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Isovalent substitutions of octahedral cations, such as Fe²⁺ for Mg²⁺, in minerals usually have a relatively small effect on the bulk moduli. However, determinations of the effect of similar isovalent substitution mechanisms involving octahedral silicon, which might be important at mantle pressures and especially in perovskites of the lower mantle, have been hampered by a lack of samples. Existing data on the effect of the exchange of Si and Ti in Ca(Ti,Si)O₃ perovskites suggest that, despite the presence of structural phase transitions, the order of the induced change in bulk modulus for complete exchange of Si for Ti remains around 10-20%. The recent discovery of a titanite-structured phase of CaSi^VISi^IVO₅ (see 3.3f this Annual Report), and a complete solid solution between it and titanite, CaTi^VISi^IVO₅, at high temperatures and pressures provides another opportunity to examine the effect of a Si for Ti exchange on the elasticity of solids.

The variation with pressure of the unit-cell volumes of CaTiSiO₅ and Ca(Ti_0.5Si_0.5)SiO₅ were measured by X-ray powder diffraction at the ESRF, Grenoble. The ESRF synchrotron source provides on beamline ID30 a monochromatic X-ray beam of sufficiently high intensity that diffraction patterns from powders held at pressures inside diamond cells can be collected in times of about 10-15 minutes. Both samples were studied to a maximum pressure of ~8 GPa. In addition to measuring its equation of state, the P2₁/a to A2/a phase transition in CaTiSiO₅ was located at 3.6 GPa and shown to be second-order in character. Data for CaSi₂O₅ were collected from a single crystal with the Huber diffractometer in Bayreuth, previously described in the Annual Reports of 1995 and 1996.

Equation of state parameters for the three compositions were determined from the volume-pressure data measured in the diffraction experiments. In the A2/a phase of all three samples (above 3.6 GPa for CaTiSiO₅, above 0.2 GPa for CaSi₂O₅ (section 3.3f), at all pressures for Ca(Ti_0.5Si_0.5)SiO₅) the pressure derivative K' of the bulk modulus does not differ significantly from 4. The bulk moduli (K_0T) obtained from fits of a Birch-Murnaghan EoS with K' = 4 are given in Fig. 3.3-9. The ~47 GPa (30%) increase in bulk modulus arising from the complete substitution of Si for Ti is far in excess of the 13% expected from density - bulk modulus systematics and indicates that partial substitution of Si for other octahedral cations in high-pressure phases minerals might have large and unexpected effects on the elasticity of mantle minerals.
 

Fig. 3.3-9: Volume-pressure data for three A2/a titanites. The lines are Birch-Murnaghan equation of states fitted to the data points (only data above 3.6 GPa were used for CaTiSiO5). Note the large change in compressional behaviour on changing composition.