Introduction

Majoritic garnet is a major constituent mineral in the Earth’s mantle transition zone depths of 410–660 km along with wadsleyite and ringwoodite (Ringwood and Major 1971; Akaogi and Akimoto 1977; Irifune and Ringwood 1987). It was firstly synthesized at high pressure by Ringwood and Major (Ringwood and Major 1971) and subsequently identified in Catherwood meteorites (Coleman 1977; Mao et al. 1982) and diamond inclusions in mantle-derived xenoliths (Moore and Gurney 1985; Meyer 1987). Petrological studies have demonstrated that majoritic garnet is the most abundant mineral in basaltic layers of subducted lithosphere in the mantle transition zone depths (Irifune et al. 1986; Irifune and Ringwood 1993; Hirose et al. 1999; Ono et al. 2001). Accordingly, the physical properties of majoritic garnet are indispensable for constraining the mineralogical models of the mantle transition zone.

Previous studies have demonstrated that the simplified system Mg4Si4O12 (majorite)–Mg3Al2Si3O12 (pyrope) is the most relevant and dominant solid system in the mantle transition zone (Irifune and Ringwood 1987, 1993; Irifune et al. 1996; Gasparik 1990, 1992; Kubo and Akaogi 2000; Akaogi et al. 2002). However, the elastic properties of majoritic garnets along the majorite–pyrope system investigated by earlier Brillouin scattering (Bass and Kanzaki 1990; Yeganeh-Haeri et al. 1990; Pacalo and Weidner 1997; Sinogeikin et al. 1997, Sinogeikin and Bass 2002a, b) and ultrasonic interferometry (Rigden et al. 1994; Liu et al. 2000; Gwanmesia et al. 2006, 2009; Zou et al. 2012) were largely scattered; for example, the pressure derivatives of the elastic moduli ranged from 3.2 to 6.7 and 1.0 to 2.1 for K Sʹ and Gʹ, respectively. The high sound velocity gradients, characteristic of this region (Bass and Anderson 1984; Sinogeikin and Bass 2002a), may be caused by the unusually high-pressure derivatives of the elastic moduli of the majoritic garnets in this solid system (Gwanmesia et al. 1998; Kavner et al. 2000; Liu et al. 2000). The discrepancies on the elastic properties of the majoritic garnets in this system have impeded to interpret the seismic velocity profile of the mantle transition zone.

In addition, these earlier studies were performed at ambient conditions (Bass and Kanzaki 1990; Yeganeh-Haeri et al. 1990; Pacalo and Weidner 1997; Sinogeikin et al. 1997; Gwanmesia et al. 2000), high pressures at room temperature (Sinogeikin and Bass 2002a; Liu et al. 2000) or high temperatures at room pressure (Sinogeikin and Bass 2002b). There have been virtually no experimental studies on elastic properties of majoritic garnets at high-pressure and high-temperature conditions of the mantle transition zone, where majoritic garnet is believed to be stable and abundant volumetrically. The development of state-of-the-art experimental techniques of ultrasonic interferometry in conjunction with synchrotron X-ray diffraction allows us to investigate sound velocities of minerals at pressure and temperature conditions of the Earth’s deep interior (Li et al. 1996, 2001, 2004, Li and Liebermann 2007; Higo et al. 2008, 2009). Gwanmesia et al. (2009) measured the elastic parameters of Mj40Py60 and Mj50Py50 garnets up to 8 GPa and 1,000 K. More recently, Zou et al. (2012) reported the elastic wave velocity of pyrope to 19 GPa and 1,700 K. To date, however, the elastic wave velocity studies on the majorite–rich garnets have been very limited; only the exception is Irifune et al. (2008), which reported the elastic wave velocity of majorite with a pyrolite minus olivine composition under high-pressure and high-temperature conditions of the mantle transition zone region. The majoritic garnet sample used in this study, however, has a more complex chemical composition than the end-member majorite in the majorite–pyrope system, the results of which are applicable only to address the behaviors of majorite with a pyrolite composition.

Here we performed in situ X-ray diffraction and ultrasonic measurements on a majoritic garnet in the majorite–pyrope system at simultaneous high pressures and high temperatures in a Kawai-type multi-anvil apparatus. The elastic moduli and their pressure and temperature derivatives are determined from the current experimental data. The newly obtained results are compared with those from the previous studies on other majoritic garnets with various compositions along the majorite–pyrope system.

Experimental method

Synthetic polycrystalline Mj80Py20 garnet

The polycrystalline majoritic garnet was synthesized at 19 GPa and 1,700 °C for 2 h from a glass with composition of 95 mol % MgSiO3 and 5 mol % Al2O3 [i.e., 80 mol % Mg4Si4O12 (Mj) and 20 mol % Mg3Al2Si3O12 (Py)] using a Kaiwai-type multi-anvil apparatus (Orange-3000) at the Geodynamics Research Center, Ehime University, Japan. The hot-pressed specimen was well sintered, translucent, and cylindrical in shape, with ~2 mm in diameter and ~1.5 mm in length. The recovered sample was confirmed to be a single-phase garnet with an average grain size of ~3 μm by X-ray diffraction and Field-Emission Scanning Electron Microprobe (FE-SEM; JEOL-7000F) observations. We noted that the polycrystalline Mj80Py20 garnet was essentially anhydrous by the absence of OH adsorption bands in the Fourier-transform infrared spectroscopy (FTIR). The bulk density of the sample ρ 0 = 3.521 ± 0.021 g cm−3 determined by Archimedes’ method is close to the density ρ 0  = 3.528 ± 0.001 g cm−3 calculated from the X-ray diffraction pattern, suggesting a very low porosity of the recovered sample.

Ultrasonic system in conjunction with in situ X-ray diffraction measurements

Ultrasonic measurements at simultaneous high pressures and high temperatures were conducted with a 1,500-ton Kawai-type multi-anvil apparatus (SPEED-1500) located at the beamline BL04B1 in SPring-8. The detailed information about the ultrasonic system, in situ X-ray diffraction, and X-radiography techniques has been described by Higo et al. (2008, 2009). We adopted the same 11/5 (OEL/TEL = Octahedral Edge Length of pressure medium/Truncated Edge Length of anvil) cell assemblage with that of Kono et al. (2010a) for ultrasonic and in situ X-ray diffraction measurements. A dense Al2O3 rod was used as a buffer rod between the sample and tungsten carbide anvil. Thin gold foils (2.5 μm in thickness) were placed on the interfaces between anvil, buffer rod, sample, and pressure marker to improve mechanical coupling. A rhenium foil tube was used as heater and an MgO window was placed in a LaCrO3 sleeve for obtaining X-ray diffraction of the sample and pressure marker (Au + NaCl + BN). Temperature was measured by a W97Re3–W75Re25 thermocouple with the hot junction near the pressure marker.

Both ends of the polycrystalline rod sample were polished to mirror surfaces using 0.5-μm diamond powders. The travel times of ultrasonic P- and S-waves through the sample were determined by a pulse echo overlap method (Li et al. 2002, 2004; Higo et al. 2008, 2009; Kono et al. 2010a). A 10° Y-cut LiNbO3 transducer, generating and receiving both compressional and transverse waves simultaneously, was bonded on the well-polished backside corner of the truncated anvil cube. Acoustic frequencies of 60 MHz for P-wave and 40 MHz for S-wave were used to determine the travel times in our study. The uncertainties of two-way travel times are ±2 ns. The sample at simultaneous high pressures and high temperatures was monitored by X-ray radiography with a high-resolution CCD camera. The precise sample length was calculated using the calibrated image pixels (1 pixel = –2 μm, in this study) multiplied by the observed distance between the gold foils placed on the top and bottom surfaces of the sample. Uncertainties in the sample length are within ±2 μm.

In situ X-ray diffraction measurements were conducted by an energy-dispersive system with a fixed diffraction angle (6°). The unit-cell volumes of the sample and the gold pressure marker were refined by reducing full diffraction patterns following the LeBail method (Le Bail et al. 1988) with the multi-phase profile-fitting technique implemented in the EXPGUI/GSAS software package (Larson and Von Dreele 2000; Toby 2001). The experimental pressures were evaluated from the equation of state of Au (Tsuchiya 2003) from its unit-cell volume at each P–T condition.

Experimental procedures

Two in situ X-ray diffraction and ultrasonic measurements were conducted at the P–T range of 0–21 GPa and 300 ~ 2,000 K (Table 1). As shown in Fig. 1, the sample was firstly compressed to the desired pressure at room temperature and then heated to the maximum temperature to release the non-hydrostatic stress. The X-ray diffraction data, ultrasonic travel times, and sample images were then collected during the cooling process down to room temperature with 200-K temperature intervals in each cycle. In run S2888, we performed four cycles of this process up to 21 GPa and 1,300 K in the metastable field of Mj80Py20 garnet. In run S2907, the measured P–T conditions of the last cycle were up to 16 GPa and 2,000 K within the stability of Mj80Py20 garnet. When the temperature decreased from 2,000 to 1,800 K at the constant load, only X-ray diffraction data were collected without ultrasonic data due to the deterioration of the LiNbO3 transducer. The samples remained as a single phase of garnet in above runs and no secondary phase was observed in the recovered samples by FE-SEM.

Table 1 P–V–T, sound velocity, and elasticity data of Mj80Py20 garnet at various high pressures and high temperatures
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Fig. 1
figure 1

Experimental pressure and temperature paths for ultrasonic and X-ray diffraction measurements on the polycrystalline Mj80Py20 garnet plotted on the phase diagram for MgSiO3 (Gasparik 1990). The phase boundaries in red lines are stability field of Mj80Py20 garnet (Gasparik 1992). The arrows indicate the P–T paths for these measurements. Opx orthopyroxene, Cpx clinopyroxene, HP-Cpx high-pressure clinopyroxene, β wadsleyite, γ ringwoodite, St stishovite, Mj majorite, II ilmenite, Pv perovskite

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Experimental results

Figure 2 shows some representative in situ synchrotron X-ray diffraction patterns collected at ambient condition and high pressures and high temperatures. In all diffraction patterns, the major reflections are assigned to the garnet structure, while minor peaks are originated from the rhenium heater and gold foil in the measured cell assembly. Parise et al. (1996) and Heinemann et al. (1997) suggested that majorite containing about 20 mol % pyrope in the pyrope–majorite system adopted a tetragonal structure, although the structure for the Mj80Py20 garnet in their studies was not obvious. In our study, we could not unambiguously identify peak-splitting or appearance of new peaks as evidence for the tetragonal structure (Parise et al. 1996). This is because the energy-dispersive X-ray diffraction technique at a fixed angle bears a certain limitation in resolving the small structural distortions. Thus, we refined the cell parameters on the basis of pseudocubic structure for Mj80Py20 garnet. The zero-pressure unit-cell volume V 0 = 1,513.24 ± 0.17 Å3 in our study agrees well with V 0 = 1,513.8 ± 1.0 Å3 (Sinogeikin et al. 1997) and is about 0.1 % smaller than the value of 1,514.1 Å3 (Morishima et al. 1999), which were also calculated with the cubic symmetry for Mj80Py20 garnet. The tetragonal distortion may be very small for Mj80Py20 garnet, if any, as our result is also comparable to the value of 1,513.6 ± 0.1 Å3 reported for the same composition garnet with the tetragonal structure by Parise et al. (1996).

Fig. 2
figure 2

Some examples of in situ X-ray diffraction patterns of Mj80Py20 garnet at a ambient condition (S2888), b 19.9 GPa, 1,300 K (S2888), and c 16.0 GPa, 2,000 K (S2907). The diffraction peaks from rhenium heater and gold foil are indicated by short lines

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The unit-cell volumes of Mj80Py20 garnet at various high pressures and high temperatures are determined through in situ X-ray diffraction measurements and then fitted to the high-temperature third-order Birch–Murnaghan equation of state (HTBM; Fig. 3). The densities of Mj80Py20 garnet at various P–T conditions are determined by its molecular weight divided by the unit-cell volumes (Table 1). Fitting P–V–T data to the HTBM equation of state gives the thermoealstic parameters as follows: K T = 160 (4) GPa, K Tʹ = 4.5 (5), ∂K T/∂T = −0.012 (6) GPaK−1, and α = a + bT with values of a = 2.15 (33) × 10−5 K−1 and b = 0.43 (8) × 10−8 K−1. As shown in Table 2, the K T = 160 (4) GPa determined in this study is slightly higher than the value (K T = 156 (2) GPa) derived at the fixed thermal expansion of 2.88 × 10−5 K−1 (Morishima et al. 1999), whereas the K Tʹ agrees well with K Tʹ = 4.4 (3) of their study.

Fig. 3
figure 3

P–V–T data of Mj80Py20 garnet with calculated isothermal compression curves. The solid curves are calculated from thermoelastic parameters derived from high-temperature third-order Birch–Murnaghan equation of state. The color solid circles are from one experiment result of Mj80Py20 garnet at 0~12.9 GPa (Morishima et al. 1999)

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Table 2 Elastic properties of majoritic garnets along the majorite–pyrope system
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Figure 4 shows the P-wave (V P) and S-wave (V S) velocities of Mj80Py20 garnet at various temperatures as a function of pressure. Both V P and V S increase almost linearly with increasing pressure, while they decrease with increasing temperature. The linear dependence on pressure and temperature of both V P and V S was also reported in earlier studies on grossular (Kono et al. 2010b) and pyrope (Zou et al. 2012), in contrast to the significantly nonlinear temperature dependences of V P and V S observed for majorite with a pyrolite minus olivine composition (Irifune et al. 2008), ringwoodite (Higo et al. 2008), and akimotoite (Zhou et al. 2013a) using the same technique. Here, we adopt the two-dimensional (2D) linear fitting (Li et al. 1998, 2001; Gwanmesia et al. 2006; Irifune et al. 2008; Higo et al. 2008; Kono et al. 2010b; Zou et al. 2012; Zhou et al. 2013a):

$$M = M_{0} + {\text{d}}M/{\text{d}}P \times P + {\text{d}}M/{\text{d}}T \times (T{-}300)$$

where M is V P or V S and dM/dP and dM/dT are their first-order pressure and temperature derivatives. A least square fitting of all the data yields: V P = 8.93 (1) + 5.95 (8) × 10−2 × P − 2.78 (3) × 10−4 × (T − 300) and V S = 4.93 (1) + 2.14 (4) × 10−2 × P − 1.90 (2) × 10−4 × (T − 300), respectively. The derived V P = 8.93 (1) km/s of Mj80Py20 garnet at ambient condition is slightly higher than the result (V P  = 8.82 (1) km/s) for the majoritic garnet with the same composition using Brillouin scattering method (Sinogeikin et al. 1997), while the present V S = 4.93 (1) km/s at ambient condition agrees well with V S = 4.91 (2) km/s in their study.

Fig. 4
figure 4

P (a) and S (b) wave velocities of Mj80Py20 garnet at high pressures and high temperatures. The solid lines represent the two-dimensional linear fitting curves. Error bars indicate the uncertainties of velocities

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The adiabatic bulk (K S) and shear (G) moduli of Mj80Py20 garnet at high pressures and high temperatures are determined using the data in Table 1 and the relations K S = ρ(V 2p  − 4V 2S /3) and G = ρV 2S . Figure 5 shows the variations of adiabatic bulk and shear moduli of Mj80Py20 garnet as a function of pressure and temperature. The data of adiabatic bulk and shear moduli are also fitted with the 2D linear fitting method, yielding: K S = 161.5 (7) + 4.42 (4) × P − 1.54 (2) × 10−2 × (T − 300) and G = 86.2 (2) + 1.28(1) × P − 0.96 (5) × 10−2 × (T − 300). The present bulk modulus and shear modulus at ambient condition are consistent with the results of Sinogeikin et al. (1997) within the uncertainties, while our results are lower by 2.5 and 3 % than those of Gwanmesia et al. (2000). The thermoelastic parameters of Mj80Py20 garnet in the present study are also obtained by fitting to the functions of Eulerian strain to third order (Davis and Dziewonski 1975; Gwanmesia et al. 2006, 2009, 2013). The derived elastic properties are as follows: K S = 158 ± 5 GPa, K Sʹ = 4.7 ± 0.5, ∂K S/∂T = −0.015 ± 0.003 GPa/K, G = 84 ± 3 GPa, Gʹ = 1.24 ± 0.17, and ∂G/∂T = −0.011 ± 0.001 GPa/K. All the values derived from the linear fitting are within uncertainties of results obtained by the finite-strain fitting method.

Fig. 5
figure 5

Adiabatic Bulk (a) and shear (b) moduli of Mj80Py20 garnet at high pressures and high temperatures. The solid lines represent the two-dimensional linear fitting curves. Error bars indicate the uncertainties of elastic moduli

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Discussion

The elastic properties of Mj80Py20 garnet obtained in this study and previous studies on the solid solutions in the majorite–pyrope system are summarized in Table 2. At ambient conditions, the differences of elastic moduli of the garnets with various compositions in the majorite–pyrope system are relatively small. Sinogeikin et al. (1997), based on earlier studies (Yeganeh-Haeri et al. 1990; Bass and Kanzaki 1990; Yagi et al. 1992; Pacalo and Weidner 1997), proposed two models for the dependence of elastic moduli on the majorite content in this system: (1) a small linear decrease in K S and G from Py100 to Mj100; (2) constant K S and G from Mj100 to Mj70Py30, followed by a step-like decrease at Mj70Py30–Mj80Py20 and a gradual increase to Mj100. As shown in Fig. 6, our results are rather compatible with the model (2), although we cannot rule out the possibility of the linear dependence (Pacalo and Weidner 1997; Gwanmesia et al. 2000). The different synthesis conditions, quench history, and measured methods make it difficult to describe the scattering nature of the elastic moduli data on the majoritic garnets along the majorite–pyrope system, especially the compositional dependency of elastic moduli in this system. It is also unclear whether the cubic-tetragonal symmetry transformation at Mj75Py25 (Parise et al. 1996) affects the elastic moduli of majoritic garnets in this system. Further systematic studies are required to clarify this issue, although the effects of this phase transformation seem not to be very significant (Sinogeikin et al. 1997).

Fig. 6
figure 6

Ambient elastic moduli (K S and G) as a function of the majorite composition in the majorite–pyrope system. Open and solid symbols represent those measured with Brillouin scattering and ultrasonic techniques, respectively. The open diamond, circle, triangle and square symbols are from Pacalo and Weidner (1997) and Sinogeikin et al. (1997), Sinogeikin and Bass (2002a, b), while the large solid circle, triangle, diamond, pentagon, star, and hexagon symbols are from this study, Gwanmesia et al. (2000), Liu et al. (2000), Gwanmesia et al. (2006), Gwanmesia et al. (2009), and Zou et al. (2012). The dashed and solid lines represent the compositional dependence proposed by Sinogeikin et al. (1997)

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The newly obtained pressure derivatives of the adiabatic bulk modulus K Sʹ = (∂K S/∂P)T and the shear modulus G′ = (∂G/∂P)T of Mj80Py20 garnet are 4.42 (4) and 1.28 (1), respectively, which are nearly identical with the results of Py100 [K S′ = 4.51 (3), G′ = 1.51 (2); Zou et al. 2012] and slightly lower than those of Mj50Py50 and Mi40Py60 (Mj50Py50 : K S′ = 5.29 (4), Gʹ = 1.49 (2); Mj40Py60 : K Sʹ = 5.34 (5), Gʹ = 1.53 (3); Gwanmesia et al. 2009) using the similar experimental methods. Furthermore, the pressure derivatives of elastic moduli for Mj80Py20 garnet in the present study are in good agreement with those of Mj100 and Mj50Py50 determined by Brillouin scattering techniques (Sinogeikin and Bass 2002a). On the other hand, our data are contradictory to the large pressure derivatives for Mj50Py50 (K′ = 6.4, G′ = 2.1) and Mj38Py62 (K′ = 6.2, G′ = 1.9) reported by Liu et al. (2000). Their high-pressure derivatives may be caused by the non-hydrostatic stresses on the cell assembly without heating at high pressures (Gwanmesia et al. 2006). It should also be noted that the K Tʹ of Mj80Py20 garnet determined in this study is also compatible with those derived from the isothermal static compression of Mj80Py20 (Morishima et al. 1999) and Mj38Py62 (Wang et al. 1998). Thus, we conclude that the pressure derivatives of elastic moduli are not sensitive to the majorite content in the majorite–pyrope system, in contrast to the results by Liu et al. (2000).

The temperature derivatives of the elastic moduli for Mj80Py20 garnet and other majorite–pyrope solid solutions are listed in Table 2. The values of (∂K S/∂T)P = −1.54 (2) × 10−2 GPa/K and (∂G/∂T)P = −0.96 (5) × 10−2 GPa/K of Mj80Py20 garnet in this study are in agreement with those derived from Brillouin scattering measurements on the same composition and also comparable to those of Mj50Py50 and Py100 garnets (Sinogeikin and Bass 2002b). Moreover, our results are also essentially identical with those of Mj50Py50 and Mj40Py60 garnets using the similar experimental method by Gwanmesia et al. (2009). When compared with the results of Py100 (Zou et al. 2012), our results are higher by about 10 and 11 %, respectively. The temperature derivatives of elastic moduli of Mj80Py20 garnet in this study are close to those of other majoritic garnets in the majorite–pyrope system, indicating that temperature derivatives of elastic moduli are insensitive to the majorite content in this system, as proposed by Wang et al. (1998) from the isothermal static measurement on Mj38Py62 and Py100 garnets.

The temperature dependences in elastic velocities of mantle minerals are important to constrain the velocity profile and mineralogy of the mantle transition zone. In Fig. 7, the V P and V S of Mj80Py20 garnet calculated from current experimental data decrease linearly with the increasing temperature at the selected pressures of 16, 18, and 20 GPa, although a nonlinear behavior in the majorite with a pyrolite minus olivine composition was reported by Irifune et al. (2008). The discrepancy may be explained by the difference in the mineral composition (Zou et al. 2012) and the limitation of the measured temperatures range in elastic velocity study (Zhou et al. 2013a). Further studies on other minerals at higher temperatures are needed to clarify this issue.

Fig. 7
figure 7

Variations of sound velocities of Mj80Py20 garnet as a function of temperature at selected pressures in the mantle transition zone region. The solid curves show the P- and S-wave velocities (V P and V S) derived from the present study. The dashed curves represent those from the sound velocity measurements on the majorite with the pyrolite composition (Irifune et al. 2008)

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In Fig. 8, we evaluate the sound velocity profiles of Mj80Py20 garnet and other solid solutions in the majorite–pyrope system (pyrope, Zou et al. 2012; Mg4Si4O12 majorite, Zhou et al. 2013b) along a typical adiabatic geotherm in the mantle transition zone (Brown and Shankland 1981). The present Al-bearing majoritic garnet (Mj80Py20) produces slightly higher velocities than the Mg4Si4O12 majorite, while lower than those of pyrope and the typical seismological models. Therefore, petrological model with the majorite-rich garnet (e.g., pyrolite,MORB or eclogite) would produce lower velocities than PREM/AK135 in the mantle transition zone, especially for the lower part of this region (Irifune et al. 2008; Kono et al. 2012).

Fig. 8
figure 8

Comparison of velocities of the majoritic garnets in the majorite–pyrope system along a typical adiabatic mantle geotherm in mantle transition zone (Brown and Shankland 1981). Black solid and dashed lines show the velocity profiles from seismic models of PREM (Dziewonski and Anderson 1981) and AK135 (Kennett and Engdahl 1991). Blue, pink, and olivine solid lines are calculated from the velocity data of Mj80Py20 (this study), majorite (Mj100, Zhou et al. 2013b), and pyrope (Py100, Zou et al. 2012)

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The majoritic garnet is a dominated phase in the mantle transition zone (Ringwood and Major 1971; Akaogi and Akimoto 1977; Irifune and Ringwood 1987). The study of elastic properties of majoritic garnet will thus contribute significantly to modeling the sound velocity profile of the mantle transition zone. For example, the high velocity gradients in the mantle transition zone at depths of 410–520 km have been attributed to the gradual dissolution of the clinopyroxene into the majoritic garnet with increasing depth (Bass and Anderson 1984; Irifune and Ringwood 1987; Irifune and Isshiki 1998; Sinogeikin and Bass 2002a), while a recent study based on sound velocity measurements on the majoritic garnet with a pyrolite minus olivine composition suggested a smaller velocity gradient for the mantle transition zone (Irifune et al. 2008). Therefore, we evaluate the velocity gradient ∂V S /∂Z of Mj80Py20 garnet [~0.7 (m/s)/km, this study], Mg4Si4O12 majorite [~0.4 (m/s)/km, Zhou et al. 2013b] and pyrope [~0.8 (m/s)/km, Zou et al. 2012], which are 3–6 times lower than the observed velocity gradients of PREM/AK135 [2.1–2.6 (m/s)/km, Dziewonski and Anderson 1981; Kennett and Engdahl 1991] in the mantle transition zone. The majoritic garnets in the majorite–pyrope system do not yield steep velocity slopes to account for the large velocity gradient in the mantle transition zone. Moreover, the velocity slope of the ~5 wt% iron-bearing majorite [~0.591 (m/s)/km; Murakami et al. 2008] is comparable to that of the majorite–pyrope system. It has also been suggested that the gradual formation of CaSiO3 perovskite from the majoritic garnet in a pyrolite minus olivine composition or the presence of chemical heterogeneity may account for the steep slope of seismic velocity in the deeper regions of the mantle transition zone (Irifune et al. 2008). Further studies about the effect of chemical composition such as calcium and sodium impurities, as well as that of the lithology of the mantle transition zone on the seismic velocities, are needed to constrain the mineralogical model of this region in the Earth’s mantle.