MICROSTRAIN IN DRY PYROPE-GROSSULAR GARNET SOLUTIONS

Garnet shows twin peaks of lattice microstrain vs. Ca-Mg composition (Du et al. 2017, Am.Min.,in press). Microstrain is zero at the pyrope and grossular end members (and also at Mg≈Ca) by XRD Williamson-Hall analysis. Intermediate excess microstrains are caused by Ca-Mg mixing and develop from specific site pairings of the same substituent cations [Mg-Mg or Ca-Ca]. The rate at which Ca-Ca pairs form and strain accumulates in pyrope goes as X_Gr² and the rate at which Mg-Mg pairs form in grossular goes as X_Py². Thus if the substitution is random, the microstrains should vary as the cation fractions squared. The total strain in pyrope depends upon the contrast in number between the Mg-Mg pairs of the matrix and the Ca-Ca pairs which increase in number through substitution of Ca for Mg. So strain will vary as the difference of the squares of the cation fractions. As Ca is substituted at random, not only do Ca-Ca pairs become larger in number, but so do Ca-Mg pairs, which discounts the strain contrast produced by the Ca-Ca vs. Mg-Mg pairs within pyrope. This discount of strain contrast between the growing Ca-Ca pairs and the faster-shrinking number of Mg-Mg pairs means that microstrains reach a maximum value well before equal numbers of Ca substitute for Mg, and reach a minimum in microstrain near subequal amounts of Ca and Mg in the structure. With further Ca substitution, a second peak of microstrain develops as the solution becomes Mg-poor grossular. These considerations are captured by a Margules-like formulation:

Microstrain(excess) = X_PyX_Gr(X_PyW_Gr + X_GrW_Py)·(abs(W_Gr²-W_Py²) - W_o)

W_o (0.07±0.01%), W_Py (1.49±0.16%) and W_Gr (1.19±0.04%) are found by fitting the data of Du et al, (2017). Because W_o is small and W_Py and W_Gr are near-symmetric (and reproducible in our data collected on different sample sets on two different diffraction platforms: ALS and BNL), random placement of Ca and Mg adequately models microstrain in our dry garnet solution. Strain in our dry garnet solutions does not follow the single-peaked enthalpy and strain variations of hydrothermally-assisted garnets.