Crystal Chemistry of Six Grossular Garnet Samples from Different Well-Known Localities

: Two isotropic grossular (ideally Ca 3 Al 2 Si 3 O 12 ) samples from (1) Canada and (2) Tanzania, three optically anisotropic grossular samples (3, 4, 5) from Mexico, and one (6) anisotropic sample from Italy were studied. The crystal structure of the six samples was reﬁned in the cubic space group Ia 3 d , using monochromatic synchrotron high-resolution powder X-ray diffraction (HRPXRD) data and the Rietveld method. The compositions of the samples were obtained from electron microprobe analyses (EPMA). The HRPXRD traces show a single cubic phase for two isotropic samples, whereas the four anisotropic samples contain two different cubic phases that were also resolved using X-ray elemental line scans, backscattered electron (BSE) images, and elemental maps. Structural mismatch from two cubic phases intergrown in the birefringent samples gives rise to strain-induced optical anisotropy. Considering the garnet general formula, [8] X 3[6] Y 2[4] Z 3[4] O 12 , the results of this study show that with increasing unit-cell parameter, the Y-O distance increases linearly and rather steeply, the average <X-O> distance increases just slightly in response to substitution mainly on the Y site, while the Z-O distance remains nearly constant. The X and Z sites in grossular contain Ca and Si atoms, respectively; both sites show insigniﬁcant substitutions by other atoms, which is supported by a constant Z-O distance and only a slight increase in the average <X-O> distance. The main cation exchange is realized in the Y site, where Fe 3+ (ionic radius = 0.645 Å) replaces Al 3+ (ionic radius = 0.545 Å), so the Y-O distance increases the most.


Introduction
In a recent study on grossular, ideally Ca 3 Al 2 Si 3 O 12 , four different samples were investigated: three anisotropic samples (two from Asbestos, Quebec and one from Tanzania) contain an intergrowth of two different cubic phases, whereas the isotropic sample from Afghanistan contains one cubic phase [1]. In this study, four additional anisotropic grossular samples from Mexico and Italy, and two isotropic grossular samples from Canada and Tanzania were investigated. The results from these ten different samples are used to examine structural trends in grossular-andradite [Ca 3 (Al,Fe) 2 Si 3 O 12 ] solid solutions. The three samples from Mexico were selected because they were described as birefringent [2]. Based on some recent studies, these samples are expected to contain multiple cubic phases [1,[3][4][5][6][7][8]. This study was carried out to confirm this expectation. Based on synthetic samples, structural data are available for grossular-andradite solid solutions [9].
Birefringence in garnet was reported over a century ago [10][11][12], but the origin still remains questionable. Many garnet samples are cubic, but some almandine, grossular, spessartine, andradite, uvarovite, and hydrogarnet samples are anisotropic under crosspolarized light, which indicates that they are not optically cubic, e.g., [13][14][15][16][17]. Several reasons were given as the cause of the birefringence, but the main one appears to be cation order in the X and Y sites that cause symmetry reduction [13,[18][19][20][21][22][23][24][25][26][27][28]. These studies observed unit-cell parameters that do not deviate significantly from a cubic unit-cell parameter. In an IR study of four birefringent samples, including grossular from Asbestos and Eden Mills, This study examines the crystal structure of four anisotropic and two isotropic grossular samples. The two isotropic samples are single cubic phases. The four birefringent samples contain two cubic phases that cause strain-induced optical anisotropy. X-ray

Synchrotron High-Resolution Powder X-ray Diffraction (HRPXRD)
The samples 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 the sample was crushed to a fine powder using a corundum mortar and pestle. The crushed sample was loaded into a Kapton capillary (0.8 mm internal diameter) and rotated during the experiment at a rate of 90 rotations per second. The data were collected at 23 • C to a maximum 2θ of about 50 with a step size of 0.001 and a step time of 0.1 s per step. The HRPXRD traces were collected with a multianalyzer detection assembly consisting of twelve independent silicon (111) crystal analyzers and LaCl 3 scintillation detectors that reduce the angular range to be scanned and allow for rapid acquisition of data. An external silicon (NIST 640c) and alumina (NIST 676a) standard (mixed in a ratio of 1 / 3 Si: 2 /3 Al 2 O 3 by weight) was used to calibrate the instrument and refine the monochromatic wavelength used in the experiment (see Table 2). Additional details of the experimental set-up are given elsewhere [46][47][48]. The experimental techniques used in this study are well established [49][50][51][52][53][54][55][56][57][58][59].  [60]. For example, ∆a = a(phase-3a) − a(phase-3b). † The profile term LY is also a measure of strain. ** Isotropic strain (%) = 100 × LY × (π/18000). The minor phase is under more strain than the dominant phase and causes strain-induced birefiringence in cubic garnets. ‡ R (F 2 ) = Overall R-structure factor based on observed and calculated structure amplitudes

Rietveld Structural Refinement
The HRPXRD data were analyzed with the Rietveld method [61], as implemented in the GSAS program [62], and using the EXPGUI interface [63]. Scattering curves for neutral atoms were used. The starting atom coordinates, cell parameter, and space group, Ia3d, were taken from Antao [1]. The background was modelled using a Chebyschev polynomial (eight terms). In the GSAS program, the reflection-peak profiles were fitted using type-3 profile pseudo-Voigt [64,65]. A full-matrix least-squares refinement was carried out by varying the parameters in the following sequence: a scale factor, unit-cell parameter, atom coordinates, and isotropic displacement parameters. Examination of the HRPXRD traces shows a single cubic phase for samples-1 and -2 and two separate cubic phases with different unit-cell parameters for samples-3, -4, -5, and -6. There are no impurities, or un-indexed peaks. The Y site was constrained to Fe + Al = 1. Toward the end of the refinement, all the parameters were allowed to vary simultaneously and the refinements proceeded to convergence. The unit-cell parameters and Rietveld refinement statistical indicators for the samples are summarized in several tables that follow.

Chemical Analyses
All the samples were analyzed quite well as indicated by the total weight percent oxides, which is close to 100% (Table 1). Based on the general garnet formula X 3 Y 2 Z 3 O 12 , the sum of the X, Y, and Z cations are close to this ideal formula. The EPMA results for the six grossular samples show that the X site is nearly filled with Ca atoms and with minor amounts of Mn atoms to make a total of 3.0 X cations. (Table 1). The raspberry-red colour in grossular was attributed to Mn atoms [2]. Samples-3 and -4 contain small amounts of the Mn atoms and both are red to pink in colour ( Figure 2). The Z site is filled with only Si atoms. The X and Z site contents do not influence the structural variations that are controlled mainly by the Al 3+ and Fe 3+ cations in the Y site in the grossular (Ca 3 Al 2 Si 3 O 12 )-andradite (Ca 3 Fe 2 Si 3 O 12 ) solid solutions. Sample-6 contains the most Fe 3+ cations, whereas sample-1 contains the least amount. The structure refinements, as shown below, indicate that the sofs for the Y sites are different for the two different cubic phases in the birefringent grossular samples. This study advances some recent work on several garnet-group minerals [66][67][68][69][70][71].
In general, separate phases in a multiphase assemblage of birefringent garnets are difficult to detect with EPMA results, especially if the crystals are randomly oriented in thin sections, or if the intergrowths occur on a fine scale. The electron beam may cover both phases and an average composition for both phases may be obtained by EPMA. Lamellar zoning in grossular and andradite occur along (110) planes and only if such planes are imaged or analyzed along a direction normal to (110) (i.e., edge on to the lamellae) may compositional differences between zones be observed. Lamellar zoning along (110) are Alor Fe 3+ -rich in an inverse relation, e.g., [18,34,[72][73][74]. Moreover, to simulate cation order in garnet, many single-crystal studies were carried out in space groups that are lower than cubic symmetry (see Section 1). However, this study and other recent studies show that such lamellar zones represent two or three different cubic phases [1,[3][4][5][6][7][8]. The separate cubic phases are quite evident from HRPXRD traces as well as in optical micrographs, and backscattered electron (BSE) images obtained with the electron probe. The HRXPRD technique was also used to observe two-phase intergrowths in other minerals [75][76][77][78][79].

Optical Light Microscopy, Backscattered Electron (BSE) Images and X-ray Elemental Maps
Samples-1 and -2 are single cubic phases that are optically isotropic and chemically homogeneous. Samples-1 and -2 show no contrast variations in optical micrographs or BSE images. However, the other samples are birefringent and some contain lamellar features or zoning (Figures 3 and 4).  The two-phase birefringent grossular samples in this study have compositional variations (Table 1), and different Y(sofs; Table 3) as indicated by line scans, BSE images, and elemental maps. The BSE image for the sample-3 shows sharp linear features and the line scan shows an inverse relation between Fe and Al atoms ( Figure 5). Average compositions were reported for grossular samples from Coahuila, Mexico [2]. They observed optical anisotropy in the form of birefringence and little compositional heterogeneity or zonation, and reported an average composition of {Ca 2 . 94        Sample-4 from Chihuahua, Mexico clearly shows two separate phases with sharp contact boundaries ( Figure 6). Line scans and cation content across the separate phases that occur as lamellar features (Figure 7a,b) show that the Al 3+ and Fe 3+ cations are inversely correlated. The elemental maps for sample-4 clearly indicate two separate phases that contain different amounts of Al 3+ and Fe 3+ cations (Figure 6b-d), whereas Ca atoms are distributed homogeneously throughout the crystal (Figure 6b). Chemical analyses from specific points (points 1 to 9 shown in Figures 6a and 7b) indicate the composition of the different phases. The compositions that represent phase-4a and phase-4b are given in Table 1.  Figure  11). The intergrowths of two phases have contact boundaries that are parallel to northwest. Cations from the points marked 1 to 9 in (a) are shown in Figure 7b. A line scan from A to B in (a) across the crystal is provided (Figure 7a).  (Figure 6a) showing the inverse relation between Fe 3+ and Al 3+ cation content and nearly homogeneous Ca content for sample-4 from Chihuahua-p, Mexico. Two separate phases may be deduced from the line scans and the elemental maps in Figure 6, but such phases are most easily detected by HRPXRD ( Figure 11).  Sample-6 from Aosta, Italy, appears homogeneous in plane-polarized light (PPL) and is birefringent in cross-polarized light (XPL; Figure 9a,b). The BSE image contains concentric growth features with light and dark contrasts that indicate slightly different compositions (Figure 9c). The brighter areas (higher mean atomic number) correspond to Fe-rich grossular, whereas the darker areas (lower mean atomic number) correspond to Alrich grossular, ideally Ca 3 Al 2 Si 3 O 12 . The X-ray elemental maps show the distribution of Al, Fe, and Ti atoms, and subtle variations are observed, especially for Ti atoms (Figure 3d-f). Quantitative chemical analyses were obtained with EPMA from the points marked 1 to 10 ( Figure 3c; Table 1). The scans along the line AB show an inverse relation between Fe 3+ and Al 3+ cations, homogeneous Ca, and slightly variable Ti distributions (Figures 9c and 10). Two separate compositions may be deduced from the line scans, the elemental maps, and quantitative spot analyses (Table 1).   Table 1). Note that Fe + Al = 2 apfu. The line scan units are arbitrary.

High-Resolution Powder X-Ray Diffraction (HRPXRD) Traces
In Rietveld structure refinements, it is necessary to show the fit of the complete trace to show how well the structure was modelled. In addition, expanded parts of the trace are also needed to observe splitting, asymmetry, width, and sharpness of diffraction peaks. Multiple cubic phases in garnets are easily observed with HRPXRD. An example of a complete HRPXRD trace is shown for a single cubic phase of sample-1 ( Figure 11a) and two cubic phases in sample-4 ( Figure 11b). The complete traces for the other samples are also given (Figures 12-14). The expanded HRPXRD traces for sample-1 shows a single cubic phase, where the peaks are very sharp and symmetrical (Figure 15a), whereas the two cubic phases in sample-4 are indicated by split peaks, especially for reflections 664, 12,8,2, and 12,6,6 ( Figure 15b).  Table 1). Note that Fe + Al = 2 apfu. The line scan units are arbitrary.

High-Resolution Powder X-ray Diffraction (HRPXRD) Traces
In Rietveld structure refinements, it is necessary to show the fit of the complete trace to show how well the structure was modelled. In addition, expanded parts of the trace are also needed to observe splitting, asymmetry, width, and sharpness of diffraction peaks. Multiple cubic phases in garnets are easily observed with HRPXRD. An example of a complete HRPXRD trace is shown for a single cubic phase of sample-1 ( Figure 11a) and two cubic phases in sample-4 ( Figure 11b). The complete traces for the other samples are also given (Figures 12-14). The expanded HRPXRD traces for sample-1 shows a single cubic phase, where the peaks are very sharp and symmetrical (Figure 15a), whereas the two cubic phases in sample-4 are indicated by split peaks, especially for reflections 664, 12,8,2, and 12,6,6 ( Figure 15b).
Sample-2 from Tanzania contains a single cubic phase with sharp, symmetric, and narrow peaks with no splitting of reflections (Figure 16a). The two phases in sample-3 are evident from the asymmetry in peaks (Figure 16b).
Both the yellow core of sample-5 and the white outer layer contains two cubic phases. The two phases in the yellow core (Chihuahua-y) of sample-5 are evident from the asymmetry in peaks (Figure 17a), whereas the white outer layer (Chihuahua-w) of the crystal clearly shows split reflections (Figure 17b). The two phases in sample-6 from Italy is indicated by the asymmetry in the reflections (Figure 18).
Diffraction peaks from garnets showing splitting were interpreted as arising from different phases, e.g., [31][32][33][34][35][36][37][38], which was confirmed from recent studies [1,3,4,[6][7][8]. Hirai and Nakazawa [34] observed stratified (110) layers in an iridescent grandite garnet where the layers are composed of Fe-rich (Adr 87 ) and Al-rich (Adr 78 ) lamellae. Their selected-area electron diffraction (SAED) pattern shows the presence of two phases because of splitting of spots that are normal to the lamellae. From the split reflections, the difference in unit-cell size for the two phases was estimated to be about 0.02 Å. They interpreted the layered structure as arising from exsolution, that is, different phases [33,34] instead of oscillatory zoning, e.g., [18,73,74,80]. Pollok et al. (2001) observed oscillatory zoning on a very fine scale in grandite garnets and their HRTEM images show that the compositional interfaces are sharp and coherent. However, their TEM image and SAED pattern show nonperiodic lamellae with interfaces normal to (110) and small diffraction peak splitting, which was not interpreted as two separate phases, as was done by Hirai and Nakazawa [33,34]. In a recent study on an andradite that contains stratified layers, Antao and Klincker [6] observed three separate cubic phases (Adr 97 , Adr 93 , and Adr 87 ) and the crystal structure of the three phases were refined using HRPXRD data. The differences in cell parameters among the three phases are 0.007 and 0.070 Å. Figure 11. Complete HRPXRD traces for (a) sample-1 from Lytton, Canada, and (b) sample-4 from Chihuahua-p, Mexico. Data for sample-4 were modelled using two slightly different cubic phases, whereas sample-1 was modelled with a single cubic phase. The difference curve (I obs − I calc ) is shown at the bottom. Short vertical lines indicate allowed reflection positions. The intensities and difference curves that are above 20 • and 40 • 2θ are multiplied by 10 and 40, respectively. Similar features are displayed in other traces shown. To avoid repetition, these descriptions will not be repeated. . Data for sample-3 was modelled using two slightly different cubic phases, whereas sample-2 was modelled with a single cubic phase.
Allen and Buseck [13] studied anisotropic near-endmember grossular samples using XRD, FTIR, TEM (SAED and HRTEM), and EPMA. They observed homogeneous compositions and did not observe any split reflections in electron diffraction patterns. They used unit-cell parameters that are nearly cubic to refine the crystal structure in a lower symmetry space group I1 and indicated that there may be cation order in the X and Y sites. They suggested that such cation order gives rise to birefringence in near-endmember grossular. Crystal structures that were refined in unnecessarily low symmetry space groups were heavily criticized [81,82].      The crystal structure of several uvarovite samples was examined in symmetry lower than the standard cubic symmetry for garnet [26,83]. They observed Cr 3+ -Al order on the Y-site and OH distribution in a noncubic manner; these features were attributed to the reduction in cubic symmetry. However, they stated: "The SAED patterns gave no evidence of a deviation from cubic symmetry. HRTEM images exhibit no indications for the occurrence of micro-twinning" [83]. In addition, their EPMA analyses of four analyses per prepared crystal reveal that their samples are chemically homogenous. Therefore, compositional zoning can be ruled out as a possible reason for optical anisotropy. The EPMA data confirmed that these garnets are, to a good approximation, simple binary uvarovite-grossular solid solutions [83].

Rietveld Refinements and Structural Variations across Grossular-Andradite Solid Solutions
In this study, the sofs calculated from the chemical analysis are similar to those obtained by the Rietveld refinements (Table 3). The EPMA sofs for the six samples are close to 1, including the Ca atom in the Y site and Si atom in the Z site. The sum of the Al and Fe atoms in the Y site is also close to 1. Samples-5 and -6 contain significant amounts of Fe 3+ cations replacing Al atoms. Except for samples-1 and -2, the two phases in each of the other samples have significantly different Y(sof ) that are expected to give rise to different Y-O distances (Table 4).  The EPMA results show that the Z site is filled with Si atoms, so the Z(sof ) can be fixed to 1. However, Z(sof ) was refined in this study and is >0.92 for all the samples (Table 3). These slight deficiencies for the Si(sof ) (<0.08) may be experimental error or may indicate minor (O 4 H 4 ), but such substitutions are insignificant in these samples because the Si-O bond distances are nearly constant (Table 4). If (O 4 H 4 ) substitution occurs in grossular, then Z(sof ) is <1, the unit-cell edge increases, the Si-O bond distances increase, and simultaneously the Y-O distances decrease from their corresponding values in the hydrous phase (see Figure 8 in Antao [84]). Small amounts of OH in near-endmember grossular were detected by IR in several studies [13,17,29]. It is possible that some of the grossular samples may contain minor amounts of (O 4 H 4 ) substitution, but because the amount is small, this discussion is reserved for samples that contain a significant amount of Si atom deficiencies, where the (O 4 H 4 ) substitution can be detected by X-ray diffraction. Examples of such samples are pink and green "jade" from South Africa [84]), or katoite samples, e.g., [36,85,86].
The EPMA results indicate the X site is filled with Ca atoms, which is also confirmed by the Rietveld refinements. The difference between the sofs obtained by the two methods is quite small, which is also the case for the Y site ( Table 3).
The unit-cell and bond distances for grossular samples from this study and the literature are compared ( Figure 19). Data from all the single-crystal structure refinements shown in Figure 19 were done in the cubic space group, Ia3d, where only single phases and no split reflections were observed. The bond distances obtained by the single-crystal method are similar to those obtained by HRPXRD (Figure 19), so both methods give similar structural results. Grossular data are included in Figure 19 if their unit-cell parameters are between 11.840 and 11.951 Å. End member grossular and andradite have a ≈ 11.85 and a ≈ 12.05 Å, respectively. In Figure 19, the data points with the maximum unit-cell parameters are for a two-phase sample from Tanzania [1], and these are similar to a hydrogarnet with a ≈ 11.94 Å [87], and different from the single-phase "hessonite" from Tanzania (grossular sample-2 in this study). There is a cluster of three data points from single-crystal studies on grossular samples from Asbestos, Quebec [88], Ramona, California [89], and a synthetic grossular sample [90]; all with nearly the same unit-cell edge between 11.84 and 11.85 Å (Figure 19). Three other samples are classified as hydrogarnets and have unit-cell parameters between 11.87 and 11.90 Å [91]. Several data points obtained with HRPXRD have a ≈ 11.85 Å. Sample-6 from Italy with the most Fe 3+ content has the largest unit-cell parameter among the samples used in this study ( Figure 19). Data for a few samples appear to show minor (O 4 H 4 ) substitution, in particular, those hydrogarnet samples studied by Basso et al. [91]. with the a unit-cell parameter that range from 11.840 to 11.951 Å. The range on the y-axis (0.08 Å) is the same in each plot, so the differences in each plot can be compared (also from the slopes of the trend lines). Straight lines are meant as guide to the eyes. The Z-O distances are nearly constant. The average <X-O> and <D-O> distances change by small amounts compared to the Y-O distance that changes the most and has the steepest slope. The Y site controls the structural variations. Data from Antao [1] for grossular samples from Quebec, Tanzania, and Afghanistan are shown as open circles. Single-crystal data for seven samples are shown as triangles [87][88][89][90][91]. Errors bars are smaller than the symbols. Data from this study shows details that were not observed in previous SCXRD studies, which is an inappropriate technique to examine multiphase samples.
The O atom is on a general O atom position in the garnet structure and the positions for all the cation sites are fixed. Because each O atom is four coordinated by one Z, one Y, and two X sites in a tetrahedral configuration, substitution on any one cation site has only minor effects on the other sites, as reflected in their bond distances [3]. The Z-O distances are nearly constant and are within the range 1.64 to 1.65 Å (Figure 19d) because the Z site is filled with Si atoms. The X site is filled exclusively with Ca atoms, so the <X-O> distance increases slightly in response to substitution on the Y site (Figure 19a). The Z and X sites have minor influence on the structural variations in grossular, which is controlled mainly by atoms in the Y site.
The Y site contains negligible amounts of other atoms besides Al and Fe atoms ( Table 1). The major variations occur for the dominant Al and Fe atoms with sample-6 containing the most Fe 3+ cations (Table 1). EPMA results shows that the Y(sofs) are different for the six samples in this study, which is confirmed by the structure refinements (Table 3). Each two-phase sample have different Y-O distances (Figure 19c).
The Y-O distance increases the most because of the substitution of Fe 3+ (radius = 0.645 Å) for Al 3+ (radius = 0.535 Å), as expected for a solid solution from anhydrous grossular, Ca 3 Al 2 Si 3 O 12 , towards anhydrous andradite, Ca 3 Fe 3+ 2 Si 3 O 12 . For some samples, there appears to be an increase in Z-O distance and a corresponding decrease in Y-O distance, which may indicate minor hydrogarnet substitution, especially for the hydrogarnet samples studied by Basso et al. [91] and the green grossular labelled Quebec-g with the smaller unit-cell edge (Figure 19c,d).
The  (Figure 19a,c,d). Satisfactory coordination of the O atom appears to be most important for the garnet structure.
The HRPXRD results are of comparable accuracy and are very similar to the singlecrystal results shown in Figure 8. However, none of the single-crystal studies observed multiple phases. Single crystal is not the appropriate technique to study a multiplephase assemblage. Moreover, TEM studies on near-endmember grossular did not observe multiple phases [13].

Is There a Miscibility Gap between Grossular and Andradite Solid Solutions?
The two-phase intergrowths may be considered as exsolution, as was predicted by theoretical calculations, e.g., [92,93], and was also interpreted as exsolution by Hirai and Nakazawa [33,34]. However, it is puzzling to rationalize exsolution in near-endmember grossular because exsolution usually occurs midway in a solid-solution series as in the alkali feldspars and pyroxenes. Oscillatory compositional zoning in garnet is relatively common and has been attributed to changing chemical or physical conditions during growth [73,94].
Formation of a two-phase intergrowths in grossular samples may be related to crystal growth and changes in oxygen fugacity (f O2 ), activity of SiO 2 (a SiO2 ), etc., as the crystals grow at relatively low temperature (<300 • C) that prevents diffusion or homogenization. Near-endmember grossular occurs in rocks that were formed by metasomatism below 300 • C [95]. Strain arises from structural mismatch of two cubic phases and gives rise to anisotropy. This study shows two-phase intergrowths in several grossular samples; each phase has different amounts of atoms on the Y site, as judged by the variation in Y-O distances and Y(sofs). Some of these ideas are confirmed in sample-5 where the yellow core is about 77% Grs and the white rim is 78 to 87% Grs, whereas the boundary is about 44% Adr, which clearly shows that the chemical conditions had changed during crystal growth.