ORDER AND ANTI-ORDER IN OLIVINE II: THERMODYNAMIC ANALYSIS AND CRYSTAL-CHEMICAL MODELLING

Abstract

The equilibrium order/anti-order behavior in olivine Fe0.48Mg0.52[SiO4]is analysed in terms of the Thompson (1969, 1970) model for the Gibbs energy due to ordering, Gord, Gord=-1/2ΔGexch0 Q-TSconford ΔGexch0 = ΔHexch0 -TΔSexch0 relates to the exchange reaction FeM2 + MgM1 ↔ FeM1 + MgM2. Since for the investigated olivine both ΔHexch0 and ΔSexch0 are positive (ΔHexch0=1.2 kJ/mol, ΔSexch0 =3.7 J/mol K), an ordered Fe2+, Mg configuration is favoured by the enthalpic part of ΔGexch0 whereas the vibrational entropic part favours anti-ordering. As a result, at low temperature, where ΔHexch0 > TΔSexch0 Fe2+ prefers M2. Since, however, the energy TΔSexch0 steadily increses with incresing temperature it promotes Fe2+ into M1 and full disorder is attained at a crossover temperature Tco where ΔHexch0 = TcoΔ Sexch0. Above Tco, TΔSexch0 becomes progressively larger than ΔHexch0 and stimulates further fractionating of Fe2+ into M1 corresponding to incressing anti-order. The unusual phenomenon of anti-order increasing at incresing temperatures is due to ΔHexch0 being relatively small in FeMg olivine compared to the temperature proportional energy TΔSexch0. In other AB olivines (A,B = Mn, Fe, Co, Ni, Mg) the exhange enthalpies are much larger, between 9 and 20 kJ/mol, so that they dominate ΔGexch0 to a degree that precludes a crossover from ordered to anti-order states up to the melting point. The exchange enthalpies reported for MnMg, FeMg, CoMg, NiMg and MnFe olivines can be rationalized in terms of cation radius (r) and electronegativity (χ) ratios of the A and B cations. In a novel approach, both radii and electronegativities have been derived from topologic analyses of the procrystal electron density distributions of pure M2[SiO4] olivines (M = Mn, Fe, Co, Ni, Mg) yielding a very satisfactory description by ΔHexch0=252.6(±6.1)[r(A)/ r(B)-1]-75.8(±1.9)[χ(A)/χ(B)-1]. Accordingly, the small value of ΔHexch0 found for FeMg olivine is a consequence of opposite radius and electronegativity contributions which almost cancel. In MnFe olivine, although both contributions are small, they cooperate resulting in a moderate value of ΔHexch0. In MnMg olivine, it is the radius ratio that dominates, contrary to CoMg and NiMg olivine where the electronegativity ratios control ΔHexch0. Consequently, Mn prefers M2, and Co and Ni segregate into M1. ΔSexch0 can be split into vibrational, ΔSexch0,vib, and electronic exchange entropies, ΔSexch0,el. Describing the first in terms of a new octahedral distortion parameter, Df, and estimating the second from the Boltzmann distribution of the 3d-electrons, ΔSexch0 can be satisfactorily modelled by ΔSexch0 = 35.76(±0.34) {[Df(A)M1 + Df(B)M2]/[Df(B)M1 + Df(A)M2]-1} + ΔSexch0,el. The resulting lnKD =-(ΔHexch0 - TΔSexch0)/RT allows, for the first time and to the best of our knowledge, an exclusively electron density based description of the experimentally observed temperature variations of the site occupances in AB olivines. This modelling of lnkD allows also for predicting the temperature variations of equilibrium cation distributions in AB olivines not investigated so far. © 2006 E. Schweizerbart'sche Verlagsbuchhandlung, D-70176 Stuttgart.