VARIATIONALLY INDUCED BREATHING EQUATIONS OF STATE OF PYROPE, GROSSULAR, AND MAJORITE GARNETS

We have completed the first non-empirical fully optimized calculations of the equations of state for pyrope, grossular, and MgSiO3 majorite garnets. The static Gibbs free energy of the 160-atom unit cell was mi nimized relative to all 27 structural parameters for the tetragonal st ructure. Zero point vibration and thermal effects were estimated with a Debye-like model and Debye temperatures obtained from the equations of state. Calculated zero-pressure densities differ from experimental values by less than 1%, while the bulk-moduli are systematically large r than those obtained spectroscopically. Nevertheless, the calculation s strongly support experimental evidence that the bulk modulus of MgSi O3 majorite is close to that of pyrope and further indicate that its ( partial derivative K-T/partial derivative P)(0) is not distinctly larg er than that of other silicate garnets. If these properties are close to those of real majorite, the steep gradient of the bulk modulus in t he transition zone is at best marginally consistent with a lherzolitic composition.