Revised PVT equations of state for almandine and spessartine garnets: implications for piezobarometry

Previously published thermal expansion data for almandine and spessartine garnets are sparse and inconsistent. We have therefore measured the thermal expansion of two garnets of compositions Alm90 Grs2.7 Py2.3 Ski4.5 (sample Alm90) and Sps81 Alm15 Grs3 And1 (sample Sps81) from ca. 90 K to ca. 780 K by synchrotron X-ray powder diffraction using quartz as an internal calibrant for temperature. The adiabatic elastic tensors of these two samples have been determined by single-crystal Brillouin scattering at room conditions; for the Alm90 sample c11 = 302.0(5), c12 = 111.3(4), c44 = 93.3(1), giving KS = 174.9(4) GPa, and for the Sps81 sample c11 = 303.1(4), c12 = 109.5(4), c44 = 93.6(2), giving KS = 174.0(4) GPa. These new data have been used in combination with P-V, P-T-V and P-T-Ks data from the literature to determine the equations of state (EoS) of end-member almandine and spessartine. The parameters of q-compromise Mie-Grüneisen-Debye thermal pressure EoS with a third-order Birch-Murnaghan EoS to describe the compressional properties at room temperature are: (Table presented.) The parameters are available in.eos files for the EosFit suite of programs in the supplementary data, and from www.rossangel.com and www.mineralogylab.com. The most significant changes from the previous EoS are the lower Debye temperatures because our data show higher thermal expansion above room temperature. The biggest consequence for host-inclusion piezobarometry is that these new EoS lead to lower entrapment temperatures for zircon inclusions in garnet. We also show that there is no significant difference in the P-V/V0 behaviour of almandine and spessartine and that the available experimental data for intermediate compositions does not indicate any significant non-ideality in the compressional or thermal expansion behaviour of almandine-spessartine garnets.