Introduction

Calcium chromite, CaCr2O4, is one of the important components of materials for many high-temperature applications in metallurgy, ceramics and solid oxide fuel cells (Róg et al. 2007). There are two polymorphs of CaCr2O4, α- and β-CaCr2O4, corresponding to high- and low-temperature form, respectively (Lee and Nassaralla 1997). Unlike most chromites crystallized as cubic spinel oxides, both α- and β-CaCr2O4 are in orthorhombic structures with space groups of Pmmn (No. 59) (Pausch and Müller-Buschbaum 1974) and Pnam (No. 62) (Hill et al. 1956), respectively. The phases were widely investigated recently because of their magnetic and magnetoelectric properties (Damay et al. 2010; Dutton et al. 2010; Singh et al. 2011; Töth 2012; Androš et al. 2014; Sakurai 2014; Songvilay et al. 2015).

As reported in previous studies (Hill et al. 1956; Hörkner and Müller-Buschbaum 1976), β-CaCr2O4 is isostructural with CaFe2O4. The CaFe2O4-type structure was believed as the high-pressure form of many spinels at the pressure and temperature conditions corresponding to the mantle transition zone and upper border of the lower mantle of the Earth (Irifune et al. 1991; Kesson et al. 1994; Kirby et al. 1996; Funamori et al. 1998; Akaogi et al. 1999). Thus this type of mineral is considered as a potential geochemical reservoir for alkaline and other large cations in the mantle (Chen et al. 2003; Merlini et al. 2010). However, rare natural mineral with CaFe2O4-type structure was found. Chen et al. (2003) reported a CaFe2O4-type FeCr2O4 in the shock veins of the Suizhou meteorite. Galuskina et al. (2014) discovered a natural occurrence of CaFe2O4 in pyrometamorphic larnite rocks and named it as harmunite. Quite recently Kaminsky et al. (2015) found a new Ca–Cr oxide mineral (Ca1.07Mg0.02Mn0.02)1.11(Cr1.71Fe 3+0.06 V0.06Ti0.03Al0.03)1.89O4, chemically and structurally similar to synthetic β-CaCr2O4, as a part of an inclusion in a diamond. This Ca–Cr oxide was believed to be a lower mantle origin (Kaminsky et al. 2015). Therefore, β-CaCr2O4 chromite might be a stable phase and potential host for Ca and Cr in the deep mantle.

The physical properties under high-temperature and high-pressure conditions are important for understanding the behavior of β-CaCr2O4 chromite in deep mantle. In previous studies, the thermodynamic properties of β-CaCr2O4 have been examined by various measurements at high temperatures and ambient pressure (Rajagopalan et al. 1989; Jacob et al. 1992; Lee and Nassaralla 2001; Róg et al. 2007). However, the physical properties of β-CaCr2O4 under high pressure have not been investigated yet. The purpose of this study is to characterize the synthesized polycrystalline β-CaCr2O4 chromite at high pressure using in situ X-ray diffraction and Raman spectroscopic measurements. Furthermore, the isothermal bulk moduli of CaFe2O4-type phases will be compared and the thermal Grüneisen parameter of Raman vibrations for β-CaCr2O4 will be determined and compared with available values of CaFe2O4-type phases.

Experimental

High-purity β-CaCr2O4 was prepared by solid-state reaction from CaCO3 and Cr2O3. Reagent-grade CaCO3 and Cr2O3 powders were mixed in the proportion corresponding to the CaCr2O4 stoichiometry, and the mixture was ground sufficiently and pressed into pellets with a diameter of 5 mm under uniaxial pressure of 30 MPa. Based on the phase diagram of CaCr2O4 (Lee and Nassaralla 1997), the pellets were sintered at 1673 K in a furnace for 12 h. The sintered product was ground finely and confirmed by a powder X-ray diffractometer as a single β-CaCr2O4 phase.

In situ high-pressure energy-dispersive X-ray diffraction experiment was performed using a multi-anvil high-pressure apparatus, SPEED 1500, at beamline BL04B1 of SPring-8, Japan. A mixture of β-CaCr2O4 plus about 10 wt% Au, the internal pressure marker, was used as the sample. The experimental method was similar to that described by Zhai et al. (2011, 2013). Kawai-type cell assembly composed of eight cubic second-stage tungsten carbide anvils with edge length of 26 mm and truncated edge length of 2 mm was adopted. A semi-sintered octahedron with 6.5-mm edge length made of MgO was used as the pressure medium, and pyrophyllite as the gasket. The tubing heater and sample capsule were made of TiB2, due to its high transparency for X-ray. The high-pressure system is combined with a synchrotron radiation source and an energy-dispersive X-ray diffraction system with a Ge solid-state detector (SSD) and a charge-coupled device (CCD) camera for radiographic imaging of the sample. A polychromatic X-ray beam collimated to the dimensions of 0.05 mm horizontally and 0.2 mm vertically was directed to the sample through pyrophyllite gasket and pressure medium. A multi-channel analyzer was used to acquire photons in a range of 20–150 keV, which was calibrated with characteristic fluorescence X-ray lines of several reference metals, including Cu, Mo, Ag, Ta, Pt, Au, Pb. The precision of the energy measurements was approximately ±30 eV per channel. The 2θ angle of SSD was set at ~6° with respect to the incident beam direction and accurately calibrated using known diffraction peaks from a standard material such as gold. The uncertainty of the diffraction angle after calibration was typically ±0.002°. In order to release deviatoric stress accumulated during the compression steps, the sample assembly was heated to about 900 K. It is noted that no thermocouple was adopted, and the temperature was estimated from the power–temperature relationship of the heater. The sample was quenched to room temperature after keeping at ~900 K for 5 min, and then the X-ray diffraction pattern was collected. The diffraction peak positions were determined using XrayAna program, and the lattice parameters were obtained by REFINE program (Bartelmehs et al. 1993). Pressure was determined using the equation of state of gold (Tsuchiya 2003) using (111), (200), (220), (311) and (222) diffraction lines. In some cases, one or two lines were unavailable to determine pressure when the diffraction peaks of gold overlapped with those of the sample. Uncertainties in the pressure determination were mostly within ±0.1 GPa.

The high-pressure Raman measurements were carried out by adopting a symmetric type of diamond anvil cell with a pair of 300-μm-culet diamond anvils. The experimental method used in this study was similar to previous studies (Shi et al. 2012; Zhai et al. 2015). The synthetic sample was loaded into a rhenium gasket with a hole of 100 μm in diameter, with Ar as the pressure medium. Tiny ruby (Cr3+ doped α-Al2O3) spheres with diameters in 5 μm as pressure marker were carefully placed inside the gasket sample chamber. The sample pressures were determined based on the modern ruby scale proposed by Sokolova et al. (2013). Micro-Raman spectra were collected by a custom-built Raman system at University of Western Ontario. An argon-ion laser with a wavelength of 514.5 nm was used as exciting source, and a spectrometer with a liquid nitrogen-cooled CCD detector was used to collect the Raman data. The spectrometer was calibrated using a neon lamp, and the precision of the frequency determination was about 1 cm−1. The data collection time was typically 120 s for each spectrum, and five spectra were collected for each pressure step. Therefore, the reported Raman spectra are average data. The Raman shift of each band was obtained by Lorentzian curve fitting to get a reasonable approximation by using PeakFit program (SPSS Inc., Chicago).

Results and discussion

P–V equation of state

The powder X-ray diffraction pattern of β-CaCr2O4 at ambient conditions yielded the orthorhombic structure (space group Pnam) with unit-cell dimensions of a = 9.083(2) Å, b = 10.629(2) Å and c = 2.971(1) Å. The observed and calculated X-ray diffraction patterns of β-CaCr2O4 at ambient conditions are listed in Table 1. The volume of β-CaCr2O4 at ambient conditions is 286.8(1) Å3. The unit-cell parameters and volume of β-CaCr2O4 determined in this study are consistent with those values reported by Hill et al. (1956) (i.e., a = 9.07 Å, b = 10.61 Å, c = 2.99 Å, V 0 = 287.7 Å3) and Hörkner and Müller-Buschbaum (1976) (i.e., a = 9.094 Å, b = 10.639 Å, c = 2.960 Å, V 0 = 286.4 Å3).

Table 1 Observed and calculated X-ray diffraction patterns of β-CaCr2O4 at ambient conditions
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The high-pressure X-ray diffraction data were collected up to 16.2 GPa at ambient temperature after annealing. Figure 1 shows representative X-ray diffraction patterns obtained in this study. In addition to the diffraction peaks from β-CaCr2O4, there were diffraction and fluorescence peaks arising from the internal pressure calibrant of gold, as well as some peaks from heater (TiB2) at high pressures. Since the X-ray diffraction patterns were collected after quenching from about 900 K to room temperature, the deviatoric stress was released and the uncertainty in the pressure determination was mostly within 0.1 GPa based on the volume calculated from lattice parameters determined using the different diffraction lines of gold.

Fig. 1
figure 1

Representative X-ray diffraction patterns of β-CaCr2O4 obtained in this study. Abbreviations indexed to the diffraction peaks: S = β-CaCr2O4; Au = gold; * = X-ray fluorescence of Au; T = TiB2 heater

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The results of unit-cell parameters and volume of β-CaCr2O4 at various pressures are shown in Table 2. The pressure–volume data were fitted to the third-order Birch–Murnaghan equation of state (Birch 1947) to determine the elastic parameters:

$$P\, = \,\frac{{3\,K_{0} }}{2}\left[ {\left( {\frac{{V_{0} }}{V}} \right)^{7/3} - \,\left( {\frac{{V_{0} }}{V}} \right)^{5/3} } \right]\times\,\left\{ {1 + \frac{3}{4}\left( {K_{0}^{{\prime }} - 4} \right)\,\,\left[ {\left( {\frac{{V_{0} }}{V}} \right)^{2/3} - 1} \right]} \right\}$$

where P, K 0, K 0′, V 0 and V are pressure, isothermal bulk modulus, the first pressure derivative of the isothermal bulk modulus, zero-pressure volume and high-pressure volume, respectively. The results from a least-squares fitting using an EosFit program (Angel 2001) are V 0 = 286.8(1) Å3, K 0 = 183(5) GPa and K 0′ = 4.1(8), respectively. The unit-cell volume as a function of pressure and the compression curve calculated from the fitted parameters are plotted in Fig. 2. If the value of K 0′ was set as 4, then K 0 = 184(2) GPa was obtained. By using a 3, b 3 and c 3 to substitute V in the second-order Birch–Murnaghan equation of state, we can obtain the axial compressible parameters as K a  = 167(4) GPa, K b  = 190(6) GPa and K c  = 191(5) GPa for a-, b- and c-axis, respectively. The a-axis is more compressible than the b- and c-axis, which shows an anisotropic elasticity for β-CaCr2O4.

Table 2 Unit-cell parameters of β-CaCr2O4 at various pressures and room temperature
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Fig. 2
figure 2

Volume of β-CaCr2O4 at high pressures and ambient temperature. Solid curve represents the third-order Birch–Murnaghan equation fit with K 0 and K 0′ of 183 GPa and 4.1, respectively. The uncertainties of pressure and volume are also shown

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Comparisons of elastic parameters for CaFe2O4-type MgAl2O4, NaAlSiO4, CaFe2O4 and CaCr2O4 are listed in Table 3. It is noted that these phases were investigated by different experimental technique adopting different pressure markers. Even for the same marker, different scales were using in different studies. Therefore, an effect of pressure scales on the obtained elastic parameters exists though all of these studies adopted third-order Birch–Murnaghan equation of state to fit the P–V data. Among these CaFe2O4-type phases, β-CaCr2O4 shows a moderate isothermal bulk modulus. Though different values were obtained for the same CaFe2O4-type phase in various studies with a noticeable scatter of the data, it seems that the general relationship K 0 × V 0 = const (Anderson and Anderson 1970) for a crystal structure is followed (Fig. 3). Based on these results, the density profiles of CaFe2O4-type phases, except that of CaAl2O4 due to the lack of elastic parameters, can be calculated up to high pressure. As shown in Fig. 4, the densities of CaFe2O4-type NaAlSiO4 and MgAl2O4 are similar, whereas the density discrepancy between CaFe2O4 and β-CaCr2O4 increases with pressure. It is noted that the density profiles were calculated at ambient temperature since not enough thermoelastic parameters of CaFe2O4-type phases are available. Therefore, further studies are required to determine the stability of β-CaCr2O4 and thermoelastic parameters of CaFe2O4-type phases in deep mantle.

Table 3 Elastic parameters of CaFe2O4-type phases (at 300 K)
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Fig. 3
figure 3

Isothermal bulk modulus–volume relationship for CaFe2O4-type phases (data sources listed in Table 3)

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Fig. 4
figure 4

Observed (solid cycle) and calculated density profiles of CaFe2O4-type phases as a function of pressure at room temperature. The elastic parameters for β-CaCr2O4, CaFe2O4, MgAl2O4 and NaAlSiO4 are from this study, Merlini et al. (2010), Sueda et al. (2009) and Guignot and Andrault (2004), respectively

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Pressure dependence of Raman spectra

Similar to the Raman-active modes of CaFe2O4-type phases (Kojitani et al. 2003, 2013; Kolev et al. 2003; López-Moreno et al. 2011), the orthorhombic β-CaCr2O4 is associated with the following Raman-active modes:

$$\varGamma = 14{\text{A}}_{{1{\text{g}}}} + 7{\text{B}}_{{1{\text{g}}}} + 14{\text{B}}_{{2{\text{g}}}} + 7{\text{B}}_{{3{\text{g}}}}$$

Therefore, the orthorhombic β-CaCr2O4 structure has 42 Raman-active modes. The Raman spectrum of β-CaCr2O4 at ambient condition is illustrated in Fig. 5, showing a strongest typical peak at 600 cm−1. Due to the very low intensity and/or overlapping of some modes, the number of observed Raman vibrations is fewer than predicted. The Raman spectrum was not analyzed by full range from 100 to 800 cm−1, but by four separated ranges of 100–375, 375–570, 570–620 and 620–800 cm−1 using PeakFit Program (SPSS Inc., Chicago). Therefore, the peaks can be positioned well. Totally 23 Raman bands were observed for β-CaCr2O4 at ambient conditions, as listed in Table 4. It should be pointed out that it is difficult to assign the vibrational modes without theory calculation, as reported in previous studies of other CaFe2O4-type phases (Kojitani et al. 2003).

Fig. 5
figure 5

Typical Raman spectra of β-CaCr2O4 at different pressures. The peak no. was indexed according to those listed in Table 4

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Table 4 Constants determined in the expressions of ν i  = ν i0 + βP and γ i  = K 0 (∂ ln ν i /∂ P) for β-CaCr2O4
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The Raman shift versus pressure plot of β-CaCr2O4 is illustrated in Fig. 6. It is noted that during compression some vibrations of β-CaCr2O4 become weaker and undistinguished, and two overlapping bands appear around 8 GPa. According to the high-pressure X-ray diffraction patterns, no phase transition occurs up to at least 16 GPa. The Raman shifts of vibrations in β-CaCr2O4 increase with pressure, and the slopes vary with different modes. In this study, argon was used as pressure medium, which gives a hydrostatic limit of about 10 GPa (Klotz et al. 2009). Therefore, in order to avoid the effect of non-hydrostatic compression, the pressure coefficients (β) of different Raman vibrations of β-CaCr2O4 were determined using the data below 10 GPa. The values of β, varying from 0.89 to 4.16 cm−1/GPa except those of the peaks at 143 and 322 cm−1 in the spectrum at ambient conditions, are also listed in Table 4. Considering the uncertainties, the pressure coefficients of peaks at 143 and 322 cm−1 in the spectrum at ambient conditions were independent of pressure. The isothermal bulk modulus can be used to calculate the mode Grüneisen parameters which are required in many theoretical calculations. The mode Grüneisen parameters (Grüneisen 1912) were calculated by the equation:

$$\gamma_{i} = \left( {\delta \nu_{i} /\delta P} \right)K_{0} /\nu_{i}$$

where ν i is the Raman shift of the ith vibrational mode and K 0 is the isothermal bulk modulus. The zero-pressure isothermal bulk modulus, K 0 of 183(5) GPa obtained in this study, was used, and the calculated mode Grüneisen parameters are shown in Table 4. The thermal Grüneisen parameter (γ th) can be calculated by the weighted average of the mode Grüneisen parameters (γ i ) determined experimentally, using the following equation (e.g., Chopelas 1996):

$$\gamma_\text{th} =\frac{\sum_iC_{V_{i}}\gamma_{i}}{\sum_iC_{V_{i}}}$$

where \(C_{V_{i}}\) is a harmonic heat capacity contribution of the ith vibrational mode. The \(C_{V_{i}}\) values were estimated from the Einstein function:

$$C_{{V_{i} }} = k\,\left( {\frac{{h\,v_{i} }}{k\,T}} \right)^{2} \,{{\exp \left( {\frac{{h\,v_{i} }}{k\,T}} \right)} \mathord{\left/ {\vphantom {{\exp \left( {\frac{{h\,v_{i} }}{k\,T}} \right)} {\left[ {\exp \left( {\frac{{h\,v_{i} }}{k\,T}} \right) - 1} \right]^{2} }}} \right. \kern-0pt} {\left[ {\exp \left( {\frac{{h\,v_{i} }}{k\,T}} \right) - 1} \right]^{2} }}$$

where ν i is the vibrational frequency of the ith mode given in 1/s, T is the temperature in K, while k and h are the Boltzmann and Plank constants, respectively. In this study, we calculated \(C_{V_{i}}\) using ν 0 observed at ambient conditions.

Fig. 6
figure 6

Pressure dependence of the Raman bands of β-CaCr2O4 at room temperature

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The thermal Grüneisen parameter γ th of β-CaCr2O4 was obtained as 0.93(2) using 22 γ i values listed in Table 4 at 300 K. Ideally, all vibrational modes should be used to estimate the thermal Grüneisen parameter. However, some vibrational modes were not observed. In previous studies of CaFe2O4-type MgAl2O4 and CaAl2O4, Kojitani et al. (2013) concluded that the thermal Grüneisen parameter calculated using the observed Raman-active modes is consistent with that calculated using all vibrational modes. The γ th of β-CaCr2O4 is smaller than those of CaFe2O4-type MgAl2O4 (1.50) and CaAl2O4 (1.30). In the CaFe2O4-type structural phases, two kinds of AO8 (A = Ca, Mg) and MO6 (M = Al, Fe, Cr) polyhedra exist. Table 5 summarizes the average bond length of A-O and M–O and available thermal Grüneisen parameter γ th for CaFe2O4-type phases. It seems that the thermal Grüneisen parameter γ th for CaFe2O4-type phases increases with average bond-length decreasing, though no detailed information of the polyhedral evolutions in CaFe2O4-type phases under high pressures is available. Therefore, the thermal Grüneisen parameter γ th for CaFe2O4 is deduced to be less than that of β-CaCr2O4.

Table 5 Average bond length and γ th for CaFe2O4-type phases
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Generally, for relatively incompressible oxide crystals without polymerized tetrahedral, bulk Grüneisen parameters lie uniformly in the range from 0.8 to 2 (Shankland and Bass 1988). Moreover, the bulk thermal Grüneisen parameter, which is equal to αK 0 V/C v (where α is the thermal expansion, K 0 is the bulk modulus, V is the molar volume and C v is the volume constant heat capacity) (Grüneisen 1912), is still poor-constrained for β-CaCr2O4 because of the lack of thermal expansion and heat capacity data.