Thermal equation of state of Cr-pyrope: implications for entrapment pressure of Cr-pyrope inclusion in diamond

Cr-pyrope is one of the most abundant mineral inclusions in peridotitic diamonds and its thermal equation of state (EoS) is a prerequisite for accurately determining its entrapment pressure ( P e ), which is important to understanding the physicochemical environment of diamond formation. We present in situ single-crystal X-ray diffraction (XRD) experimental results of five natural Cr-pyropes (Cr# = 0.3–22.4, Cr# = Cr/(Cr + Al)) at high pressure ( P ), high temperature ( T ), and high P – T up to 13.2 GPa and 950 K. The obtained P –volume( V )– T data were used to derive EoS parameters. The results indicated that the compressional behaviors of these Cr-pyropes are close (up to 2.8% difference), but the differences between their thermal expansivities are up to 8.8%. The thermal expansivities of the Cr-pyropes are significantly higher than that of end-member garnets (pyrope, almandine, and grossular) obtained by room- P high- T XRD, but they are consistent with the end-member thermal expansivities obtained by high P – T XRD. To investigate the compositional effects on the estimation of P e of Cr-pyrope, the obtained EoS parameters were used to calculate the P e in diamond. The results indicated that the variation in thermal expansion behavior plays a more significant role in influencing the P e in comparison with the compressional behavior. In addition, the P e of the Cr-pyropes are compared with the P e of end-member garnets (pyrope, almandine, grossular, and uvarovite), which indicates that the low-Cr (Cr# = 0.3–4.4) pyropes are closer to pyrope in P e while the high-Cr (Cr# = 9.3–22.4) pyropes are closer to grossular.