Phase Transition Properties of Solids: The Crylites, A₃MF₆ (1977)
AuthorsBall, G. F. A.show all
This thesis discusses structural phase transitions that occur in various cryolite compounds. The cryolites are characterised by the chemical formula A₃MF₆, where A and M are cations with valency 1 and 3 respectively. At high temperatures these compounds tend to possess a characteristic face-centred cubic form (space group O⁵h). On cooling, this is often transformed to a lower symmetry structure; the particular structure assumed varies from compound to compound. Structural transitions of this type are often associated with the reduction in frequency ("softening") of just one particular lattice vibrational mode of the high temperature form. Landau's theory of phase transitions provides a means of predicting this mode, given just the crystal structures existing on each side of the transition. A summary of the group theory of lattice dynamics is given to provide a basis for using Landau's approach. This group theory is used to derive all the vibrational modes which, according to Landau's results, can be associated with a second-order structural phase transition from the face-centred cubic cryolite form. A complete analysis is performed for a transition to the tetragonal (D⁶₄ h) structure; this transition is predicted to be associated with the x²⁺ mode of the high temperature form. Experimental approaches and results described in the literature are surveyed. In the current work it has been generally necessary to use powder rather than crystal samples, and the emphasis has been on appropriate X-ray diffraction methods. The design and operation of a variable temperature (~-140 to 100°C) system for taking Debye-Scherrer x-ray photographs is described, as well as the development of facilities for digitizing and processing the resultant data. Previously undetected transitions, observed using differential thermal analysis (D.T.A.), are reported for (NH₄) ₃VF₆ (three) and (NH₄) 3CrF₆. Some preliminary X-ray data on the low temperature structures of (NH₄) ₃FeF₆, (NH₄) ₃CrF₆ and (NH₄) ₃AlF₆ are discussed.