ELASTIC ANOMALIES IN MINERALS DUE TO STRUCTURAL PHASE-TRANSITIONS

Landau theory provides a formal basis for predicting the variations of elastic constants associated with phase transitions in minerals. Thes e elastic constants can show substantial anomalies as a transition poi nt is approached from both the high-symmetry side and the low-symmetry side. In the limiting case of proper ferroelastic behaviour, individu al elastic constants, or some symmetry-adapted combination of them, ca n become very small if not actually go to zero. When the driving order parameter for the transition is a spontaneous strain, the total exces s energy for the transition is purely elastic and is given by: G(elast ic) = 1/2 Sigma(i,k)C(ik)e(i)e(k) + 1/3!Sigma(i,k,l)C(ikl)e(i)e(k)e(l) + 1/4!Sigma(i,k,l,m)C(iklm)e(i)e(k)e(l)e(m) + ... which has the same form as a Landau expansion. In this case, the second-order elastic con stant C-ik softens as a linear function of temperature with a slope in the low-symmetry phase that depends on the thermodynamic character of the transition. If the driving order parameter, Q, is some structural feature other than strain, the excess energy is given by: G = 1/2(T-T -c)Q(2) + 1/4bQ(4) + ... + Sigma(i,m,n)lambda(i),(m,n)e(i)(m)Q(n) + 1/ 2 Sigma(i,k)C(ik)(0)e(i)e(k) In this case, the effect of coupling, des cribed by the term in lambda e(m)Q(n), is to cause a great diversity o f elastic variations depending on the values of m and n (typically 1, 2 or 3), the thermodynamic character of the transition and the magnitu des of any non-symmetry-breaking strains. The elastic constants are ob tained by taking the appropriate second derivatives of G with respect to strain in a manner that includes the structural relaxation associat ed with Q. The symmetry properties of second-order elastic constant ma trices can be related to the symmetry rules for individual phase trans itions in order to predict elastic stability limits, and to derive the correct form of Landau expansion for any symmetry change. Selected ex amples of ''ideal'' behaviour for different types of driving order par ameter, coupling behaviour and thermodynamic character have been set o ut in full in this review. Anomalies in the elastic properties on a ma croscopic scale can also be understood in terms of the properties of a coustic phonons, These microscopic processes must be considered if ela stic anomalies due to dynamical effects are to be accounted for correc tly. Such additional anomalies are characterised by softening of the f orm Delta C-ik = A(ik) \T - T-c\(K) as the transition is approached fr om the high-symmetry side. The A coefficient is a property of the mate rial, and K depends on how the branches of the critical acoustic mode soften in three dimensions. Adopting this approach allows the quantita tive description of elastic variations in ''real'' systems. Albite pro vides a likely example of proper ferroelasticity in minerals, and valu es for the required coefficients, extracted from experimental data, yi eld a complete picture of the expected elastic properties. The beta re versible arrow alpha transition in quartz provides an example of co-el astic behaviour. Data for TeO2, BiVO4 and KMnF3 (a perovskite) have be en reviewed to illustrate the full range of elastic anomalies that sho uld be expected at structural phase transitions in natural minerals.