Elasticity of Corundum at High Pressures and Temperatures: Implications for Pyrope Decomposition and Al‐Content Effect on Elastic Properties of Bridgmanite

Abstract

The thermodynamic and elastic properties of corundum at high pressures and temperatures are calculated based on density functional theory within the local density approximation. The calculated results agree well with the available experimental results and provide reliable data up to 80 GPa and 2,500 K. Our results confirm that C14 should be positive at ambient conditions. Elastic moduli of corundum, especially its shear modulus, exhibit noticeable nonlinear dependences with pressure and thereby result in the nonlinear pressure dependences of wave velocities. The decomposition of pyrope into the assemblage of bridgmanite and corundum is also investigated within the generalized gradient approximation. The calculated phase boundary is comparable to experimental results and has a positive Clapeyron slope of +2.1 MPa/K. Pyrope decomposition can result in VP, VS, and density jumps of 12.4%, 20%, and 9.8%, respectively. A small amount of pyrope dissociation can cause a large impendence contrast and may partially account for the observed discontinuities below 660 km at the subduction zone. Combining our calculations with results from the previous study, we suggest that the incorporation of Al into bridgmanite shows no discernable effect on its elastic moduli and wave velocities. This may impede the detection of Al content in bridgmanite through seismological methods.

Thermodynamic and Elastic Properties of Grossular at High Pressures and High Temperatures: A First‐Principles Study

“…The calculated elastic constants at static conditions are consistent with previous LDA calculations (Kawai & Tsuchiya, ), but larger than those calculated using generalized gradient approximation (Kawai & Tsuchiya, ) and hybrid functional B3LYP (Erba, Mahmoud, Belmonte, et al, ). This is because the generalized gradient approximation and B3LYP calculations predict a much larger volume than the LDA calculations and elasticity is sensitive to the volume (e.g., Maul et al, ; Wang & Wu, ). The vibrational contribution expands volume of grossular by ~2% (Figure ) and hence decreases C 11 , C 12 , and C 44 by ~5.6%, ~6.8%, and ~3.0% (Figure ) at ambient conditions, respectively.…”

“…In order to check whether the decomposition of grossular can be seismically detectable, we calculated the wave velocities and density contrasts between grossular and the assemblage of Ca‐perovskite and corundum along the normal mantle on the basis of our results and previous elastic data for corundum and Ca‐perovskite (Kawai & Tsuchiya, ; Wang & Wu, ). Our results show that if grossular decomposes into the mixture of Ca‐perovskite and corundum at around 23 GPa, the V P , V S , and density jumps would be ~7.2%, 11.5%, and 13.3%, respectively.…”

“…The decomposition of a small amount of grossular would produce considerable velocities and density jumps that can probably be seismically detected. In addition, Wang and Wu () found that the decomposition of pyrope into the assemblage of bridgmanite and corundum can also produce considerable velocities and density contrasts (12.4% in V P , 20% in V S , and 9.8% in density), which are significantly larger than those induced by the decomposition of grossular (Figure ). They also inferred that the phase transition from majorite to bridgmanite could cause slightly larger velocities jumps than those resulted from the decomposition of pyrope.…”

“…Although the actual velocity and density jumps depend on the amount of garnet, the phase transition of garnet may account for the detected complicated multiple discontinuity around 660 km (Cottaar & Deuss, ; Deuss, ; Simmons & Gurrola, ). The Clapeyron slope might be helpful to distinguish one phase transition from others (e.g., ~0 MPa/K for grossular; ~ +2.1 MPa/K for pyrope; ~1.2 MPa/K for majorite; and −2.9 MPa/K for ringwoodite; e.g., Akaogi et al, ; Hirose et al, ; Wang & Wu, ; Yu et al, ; Yu et al, ), but more researches are needed to clarify their phase boundaries, especially the one for grossular.…”

“…An isotropic distribution function of strain Grüneisen azimuth angles is assumed in this method, which is true for isotropic material, and the anisotropy of the crystal is considered through the anisotropic pressure dependence of lattice parameters. The method has been applied successfully to many minerals, including MgO (Wu & Wentzcovitch, ), ferropericlase (Wu et al, ), bridgmanite (Shukla et al, ), stishovite and the CaCl 2 ‐type silica (Yang & Wu, ), superhydrous phase B (Yang et al, ), ringwoodite (Núñez Valdez et al, ), olivine and wadsleyite (Núñez Valdez et al, ), pyrope (Hu et al, ), Orthoenstatite (Qian et al, ), diopside (Zou et al, ), and Corundum (Wang & Wu, ).…”