University:
Widener University
Course:
PHYS-313 | Classical Mechanics
Academic year:

2023
Views:

447

Pages:

14
Author:

biologizetyf

Strength and Elasticity of SiO2 across the Stishovite-CaCl2type Structural Phase Boundary 1. Introductions Stishovite: a dense tetragonal polymorph of quartz that is formed under great pressure and is often associated with meteoroid impact. (from Dictionary) z Why Stishovite important? 1. may explain some seismic structure in the mantle 2. a prototype for the six-coordinated silicates 3. transformation: stishovite Æ orthorhombic CaCl2 structure at ~ 50 GPa z Elastic properties is important for the understanding of phase transformation. However,direct experimental measurements of the elastic properties, strength and plastic deformation behavior of stishovite at high pressure is very limited. z This Paper: use lattice strain meas. under nonhydrostatic compression in a diamond anvil cell to examine dense SiO2 over a broad pressure range. z 2. Experiment Pure stishovite powder z Au foil: pressure marker and reference for the x-ray position z Diamond anvil cell: compress the sample z Using energy dispersive x-ray diffraction z 3. Data analysis Using lattice strain theory to analyze data z Def. of differential stress t = σ3 – σ1 σ3 : stress along the diamond cell axis σ1 : the radial stress z The supported t is a lower bound to the yield strength z z z z z z z dm(hkl) : measured interplanar spacing for plane (hkl) (?) dp(hkl) : d spacing resulting from the hydrostatic component of stress Ψ: the angle between the diffracting plane normal and the loading direction GXR(hkl): x-ray shear modulus under Reuss (isostress) condition GV(hkl): x-ray shear modulus under Voigt (isostrain) condition α: 0 – 1, weighting factor considerations. dm(hkl) = dp(hkl) when Ψ = 54.7o z t can be estimated from the shear modulus G and the average Q(hkl) value from all measured reflections: z z Image removed due to copyright considerations. Please see: Peaks shift to lower Energies as Ψ increases Shieh, S. R., et al. "Strength and elasticity of SiO2 across the stishovite-CaCl2-type structural phase boundary." Physical Review Letters 89 (2002): 255507. he interaction of a subducting lithospheric slab with GR 89 (1984): 4389-4402. ext z Assume that the measured d spacings correspond to volume compression under hydrostatic stress ( ? ) Image removed due to copyright considerations. Please see: Shieh, S. R., et al. "Strength and elasticity of SiO2 across the stishovite-CaCl2-type structural phase boundary." Physical Review Letters 89 (2002): 255507. Compression curve is strongly sensitive to Orientation Ψ: Ψ ↑ Æ d ↑ Æ V/V0 ↑ (less incompressible) Elastic properties reflect the bond strength and directionality, but insufficient for complete characterization since shear strength can vary greatly. z The ratio of shear strength τ to shear modulus G: τ/G Æ reflects the contribution of both plastic and elastic deformation. z This study examines t/G : can be obtained from the average slope of d spacing VS (13cos2Ψ ) term (why t, not τ?) z 15 – 60 GPa 0.019 – 0.037 Image removed due to copyright considerations. Please see: Shieh, S. R., et al. "Strength and elasticity of SiO2 across the stishovite-CaCl2-type structural phase boundary." Physical Review Letters 89 (2002): 255507. The ratio for Stishovite is i about half the value for oliven and ringwoodite Below 30 GPa Differential stresses supported by stishovite are significantly lower than those of ringwoodite, consistent with measurements on SiO2 glass Image removed due to copyright considerations. Please see: Shieh, S. R., et al. "Strength and elasticity of SiO2 across the stishovite-CaCl2-type structural phase boundary." Physical Review Letters 89 (2002): 255507. z z z z Use lattice strain equations to recover full elastic stiffness tensor ant high P. Shishovite in tetragonal system has six independent elastic stiffness (C11, C12, C13, C33, C44, C66). Lattice equations are insensitive to C44 and C66, so these two were fixed to theoretical values. Æ 4 unknowns 6 knowns (4 independent lattice reflections, compressibility, c/a ratio) Inversion equations: Image removed due to copyright considerations. Please see: Shieh, S. R., et al. "Strength and elasticity of SiO2 across the stishovite-CaCl2-type structural phase boundary." Physical Review Letters 89 (2002): 255507. 4. Conclusions The ratio of differential stress to shear modulus t/G is 0.019 – 0.037 at P = 15-60 GPa z The ratio for octahedrally coordinated stishovite is lower by a factor of 2 than observed in fourcoordinated silicates. z The differential stress of stishovite is about 4.5 (1.5) GPa below 40 GPa and to decrease sharply as the stishovite-CaCl2-type phase transition boundary is approached. z Inversion of measured lattice strains provides direct experimental evidence for softening of C11 - C12 z