Time-temperature-transformation (TTT) analysis of cation disordering in omphacite

Abstract

The kinetics of cation disordering in a natural ordered (P2/n) omphacite have been followed at P=18 and 30 kb, T= 750–1,260° C, for times of between 1.5 min and 16 days in a piston-cylinder apparatus. Time-temperature-transformation (TTT) analysis of the experimental data, using the presence or absence of the 11¯1 reflection in single crystal X-ray precession photographs to indicate the extent of reaction, yields an equilibrium order/disorder temperature (T _ord) of 865±10° C, an activation enthalpy (1 bar) of 71±6 kcal mole⁻¹ and an activation volume of 9±4 cm³ mole⁻¹ (plus and minus figures represent the precision of a best fit between experimental data and TTT theory rather than absolute errors). The activation volume is consistent with a vacancy mechanism of cation diffusion. H₂O, added in the form of oxalic acid, appears to speed the process up slightly. The overall transformation mechanism is continuous, involving neither the nucleation of a disordered phase nor a change in antiphase-domain distribution. This is consistent with both first- and non-first-order character for the C2/c⇋P2/n transformation, though a range of ordered states below T _ord is indicated by the weakening of h+k=odd reflections. A simple extrapolation of the disordering rates to geological conditions leads to the first estimate of how long disordered omphacites would take to order in nature, ranging from less than one year at T≈800° C to more than 10⁷ years at T<350° C.