Model pyroxenes III: Volume of C2/c pyroxenes at mantle P, T, and x

Variations in unit-cell volumes of mantle minerals as functions of P and T are important parameters in the description of the interior of the Earth and the behavior of materials, Recently, Thompson and Downs (2004) presented a model for the crystal structures of pyroxenes parameterized in terms of the O3-O3-O3 angle, χ, and the oxygen radius, r. This model has proven useful in the analysis of compression and expansion mechanisms in pyroxenes, providing an understanding of χ and r as functions of P and T. However, it did not provide a basis for analyzing changes in some properties that are strongly dependent on composition. In this paper, we show that ambient unit-cell volumes of the C2/c pyroxenes are correlated with M1 cation radius. This relationship can be used to calculate model ambient unit-cell volumes as a function of chemistry. From this starting point, pyroxene unit-cell volume variation with P and T can be modeled as a function of χ(P,T) and r(P,T). These relationships are investigated for diopside, heden-bergite, acmite, jadeite, and kosmochlor. The model reproduces observed unit-cell volumes of these phases recorded at P to within 0.09% and at T to within 0.10%, at simultaneous P and T for jadeite to within 0.57%, and at simultaneous P and T for diopside to within 1.20%. K_o and K¹ from third-order Birch-Murnaghan fits to the observed volume vs. pressure relationships and those calculated from the Thompson-Downs model are statistically the same. The fit of the Thompson-Downs EOS to the observed data is compared to the fit of the third order Birch-Murnaghan. The model is used to create an algorithm that estimates volumes for C2/c pyroxenes as a function of P, T, and x.