Crystal-Chemical Properties of Synthetic Almandine-Pyrope Solid Solution by X-Ray Single-Crystal Diffraction and Raman Spectroscopy

Crystal-chemical properties of synthetic Almandine-Pyrope (Alm-Pyr) solid solutions were investigated by X-ray single-crystal diffraction and Raman spectroscopy. Garnet solid solution with different compositions were synthesized from powder at 4.0 GPa and annealed at 1200 °C for 48 h by a multi-anvil pressure apparatus. Garnet crystals with different sizes (about 60-1000 μm) were obtained from synthesis. The results of X-ray single-crystal diffraction show that the unit cell constants decrease with increasing Pyr contents in the synthetic Alm-Pyr crystals due to the smaller ionic radius of Mg2+ in eightfold coordination than that of Fe2+. The data exhibit obviously positive deviations from ideal mixing volumes across the Alm-Pyr join which may be caused by the distortion of the SiO4 tetrahedron. Moreover, the significant decrease in the average M-O bond length and volume of the [MgO8]/[FeO8] dodecahedron with increasing Pyr contents are the most important factors to the decrease in the Alm-Pyr crystal unit cell constant and volume. On the other hand, selected bond distances (average , , and  distances) have a linear correlation with the unit-cell parameter, but the  distance has nonlinear correlation. With increasing the unit-cell parameter, the average  distance increases significantly, followed by the average  and  distances. While the  distance changes negligibly further confirming the conclusion that the significant decrease of the average M-O bond length of the [MgO8]/[FeO8] dodecahedron with increasing Pyr contents are the most important factors to the decrease in the Alm-Pyr crystal unit cell volume. In the Raman spectra collected for the Alm-Pyr solid solutions, Raman vibration mode assignments indicate that the Raman vibrational spectra change along the Alm-Pyr binary solution. The mode frequencies of Si-O stretching, Si-O bending, and the rotation of the SiO4-tetrahedron (R(SiO4)) decrease linearly, while the translational modes of the SiO4-tetrahedron (T(SiO4)) increase with increasing Alm contents.


Introduction
Garnet is not only one of the most important mineral in the upper mantle [1], but also an important phase in metamorphic rocks [2]. Hence, garnet is stable over a wide range of pressures and temperatures in the Earth. In addition, garnet plays a prominent role in many geothermobarometers used to calculate the pressure and temperature of the mantle and metamorphic rock [3,4]. Therefore, the crystal-chemical properties concerning the elastic-strain, thermodynamic and trace-element substitution behavior of garnet are important for constraining the compositions, thermodynamic and physical properties of rocks in the middle-low crust and upper mantle.
The garnet group is a variety of nesosilicate minerals with an isolated group of [SiO4] as its basic skeleton, including all garnets of essentially the same structure and chemically similar elements, and belongs to the cubic system and space group 3 . The general formula for the garnet group is X3Y2Z3O12, where X, Y, and Z refer to dodecahedral, octahedral, and tetrahedral sites, respectively [5] ( Figure 1). Generally, the X site is occupied by Mg 2+ , Fe 2+ , Mn 2+ , Ca 2+ , etc. The Y site is occupied by Al 3+ , Fe 3+ , Cr 3+ , Ti 4+ , etc. Si 4+ and Al 3+ occupy the Z site. The minerals of the garnet group are divided into two series, pyralspite and ugrandite, depending on the cation in the X site. If the X site of garnet is mainly occupied by Mg 2+ , Fe 2+ , and Mn 2+ , it is pyralspite, while if the X site is mainly occupied by Ca 2+ , it is ugrandite. However, most of garnet group samples in nature occur as multi-component solid solutions. For example, the pyrope (Pyr) component of garnet found in diamonds of peridotitic and eclogitic origin can be as high as about 79 mol.% and 43 mol.%, respectively, and the almandine (Alm) component is about 11 mol.% and 33 mol.%, respectively [6]. The structure, elastic properties, and electrical conductivity of garnet end-members have been extensively studied, but detailed studies on structure by X-ray single-crystal diffraction and Raman spectroscopy of garnet solid solutions are limited. In particular, Raman spectroscopy studies have only focused on grossular-andradite join, pyrope-grossular join, and almandine-pyrope (Alm-Pyr) join [7][8][9][10]. To date, even in the most studied Alm-Pyr join, the structural properties of Alm-Pyr solid solution by the X-ray single-crystal diffraction are very limited, only several garnet compositions along the Alm-Pyr solid solution have been investigated by the X-ray single-crystal diffraction in details [11]. However, only when the strictly binary solid-solution compositions are available can we fully understand how the natural garnet structure changes as a function of composition. Therefore, the crystal-chemical properties of the Alm-Pyr solid solution require further systematic research. The structure, elastic properties, and electrical conductivity of garnet end-members have been extensively studied, but detailed studies on structure by X-ray single-crystal diffraction and Raman spectroscopy of garnet solid solutions are limited. In particular, Raman spectroscopy studies have only focused on grossular-andradite join, pyrope-grossular join, and almandine-pyrope (Alm-Pyr) join [7][8][9][10]. To date, even in the most studied Alm-Pyr join, the structural properties of Alm-Pyr solid solution by the X-ray single-crystal diffraction are very limited, only several garnet compositions along the Alm-Pyr solid solution have been investigated by the X-ray single-crystal diffraction in details [11]. However, only when the strictly binary solid-solution compositions are available can we fully understand how the natural garnet structure changes as a function of composition. Therefore, the crystal-chemical properties of the Alm-Pyr solid solution require further systematic research.
In this study, we firstly synthesize 11 garnet compositions along the Alm-Pyr solid solution at high pressure and high temperature. Then we select 10 garnets for X-ray single-crystal diffraction and 9 garnets for Raman spectroscopy studies. Finally, we discuss the effect of composition on the crystal-chemical properties along the Alm-Pyr binary.

Crystal Synthesis
Eleven single crystals of Alm-Pyr garnet (Alm 100 , Pyr 9 Alm 91 , Pyr 14 12 , and Pyr 100 ) used in this study were synthesized at high pressure and high temperature using a multi-anvil pressure apparatus (YJ-3000t) at the Institute of Geochemistry, Chinese Academy of Sciences, Guiyang, China. The sample assembles and synthesis process were similar to those used by Fan et al. (2017) and Xu et al. (2018) [12,13], and were briefly described here.
The starting materials used in the synthesizing experiments were stoichiometric amounts of high-purity magnesium oxide (MgO), aluminum oxide (Al 2 O 3 ), silica (SiO 2 ), Iron (Fe), and Ferric oxide (Fe 2 O 3 ). The mixture was grounded in acetone at an agate mortar for 3 h and then heated for more than 12 h at 200 • C in a muffle furnace to eliminate adsorbed water. Finally, the mixture was encapsulated in the platinum capsules with 1 weight percent (wt.%) of deionized water. The graphite tube was used as the heater and the pressure transmitting medium was pyrophyllite. All complete assemblies were heated for more than 10 h at 200 • C in a muffle furnace before being loaded into the apparatus.
The sample assembly was first compressed to 4.0 GPa for over 20 min by a multi-anvil pressure apparatus (YJ-3000t) and then heated to 1200 • C in 20 min. After a run duration of 48 h, the garnet crystals with different sizes (about 60-1000 µm) were obtained from the quenched run product.

Analysis Methods
The synthetic single garnet crystals were observed by the stereoscopic microscope. The compositions of garnet crystals with sizes larger than~100 µm were performed at the Institute of Geochemistry, Chinese Academy of Sciences, Guiyang, China with an electron microprobe analysis (EMPA, JEOL Hyperprobe JXA-8500F microscope), operating at a 15 kV accelerating voltage, 20 nA beam current, and a beam size of 10 µm.
The synchrotron X-ray single-crystal diffraction experiments at ambient condition were carried out with a six-circle diffractometer at 13-BM-C experimental station of the Advanced Photon Source, Argonne National Laboratory. The wavelength of the incident X-ray was 0.4340 Å, and the beam size was 12 µm × 18 µm. Diffraction images were acquired on Dectris Pilatus 1M detector and calibrated using the ambient LaB 6 as the diffraction standard [14]. Stepped ϕ rotation exposures were collected for the single-crystal sample of different components, with an exposure time of 1 s/deg. The ϕ-rotation (from −170 • to 170 • ) axis was horizontal and perpendicular to the incident X-ray direction. The diffraction images were analyzed using the Bruker APEX3 software. Crystal structures were refined from the intensity data using the SHELXL software, facilitated by Olex 2 user interfaces [15,16]. Table S1 in the supplements shows the unit-cell parameters and details of the structural refinement of the samples.
Raman spectra in this study were collected with the Renishaw Raman spectrometer equipped with a Peltier-cooled charge-coupled device (CCD) detector. The laser exciting the sample was 532 nm in wavelength. The laser light was focused on samples by using the Leica microscope with a long-distance 20× objective to a beam size of about 2 µm diameter and the laser power was 2 mW. Each Raman spectrum was collected with a total exposure time of 300 s. Nine spectra were collected from different points on each garnet sample and measured Raman data from 100 cm −1 to 1200 cm −1 . We fitted the Raman peaks and obtained peak parameters, Raman mode frequencies, and peak widths [full width at half-maximum (FWHM)] from these spectra.

Synthetic Garnet Crystal
The microphotographs of the synthetic Alm-Pyr crystals are shown in Figure 2 and Figure S1 in the supplements. The synthetic Alm-Pyr crystals are available in a variety of colors and optical characteristics. The color of the crystals gradually changes from colorless to orange and maroon with the increase of Alm contents in the Alm-Pyr crystals from 0 mol.% to 100 mol.%. In the meantime, the Alm-Pyr crystals also gradually vary from transparent to translucent, and finally to nearly opaque. The typical dimension of Alm-Pyr crystals with granular forms ranges from about 60 µm up to more than 1 mm with the increase of Alm contents ( Figure 2).

Synthetic Garnet Crystal
The microphotographs of the synthetic Alm-Pyr crystals are shown in Figure 2 and Figure S1 in the supplements. The synthetic Alm-Pyr crystals are available in a variety of colors and optical characteristics. The color of the crystals gradually changes from colorless to orange and maroon with the increase of Alm contents in the Alm-Pyr crystals from 0 mol.% to 100 mol.%. In the meantime, the Alm-Pyr crystals also gradually vary from transparent to translucent, and finally to nearly opaque. The typical dimension of Alm-Pyr crystals with granular forms ranges from about 60 μm up to more than 1 mm with the increase of Alm contents ( Figure 2). The Alm-Pyr crystals have different grain size and morphology because the anisotropy of the growth fronts depends on the chemical composition [17] (Figures 2 and S1). The microphotographs show that the largest grains are from sample Alm100 having a size of about 1000 μm. All samples have a combined form of rhombic dodecahedron {110} and tetragonal trisoctahedron {211}. Moreover, the faces of rhombic dodecahedron are more developed than those of tetragonal trisoctahedron ( Figure  S1).

Chemical Composition
All the 11 synthetic garnet compositions along the Alm-Pyr solid solution are given in Table 1. In addition, garnet crystal-chemical formulae were calculated according to the recommendations of Grew et al. (2013) [18] and also reported in Table 1. The Alm-Pyr crystals have different grain size and morphology because the anisotropy of the growth fronts depends on the chemical composition [17] (Figure 2 and Figure S1). The microphotographs show that the largest grains are from sample Alm 100 having a size of about 1000 µm. All samples have a combined form of rhombic dodecahedron {110} and tetragonal trisoctahedron {211}. Moreover, the faces of rhombic dodecahedron are more developed than those of tetragonal trisoctahedron ( Figure S1).

Chemical Composition
All the 11 synthetic garnet compositions along the Alm-Pyr solid solution are given in Table 1. In addition, garnet crystal-chemical formulae were calculated according to the recommendations of Grew et al. (2013) [18] and also reported in Table 1. The EMPA results indicate that the synthesized garnet crystals consist almost entirely of Pyr and Alm, where the components of the Pyr and Alm are always greater than 99.6 mol.% and little grossular and spessartine (<0.4 mol.%) are also presented (Table 1). However, as shown in the Figure 3, except for the end members of Alm and Pyr garnets, the compositions of the other 9 synthetic Alm-Pyr crystals are obviously different from the nominal compositions of the starting material with Pyr contents less than those of nominal compositions ( Figure 3). The result is basically consistent with occupancy factors obtained by structural refinement of the samples (Table 1 and Table S1). Expect for the samples with 10 mol.% and 40 mol.% Pyr in nominal composition and the end members of Alm and Pyr garnets, the measured compositions of the other 6 synthetic Alm-Pyr crystals are obviously different from the nominal compositions of the starting material with Pyr contents less than those of nominal compositions ( Figure 3). The EMPA results indicate that the synthesized garnet crystals consist almost entirely of Pyr and Alm, where the components of the Pyr and Alm are always greater than 99.6 mol.% and little grossular and spessartine (<0.4 mol.%) are also presented (Table 1). However, as shown in the Figure  3, except for the end members of Alm and Pyr garnets, the compositions of the other 9 synthetic Alm-Pyr crystals are obviously different from the nominal compositions of the starting material with Pyr contents less than those of nominal compositions ( Figure 3). The result is basically consistent with occupancy factors obtained by structural refinement of the samples (Tables 1 and S1). Expect for the samples with 10 mol.% and 40 mol.% Pyr in nominal composition and the end members of Alm and Pyr garnets, the measured compositions of the other 6 synthetic Alm-Pyr crystals are obviously different from the nominal compositions of the starting material with Pyr contents less than those of nominal compositions (Figure 3).

Characteristics of Unit-Cell Parameters
The unit-cell parameters and the unit-cell volumes of the Alm-Pyr Crystals refined from the Xray single-crystal diffraction are summarized in Table 2, along with the results of the previous studies for comparison [11,19,20]. Our results clearly showed that the unit cell constants decrease systematically with increasing Pyr contents in the synthetic Alm-Pyr crystals, due to the smaller ionic radius of Mg 2+ in eightfold coordination (0.89 Å) than that of Fe 2+ (0.92 Å) (Figure 4) [21].
The unit-cell measurements on the Alm-Pyr solid solutions exhibited considerably more scatter and positive deviations from ideal volumes of mixing across the Alm-Pyr join (Figure 4), which is contrary to the results obtained by the X-ray powder diffraction previously [22,23]. In theory, any solid solution deviates from the ideal solution properties to some extent. In the present case, the

Characteristics of Unit-Cell Parameters
The unit-cell parameters and the unit-cell volumes of the Alm-Pyr Crystals refined from the X-ray single-crystal diffraction are summarized in Table 2, along with the results of the previous studies for comparison [11,19,20]. Our results clearly showed that the unit cell constants decrease systematically with increasing Pyr contents in the synthetic Alm-Pyr crystals, due to the smaller ionic radius of Mg 2+ in eightfold coordination (0.89 Å) than that of Fe 2+ (0.92 Å) (Figure 4) [21].
The unit-cell measurements on the Alm-Pyr solid solutions exhibited considerably more scatter and positive deviations from ideal volumes of mixing across the Alm-Pyr join (Figure 4), which is contrary to the results obtained by the X-ray powder diffraction previously [22,23]. In theory, any solid solution deviates from the ideal solution properties to some extent. In the present case, the rotation of the SiO 4 tetrahedra is a possible cause of the positive deviations from ideal mixing volumes.       (Table 3) (Table 3) (9) 11.52701 (11) 11.5241 (3) 11.52759 (16) 11.51055 (6) 11.50955 (6) 11.5013 (4) 11.4887 (3) 11.48023 (8)  To eliminate the compositional variable, we also plot the bond distances versus the unit-cell parameter figures to the structural variations cross the Alm-Pyr solid solution. These figures show that the selected bond distances (average <M-O>, <Al-O>, and <D-O> distances) have a linear correlation with the unit-cell parameter, but the <Si-O> distance has nonlinear correlation which R 2 = 0.284. With increasing the unit-cell parameter, the average <M-O> distance increases significantly, followed by the average <D-O> and <Al-O> distances. However, the <Si-O> distance change negligibly (Table 3, Figure 6). Comparing our data with the previous study of Antao et al. (2014), we can find that our synthetic samples match those of natural samples quite well ( Figure 6) [24]. The average <D-O> distance present optimal linear with the unit-cell parameter of all the data and other bond distances show more scatter than that for the average <D-O> distance, which may mean that satisfactory coordination of the O atom is most important for the garnet structure. To eliminate the compositional variable, we also plot the bond distances versus the unit-cell parameter figures to the structural variations cross the Alm-Pyr solid solution. These figures show that the selected bond distances (average <M-O>, <Al-O>, and <D-O> distances) have a linear correlation with the unit-cell parameter, but the <Si-O> distance has nonlinear correlation which R 2 = 0.284. With increasing the unit-cell parameter, the average <M-O> distance increases significantly, followed by the average <D-O> and <Al-O> distances. However, the <Si-O> distance change negligibly (Table 3, Figure 6). Comparing our data with the previous study of Antao et al. (2014), we can find that our synthetic samples match those of natural samples quite well ( Figure 6) [24]. The average <D-O> distance present optimal linear with the unit-cell parameter of all the data and other bond distances show more scatter than that for the average <D-O> distance, which may mean that satisfactory coordination of the O atom is most important for the garnet structure.

Excess Mixing Volume in Solid Solutions
As we can see, the unit-cell measurements on the Alm-Pyr solid solutions in our study exhibited considerably more scatter and positive deviations from ideal volumes of mixing across the Alm-Pyr join, which shows non-ideal mixing properties (Figure 7). However, our results should show nearideal mixing properties because of the small difference in ionic radii of Mg 2+ (0.89 Å) and Fe 2+ (0.92 Å) in eightfold coordination [21]. There are lots of possible factors that could have caused excess volume such as dampness, synthesizing some unidentified phase and the distortion of the SiO4 tetrahedra, etc. [9,25]. In this study, we think the cause might be the rotational orientation of the SiO4 tetrahedra. As mentioned above, satisfactory coordination of the O atom is most important for the garnet structure and the relationship between the average <M-O> distance and the unit-cell parameter has

Excess Mixing Volume in Solid Solutions
As we can see, the unit-cell measurements on the Alm-Pyr solid solutions in our study exhibited considerably more scatter and positive deviations from ideal volumes of mixing across the Alm-Pyr join, which shows non-ideal mixing properties (Figure 7). However, our results should show near-ideal mixing properties because of the small difference in ionic radii of Mg 2+ (0.89 Å) and Fe 2+ (0.92 Å) in eightfold coordination [21]. There are lots of possible factors that could have caused excess volume such as dampness, synthesizing some unidentified phase and the distortion of the SiO 4 tetrahedra, etc. [9,25]. In this study, we think the cause might be the rotational orientation of the SiO 4 tetrahedra. As mentioned above, satisfactory coordination of the O atom is most important for the garnet structure and the relationship between the average <M-O> distance and the unit-cell parameter has more excellent linearity than the bond distances of <Al-O> and <Si-O>. Figure 8 shows the polyhedron structural variations across the Alm-Pyr solid solutions. The bond distances of <M-O> and <Al-O> vary linearly with their polyhedron volumes, but the <Si-O> distance exhibits more scatter and deviation from linearity (Table 3). Moreover, SiO 4 tetrahedra with the near-equal <Si-O> distance have different tetrahedra volumes, indicating the distortion of the SiO 4 tetrahedron. The possible reason for this is the substitution of Mg 2+ and Fe 2+ cations in the dodecahedral sites. The smaller ionic radius of Mg 2+ in eightfold coordination (0.89 Å) than that of Fe 2+ (0.92 Å) causes the shorter Mg-O bond length than Fe-O bond length, then causes the distortion of the SiO 4 tetrahedron. Therefore, we consider that the distortion of the SiO 4 tetrahedron is a possible reason leading to excess volume in this study.
Crystals 2019, 9, 541 11 of 18 more excellent linearity than the bond distances of <Al-O> and <Si-O>. Figure 8 shows the polyhedron structural variations across the Alm-Pyr solid solutions. The bond distances of <M-O> and <Al-O> vary linearly with their polyhedron volumes, but the <Si-O> distance exhibits more scatter and deviation from linearity (Table 3). Moreover, SiO4 tetrahedra with the near-equal <Si-O> distance have different tetrahedra volumes, indicating the distortion of the SiO4 tetrahedron. The possible reason for this is the substitution of Mg 2+ and Fe 2+ cations in the dodecahedral sites. The smaller ionic radius of Mg 2+ in eightfold coordination (0.89 Å) than that of Fe 2+ (0.92 Å) causes the shorter Mg-O bond length than Fe-O bond length, then causes the distortion of the SiO4 tetrahedron. Therefore, we consider that the distortion of the SiO4 tetrahedron is a possible reason leading to excess volume in this study.    Figure 9 shows the 9 Raman spectra collected from our Alm-Pyr solid solution series. Raman frequencies of peaks in these spectra and assigned Raman vibration modes are contained in Table 4. The peak positions in our study agree well with those of standard Raman spectra, and can be grouped into three distinct regions: low-frequency region between 167 cm −1 and 375 cm −1 ; medium energy peaks (475-688 cm −1 ); and high energy peaks (759-1060 cm −1 ). The symmetry for the total vibrational modes of garnet calculated by factor group analysis (FGA) is given as follows [26][27][28]:

Characteristics of Raman Spectroscopy
A total of 25 Raman active (3A 1g + 8Eg + 14F 2g ) and 17 infrared-active (17F 1u ) are expected. However, the observed vibrational modes are only 14 modes, which is less than the expected mode, and the peak around 330 cm −1~3 50 cm −1 is mixed by J mode. The observed vibrational modes are grouped into three main regions (Figure 9).  4 )). In addition, the mode at around 210 cm −1 (L) is due to translational motions of SiO 4 (T(SiO 4 )) [29]. The mode at around 168 cm −1 (M) is due to the translation motion of Fe 2+ [30], which appears in the samples with the Alm content higher than 52 mol.% (Figure 9).  Figure 9 shows the 9 Raman spectra collected from our Alm-Pyr solid solution series. Raman frequencies of peaks in these spectra and assigned Raman vibration modes are contained in Table 4. The peak positions in our study agree well with those of standard Raman spectra, and can be grouped into three distinct regions: low-frequency region between 167 cm −1 and 375 cm −1 ; medium energy peaks (475-688 cm −1 ); and high energy peaks (759-1060 cm −1 ). The symmetry for the total vibrational modes of garnet calculated by factor group analysis (FGA) is given as follows [26][27][28]:

Characteristics of Raman Spectroscopy
Γtotal = 3A1g + 5A2g + 8Eg + 14F1g + 14F2g + 5A1μ + 5A2μ + 10Eμ + 18F1μ + 16 F2μ A total of 25 Raman active (3A1g + 8Eg + 14F2g) and 17 infrared-active (17F1u) are expected. However, the observed vibrational modes are only 14 modes, which is less than the expected mode, and the peak around 330 cm −1~3 50 cm −1 is mixed by J mode. The observed vibrational modes are grouped into three main regions (Figure 9)  SiO4)). In addition, the mode at around 210 cm −1 (L) is due to translational motions of SiO4 (T(SiO4)) [29]. The mode at around 168 cm −1 (M) is due to the translation motion of Fe 2+ [30], which appears in the samples with the Alm content higher than 52 mol.% (Figure 9).    [31] and Theodore (2013) [32]. Figure 10 shows plots of different mode frequencies along Alm-Pyr binary. We can see that the Si-O stretching and Si-O bending modes frequencies decrease linearly with the Alm content. The A 1g spectra of the silicate garnets contain three modes around 350 cm −1 , 550 cm −1 and 900 cm −1 , and these modes have the maximum intensities. These selected A 1g mode and E g mode frequencies of SiO 4 translation (T(SiO 4 )) as functions of composition along Alm-Pyr binary are shown in detail in Figure 11. The (Si-O) str modes show stronger dependence on composition than the (Si-O) bend . The Raman mode frequencies of the rotation of the SiO 4 -tetrahedron (R(SiO 4 )) decrease linearly with increasing Alm content, but the translational modes of the SiO 4 -tetrahedron (T(SiO 4 )) increase with increasing Alm content. The variation of the trends is attributed to a coupling between the vibrations of the translational modes of the SiO 4 -tetrahedron and those of the translational modes of the X-site cations [9,29].
Crystals 2019, 9,541 15 of 18 Figure 10 shows plots of different mode frequencies along Alm-Pyr binary. We can see that the Si-O stretching and Si-O bending modes frequencies decrease linearly with the Alm content. The A1g spectra of the silicate garnets contain three modes around 350 cm −1 , 550 cm −1 and 900 cm −1 , and these modes have the maximum intensities. These selected A1g mode and Eg mode frequencies of SiO4 translation (T(SiO4)) as functions of composition along Alm-Pyr binary are shown in detail in Figure  11. The (Si-O)str modes show stronger dependence on composition than the (Si-O)bend. The Raman mode frequencies of the rotation of the SiO4-tetrahedron (R(SiO4)) decrease linearly with increasing Alm content, but the translational modes of the SiO4-tetrahedron (T(SiO4)) increase with increasing Alm content. The variation of the trends is attributed to a coupling between the vibrations of the translational modes of the SiO4-tetrahedron and those of the translational modes of the X-site cations [9,29].

Conclusions
In summary, the crystal-chemical properties of the synthetic Alm-Pyr solid solution were carried out by X-ray single-crystal diffraction and Raman spectroscopy. Our results clearly show that the unit cell constants decrease with increasing Pyr contents (XPyr) in the synthetic Alm-Pyr crystals owing to  Figure 10 shows plots of different mode frequencies along Alm-Pyr binary. We can see that the Si-O stretching and Si-O bending modes frequencies decrease linearly with the Alm content. The A1g spectra of the silicate garnets contain three modes around 350 cm −1 , 550 cm −1 and 900 cm −1 , and these modes have the maximum intensities. These selected A1g mode and Eg mode frequencies of SiO4 translation (T(SiO4)) as functions of composition along Alm-Pyr binary are shown in detail in Figure  11. The (Si-O)str modes show stronger dependence on composition than the (Si-O)bend. The Raman mode frequencies of the rotation of the SiO4-tetrahedron (R(SiO4)) decrease linearly with increasing Alm content, but the translational modes of the SiO4-tetrahedron (T(SiO4)) increase with increasing Alm content. The variation of the trends is attributed to a coupling between the vibrations of the translational modes of the SiO4-tetrahedron and those of the translational modes of the X-site cations [9,29].

Conclusions
In summary, the crystal-chemical properties of the synthetic Alm-Pyr solid solution were carried out by X-ray single-crystal diffraction and Raman spectroscopy. Our results clearly show that the unit cell constants decrease with increasing Pyr contents (XPyr) in the synthetic Alm-Pyr crystals owing to

Conclusions
In summary, the crystal-chemical properties of the synthetic Alm-Pyr solid solution were carried out by X-ray single-crystal diffraction and Raman spectroscopy. Our results clearly show that the unit cell constants decrease with increasing Pyr contents (X Pyr ) in the synthetic Alm-Pyr crystals owing to the smaller ionic radius of Mg 2+ in eightfold coordination (0.89 Å) than that of Fe 2+ (0.92 Å). However, the data show considerably more scatter and positive deviations from ideal volumes of mixing across the Alm-Pyr join that may be caused by the distortion of the SiO 4 tetrahedron. On the other hand, the average <M-O>, <Al-O>, and <D-O> bond distances have a linear correlation with the unit-cell parameter, while the <Si-O> distance has nonlinear correlation. Furthermore, the average <D-O> distance present optimal linear with the unit-cell parameter of all the data and other bond distances show more scatter than that for the average <D-O> distance, which may mean that satisfactory coordination of the O atom is most important for the garnet structure.
In addition, Raman mode frequencies of garnets along the Alm-Pyr solid solution series show the vibrational spectra change with the composition. The Si-O stretching, Si-O bending, and the rotation of the SiO 4 -tetrahedron (R(SiO 4 )) mode frequencies decrease linearly, but the translational mode frequencies of the SiO 4 -tetrahedron (T(SiO 4 )) increase with the Alm content. The variation of the trends is a result of the coupling between the vibration of the translational mode of the SiO 4 -tetrahedron (R(SiO 4 )) mode and that of the translational mode of the X-site cations.