Origin of birefringence in andradite from Arizona, Madagascar, and Iran

Abstract

The crystal structure of four birefringent andradite samples (two from Arizona, one from Madagascar, and one from Iran) was refined with the Rietveld method, space group $Ia\overline{3} d$, and monochromatic synchrotron high-resolution powder X-ray diffraction (HRPXRD) data. Each sample contains an assemblage of three different cubic phases. From the electron-microprobe (EMPA) results, fine-scale intergrowths in the Arizona-2 and Madagascar samples appear homogeneous with nearly identical compositions of {Ca_2.99Mg_0.01}_Σ3[${\text{Fe}}_{1.99}^{3 + }$ ${\text{Mn}}_{0.01}^{3 + }$]_Σ2(Si_2.95Al_0.03 ${\text{Fe}}_{0.02}^{3 + }$)_Σ3O₁₂, Adr₉₈ (Arizona-2), and Adr₉₇ (Madagascar). Both samples are near-end-member andradite, ideally {Ca₃}[${\text{Fe}}_{2}^{3 + }$](Si₃)O₁₂, so cation ordering in the X, Y, or Z sites is not possible. Because of the large-scale intergrowths, the Arizona-1 and Iran samples contain three different compositions. Arizona-1 has compositions Adr₉₇ (phase-1), Adr₉₃Grs₄ (phase-2), and Adr₈₇Grs₁₁ (phase-3). Iran sample has compositions Adr₈₆Uv₁₂ (phase-1), Adr₆₉Uv₃₀ (phase-2), and Adr₇₆Uv₂₂ (phase-3). The crystal structure of the three phases within each sample was modeled quite well as indicated by the Rietveld refinement statistics of reduced χ² and overall R (F ²) values of, respectively, 1.980 and 0.0291 (Arizona-1); 1.091 and 0.0305 (Arizona-2); 1.362 and 0.0231 (Madagascar); and 1.681 and 0.0304 (Iran). The dominant phase for each sample has the following unit-cell parameters (Å) and weight fractions (%): a = 12.06314(1), 51.93(9) (Arizona-1); 12.04889(1), 52.47(1) (Arizona-2); 12.06276(1), 52.21(8) (Madagascar); and 12.05962(2), 63.3(1) (Iran). For these dominant phases, the distances and site occupancy factors (sofs) in terms of neutral atoms at the Ca(X), Fe(Y), and Si(Z) sites are as follows: <Ca–O> = 2.4348, Fe–O = 2.0121(6), Si–O = 1.6508(6) Å; Ca(sof) = 0.955(2), Fe(sof) = 0.930(2), and Si(sof) = 0.917(2) (Arizona-1); <Ca–O> = 2.4288, Fe–O = 2.0148(7), Si–O = 1.6476(7) Å; Ca(sof) = 0.953(2), Fe(sof) = 0.891(2), and Si(sof) = 0.927(2) (Arizona-2); <Ca–O> = 2.4319, Fe–O = 2.0220(6), Si–O = 1.6460(6) Å; Ca(sof) = 0.955(2), Fe(sof) = 0.941(2), and Si(sof) = 0.939(2) (Madagascar); and <Ca–O> = 2.4344, Fe–O = 2.0156(8), Si–O = 1.6468(8) Å; Ca(sof) = 0.928(2), Fe(sof) = 0.908(2), and Si(sof) = 0.932(3) (Iran). The sofs based on the EMPA results are similar to those obtained from the Rietveld refinement. Each phase in the HRPXRD results can be correlated with a specific chemical composition. For example, the Iran sample composition Adr₆₃Uv₃₀ corresponds to phase-3 that has the smallest unit-cell parameter; Adr₇₆Uv₂₂ corresponds to phase-1 that has the intermediate cell value; and Adr₈₆Uv₁₃ corresponds to phase-2 that has the largest unit-cell parameter. The bond distances compare well with those obtained from radii sum. The three different cubic phases in each sample cause strain that arises from the mismatch of the cubic unit-cell parameters and give rise to birefringence.