Landau Free-Energy and Order Parameter Behavior of the Alpha/Beta Phase-Transition in Cristobalite
Zeitschrift Fur Kristallographie 201(1-2): 125-145
Cristobalite, the high-temperature phase of silica, SiO2, stable between 1743 K and the melting point at 1898 K, exists in metastable form at lower temperatures. The cristobalite tetrahedral framework distorts from cubic Fa3mBAR to tetragonal P4(1)2(1)2 symmetry at a strongly first order phase transition near 533 K with a latent heat of 1256 Jmol-1. The transition involves a large (5%) volume discontinuity such that single crystals tend to shatter. We measured the thermal evolution of the structural order parameter of the alpha/beta-cristobalite transition and the unit cell strain by neutron time-of-flight and X-ray Guinier powder diffractometry. The system is well described by a single-domain approach with only one active order parameter component, and there is no evidence for a coupling mechanism between the six possible order parameter components. The transition follows a Landau free energy expansion up to sixth order according to G = G0 + 1/2-alpha(N) (T - T0) Q(N)2 + 1/4 b(N) Q(N)4 + 1/6 c(N) Q(N)6 where T0 = 287 K (= T(c) - 246 K) and the coefficients alpha(N) = 7.44 J (mol K)-1, b(N) = -11.55 kJmol-1, c(N) = 13.70 kJmol-1 include strain coupling energies and are normalized to give Q(N)(0 K) = 1. The fourth order term remains strongly negative after subtraction of the strain-renormalization effects. Our analysis shows that Landau theory may be successfully applied to the quantitative analysis of strongly first order phase transformations, and that the first order character of the alpha/beta-cristobalite inversion is neither strain- nor fluctuation induced. Although the order parameter step DELTA-Q(N) at the first order discontinuity is as large as 0.8, the thermal expansion of the low temperature phase as well as the strain discontinuity are quantitatively governed by linear coupling of the strain to the square of the order parameter amplitude, corresponding to improper ferroelastic behaviour.