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 minimized relative to all 27 structural parameters for the tetragonal structure. 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 larger than those obtained spectroscopically. Nevertheless, the calculations strongly support experimental evidence that the bulk modulus of MgSiO3 majorite is close to that of pyrope and further indicate that its (∂KT/∂P)o is not distinctly larger than that of other silicate garnets. If these properties are close to those of real majorite, the steep gradient of the bulk modulus in the transition zone is at best marginally consistent with a Iherzolitic composition.