Elasticity of magnesite and dolomite from a genetic algorithm for inverting Brillouin spectroscopy measurements

A hybrid numerical scheme that simultaneously retrieves single-crystal elastic constants, C_ij, and wave-normal directions is applied to determine the elasticity of natural samples of both magnesite and dolomite, as measured by Brillouin spectroscopy at ambient conditions. The scheme incorporates the genetic algorithm (GA) as a global searching tool and a final local linearization to overcome the intrinsic difficulty of fitting non-linear Christoffel's equation. To compensate for the stochastic nature of GA, especially when the misfit function of the problem manifests highly rugged topography in the model space, the procedure was repeated for multi-runs. This is to assure that the best solution is captured by examining the statistics among the runs that yield the fittest solutions. The resultant elastic constants C₁₁, C₁₂, C₁₃, C₁₄, C₃₃ and C₄₄ are, respectively, 260.3(2.6), 82.9(4.5), 59.6(3.1), (-)20.1(1.3), 153.7(4.1) and 59.7(1.4) GPa for magnesite. For dolomite, C₁₁, C₁₂, C₁₃, C₁₄, C₁₅, C₃₃ and C₄₄ are, respectively, 204.1(2.2), 68.5(3.4), 45.8(4.4), 20.6(1.3), 6.7(1.5), 97.4(5.3) and 39.1(1.5) GPa. Unfortunately, the results for dolomite are statistically non-unique in the numerical calculation. The above data were adopted because the cleavage plane of dolomite was used in the experiment. The results for both magnesite and dolomite are compatible with those determined earlier by ultrasonic methods. It is anticipated that the new method developed in the present study should be applicable to less symmetric crystals, since there are no particular assumptions on the crystal symmetry embedded within the scheme.