1 Introduction
Silicate garnets constitute a large family of rock-forming minerals that are considered to be a major constituent of the Earth's upper mantle (Bass and Anderson, 1984; Green and Ringwood, 1967). Among mantle garnets, Cr-rich garnets are less common minerals that form in mafic and ultramafic rocks that have undergone metasomatic reactions at relatively low temperature and pressure (Challis et al., 1995; Mogessie and Rammlmair, 1994; Proenza et al., 1999). However, geological and petrological studies have demonstrated that the chromium concentration in garnet increases with depth, along with the spinel-garnet transformation up to 7 GPa (Klemme, 2004), which has important implications for the geobarometry of rock samples returned from the deep mantle (Grutter et al., 2006). Despite constituting a minor fraction of mantle garnets, Cr-garnet might become more important at the bottom of the upper mantle when Cr-rich spinel decomposes through metasomatic reactions. Therefore, knowledge of the elasticity of Cr-garnet is important to estimate the effect of Cr3+ incorporation on the physical properties of mantle garnets and its possible implications for the interpretation of deep-Earth structures.
Mantle garnets form complex non-ideal solid solutions, whose physical properties may change as a function of pressure, temperature and chemical composition. The structure of silicate garnets consists of a mixed framework of corner-sharing SiO4 tetrahedra and YO6 octahedra, with twisted XO8 cubes lying in between. In natural garnet the X-site is exclusively occupied by divalent cations (Mg2+, Fe2+, Ca2+, Mn2+), whereas the Y-site normally hosts trivalent cations (Al3+, Fe3+, Cr3+) (Deer et al., 1962). The variety of the garnet chemistry makes it difficult to establish a relation between chemical composition and elasticity by a direct study at high pressure and temperature. For this reason, previous studies have been investigating the elasticity of garnet endmembers at high P and T (among many others, Bass, 1989; Conrad et al., 1999; Gréaux and Yamada, 2013; Gréaux et al., 2010; Pavese et al., 2001; Sinogeikin and Bass, 2002; Zou et al., 2012b), from which they derived the elasticity of more complex solid solutions.
In the Earth's mantle, Ca3Cr2Si3O12 uvarovite and Mg3Cr2Si3O12 knorringite are of the most relevant Cr-garnet endmembers and are commonly found in xenoliths and inclusions in diamonds from the deep mantle (Deer et al., 1962; Irifune et al., 1982; Klemme, 2004). Uvarovite garnet was reported to be stable in a wide range of pressures and temperatures, and hence is found in various metamorphic rocks in the form of aggregates of tiny crystals that usually contain significant amounts of grossular and andradite (Deer et al., 1962). On the other hand, phase relation and stability of knorringite, despite remaining controversial (Klemme, 2004; Zou and Irifune, 2012), suggested that this endmember may not be stable in upper mantle conditions. Therefore, uvarovite garnet might be the most relevant Cr-garnet endmember to investigate the effect of Cr3+ incorporation on the physical properties of silicate garnets in upper mantle conditions.
The elasticity of uvarovite garnet was formerly studied by Brillouin spectroscopy on single crystals at room conditions (see Bass, 1986, and references therein). Subsequently, experiments at high pressure and room temperature were conducted to investigate the elasticity of natural and synthetic uvarovite specimens (Bass, 1986; Diella et al., 2004; Léger et al., 1990>). Léger et al. (1990) reported the isothermal compressibility of a polycrystalline aggregate at 300 K by using a diamond anvil cell (DAC) and proposed the first pressure derivative K’ = 4.7 assuming the bulk modulus K0 = 162 GPa given by Bass (1986). More recent experiments on the basis of in situ X-ray measurements in a laser-heated diamond anvil cell up to 16.2 GPa and 900 K (Fan et al., 2015) reported K0 = 162 GPa and K’ = 4.0–4.5 and the thermal expansion α0 = 2.72 × 10−5 K−1, which is slightly larger than α0 = 2.15 × 10−5 K−1 proposed by lattice energy and vibrational energy calculations (Ottonello et al., 1996).
Here we investigated the pressure–volume–temperature relation of a synthetic uvarovite garnet Ca3Cr2Si3O12 up to 12.7 GPa and 1100 K using a multi-anvil apparatus combined with synchrotron Energy-Dispersive X-Ray Diffraction (EDXRD) measurements at the beamline AR-NE5 C (KEK-Photon Factory, Japan). The use of a large-volume apparatus allowed for precise control of pressure and temperature, while energy-dispersive X-ray diffraction (EDXRD) measurements were carried out in situ at high pressures and temperatures up to 12.7 GPa and 1100 K. Thermoelastic properties of uvarovite garnet were derived using the high-temperature equation of state (EoS). Results are discussed relative to other garnet endmembers and garnet solid solutions to estimate the effect of Cr3+ on the density of mantle garnets in P and T conditions of the upper mantle.
2 Material and methods
Starting materials were prepared as a mechanical mixture of reagent-grade oxides in the molar proportions: 3CaCO3·1Cr2O3·3SiO2. The mixture was placed ∼20 h at 1173 K to remove carbonate and then hot-pressed at ∼7 GPa and 1673 K for 2 h using a Kawai-type multi-anvil press apparatus ORANGE2000 at the Geodynamics Research Center (Ehime University, Matsuyama, Japan). The recovered sample was sintered and consisted mainly of uvarovite garnet, with minor amounts of Cr2O3 and CaO from the starting material. The chemical composition of the uvarovite garnet was analyzed by a Field-Emission Scanning Electron Microscope (FE-SEM) equipped with an Energy-Dispersive X-ray Spectrometer (EDS), which yielded the composition (in wt% with standard deviation in parentheses): CaO, 33.8(1); Cr2O3, 30.9(1); SiO2, 35.5(1); i.e. Ca3.02Cr2.04Si2.96O12 on the basis of 12 oxygens. Micro-focused X-ray diffraction analysis of the sample yielded a0 = 12.002 ± 0.002 Å, which is compatible with previous reports that scatter within 11.988–12.010 Å (Andrut and Wildner, 2002; Bass, 1986; Léger et al., 1990; Novak and Gibbs, 1971).
High-pressure and high-temperature in situ experiments were carried out in a DIA-type multi-anvil press apparatus, MAX-80, located at the beamline AR-NE5 C of KEK-Photon Factory (Tsukuba Pref., Japan). High pressure was generated within what is called a 6-6-type cell assembly (Nishiyama et al., 2008) adapted for 4.0-mm truncation edge-length tungsten carbide anvils. The cell assembly consisted of a boron epoxy cubic pressure medium with a side length of 7.0 mm, a cylindrical graphite heater contained in a ZrO2 insulator (Fig. 1), to reduce temperature gradients in the cell assembly. Pressure was estimated using the equation of state (EoS) of gold (Tsuchiya, 2003), which was mixed with MgO at a ratio of 10:1 (in wt.%) and placed near the hot junction of a W97Re3-W75Re25 thermocouple that was used to monitor temperature. The sample and pressure marker were surrounded by MgO to ensure a pseudo hydrostatic environment.
![](/geoscience/article/CRGEOS_2019__351_2-3_95_0/jpg/src/tex/figures/gr1.jpg)
Experimental cell assembly.
First, the sample is pressurized to 5.1 GPa and heated to 900 K. Temperature was maintained at 900 K for about 30 min to reduce non-hydrostatic stresses that can develop during cold compression. EDXRD measurements were carried out upon decrease of temperature to 300 K in steps of 200 K. All measurements in a given cooling cycle were done over a total duration of about 1 h. The heating/collecting data procedure was repeated after each increment of pressure to 5.8, 7.8, 11.5, and 12.7 GPa, respectively. Further details about the procedures of the high-pressure and high-temperature measurements can be found in Gréaux and Yamada (2013).
All EDXRD patterns were collected at a fixed diffraction angle of ∼6 degrees, which was calibrated on the basis of the diffraction pattern of gold at zero pressure; this method yielded an estimated error of 0.08 GPa in room conditions. Analyses of all XRD patterns were carried out by means of multi-peak fitting technique as implemented in the PDIndexer software package (Seto et al., 2010). XRD patterns of the pressure marker at high P and T were collected in between the hot-junction of the thermocouple and the sample (Fig. 1), while XRD patterns of the sample were collected at the closest location to the sample/pressure marker interface. The temperature gradient between the thermocouple hot-junction and the sample was estimated to be about ± 25 K at 500 K and ± 40 K at 1100 K, on the basis of the two EoS of gold (Tsuchiya, 2003) and MgO (Tange et al., 2009) in the pressure marker. The precision upon the pressure was estimated from the uncertainties on the unit-cell volume of gold propagated to the pressure through the EoS of gold (Tsuchiya, 2003). The unit-cell volume of the uvarovite garnet and the corresponding pressure (Au-scale) and temperature are given in Table 1.
Experimental pressure, temperature and volume of uvarovite garnet.
Pressure (GPa) | Temperature (K) | Volume (Å3) | Pressure (GPa) | Temperature (K) | Volume (Å3) |
0a | 300 | 1735.8(1) | 7.32(4) | 700 | 1680.0(5) |
5.44(5) | 900 | 1704.6(15) | 6.97(4) | 500 | 1675.1(6) |
4.89(5) | 700 | 1703.3(12) | 6.70(4) | 300 | 1672.0(8) |
4.43(5) | 500 | 1699.7(11) | 11.55(4) | 1100 | 1656.6(7) |
4.27(5) | 300 | 1693.7(8) | 10.97(4) | 900 | 1655.4(7) |
6.50(5) | 900 | 1694.3(8) | 10.53(4) | 700 | 1652.3(9) |
5.95(4) | 700 | 1692.0(8) | 10.08(4) | 500 | 1649.6(8) |
5.49(4) | 500 | 1689.1(8) | 9.86(4) | 300 | 1635.9(7) |
5.12(5) | 300 | 1685.3(10) | 13.08(5) | 1100 | 1644.5(6) |
8.43(4) | 1100 | 1684.1(9) | 10.97(6) | 300 | 1635.9(7) |
7.81(4) | 900 | 1682.7(8) | 0.94(3) | 300 | 1726.0(2) |
a XRD pattern collected before compression.
Fig. 2 shows the analysis results of the recovered sample. The ambient condition XRD profile is mainly explained by the diffraction peaks of the uvarovite garnet with minor peaks corresponding to excess Cr2O3 eskolaite, CaO lime from the starting material and two unidentified peaks (Fig. 2a). The FE-SEM observations of the recovered sample shows uvarovite garnet and minor amounts of Cr2O3 and CaO (Fig. 2b). No other phase was found in the sample. SEM-EDS analysis of the recovered sample yielded the composition CaO, 33.7(2); Cr2O3, 30.6(4); SiO2, 35.7(2); i.e. Ca3.01Cr2.02Si2.98O12, which is close to the composition of the starting material, suggesting that no reaction occurred between the garnet sample and surrounding materials during P–V–T measurements.
![](/geoscience/article/CRGEOS_2019__351_2-3_95_0/jpg/src/tex/figures/gr2.jpg)
X-ray diffraction (XRD) pattern and scanning electron microscope (SEM) backscattered electron image of the recovered uvarovite sample. The XRD pattern could be explained by uvarovite garnet (Uva), eskolaite (Esk), lime (Lim) and two unidentified peaks (a). SEM observations of the sample showed mainly uvarovite garnet with minor amounts of Cr2O3 (Esk) and CaO (Lim) from the starting material (b). No other phase was found in the sample.
3 Results and discussion
3.1 Pressure–volume data at room temperature
The volume–pressure data relations have been determined by a least-square fitting of room-T data (Table 1) to the third-order Birch–Murnaghan (BM) equation of state whose general form is as follows:
(1) |
where K0, K’0, and V0 are the isothermal bulk modulus, its pressure derivative, and the zero-pressure unit-cell volume, respectively. Fitting of all parameters simultaneously using 300-K data collected at the end of each heating cycle, however, yielded large uncertainties (K0 = 166.2 ± 2.4 GPa, K’0 = 3.6 ± 0.4, and V0 = 1735.7 ± 0.3 Å3), suggesting that all parameters cannot be resolved simultaneously due to the limited pressure range in this study. Therefore, we chose to fix the pressure derivative K’0 at 4 here, which is compatible with the slightly positive slope of the normalized pressure against the Eulerian strain (inset of Fig. 3) that indicates a value of K’0 ≥ 4 (Angel, 2000). Fitting of equation (1) with K’0 fixed at 4 yielded the bulk modulus K0 = 164.2 ± 0.7 GPa, which is in excellent agreement with K0 = 164 ± 1 GPa (K’0 = 4) proposed by Fan et al. (2015) on the basis of angle-dispersive XRD in the diamond-anvil cell. Another fitting of equation (1) with K’0 fixed at 4.5 gave K0 = 161.6 ± 0.9 GPa (V0 = 1736.1 ± 0.3 Å3), which is also in good agreement with K0 = 162 ± 2 GPa, K’0 = 4.5 ± 0.3 derived by Fan et al. (2015) when they refined all parameters simultaneously (Table 2). The agreement on the results of elastic parameters and the small offset between data sets (Fig. 3), despite using two different techniques, suggests limited experimental uncertainties in our study and that of Fan et al. (2015).
![](/geoscience/article/CRGEOS_2019__351_2-3_95_0/jpg/src/tex/figures/gr3.jpg)
Pressure–volume data of uvarovite garnet obtained in this study (plain circle), compared with the former experimental studies of Léger et al. (2000, open triangles) and Fan et al. (2015, open circle), while the broken line represents the uvarovite compression curve derived from theoretical calculations (Milman et al., 2001). Cross symbols represent data obtained by Diella et al. (2004) for a natural uvarovite-grossular garnet. Fitting of our P–V data (solid line) by a third-order Birch–Murnaghan equation of state fit yielded K0,300 = 165.0 ± 2.6 GPa, K’0,300 = 4.0 ± 0.4 and V0,300 = 1735.8 ± 0.4 Å3. Error bars on the pressure and volume measurements are within the size of the symbols. Inset in the figure shows the normalized pressure versus the Eulerian strain plot based on the Birch–Murnaghan EoS at 300 K, where the solid line represents the linear fit through the data.
Elasticity of uvarovite at 300 K.
K0,300 (GPa) | K’ 0,300 | V0,300 (Å3) | Reference | Methods |
166.2 (24) | 3.6 (4) | 1735.7 (3) | This study | XRD-LVP |
164.2 (7) | 4.0a | 1735.9 (3) | ||
161.6 (9) | 4.5a | 1736.1 (3) | ||
160.6 (10) | 4.7a | 1736.2 (4) | ||
162.1 (19) | 4.3 (3) | 1736.5 (4) | This study + Fan et al. (2015) | |
162 (2) | – | 1726.7 | Bass (1986) | BS |
162a | 4.7 (7) | 1732.3a | Leger et al. (1990) | XRD-DAC |
160 (1) | 5.8 (1) | 1697.5 | Diella et al. (2004) | XRD-DAC |
164.8 (22) | 4.7 (9) | 1731.5 | Wang and Ji (2001) | US-PC |
143 | 4.7 | 1737.1 | Milman et al. (2001) | Ab initio Calc. |
164 (1) | 4.0a | 1736.5 (3) | Fan et al. (2015) | XRD-DAC |
162 (2) | 4.5 (3) | 1736.9 (5) |
a Fixed during fitting.
When we fixed K’0 at 4.7, we obtained a smaller K0 = 160.6 ± 1.0 GPa, which, within the uncertainties, is also in agreement with the values of K0 = 162 and K’0 = 4.7 proposed by Léger et al. (1990). Our results show that it is difficult to determine a unique K0/K’0 tradeoff for uvarovite garnet. This can be explained by the lack of constraints on the first pressure derivative K’0, which is partly due to the limited pressure range addressed in all studies, respectively. One alternative way to determine the most appropriate set of moduli and derivatives would be to fit all available data simultaneously. We noted, however, that although below 10 GPa, the original P–V data of Léger et al. (1990) agree well with our data (Fig. 3), volumes at P higher than 10 GPa are larger, which is likely caused by anisotropic stress above 10 GPa due to the solidification of their methanol/ethanol pressure-transmitting medium (Léger et al., 1990), and therefore we excluded those data from the global fitting. The resulting elastic parameters K0 = 162.1 ± 1.9 GPa, K’0 = 4.3 ± 0.3 and V0 = 1736.5 ± 0.4 Å3 agree well, within uncertainties, with our data and those of Fan et al. (2015).
It is worth noting that none of the parameters fitted here can explain the correlation between bulk modulus and its pressure derivatives for natural uvarovite samples (Diella et al., 2004; Wang and Ji, 2001), suggesting the Cr3+/Al3+ ratio would have a substantial effect on the compressibility of those silicate garnets, which will be discussed a few sections below. Moreover, we cannot explain the low bulk modulus K0 = 143 ± 4 GPa for K’0 = 4.7 proposed by Milman et al. (2001) based on an ab initio calculation by the density functional theory within the generalized gradient approximation. It is, however, difficult to draw any conclusion, because their calculations did not take into account the possibility of a Jahn–Teller effect that is expected to affect the compressibility of minerals containing octahedrally coordinated transition metals (Bass and Weidner, 1984; Pacalo et al., 1992; Zhang et al., 1998).
3.2 P–V–T data and thermoelastic parameters
Fitting of the pressure–volume–temperature data was carried out by a modified third-order Birch–Murnagham equation of state with the following form:
(2) |
In this equation, the thermal dependences of the zero-pressure volume V0,T and bulk modulus K0,T are expressed using the following equations:
(3) |
(4) |
where V0,300 is the volume at room-P,T, and α0,T, the thermal expansion, which is empirically assumed to be α0,T = a0 + b0T, Eq. (3). K0,T is expressed as a linear function of temperature, its first temperature derivative (∂K0,T/∂T)P and the zero-pressure bulk modulus K0,300, Eq. (4). Here we assumed that K’0 is constant with temperature.
Fitting of our P–V–T data with all parameters simultaneously gave the following thermoelastic properties: K0,300 = 163.6 ± 2.6 GPa, K’0 = 4.1 ± 0.5, V0 = 1735.9 ± 0.4 Å3, (∂K0,T/∂T)P = –0.014 ± 0.004 GPa K−1, a0 = 2.32 ± 0.13 × 10−5 K−1, b0 = 2.13 ± 2.18 × 10−9 K−2 (e.g., α0,300 = 2.37 ± 0.20 × 10−5 K−1). The bulk modulus K0,300 and its pressure derivative determined here are consistent with our fitting of P–V data at 300 K. It is also in good agreement with K0,300 = 162 GPa and K’0 = 4.3, derived from Fan et al.’s (2015) P–V–T data. However, we found that their temperature derivative (∂K0,T/∂T)P = −0.021 GPa K−1 is ∼30% smaller than our present value, while their thermal expansion α0,300 = 2.72 × 10−5 K−1 is about ∼15% larger than our α0,300 (Table 3), which is in closer agreement with the theoretical value α0 = 2.15 × 10−5 K−1 proposed by Ottonello et al. (1996) based on lattice energy and vibrational energy calculations. The thermal gradient in our cell (see experimental methods) is likely to affect the result of our EoS fitting by ∼0.8% for KT and ∼4% for the thermal expansion, but these variations are smaller than the differences between our EoS data and those of Fan et al. (2015), and therefore cannot explain the different thermal parameters for the two studies. Although our room temperatures are in good agreement with those of Fan et al. (2015), our study suggests that unconstrained uncertainties in the data collected at high temperature might still remain between the multi-anvil-apparatus and the diamond-anvil cell, an issue that should be addressed in future experiments.
Thermoleastic parameters of uvarovite garnet compared to other ugrandite garnets.
V 0,300 | K0,300 (GPa) | K’ 0,300 | (∂K0,T/∂T)P (GPa K−1) | α0,300 (10−5 K−1) | |
Uvarovite | |||||
This study | 1735.9 (3) | 164.0 (8) | 4.0a | −0.014 (2) | 2.36(17) |
1735.9 (4) | 163.6 (26) | 4.1 (5) | −0.014 (4) | 2.37(20) | |
1736.2 (3) | 161.5 (8) | 4.5a | −0.017 (2) | 2.45(18) | |
Fan et al. (2015) | 1736.6 (6) | 164 (1) | 4.0a | −0.018 (4) | 2.69(12) |
1736.8 (8) | 162 (3) | 4.3 (4) | −0.021 (4) | 2.72(14) | |
1737.0 (6) | 161 (1) | 4.5a | −0.022 (4) | 2.76(13) | |
This study + Fan et al. (2015) | 1736.7 (6) | 161.0 (28) | 4.5 (4) | −0.018 (3) | 2.63(11) |
Grossular | |||||
Milman et al. (2001) | 1667 | 166 | 4.3 | – | – |
Gréaux et al. (2010) | 1664a | 166a | 4.0 (1) | −0.019 (1) | 2.74(23) |
Gwanmesia et al. (2013) | 1662.1 (3) | 169.7 (8) | 4.47 (1) | – | – |
Andradite | |||||
Milman et al. (2001) | 1753.2 | 147 | 4.4 | – | – |
Pavese et al. (2001) | 1753.9 (5) | 158 (2) | 4.0a | −0.017 (9) | 3.17(6) |
Jiang et al. (2004) | – | 154.5 (6) | 4.7 (1) | – | – |
Goldmanite | |||||
Milman et al. (2001) | 1762.8 | 139 | 4.7 | – | – |
a Fixed during fitting.
Fitting of Eqs. (2)–(4) by fixing the first pressure derivative resulted in variations of K0 and V0 (Table 3), due to the strong correlation between K0 and K’. In contrast, the thermal properties (∂K0,T/∂T)P and α0,300 did not change in a significant manner, indicating that the thermal properties of uvarovite are either less affected or unaffected by the variation of the bulk modulus and of its pressure derivative. A similar conclusion was reached by other experimental studies on the elasticity of silicate garnets (Fan et al., 2015; Gréaux and Yamada, 2013; Zou et al., 2012a). Fitting of all available data from our study and that of Fan et al. (2015) gave the following parameters: K0,300 = 161.0 ± 2.8 GPa, K’0 = 4.5 ± 0.4, V0 = 1736.7 ± 0.6 Å3, (∂K0,T/∂T)P = –0.018 ± 0.003 GPa K−1, α0,300 = 2.63 ± 0.11 × 10−5 K−1 (Fig. 4). The temperature derivative of the bulk modulus (∂K0,T/∂T)P is similar to those of grossular and andradite in previous studies (Gréaux et al., 2010; Pavese et al., 2001), suggesting that the values of (∂K0,T/∂T)P of ugrandite garnets are independent of the 3+ cations in the garnet octahedral site. The thermal expansion coefficient α0 = 2.40–2.53 × 10−5 K−1 is smaller than that of grossular (Gréaux et al., 2010) and andradite (Pavese et al., 2001), although the difference between uvarovite and grossular fall within their respective uncertainties. Besides, the higher value proposed for andradite could have resulted from the use of a different expression for the thermal parameters in the EoS as Pavese et al. (2001) expressed α = cste instead of α = a0 + b0T used in the present study and Gréaux et al. (2010).
![](/geoscience/article/CRGEOS_2019__351_2-3_95_0/jpg/src/tex/figures/gr4.jpg)
Unit-cell volume of uvarovite garnet as a function of pressure and temperature. Data at 300 K (plain circle), 500 K (open circle), 700 K (plain square), 900 K (open triangle), and 1100 K (plain diamond) are represented respectively. Large symbols represent our data, while small symbols are from Fan et al. (2015). For all our data, pressure and volume error bars are within the size of the symbols. Solid lines represent the isothermal compression curves obtained from fitting all the data to a Birch–Murnaghan EoS.
4 Discussion
4.1 Comparison with other garnets of the ugrandite group
The ugrandite is a family of isostructural garnets with the formula Ca3Y2Si3O12, where the Y-site is commonly occupied either by Al (grossular), Fe (andradite), Cr (uvarovite), or V (goldmanite). The bulk moduli K0 = 162–165 GPa determined in this study showed that the compressibility of uvarovite is in between that of andradite (K0 = 154–158 GPa) (Jiang et al., 2004; Pavese et al., 2001) and grossular (K0 = 166–171.5 GPa) (Gréaux et al., 2010; Gwanmesia et al., 2013), although differences in K0 depend on the value of K’ adopted in the respective studies. In their study, Fan et al. (2015) neglected this aspect when they proposed representing the bulk modulus of ugrandite garnet as a linear function of the unit-cell volume. The validity of such a relation can be tested by using the derived elastic properties to calculate the compression curve of a garnet solid solution and comparing the result to actual data.
Fig. 5 shows the calculated densities of a grossular/uvarovite solid solution compared with the experimental study of Diella et al. (2004), who reported the compressibility of a natural garnet sample containing ∼62 mol% of uvarovite using a diamond- anvil cell and synchrotron X-ray diffraction. The density of the garnet solid solution was estimated from a weighted summation of the individual elastic properties of the corresponding end members (e.g., Pamato et al., 2016). In this approach we assumed that elastic properties vary linearly as a function of the endmember proportions in the solid solution. The calculated densities are in relatively good agreement with experimental data, while both experimental and theoretical datasets stand in between the densities of the uvarovite (this study) and grossular (Gréaux et al., 2010) endmembers. The experimental densities of Diella et al. (2004) are generally smaller than those of uvarovite (Fig. 3), which can be explained by the smaller unit-cell volume of grossular (∼1662–1664 Å3) compared to that of uvarovite (∼1727–1738 Å3). We noted, however, that when using garnet endmember proportions as given by their electron probe analyses (Fig. 5, Uv62Gr33+), the calculated densities are slightly lower than the experimental data. Instead, we found a better agreement between the weighted average and experimental data (Diella et al., 2004) when we used the endmember proportions (in mol%): 65% uvarovite, 30% grossular, 2% pyrope, 1% almandine, 1% spessartine, and 1% andradite (Fig. 5, Uv65Gr30+). The amount of uvarovite that we propose here is slightly higher than the value measured with an electron probe; this difference could be derived from unconstrained uncertainties in our respective experiments. On the other hand, we can see in Fig. 5 that density calculated using Fan et al.’s (2015) linear model fits well with Diella et al.’s (2004) data at low pressure, but fails to explain densities at pressures higher than ∼5 GPa, which is likely due to their higher K’ values, as discussed above.
![](/geoscience/article/CRGEOS_2019__351_2-3_95_0/jpg/src/tex/figures/gr5.jpg)
Experimental and calculated densities of natural uvarovite-rich garnet. Open circles represent the experimental data of Diella et al. (2004), while the purple solid lines represent our calculated densities for the composition 62% uvarovite, 33% grossular, 5% spessartine and 1% andradite (Uva62Gro33+, light purple) and 65% uvarovite, 30% grossular, 2% pyrope, 1% almandine, 1% spessartine, and 1% andradite (Uva65Gro30+, dark purple). The broken line represents the same calculation for Uva65Gro30+ using the elastic parameters of Fan et al. (2015). The density curve of grossular (blue line), uvarovite (red line) and andradite (green line) ugrandite garnet endmembers are shown for comparison.
Such features could be explained based on the crystal structure of silicate garnets. The cubic garnet structure consists of large dodecahedral sites, which share edges with corner-linked chains of alternating SiO4 tetrahedra and YO6 octahedra, and with each other (Novak, 1971). Previous theoretical studies have demonstrated that the size of the dodecahedral cation likely controls the variations in the elasticity of silicate garnets with Al and Si in the octahedral site (Milman et al., 2000; Pacalo et al., 1992). However, there is no firm explanation for the lower values observed for garnets with transition metals in the octahedral site such as andradite and uvarovite garnets. In addition, the dodecahedral cavity of ugrandite garnet is filled with a large Ca2+ cation, so the rotational freedom within the corner-linked chains is limited, resulting in the structure becoming more rigid compared to other garnet groups (Milman et al., 2000; Pacalo et al., 1992). Based on the similarities in site occupancies, it is therefore likely that the characteristics of the trivalent cation and the resulting compressibility of the octahedral site might play a major role in controlling the variations of elasticity between ugrandite garnets. Our results go in that direction, showing that ugrandite garnets with a small octahedral site (e.g., grossular) have higher bulk modulus than garnets with a larger octahedral site (e.g., uvarovite, andradite). It is compatible with former studies in pyroxenes, olivines, and spinels, which showed that transition metals in octahedral coordination tend to decrease the elastic moduli of those minerals (Bass and Weidner, 1984; Pacalo et al., 1992; Zhang et al., 1998). Our results also suggest that ugrandite garnet with transition metals in the octahedral site (e.g., uvarovite, andradite) might become more incompressible upon increasing pressure, hence yielding higher K’ than garnet with Al in the octahedral site. It is, however, difficult to come to a firm conclusion about the K’ value of silicate garnets, as experimental values generally fall between 4 and 5 (Gwanmesia et al., 2006; Kono et al., 2010; Zou et al., 2012b) with differences between species barely standing outside of their respective uncertainties.
4.2 Implications for the density of the upper mantle
Petrological studies of minerals in kimberlite and alkali basalts that returned from the deep mantle revealed that the upper mantle is largely constituted of aluminous lherzolite. It is also known that lherzolite undergoes an important transition from spinel lherzolite to garnet lherzolite at high pressures between ∼2 GPa and ∼7 GPa, which strongly depends on the Cr/(Cr + Al) ratio of the system (Klemme, 2004). In this reaction, Cr and Ca increasingly substitute into the garnet with increasing pressure, resulting in an increase in the grossular and uvarovite components of mantle garnets. Using our elasticity data on uvarovite, combined with those of other garnet endmembers, we estimated the density variation in garnet lherzolite as a function of depth along an average mantle geotherm. Here we postulated that Cr is only present through the uvarovite endmember, assuming that the knorringite component may be minor at the pressures and temperatures of the upper mantle, although its proportions might increase with increasing pressure (Zou and Irifune, 2012). Either way, it is difficult to implement this parameter in our model, as the precise thermoelastic data of pure knorringite garnet are unavailable to this day.
Fig. 6 shows the calculated density profiles of simplified mantle garnets with the following compositions: 75% pyrope and 25% grossular (Py75Gr25), and 75% pyrope and 25% uvarovite (Py75Uva25), compared to those of pyrope, which is the major component of upper-mantle garnets. It is interesting to note that densities of Py75Gr25 are only ∼0.5% higher than those of pyrope, suggesting that mantle garnet may not be sensitive to variations of the grossular component; e.g., Cr/(Cr + Al) = 0. In contrast, we found a more substantial ∼2% density increase when incorporating the uvarovite component (Py75Uva25); e.g., Cr/(Cr + Al) = 1. Garnet compositions in lherzolite xenoliths from alkali basalts and kimberlites generally yield a Cr/(Cr + Al) < 0.2–0.35 (Grutter et al., 2006), which would correspond to a ∼1% density increase compared to the pyrope endmember. Higher Cr/(Cr + Al) ratios > 0.5 are reported in chromite-saturated harzburgite garnets, but those compositions are Ca-depleted, implying the formation of a knorringite-rich pyrope garnet, for which our model is non-applicable. It should also be mentioned that lherzolite garnets bear a substantial amount of Fe, although its exact chemical behavior is not well known. If we consider only Fe2+ as the main garnet species (Py75Alm25, Fig. 6), density increases drastically due to the high density of the almandine endmember. In contrast, the presence of Fe3+ would decrease density compared to Py75Alm25 due to the lower density of the andradite endmember, which is almost the same as that of uvarovite. However, the increase of andradite garnet along with the presence of Fe3+ would be incompatible with the relatively low Ca contents of garnet lherzolite (McDonough and Rudnick, 1998), suggesting that Fe2+ might be the main species in natural systems. Fig. 6 shows that high Fe2+ content is more likely to affect the bulk density of mantle garnet rather than the incorporation of Cr3+. However, because Cr3+ and Fe3+ are positively correlated in upper mantle garnets (e.g., Canil and O’Neill, 1996; Nimis et al., 2015), the presence of the Cr-rich component might also favor the formation of Fe3+, hence resulting in a decrease of the mantle garnet density. Our results emphasize that the mantle garnet density could vary substantially upon Cr/(Cr + Al) increase, which seems to occur at upper mantle depths, as Cr-rich garnets are commonly found in diamond inclusions.
![](/geoscience/article/CRGEOS_2019__351_2-3_95_0/jpg/src/tex/figures/gr6.jpg)
Model densities of mantle garnet solid solutions as a function of depth. The blue line represents densities of pyrope (i.e. Cr-free) from what we increased grossular (Py75Gr25, purple line), uvarovite (Py75Uva25, pink line) and almandine (Py75Alm25, red line) proportions respectively. The broken line represents the calculated density of a lherzolite garnet based on the chemical analyses of a fertile peridotite garnet brought up by alkali basalts (McDonough and Rudnick, 1998), which yielded the following composition: 75% pyrope, 13% almandine, 9% pyrope, 4% uvarovite, and 1% andradite.
The density of a natural garnet lherzolite was estimated based on the elasticity of garnet endmembers and the chemical analyses of a fertile peridotite garnet brought up by alkali basalts (McDonough and Rudnick, 1998); it yielded the following: 75% pyrope, 13% almandine, 9% grossular, 4% uvarovite and 1% andradite. Our estimates show that the density of garnet lherzolite would be ∼2.5% higher compared to the Cr- and Fe-free Py75Gr25 garnet (Fig. 6), which may have some implications for the seismic discontinuity at depths of 50–100 km. This discontinuity has been observed globally, but the depth is not the same everywhere (Hales, 1969; Yamasaki and Nakada, 1997); a difference that is attributed to the shift of the spinel-garnet phase boundary from ∼2 GPa in Al-rich fertile mantle compositions to ∼7 GPa in the deeper continental crust (Klemme, 2004; Klemme and O’Neill, 2000), where Al is depleted and Cr and Fe are more abundant, as a possible consequence of melting events (Walter et al., 2002). The higher density of Cr- and Fe-rich garnets further emphasizes the importance of the spinel-garnet transition and offers an alternative to thermal anomalies in order to explain the increase in seismic velocity at depths of ∼100 km (Hales, 1969; Yamasaki and Nakada, 1997). These conclusions, however, would need to be completed by the contribution of the knorringite garnet endmember, which is likely to change such behavior at higher pressure and high Cr/(Cr + Al) ratios.
5 Conclusion
In the present study, we investigated the elasticity of uvarovite garnet as a function of pressure and temperature up to 13 GPa and 1100 K, using the multi-anvil apparatus combined with in situ synchrotron X-ray diffraction. The results are generally in good agreement with a recent study that used the laser heated diamond anvil cell up to 16 GPa and 900 K, although our results suggest slightly milder pressure and temperature dependences of the bulk modulus. The present data are compatible with the compressibility of grossular/uvarovite specimens, such as what is found in natural systems. The present results highlight the effect of 3+ cations substitution on the thermoelasticity of garnets and call for more systematic studies on other ugrandite end-members (e.g., andradite, goldmanite) at simultaneous high pressure and high temperature. Based on a comparison with the elasticity of other garnet endmembers, we proposed that the incorporation of Cr3+ and Fe3+ in the Y-site of the garnet structure is likely to increase the density of ugrandite garnets, resulting in a substantial increase of density in regions where Cr-rich spinel releases chromium in the garnet through metasomatic reactions. Further constraints on the other silicate garnet end-members at high pressure and high temperature will be particularly valuable to understand the behavior of mantle garnets at high P and T, since they usually display relatively complex compositions in a natural environment.
Acknowledgments
The synchrotron radiation experiments performed at AR-NE5 C have been done with the approval of the KEK (2011G065). Authors are thankful to X. Wang for fruitful discussions. The authors acknowledge two anonymous reviewers for constructive comments. This work was partly supported by the Global-COE program “Deep Earth Mineralogy”.