Differential stress effect on the structural and elastic properties of forsterite by first-principles simulation

To understand the effect of differential stress on the properties of forsterite, changes of its structural parameters and elastic properties under different differential stress were calculated by first-principles simulations. Totally, 5 sets of different stresses results (namely x = 0, ±1 and ±2 GPa, x is the stress difference among σzz, σyy or σxx), were calculated. The effect of differential stresses on lattice constants show Poisson effect. Compared with the results under hydrostatic stress, all lattice strain (εa, εb, and εc) significantly increased at differential stress conditions. Furthermore, when the largest differential stresses are positive they more effect on lattice strain than the differential stresses are negative. Effect of different differential stress on density of forsterite is different. Compared with the density under hydrostatic pressure, positive differential stresses applied in the x direction or negative differential stresses applied in the y direction make forsterite density decreasing; however, positive differential stresses applied in the y direction or negative differential stresses applied in the x direction make forsterite density increasing. The density differences caused by differential stress are close to the upper mantle density anomaly. The effect of differential stress on density and lattice parameters is more notable when the absolutely value of Δσxx or Δσyy are the biggest among the differential stresses, namely stresses distributing along a and b axis orientation are more influenced on forsterite structural parameters than c axis orientation. Full elastic constants, bulk and shear modulus of forsterite (C11, C22, C33, C44, C55, C66, C12, C13, C23) were calculated under different stress conditions. Bulk modulus, shear modulus and elastic constants of differential stress are also different with the values at hydrostatic pressure, but the calculated results do not show any significant trends.