The elasticity of natural hypersthene and the effect of Fe and Al substitution

Compressional behavior of a natural hypersthene has been investigated at pressures up to 10.1 GPa at room temperature using in situ synchrotron X-ray diffraction in a diamond anvil cell. No phase transition was observed within the experimental pressure range. The pressure-volume data have been fitted with a third-order Birch-Murnaghan equation of state, resulting in K₀ = 113.6(6.2) GPa and and K'₀ = 7.7(2.0) for the bulk modulus and its pressure derivative with a fixed unit-cell volume V₀ = 854.0(6) ų. The unit-cell parameters, a, b, and c, decrease nonlinearly with elevated pressure and show an anisotropic axial compressibility with a ratio β_a: β_b: β_c: =1:2.05:1.3. The comparison with previous results of orthopyroxene reveals that Al substitution causes a decrease in unit-cell volume and an increase in the bulk modulus, whereas the incorporation of Fe has opposite effects. The relation between unit-cell volume and En/Ts contents has been obtained, V₀ (ų) = 873.7(1.1)-40.8(1.44) × En-90.6(14.7) × Ts, which permits the prediction of unit-cell volume for Fe-and Al-bearing orthopyroxene system.