OrientXplot calculationsThe information we report below is extracted from the "Users manual" of OrientXplot (Angel et al., 2015) and explains how it is possible to plot the orientation data from single-crystal X-ray diffraction or from other sources (i.e. Electron Backscatter Diffraction, hereafter EBSD).One of the main problems when plotting the relative crystallographic orientations of inclusions in different hosts is the possible ambiguity in indexing the diffraction patterns (or data from other sources, e.g. EBSD) coming from the symmetry of both the inclusion and the host. For example, in an orthorhombic system, the symmetry makes the [100] direction equivalent to [-100], and [010] equivalent to [0-10], and others. There is no physical approach to distinguish between these two directions. Therefore, in this case, an 'a-axis' pointing vertically upwards could equally be described as '-a' or [-100]. The possible equivalent orientations that maintain a right-hand description of the unit-cell axes of a crystal with a certain symmetry point group are described by the symmetry elements of the point sub-group that does not include any inversion symmetry and mirror planes. Accordingly, both garnet and diamond will be considered as having a point group 432 instead of m3m. In detail, to eliminate the symmetry ambiguity, we rotate the orientation matrix (determined by single-crystal X-ray diffraction) of each garnet inclusion by the symmetry elements of point group 432, oriented to coincide with the unit-cell axes of the diamond host. This generates 24 possible crystallographic orientations of garnet with respect to its diamond host (symmetrically equivalent and physically indistinguishable by any method). For each of them, there are 24 orientations, which are symmetrically-equivalent orientations of the garnet because of its symmetry.
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