions in the α-phase arise mainly from the decrease of effective deviations from the β-orientation during the collective transfer motions. It is greater than the bond-length change which contribute to the total expansion. In the β-phase, the increase of the amplitudes of the transfer motions works to cancel or overwhelms the positive effects due to the expansions of the constituting units and the increase of the transfer frequency. For this reason, the temperature variation of cell dimensions of β-phase is very small or even negative. The slight thermal expansions, experimentally observed in the range 20 to 100 K above the transition temperature, are related to the appearance of transitional states.