Garnet Solid Solutions: Microscopic-Macroscopic Strain and Implications for Thermodynamic Mixing and Trace Element Substitution Behavior

The aluminosilicate garnets (X₃Al₂Si₃O₁₂ with X = Fe²⁺, Mn²⁺, Mg, Ca) are an important rock-forming solid-solution system. We are investigating their microscopic-mesoscopic crystal chemical properties using various spectroscopic, diffraction and computational techniques. The results are used to interpret and understand the bulk physical and macroscopic thermodynamic properties. The volumes of mixing of the six binaries in this system have been determined. Positive deviations from ideal thermodynamic mixing are observed for five binaries. They are largely a result of lattice strain arising from the exchange of X-site cations of different sizes. The magnitude of nonideality is a function of the volume difference between the two end members and can be described using a quadratic function that has a physical basis in strain theory. These experimental results are in excellent agreement with static lattice energy simulations that have been carried out. The simulations show a clear quadratic dependence for the magnitude of the excess volumes of mixing versus volume difference of the end members. Excess enthalpies of mixing behave similarly. The simulations demonstrate the importance of local structural distortions and site relaxation in affecting the thermodynamic mixing properties and strain in solid solutions. IR and Raman spectroscopic measurements give a measure of local structural heterogeneity over different experimental length scales. The phonon systematics, such as nonlinear variations in the mode wavenumbers and line broadening in binary solid solutions, can be correlated with thermodynamic mixing behavior. Wavenumber shifts correlate with excess volumes and line broadening with the enthalpies of mixing. ²⁹Si NMR measurements show the presence of short-range ordering of Mg and Ca (clustering) in pyrope-grossular garnets. The degree of order is related to the temperature of equilibration and has a measurable, but secondary effect on macroscopic strain. It can be expected that trace element substitution behavior in garnet is a function of microscopic strain. Our investigations show that the `state of alternating bonds' best describes the bond behavior for the X-site cations. Thus, the presence of two quasi `sublattices' will govern trace-element substitution at the X-site.