Structural Trends and Solid-Solutions Based on the Crystal Chemistry of Two Hausmannite (Mn3O4) Samples from the Kalahari Manganese Field

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 Mn3O4 (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 AB2O4. The EPMA composition for sample-a is [Mn0.88Mg0.11Fe0.01]Σ1.00Mn2.00O4 compared to MnMn2O4 obtained by refinement. The single-crystal structure refinement in the tetragonal space group I41/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) Å3. The Jahn–Teller elongated MnO6 octahedron of the M site consists of M–O × 4 = 1.9272(5), M–O × 2 = 2.2843(7), and an average <M–O>[6] = 2.0462(2) Å, whereas the MnO4 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 [Mn0.99Mg0.01](Mn1.52Fe0.48)O4. The Rietveld refinement gave R (F2) = 0.0368. The unit-cell parameters are a = b = 5.78144(1), c = 9.38346(3) Å, and V = 313.642(1) Å3. The octahedron has M–O × 4 = 1.9364(3), M–O × 2 = 2.2595(6), and average <M–O>[6] = 2.0441(2) Å, whereas T–O × 4 = 2.0438(5) Å. The refinement gave T(sof ) = 0.820(9) Mn2+ + 0.180(9) Fe2+ and M(sof ) = 0.940(5) Mn3+ + 0.060(5) Fe3+. 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 Mn3O4.


Introduction
Numerous studies were carried out on spinels because of their chemical and structural simplicity, their geological importance, and their use as geothermometers, geobarometers, and geospeedometers (e.g., [1,2]). Spinel-supergroup minerals have the general formula, AB 2 O 4 . The A and B cation charges may be either +2 and +3 (e.g., spinel, MgAl 2 O 4 , and magnesioferrite, MgFe 2 O 4 ), or +4 and +2 (e.g., ulvöspinel, TiFe 2 O 4 , and qandilite, TiMg 2 O 4 ). The formal charge of A and B constituents can range from 0 to +6 [3]. In "normal" spinels, the A constituent occupies the 4-coordinated tetrahedral T site and the B constituent occupies the 6-coordinated octahedral metal M site [4]. In "inverse" spinels, the T site contains only B cations and the M site contains an equal number of A and B cations, so the M site is fully disordered. Intermediate spinels may be expressed as a mix of normal and inverse end-members, with the general formula, [4] [A 1−x B x ] [6] (A x B 2−x )O 4 , where the variable x is referred to as the "inversion parameter". This x is the fraction of B cations at the T site. In normal spinels x = 0, re x = 2/3) for a random arrangement of cations to Q = −0.5 in inverse spinel. The relation en Q and x is: Q = 1 -(3/2)x. Magnesioferrite, MgFe2O4, is partly inverse and partly norm ne of the most interesting ferrite spinels [6][7][8]. he structure of cubic spinels consists of T cations at 8a (1/8, 1/8, 1/8), M cations at 16d (½ nd O atoms on the body diagonals of a cube at 32e (u, u, u), where u is approximately group Fd⎯3m. In a cubic spinel structure, there are only two structural variables (ex cement parameters): the a unit-cell parameter and the O atom positional parameter, u. ausmannite, ideally Mn3O4, is a normal spinel with a distorted tetragonal structure (Figu ember hausmannite structural formula is [4] [Mn 2+ ] [6] (Mn2 3+ )O4. The T site may be occupie ent cations (e.g., Mn 2+ , Mg 2+ , Zn 2+ , or Fe 2+ ), and the Jahn-Teller elongated MO6 octahedron cupied by trivalent cations (e.g., Mn 3+ , Fe 3+ , or Al 3+ ). These two types of substitutions sh rise to different structural features. Hetaerolite, ideally ZnMn2O4, is isostructural annite [9]. Many natural samples belong to the hausmannite-hetaerolite series [MnMn 2O4], where the main substitution is between Mn 2+ and Zn 2+ cations. Such series gives ri defined structural variations in hausmannite solid solutions because the divalent cations r sizes (e.g., [10,11]). igure 1. Part of the tetragonal hausmannite structure consisting of Mn 2+ O4 tetrahedra (grey) and n 3+ O6 octahedra (pink) that contains Jahn-Teller elongation of two apical O atoms that occur in the ertical direction that is parallel to [001]; the four shorter basal Mn 3+ -O bonds of the bypyramid are early in the (100) plane. The oxygen atoms are indicated by red spheres. The hausmannite tructure is similar to the henritermierite garnet structure that also consists of Jahn-Teller elongated n 3+ O6 octahedra and SiO4, instead of Mn 2+ O4, tetrahedra (see Figure 6 in [12]).
utzmer et al. [13] reported both magnetic and non-magnetic hausmannite samples ari manganese field (KMF; samples-2 and -3 in Table 1). It seems that substitution of Gutzmer et al. [13] reported both magnetic and non-magnetic hausmannite samples from Kalahari manganese field (KMF; samples-2 and -3 in Table 1). It seems that substitution of Fe 3+ cations at the M site give rise to a magnetic sample. Substitution of Mn 3+ (0.645 Å, HS) by Fe 3+ (0.645 Å, HS) cations results in minor, but measurable changes in unit-cell parameters, and a decrease of Jahn-Teller distortion with increasing Fe 3+ concentrations [14]. Neutron diffraction results at 10 K from Baron et al. [14] indicate that Fe-rich hausmannite is not the source for high-temperature (Curie temperature of 750 K) ferrimagnetism in hausmannite-rich ores from the KMF that was described by Gutzmer et al. [13]. The authors indicated that minor amounts of Mn-bearing hematite in the hausmannite-rich ores may be the source for the unusual magnetic properties, but this was not confirmed. There appear to be two different types of hausmannite samples from the KMF. One type has substitution of divalent cations at the T site, and the other type has substitution of trivalent cations at the M site as well as at the T site. These different types of samples are investigated further in this study.
The crystal structure of hausmannite is that of a tetragonally-deformed cubic spinel structure [15]. Satomi [16] reported unit-cell parameters for a synthetic Mn 3 O 4 (sample-1; Table 1). The magnetic structure of hausmannite from a polycrystalline sample was examined by neutron methods and aspects of the structure were discussed [14,17,18]. Thereafter, several structural studies were carried out on hausmannite (Table 1). Structural data for ZnMn 2 O 4 [19] and MgMn 2 O 4 [20] are also available. Table 1. Unit-cell parameters and bond distances for hausmannite, [4] [T 2+ ] [6] (M 3+ ) 2 O 4 , where T = tetrahedral site and M = octahedral site. In hausmannite, the T and M sites are at fixed positions and the O-atom coordinate is at (0, x, y). The O atom is positioned to balance between the co-Operative Jahn-Teller distortion around the Mn 3+ site, stretching of the Mn 3+ O 6 octahedron along [001], countered by the force of the tetrahedron preserving its regular form against the tetragonal deformation of the structure [16,22]. The chemical bonds in spinels influence the cation ordering, the structural distortion, and the magnetic-exchange interactions [23]. In hausmannite, the four short Mn 3+ -O bonds around the octahedrally-co-Ordinated Mn 3+ cations are covalent, and the two longest bonds have an ionic character [23]. In contrast, the four Mn 2+ -O bonds around the tetrahedral T sites have characteristics that are between ionic and covalent.
Under normal pressure conditions, hausmannite has two crystallographic forms: a tetragonal low-temperature form and a cubic high-temperature form [24,25]. The cubic-tetragonal transition occurs at 1170 • C where there is no Jahn-Teller distortion. The structure is deformed during the transition to the tetragonal structure that contains Jahn-Teller elongation [24]. In the tetragonal hausmannite structure, the O atoms form a tetragonally distorted cubic close-packed structure where the tetrahedral and octahedral sites are occupied by Mn 2+ and Mn 3+ cations, respectively [24]. The tetragonal hausmannite crystal structure has space group I4 1 /amd [24]. The structure of a hausmannite from Langbån, Sweden is known [21].
Hausmannite is relatively uncommon, but it has a wide field of stability. It is usually found with other manganese oxide minerals in metamorphosed or hydrothermal manganese ores [24], but euhedral crystals are rare. Hausmannite occurs in a few localities such as Ilmanau, Thuringia, Germany and the Kalahari manganese field (KMF), South Africa [14]. It is typically ferrimagnetic, but a strong magnetic sample was discovered in the hydrothermally altered KMF [13]. In the KMF, the manganese ores are interbedded with the iron-rich Hotazel formation and are preserved in erosional relict basins [13]. Within the high-grade Wessels type manganese ore, normal faults acted as conduits for hydrothermal fluids which caused hematitization of the manganese ores. This high-grade manganese ore is coarse grained and contains hausmannite, bixbyite, marokite, and hematite [13].
The unit-cell parameters of Mn 3−x Fe x O 4 hausmannite indicate decreasing Jahn-Teller distortion with increasing Fe content, which also causes an increase in the Curie temperature [14]. Their study seems to indicate that Fe-rich hausmannite causes the unusual high-temperature ferrimagnetic behavior in the KMF. Iron-rich hausmannite, containing up to 11.3 wt % of Fe 2 O 3 , has unit-cell parameters that are smaller along the a axis and larger along the c axis than pure Mn 3 O 4 . These parameters shrink along the a axis and expand along the c axis, proportional to increasing Fe content [14].
This study examines the crystal chemistry of two different hausmannite samples from the KMF using electron-probe microanalysis (EPMA). The crystal structure of sample-a was obtained with single-crystal X-ray diffraction (SCXRD) data, whereas that for samples-b and -c were obtained from Rietveld structure refinement using synchrotron high-resolution powder X-ray diffraction (HRPXRD) data. These results are compared with data from the literature (Table 1).

Sample Description
The hausmannite sample-a used in this study is a black crystal that occurs with henritermierite garnet from Wessels X Mine, Kalahari manganese field (KMF), Northern Cape Province, South Africa. The hausmannite crystals are intergrown with tetragonal garnet, henritermierite, ideally Ca 3 Mn 2 [(SiO 4 ) 2 (O 4 H 4 )] Σ3 [12]. Sample-a was obtained from the Royal Ontario Museum (ROM #M54234). The hausmannite sample-b is from the KMF, where it occurs as a large massive sample that resembles a pyramidal "Christmas tree". Both samples-a and -b are non-magnetic. However, Gutzmer et al. [13] reported both magnetic and non-magnetic samples from the KMF (Table 1). We also obtained the structure of a synthetic powdered Mn 3 O 4 sample-c (97% purity from Sigma Aldrich, Oakville, ON, Canada) as a reference material. This hausmannite sample-c contains about 3% bixbyite, Mn 2 O 3 , as determined by Rietveld refinement.

Electron-Probe Microanalysis (EPMA)
Quantitative chemical compositions and backscattered electron (BSE) images were collected with a JEOL JXA-8200 WD-ED electron-probe microanalyser (EPMA). The JEOL operating program on a Solaris platform was used for ZAF correction and data reduction. The wavelength-dispersive (WD) operating conditions were 15 kV accelerating voltage, 20 nA beam current and 5 µm beam diameter. The standards used were rhodonite (Mn Kα), chromite (Mg Kα, Fe Kα), and corundum (Al Kα). Using the EPMA data, atoms per formula unit (apfu) were calculated on the basis of four oxygen atoms and three cations [10], with FeO converted to Fe 2 O 3 by multiplying by 1.1113 and MnO converted to Mn 2 O 3 by multiplying by 1.1128. The average chemical analyses from 12 points are given for samples-a and -b ( Table 2).

Single-Crystal X-ray Diffraction (SCXRD)
The hausmannite sample-a structure was studied with single-crystal X-ray diffraction (SCXRD) using a Nonius Kappa APEX2 CCD on a diffractometer using a Bruker Nonius FR591 Rotating anode with graphite monochromatized MoKα radiation. A small crystal fragment (approximately 0.05 × 0.05 × 0.06 mm 3 ) was mounted on the end of a glass fiber (0.05 mm in diameter) with epoxy and placed on a goniometer. The generator setting was 50 kV and 36 mA and the detector-to-crystal distance was fixed at 35 mm. A total of ten frames were collected for unit-cell determination. The scan settings were 1 • rotation per frame (total rotation = 10 • ) and 22 s of X-ray exposure time per frame. After obtaining satisfactory unit-cell parameters and mosaicity values (less than 1 • ), a complete dataset was collected using a 2 • per frame rotation with exposure of 42-122 s per frame. The diffraction spots were measured in full, scaled with SCALEPACK, corrected for Lorentz-polarization, and integrated using the Nonius program suite DENZO-SMN [26].
The space group I4 1 /amd was obtained based on systematic absence of reflections and structure factor statistics. Full-matrix least-squares refinements were carried out with the SHELXL program using neutral atom scattering factors [27] and the WinGX platform [28]. The starting structural model was from Jarosch [21]. Anisotropic displacement parameters were used for all of the atoms in hausmannite. The site occupancy factors (sofs) for the cations were refined together with the isotropic displacement parameters and the resulting sofs were fixed while the anisotropic displacement parameters were refined. Further details of the data collection for sample-a and refinement are given in Table 3 and those for samples-b and -c are given in Table 4. The atom coordinates, sofs, and equivalent isotropic displacement parameters are given in Table 5. Anisotropic displacement parameters are given in Table 6. Selected bond distances and angles are given in Table 7. Bond-valence sums (BVS; valence units, vu) are given in Table 8. Table 3. Crystal structure refinement data for hausmannite sample-a (cif is given as a supplementary material).

Miscellaneous
Sample-a

Synchrotron High-Resolution Powder X-Ray Diffraction (HRPXRD)
Both samples-b and -c were studied with HRPXRD that was performed at beamline 11-BM, Advanced Photon Source (APS), Argonne National Laboratory (ANL). A small fragment (about 2 mm in diameter) of sample-b was crushed under methanol to a fine powder using a corundum mortar and pestle (crystal size is unknown as no mesh was used). Sample-c was obtained as a powder. The crushed samples were loaded into Kapton capillaries (0.8 mm internal diameter) and rotated during the experiment at a rate of 90 rotations per second. The data were collected at 21 • C to a maximum 2θ of about 50 • with a step size of 0.0005 • and a step time of 0.1 s per step. The HRPXRD trace was collected with a unique multi-analyzer detection assembly consisting of 12 independent silicon (111) crystal analysers and LaCl 3 scintillation detectors that reduce the angular range to be scanned and allow for rapid acquisition of data. A silicon (NIST 640c) and alumina (NIST 676a) standard (ratio of 1 /3Si: 2 /3Al 2 O 3 by weight) was used to calibrate the instrument and refine the monochromatic wavelength used in the experiment (Table 4). Additional details of the experimental setup are given elsewhere [29][30][31]. All of the above experimental techniques were used to characterize many minerals [32][33][34][35][36][37][38][39][40][41][42][43].

Rietveld Structure Refinement
The HRPXRD data was analyzed with the Rietveld method [44], as implemented in the GSAS program [45], and using the EXPGUI interface [46]. Scattering curves for neutral atoms were used. The single-crystal results were used as the initial structural model for the Rietveld refinement. The background was modeled with a shifted Chebyschev polynomial (six terms). The reflection-peak profiles were fitted using type-3 profile (pseudo-Voigt; [47,48]). Examination of the HRPXRD trace for the hausmannite sample-b shows a single tetragonal phase. No impurities or un-indexed peaks were observed (Figure 2). The unit-cell parameters and the Rietveld refinement statistical indicators are given for both samples-b and -c ( Table 4). The atom coordinates, sofs, and equivalent isotropic displacement parameters are given in Table 5. Anisotropic displacement parameters are given in Table 6. Selected bond distances and angles are given in Table 7.

Rietveld Structure Refinement
The HRPXRD data was analyzed with the Rietveld method [44], as implemented in the GSAS program [45], and using the EXPGUI interface [46]. Scattering curves for neutral atoms were used. The single-crystal results were used as the initial structural model for the Rietveld refinement. The background was modeled with a shifted Chebyschev polynomial (six terms). The reflection-peak profiles were fitted using type-3 profile (pseudo-Voigt; [47,48]). Examination of the HRPXRD trace for the hausmannite sample-b shows a single tetragonal phase. No impurities or un-indexed peaks were observed (Figure 2). The unit-cell parameters and the Rietveld refinement statistical indicators are given for both samples-b and -c ( Table 4). The atom coordinates, sofs, and equivalent isotropic displacement parameters are given in Tables 5. Anisotropic displacement parameters are given in Table 6. Selected bond distances and angles are given in Table 7.

Results and Discussion
Backscattered electron (BSE) images of sample-a revealed the presence of hausmannite within henritermierite garnet (see Figure 8 in [12] (Table 5) Table 7). The difference in Jahn-Teller elongation of 0.034(1) Å between samples-a and -b is one of the most significant structural difference between these two samples. Neutron data from Baron et al. [14] gave structural data at 10 K for three samples (5-7; Table 1). These neutron data appear to be incorrectly calculated and reported in the American Mineralogist Crystal Structure Database at 295 K (8 to 10; Table 1). Unit-cell parameters (sample-1) from Satomi [16] are unreliable because it does not plot close to pure hausmannite that corresponds to samples-24 and -c. The neutron data at 295 K (sample-8) assume sample-1 values in its calculations. Structural data for some nearly pure Mn 3 O 4 are given (1, 4, 5, 8, and 21-23). Their deviations in values from nearly pure samples-24 and -c show what datasets are unreliable (1, 8-10 are unreliable; Figure 3), so these four data points are not considered further. Minerals 2019, 9 FOR PEER REVIEW 11 calculations. Structural data for some nearly pure Mn3O4 are given (1, 4, 5, 8, and 21-23). Their deviations in values from nearly pure samples-24 and -c show what datasets are unreliable (1, 8-10 are unreliable; Figure 3), so these four data points are not considered further.   Table 1; solid green triangles) are incorrectly calculated at 295 K (8-10; open green triangles). At room temperature, sample-c (= 25 in Table 1), which is a synthetic Mn3O4 powder, has the largest V among samples for which structures were refined, whereas sampe-13 has the smallest V because it contains small Mg cations. Samples-a (= 11) and -b (= 12) are indicated. Black lines represent atom replacement in the T 2+ site, whereas substitution at the M 3+ site occurs in samples that plot away from the trend lines. Sample-7 (10 K) and sample-b are off the trend lines and are related to Fe 3+ substituting for Mn 3+ at the M site. In addition, samples-2 to -4, especially sample-3, may contain substitutions at the M site.  Table 1; solid green triangles) are incorrectly calculated at 295 K (8-10; open green triangles). At room temperature, sample-c (= 25 in Table 1), which is a synthetic Mn 3 O 4 powder, has the largest V among samples for which structures were refined, whereas sampe-13 has the smallest V because it contains small Mg cations. Gutzmer et al. [13] presented chemical compositions and unit-cell parameters for two samples from the KMF (2 is non-magnetic and 3 is magnetic; Table 1). Sample-2 seems similar to pure Mn 3 O 4 sample-c ( Figure 3). Sample-a (= 11) plots between samples-14 and -19 ( Figure 3). Sample-b has unit-cell parameters that are different from samples-3 and -7 (10 K data), but it seems plausible that both of these samples are similar to sample-b because all three samples are off the trend lines ( Figure 3). The magnetic property of samples-3 and -7, if present, may arise from the incorporation of Fe 3+ for Mn 3+ cations in hausmannite solid solutions [14]. However our sample-b is not magnetic when tested with a hand magnet. Based on room-temperature data, sample-c has the largest V among samples for which structures are available, whereas the Mg-rich sample-13 has the smallest V.

Structural Trends for Hausmannite Solid Solutions
Minerals 2019, 9 FOR PEER REVIEW 12 All the trend lines (equations given as inserts) in Figures 3 to 5 are based on data from Bosi et al. [10,11].
Gutzmer et al. [13] presented chemical compositions and unit-cell parameters for two samples from the KMF (2 is non-magnetic and 3 is magnetic; Table 1). Sample-2 seems similar to pure Mn3O4 sample-c ( Figure 3). Sample-a (= 11) plots between samples-14 and -19 ( Figure 3). Sample-b has unit-cell parameters that are different from samples-3 and -7 (10 K data), but it seems plausible that both of these samples are similar to sample-b because all three samples are off the trend lines ( Figure 3). The magnetic property of samples-3 and -7, if present, may arise from the incorporation of Fe 3+ for Mn 3+ cations in hausmannite solid solutions [14]. However our sample-b is not magnetic when tested with a hand magnet. Based on room-temperature data, sample-c has the largest V among samples for which structures are available, whereas the Mg-rich sample-13 has the smallest V.   Table 1). Sample-13 also has the smallest unit-cell parameters because it contains the highest amount of Mg 2+ cations at the T site. Samples-b and -7 contain a   Table 1). Sample-13 also has the smallest unit-cell parameters because it contains the highest amount of Mg 2+ cations at the T site. Samples-b and -7 contain a significant amount of Fe 3+ cations at the octahedral M site, which affects the unit-cell parameters and T-O distances (Figure 4).
The average <M-O> distance varies linearly with unit-cell parameters ( Figure 5). Data for samples-a and -c falls near the linear trend lines, but samples-b and -7 are off those lines. The trend lines correspond to substitution of divalent cations at the T site. Substitution of trivalent cations at the M site causes these samples to plot off the trend lines. The presence of Fe 3+ cations at the M site causes less Jahn-Teller distortion in sample-b compared to sample-a, so the average <M-O> is shorter in sample-b (Table 7). Minerals 2019, 9 FOR PEER REVIEW 13 significant amount of Fe 3+ cations at the octahedral M site, which affects the unit-cell parameters and T-O distances (Figure 4). The average <M-O> distance varies linearly with unit-cell parameters ( Figure 5). Data for samples-a and -c falls near the linear trend lines, but samples-b and -7 are off those lines. The trend lines correspond to substitution of divalent cations at the T site. Substitution of trivalent cations at the M site causes these samples to plot off the trend lines. The presence of Fe 3+ cations at the M site causes less Jahn-Teller distortion in sample-b compared to sample-a, so the average <M-O> is shorter in sample-b (Table 7). 5 Table 1). Samples-a and -c fall close to the trend lines, but samples-b and -7 are off those lines. Pure Mn3O4 has the largest average <M-O> distance (samples-c and -24) and the Mg-rich sample-13 has a small average <M-O> distance at room temperature.
Substitution of cations at the octahedral M site causes a change in the average <M 3+ -O> distance and unit-cell parameters ( Figure 5). For the samples (13 to 24; Table 1) for which the trend lines are based, the M site is completely filled with Mn 3+ cations. Therefore, variations in the <M 3+ -O> distance arise from the influence of the T site cations. However, samples-b and -7 contain a significant amount of Fe 3+ cations at the M site, so these samples are off the trend lines ( Figure 5). With respect to pure Mn3O4 (samples-24, -c), sample-b shows an enlargement of a and contraction of the c unit-cell parameter. Samples-c and -24 have the largest average <M-O> distance, whereas the Mg-rich sample-13 has the smallest average <M-O> distance.
The Jahn-Teller elongation, Δ(M-O), is less for sample-b compared to sample-a (Table 6; Figure  6). As the difference between the a and c unit-cell parameters, (c-a), becomes smaller, the Jahn-Teller elongation, Δ(M-O), also becomes smaller ( Figure 6). For the samples in this study, sample-c has the highest Δ(M-O), whereas sample-b has the lowest Δ(M-O). At low temperature (10 K), sample-7 has the least distortion. The Mg-rich sample-13 has a small distortion. In the case of the tetragonal to  Table 1). Samples-a and -c fall close to the trend lines, but samples-b and -7 are off those lines. Pure Mn 3 O 4 has the largest average <M-O> distance (samples-c and -24) and the Mg-rich sample-13 has a small average <M-O> distance at room temperature.
Substitution of cations at the octahedral M site causes a change in the average <M 3+ -O> distance and unit-cell parameters ( Figure 5). For the samples (13 to 24; Table 1) for which the trend lines are based, the M site is completely filled with Mn 3+ cations. Therefore, variations in the <M 3+ -O> distance arise from the influence of the T site cations. However, samples-b and -7 contain a significant amount of Fe 3+ cations at the M site, so these samples are off the trend lines ( Figure 5). With respect to pure Mn 3 O 4 (samples-24, -c), sample-b shows an enlargement of a and contraction of the c unit-cell parameter. Samples-c and -24 have the largest average <M-O> distance, whereas the Mg-rich sample-13 has the smallest average <M-O> distance.
The Jahn-Teller elongation, ∆(M-O), is less for sample-b compared to sample-a (Table 6; Figure 6). As the difference between the a and c unit-cell parameters, (c-a), becomes smaller, the Jahn-Teller elongation, ∆(M-O), also becomes smaller ( Figure 6). For the samples in this study, sample-c has the highest ∆(M-O), whereas sample-b has the lowest ∆(M-O). At low temperature (10 K), sample-7 has the least distortion. The Mg-rich sample-13 has a small distortion. In the case of the tetragonal to cubic transition of hausmannnite, with increasing temperature, the a and c unit-cell parameters approach equality and ∆(M-O) also approaches 0 towards the transition at 1170 • C.