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Cubic garnet (space group Ia\overline 3 d) has the general formula X 3 Y 2 Z 3O12, where X, Y and Z are cation sites. In the tetragonal garnet (space group I41/acd), the corresponding cation sites are X1 and X2, Y, and Z1 and Z2. In both space groups only the Y site is the same. The crystal chemistry of a tetragonal (OH,F)-rich spessartine sample from Tongbei, near Yunxiao, Fujian Province, China, with composition X (Mn2.82Fe^{2+}_{0.14}Ca0.04)Σ3 Y {Al1.95Fe^{3+}_{0.05}}Σ2 Z [(SiO4)2.61(O4H4)0.28(F4)0.11]Σ3 (Sps94Alm5Grs1) was studied with single-crystal X-ray diffraction and space group I41/acd. The deviation of the unit-cell parameters from cubic symmetry is small [a = 11.64463 (1), c = 11.65481 (2) Å, c/a = 1.0009]. Point analyses and back-scattered electron images, obtained by electron-probe microanalysis, indicate a homogeneous composition. The Z2 site is fully occupied, but the Z1 site contains vacancies. The occupied Z1 and Z2 sites with Si atoms are surrounded by four O atoms, as in anhydrous cubic garnets. Pairs of split sites are O1 with F11 and O2 with O22. When the Z1 site is vacant, a larger [(O2H2)F2] tetrahedron is formed by two OH and two F anions in the O22 and F11 sites, respectively. This [(O2H2)F2] tetrahedron is similar to the O4H4 tetrahedron in hydrogarnets. These results indicate ^{X}{{\rm Mn}^ {2+}_{3}}\,^{Y}{\rm Al}_{2}^{Z}[({\rm SiO}_{4})_{2}({\rm O}_{2}{\rm H}_{2})_{0.5}({\rm F}_{2})_{0.5}]_{\Sigma3} as a possible end member, which is yet unknown. The H atom that is bonded to the O22 site is not located because of the small number of OH groups. In contrast, tetragonal henritermierite, ideally ^{X}{\rm Ca}_{3}\,^{Y}{\rm Mn}^{3+}_{2}\,^{Z}[({\rm SiO}_{4})_{2}({\rm O}_{4}{\rm H}_{4})_1]_{\Sigma3}, has a vacant Z2 site that contains the O4H4 tetrahedron. The H atom is bonded to an O3 atom [O3—H3 = 0.73 (2) Å]. Because of O2—Mn3+—O2 Jahn–Teller elongation of the Mn3+O6 octahedron, a weak hydrogen bond is formed to the under-bonded O2 atom. This causes a large deviation from cubic symmetry (c/a = 0.9534).

The crystal chemistry of two hausmannite samples from the Kalahari manganese field (KMF), South Africa, was studied using electron-probe microanalysis (EPMA), single-crystal X-ray diffraction (SCXRD) for sample-a, and high-resolution powder X-ray diffraction (HRPXRD) for sample-b, and a synthetic Mn 3 O 4 (97% purity) sample-c as a reference point. Hausmannite samples from the KMF were reported to be either magnetic or non-magnetic with a general formula AB 2 O 4 . The EPMA composition for sample-a is [Mn 2+ 0.88 Mg 2+ 0.11 Fe 2+ 0.01 ] Σ1.00 Mn 3+ 2.00 O 4 compared to Mn 2+ Mn 3+ 2 O 4 obtained by refinement. The single-crystal structure refinement in the tetragonal space groupI4 1 /amd gave R1 = 0.0215 for 669 independently observed reflections. The unit-cell parameters are a = b = 5.7556(6), c = 9.443(1) Å, and V = 312.80(7) Å 3 . The Jahn-Teller elongated Mn 3+ O 6 octahedron of the M site consists of M-O × 4 = 1.9272(5), M-O × 2 = 2.2843(7), and an average [6] = 2.0462(2) Å, whereas the Mn 2+ O 4 tetrahedron of the T site has T-O × 4 = 2.0367(8) Å. The site occupancy factors (sof ) are M(sof ) = 1.0 Mn (fixed, thereafter) and T(sof ) = 1.0008(2) Mn. The EPMA composition for sample-b is [Mn 0.99 Mg 0.01 ](Mn 1.52 Fe 0.48 )O 4 . The Rietveld refinement gave R (F 2 ) = 0.0368. The unit-cell parameters are a = b = 5.78144(1), c = 9.38346(3) Å, and V = 313.642(1) Å 3 . The octahedron has M-O × 4 = 1.9364(3), M-O × 2 = 2.2595(6), and average [6] = 2.0441(2) Å, whereas T-O × 4 = 2.0438(5) Å. The refinement gave T(sof ) = 0.820(9) Mn 2+ + 0.180(9) Fe 2+ and M(sof ) = 0.940(5) Mn 3+ + 0.060(5) Fe 3+ . Samples-a and -b are normal spinels with different amounts of substitutions at the M and T sites. The Jahn-Teller elongation, ∆(M-O), is smaller in sample-b because atom substitutions relieve strain compared to pure Mn 3 O 4 . Minerals 2019, 9, 343 2 of 16and in inverse spinels x = 1. A value of x = 2/3 corresponds to a random distribution of A and B atoms. Alternatively, an order parameter, Q, is used to express the degree of order [5]. The order parameter, Q, varies from Q = 1 for a completely ordered normal spinel to Q = 0 (where x = 2/3) for a random arrangement of cations to Q = −0.5 in inverse spinel. The relationship between Q and x is: Q = 1 -(3/2)x. Magnesioferrite, MgFe 2 O 4 , is partly inverse and partly normal, so it is one of the most interesting ferrite spinels [6][7][8].The structure of cubic spinels consists of T cations at 8a (1/8, 1/8, 1/8), M cations at 16d ( 1 /2 , 1 /2 , 1 /2 ), and O atoms on the body diagonals of a cube at 32e (u, u, u), where u is approximately 1 /4 in space group Fd3m. In a cubic spinel structure, there are only two structural variables (except displacement parameters): the a unit-cell parameter and the O atom positional parameter, u.Hausmannite, ideally Mn 3 O 4, is a normal spinel with a distorted tetragonal structure (Figure 1). End-member hausmannite structural formula is [4] [Mn 2+ ] [6] (Mn 2 3+ )O 4 . The T site may be occupied by divalent cations (e.g., Mn 2+ ...

The crystal structure of an optically anisotropic kimzeyite garnet from Magnet Cove, Arkansas, USA, where it was first discovered, was refined with the Rietveld method, cubic space group, Ia\overline 3 d, and monochromatic [λ = 0.41422 (2) Å] synchrotron high-resolution powder X-ray diffraction (HRPXRD) data. The Rietveld refinement reduced χ and overall R(F) values are 1.840 and 0.0647, respectively. The sample, with the general garnet formula XYZO, contains an intergrowth of two cubic phases that occur initially as oscillatory growth zoning, and patchy intergrowths arise later from fluid-enhanced dissolution and re-precipitation. The two compositions obtained with electron-probe microanalyses (EPMA) are Ca(ZrTiFeMn)[AlFeSi]O for phase 1a and Ca(ZrTiFe)[AlFeSi]O for phase 1b. The weight percentage, unit-cell parameter (Å), distances (Å), and site occupancy factors (s.o.f.s) for phase 1a are as follows: 42.6 (2)%, a = 12.46553 (3) Å, average 〈X-O〉 = 2.482, Y-O = 2.059 (2), Z-O = 1.761 (2) Å, Ca (X s.o.f.) = 0.960 (4), Zr (Y s.o.f.) = 0.809 (3), and Fe (Z s.o.f.) = 0.623 (2). The corresponding values for phase 1b are 57.4 (2)%, a = 12.47691 (2) Å, average 〈X-O〉 = 2.482, Y-O = 2.062 (1), Z-O = 1.762 (1) Å, Ca (X s.o.f.) = 0.957 (3), Zr (Y s.o.f.) = 0.828 (2) and Fe (Z s.o.f.) = 0.617 (2). The main structural differences between the two phases are in the unit-cell parameter, Δa = 0.01138 Å, Y(s.o.f.), and Y-O distance. Structural mismatch between the two cubic phases in a crystal gives rise to strain-induced optical anisotropy.

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Solid solutions are common in minerals, have a homogeneous composition, and are single phases that give rise to well-defined diffraction patterns. However, some minerals grow over a long period of geologic time (millions of years in some cases), so the growing conditions change. As a result, chemical compositions of such minerals are inhomogeneous. These minerals contain fine-scale chemical zoning that is similar to growth rings of a tree. The chemical composition of one zone is slightly different from another zone. There are usually a small number of such zones. Theoretically, each distinct composition should give rise to unique diffraction effects. Small compositional differences between phases can be detected by split diffraction peaks. The different compositions can be observed in back-scattered electron (BSE) maps. The Rietveld method and monochromatic short-wavelength synchrotron high-resolution powder X-ray diffraction (HRPXRD) data are used to characterize the different phases that are intergrown together. Some mineral examples will be discussed.

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