Predicting and explaining crystallographic orientation relationships of exsolved precipitates in garnet using the edge‐to‐edge matching model

Abstract

Relative alignments of mineral exsolutions and their host crystals can be described by crystallographic orientation relationships (COR). Exsolved phases in garnet from high-grade metamorphic rocks and igneous rocks may have COR, but the complexity of COR distributions has thus far restricted their use to identifying exsolved phases. Classification of COR also remains mineral-specific, leaving doubt as to what information COR preserve. To test how COR may be standardized, we calculated mismatch of low-index crystallographic planes (d-value ratios) and crystallographic directions (rows of atoms) between precipitates and garnet and defined search criteria for structural alignments likely to be energetically favourable. We analysed published electron backscatter diffraction (EBSD) data for apatite, rutile, ilmenite, corundum, and quartz precipitates in garnet (n tot = 1,296) for the presence of these alignments. Our method predicts between 88% and 98% of observed alignments across the studied minerals and requires only calculations using unit cell parameters. We further show that each exsolved mineral forms COR predicted by the edgeto-edge matching model which was developed to describe unambiguous exsolution textures in alloys. Edge-to-edge matching aligns atoms at the hostprecipitate interface by parallelism or near-parallelism of crystallographic planes of similar spacing and parallelism of crystallographic directions (rows of atoms) of similar length on the edges of those planes. Edge-to-edge matches likely facilitate coherent to semi-coherent interfaces by lowering surface free energy and strain energy, stabilizing precipitates. These matches are defined by criteria applicable to all minerals, making them an ideal tool for classifying, discovering and interpreting COR of diverse precipitates in garnet. This approach may also predict COR in other geological mineral pairs (e.g., exsolved feldspars). We find that edge-to-edge matching may explain the stability of the needle-shaped morphologies commonly observed for exsolution textures in garnet. Edge-to-edge matching COR distributions can be tested as proxies of the state of the host rock at the time of exsolution to evaluate factors such as temperature, cooling rate, degree of undercooling, and/or strain. Patterns of edge-to-edge matching COR may be paired with

Variations in orientation relationships between rutile inclusions and garnet host relate to magmatic growth zoning

“… 2015 ; Griffiths et al. 2020 ; Keller and Ague 2022 ), whereas only subordinately elongation parallel to Grt has been reported (Hwang et al. 2015 ).…”

“… 2016 , 2019 ; Keller and Ague 2019 ; Griffiths et al. 2020 ; Keller and Ague 2022 ), especially as their relative frequencies vary considerably. Still, the petrogenetic parameters that promote or suppress the development of certain CORs have not yet been constrained.…”

“… 2019 ; Keller and Ague 2019 ; Griffiths et al. 2020 ; Keller and Ague 2020 , 2022 ). Crystallographic orientation relationships (CORs) are defined as “systematic relationships between the crystallographic orientations of next-neighbour crystal pairs sharing boundary segments” (Habler and Griffiths 2017 ).…”

“…Observations of such lattice interactions between garnet host and rutile inclusions in the literature have been frequently interpreted as indicative of inclusion formation by precipitation within a pre-existing garnet crystal (Gou et al. 2014 ; Keller and Ague 2019 , 2022 ). Proposed mechanisms of this timing relationship include exsolution (Griffin et al.…”

“… 2017 ), the controlling parameters of COR formation between rutile and garnet still need to be deciphered (Griffiths et al. 2020 ; Keller and Ague 2022 ).…”