Raman and X-ray diffraction study of pressure-induced phase transition in synthetic Mg2TiO4

Synthetic Mg2TiO4 qandilite was investigated to 50 and 40.4 GPa at room temperature using Raman spectroscopy and X-ray diffraction, respectively. The Raman measurements showed that cubic Mg2TiO4 spinel transforms to a high pressure tetragonal (I41/amd, No.141) phase at 14.7 GPa. Owing to sluggish kinetics at room temperature, the spinel phase coexists with the tetragonal phase between 14.7 and 24.3 GPa. In the X-ray diffraction experiment, transformation of the cubic Mg2TiO4 to the tetragonal structure was complete by 29.2 GPa, ~5 GPa higher than the transition pressure obtained by Raman measurements, owing to slow kinetics. The obtained isothermal bulk modulus of Mg2TiO4 spinel is KT0 = 148(3) GPa when KT0’ = 6.6, or KT0 = 166(1) GPa when KT0’ is fixed at 4. The isothermal bulk modulus of the high-pressure tetragonal phase is calculated to be 209(2) GPa and V0 = 270(2) Å3 when KT0’ is fixed at 4, and the volume reduction on change from cubic to tetragonal phase is about 9%. The calculated thermal Grüneisen parameters (γth) of cubic and tetragonal Mg2TiO4 phases are 1.01 and 0.63. Based on the radii ratio of spinel cations, a simple model is proposed to predict post-spinel structures.

thermodynamic properties are needed in the Mg 2 TiO 4 system. In this study, in situ high-pressure Raman measurements and equations of states of both spinel and post-spinel structures of synthetic Mg 2 TiO 4 qandilite were investigated at room temperature. The post-spinel phase was identified and a model for prediction of post-spinel structure is also reported.

Result and Discussion
Two Raman measurements were conducted at pressure to 24.5 GPa and 50 GPa, respectively. Group theory predicts that for normal spinels at the Γ point of the Brillouin zone 27 : where R denotes Raman-active modes and u denotes infrared-active modes. Therefore, five Raman bands are predicted for the normal spinels. However, cation disorder in the inverse spinel is expected to cause splitting of the A 1g mode [28][29][30][31] . In this study, two A 1g , one E g , and three T 2g were observed for Mg 2 TiO 4 spinel, and, in addition, two weak peaks at the shoulders of T 2g (432 and 546 cm −1 ) were present (blue arrows in Fig. 1). The higher frequency peaks of A 1g modes are assigned to stretching of the MgO 4 tetrahedron and the split A 1g mode is found at about 596 cm −1 in our measurements. The E g mode corresponds to a symmetric bending vibration of the oxygens within tetragonal units. The T 2g near 506 cm −1 is caused by an asymmetric bending of O-Mg-O bonds and the other T 2g near 281 cm −1 is assigned to the translation between TiO 6 octahedron and Mg cation. The T 2g near 385 cm −1 arises from the opposing translations between cations and oxygens along one direction of the lattice. The two different shoulders of T 2g are likely related to cation substitutions. When Mg 2 TiO 4 spinel was compressed to 14.7 GPa, a new peak appeared close to 595 cm −1 . Upon further compression to 24.5 GPa, four additional new peaks were observed, strongly suggesting a new phase. To test whether the new high-pressure phase can be quenchable, the sample was gradually decompressed to ambient pressure, after which a shoulder of high frequency A 1g from the high pressure phase was retained, suggesting that the new phase did not fully back-transform and some amount of the new phase coexisted with the spinel phase (Fig. 1). The second Raman measurements were conducted to 50 GPa and the results are shown in Fig. 2 To better understand the phase transition boundary, the frequency shifts as a function of pressure are plotted in Fig. 3. A single new peak observed at slightly higher frequency near 595 cm −1 at about 14.7 GPa and is assigned to the new phase. A discontinuity was clearly observed near 24.3 GPa, as evidenced by four additional modes near 413, 558, 737, and 836 cm −1 . Our Raman data suggest that the new phase only partially transformed at about 14.7 GPa, and that the transformation is very sluggish. A two-phase mixture therefore persists between 14.7 and 24.3 GPa. The decompression results showed that the high-pressure phase was partly quenchable, and both spinel and high-pressure phases coexisted to ambient pressure. Four high-pressure modes and six cubic bands were found in the quenched Raman spectra based on two sets of Raman measurements, but the peak at about 500 cm −1 , which coincides with the position of a peak in compression data, appeared only below 4 GPa. Since this is a first-order phase transition for Mg 2 TiO 4 , we were then able to obtain the slopes of pressure dependence dν i / dP values based on two different datasets of curve fits.
The high-pressure phase of Mg 2 TiO 4 could have a tetragonal structure, based on the splitting of MgO 4 modes. Previous studies on ZnGa 2 O 4 20 and MgCr 2 O 4 22 also suggested a cubic to tetragonal transition at high pressure and room temperature. Our X-ray diffraction analyses (see below) suggest that the high-pressure phase is a tetragonal spinel (I4 1 /amd, No.141). The new peak at 413 cm −1 splits from E g at 24.3 GPa due to the different bending vibration of oxygen at tetrahedral units, and the other new peak at 558 cm −1 appeared at high pressure in the tetragonal phase because of the change of O-Mg-O bending from original higher-frequency T 2g . The cubic spinel A 1g peak at 737 cm −1 split into two peaks at 809 and 836 cm −1 , which can be attributed to differences in the shortening of bond lengths of the MgO 4 tetrahedron. As a result, the observed Raman-mode frequencies (ν), pressure dependencies (dν i /dP), and mode Grüneisen parameters (γ i ) for spinel and for the high-pressure phase are listed in Table 1. The pressure dependencies dν i /dP of Mg 2 TiO 4 spinel indicate that two higher-frequency T 2g and one A 1g are more compressible, and the lowest-frequency T 2g are stiffer. The lowest-frequency E g of the high-pressure phase is stiffer than the other Raman modes. Mode Grüneisen parameters (γ i ) are calculated from the equation where isothermal bulk moduli K T of spinel and tetragonal phase are both obtained from this study (see below). The thermal Grüneisen parameter (γ th ) 34,35 can be calculated as the weighted average of the mode Grüneisen parameters (γ i ), which are listed in Table 1. The thermal Grüneisen parameter is given by , and the harmonic heat capacity Cv i was estimated from the Einstein function: www.nature.com/scientificreports www.nature.com/scientificreports/ where temperature T is 300 kelvins, h is the Plank constant, and κ is the Boltzmann constant. Our results show that the thermal Grüneisen parameter is 1.01 for the spinel phase and 0.63 for the tetragonal phase.
No MgTiO 3 contaminant was observed during any of the X-ray diffraction measurements and the ambient-pressure unit-cell lattice parameters of synthetic Mg 2 TiO 4 spinel collected at both 13-BM-D and 13-BM-C were confirmed to be the pure phase. The ambient-pressure unit-cell parameters of the synthetic Mg 2 TiO 4 spinel are a 0 = 8.4464(2) Å and V 0 = 602.59(5) Å 3 , both of which are comparable with previous studies 9,11,14,36 . In-situ high-pressure X-ray diffraction patterns of Mg 2 TiO 4 to 27.4 GPa collected at beamline 13-BM-D (Run 1) are shown in Fig. 4a. Our two-dimensional images displayed a new feature at 15.7 GPa which could be the high-pressure tetragonal phase T101 (Fig. 4b). At pressure above 22.8 GPa, additional new peaks were observed, allowing us to determine that the structure of the high-pressure phase is tetragonal I4 1 /amd (No. 141). Note that the spinel structure was found to coexist with this high-pressure tetragonal phase, but its diffraction peaks became weaker above 27.4 GPa. As a consequence, no further data at higher pressures were collected from Run 1. Upon decompression, spinel and the tetragonal phases were found to coexist at all pressures to ambient conditions. For Run 2, the pressure was increased directly from 2.7 to 22 GPa and then gradually compressed to 34 GPa within 3 hours (Fig. 5a). Again, the high-pressure tetragonal phase coexisted with Mg 2 TiO 4 spinel from 22 to 34 GPa and the refined structure at 34 GPa is shown in Fig. 5c. However, the tetragonal phase T101 appeared at 32 GPa, which

Spinel Phase
High-Pressure Phase www.nature.com/scientificreports www.nature.com/scientificreports/ was about 18 GPa higher than Run 1, and another new peak T220 appeared at 34 GPa (Fig. 5b). For Run 3, the pressure was gently increased from 1 bar to 40.4 GPa over 9 hours (Fig. 6). At 29.2 GPa the cubic spinel had fully transformed to the tetragonal phase. After decompression, both spinel and high-pressure tetragonal phases were retained and persisted for at least 24 h after decompression to ambient conditions. The tetragonal phase T220 is critical for the structure determination but it is actually very weak. We checked all our 2D images and found the T220 only observable at 34 GPa in Run 2. In addition, for the tetragonal phase T532, it only can be assigned to the www.nature.com/scientificreports www.nature.com/scientificreports/ tetragonal phase by doubling the c-axis to 5.446 Å at 25.9 GPa in Run 3. In summary, our X-ray diffraction results suggest that the tetragonal phase transformation started at 15.7 GPa and completed at 29.2 GPa. In addition, in all three runs, the coexistences of spinel and tetragonal phases over variable ranges of pressure are likely to be a result of sluggish kinetics. Our X-ray diffraction data showed both spinel and tetragonal phases were present between www.nature.com/scientificreports www.nature.com/scientificreports/ Figure 6. Representative X-ray diffraction patterns of Mg 2 TiO 4 collected in Run 3. Cubic Mg 2 TiO 4 spinel fully transforms to tetragonal structure at 29.2 GPa. Upon decompression, both low-and high-pressure phases were present at ambient pressure. The room-pressure pattern was collected after 24 hours of decompression. (Red: compression patterns; blue: decompression patterns).

Spinel Structure
Tetragonal Structure  www.nature.com/scientificreports www.nature.com/scientificreports/ 15.7 and 29.2 GPa, but in the Raman measurements the mixture of phases is limited to a smaller pressure range. We postulate that this is owing to longer collection time in Raman measurements than in the X-ray diffraction measurements and perhaps because local atomic bonding distortions and variations detected by Raman scattering are more sensitive than the bulk structural changes measured using the X-ray diffraction method.

P (GPa) a(Å) V(Å 3 ) P (GPa) a(Å) c(Å) V(Å 3 )
The unit-cell lattice parameters and volume data of Mg 2 TiO 4 at pressure to 40.4 GPa are summarized in Table 3. The Mg 2 TiO 4 volume data with respect to pressures were fitted with a third-order Birch-Murnaghan equation of state, with all volume data expressed as molar volumes (Fig. 7). The obtained isothermal bulk modulus of Mg 2 TiO 4 spinel is K T0 = 148(3) GPa when K T0 ' = 6.6, and K T0 = 166(1) GPa when K T0 ' is fixed at 4, in agreement with previous studies 13,14 . The volume change between spinel and tetragonal phase is about 9%. The unit-cell lattice parameters of tetragonal phase obtained from this study are also listed in Table 2. The bulk modulus K T0 of the tetragonal phase is obtained as 209(2) GPa and V 0 = 270(2) Å 3 when K T0 ' is fixed at 4, based on the trend of Eulerian strain-normalized pressure plot 37 .
To evaluate the post-spinel structure for the orthotitanates, we compare several spinel phases and their post-spinel structures such as CT 38 (Table 3). The CF phase of AB 2 O 4 post-spinel was limited by the radius ratio r B /r A . In general, CF phase can be found in the range of 0.53 to The Eulerian strain-normalized pressure plot shows that K T0 ' of the high-pressure phase is close to 4.  www.nature.com/scientificreports www.nature.com/scientificreports/ 0.89, but not in the case of r B /r A < 0.53 47 . The radius ratio r B /r A of Mg 2 TiO 4 is around 1.19 which is larger than the range of CF phase but very close to Zn 2 TiO 4 with radius ratio r B /r A of 1.22. The post-spinel structure of Zn 2 TiO 4 was suggested to be CT phase 48 with an intermediate tetragonal phase 23  , where A cations do not sit in tetrahedral sites anymore and the size limit for B cations is smaller as they have to fit into tetrahedral sites. Nevertheless, whether in normal or inverse spinels, A cations are usually larger than B cations under ambient conditions. Figure 8 shows the radius ratio r A /r O with respect to r B /r O for several different spinels at ambient conditions, and two distinct trends of CM and CF are observed. Intermediate tetragonal and CT phases lie mostly between CM and CF curves. The A cations (Ti 4+ ) of Mg 2 TiO 4 , Zn 2 TiO 4 , and Co 2 TiO 4 inverse spinels are the same and the radii of B cations (Mg 2+ , Zn 2+ , and Co 2+ ) are very similar. However, they have different post-spinel structures within the area r A /r O < 0.45 and r B /r O > 0.5. The possible explanation is that when r A is smaller than r B , not only B cations can sit in both tetrahedron and octahedron but also A cations. With the exception of the CF phase, the trends of all post spinels are located within the area where radius ratio r B /r A is smaller than 1.

Conclusion
Two sets of Raman measurements were performed at pressure to 24.5 GPa and 50 GPa in this study. Our Raman results demonstrated that a phase transformation occurred at 14.7 GPa, and a two-phase mixture persisted at pressure up to 24.3 GPa. The cubic Mg 2 TiO 4 spinel fully transformed to a tetragonal phase above 24.3 GPa and the new phase persisted to 50 GPa. On decompression, the high-pressure phase was observable from 50 to about 18.7 GPa, and most Raman features were diminished with further decompression except the broad A 1g peak near 700-800 cm −1 . The high-pressure phase was partly quenchable below 18.7 GPa, and both spinel and high-pressure phases coexisted to ambient pressure. Our X-ray diffraction data suggest that the tetragonal phase transformation started at 15.7 GPa and completed at 29.2 GPa. The coexisting cubic and tetragonal phases are also shown on our decompression X-ray diffraction patterns at ambient pressure. Comparing our three X-ray diffraction runs, the coexistence of spinel and tetragonal phases extends over three different pressure ranges, and the full phase transformation pressure is ~5 GPa higher than Raman measurements, which is likely the result of slow kinetics. The obtained isothermal bulk modulus of Mg 2 TiO 4 spinel is K T0 = 148(3) GPa when K T0 ' = 6.6, or K T0 = 166(1) GPa when K T0 ' is fixed at 4. The isothermal bulk modulus of high-pressure tetragonal phase is calculated as 209(2) GPa and V 0 = 270(2) Å 3 when K T0 ' is fixed at 4, and the volume reduction from cubic to tetragonal phase is about 9%. Grüneisen parameters (γ th ) calculated from the isothermal bulk moduli K T of spinel and tetragonal phases obtained from this study are 1.01 and 0.63. A simple model to predict post-spinel structures is proposed based on the radii ratio of spinel cations and our model shows the tetragonal phases located in between the CF and CM trends. www.nature.com/scientificreports www.nature.com/scientificreports/

Experimental Methods
In situ high-pressure and room-temperature Raman and X-ray diffraction measurements on Mg 2 TiO 4 qandilite were performed at pressure to 50 and 40.4 GPa, respectively, using symmetric diamond anvil cells. Mg 2 TiO 4 qandilite starting material was synthesized at 1673 K for 52 h from a mixture of MgO and TiO 2 . The product was examined by electron probe microanalysis and conventional X-ray diffraction. The results show Mg 2 TiO 4 with less than 5% of MgTiO 3 14 . We used a pair of 300-µm diamond culets for both Raman and X-ray diffraction measurements in the high-pressure diamond anvil cell study. Rhenium gaskets were pre-indented to 35-40 µm thickness and a 150-µm hole was drilled to create a sample chamber. Neon was used as a pressure-transmitting medium, together with 1 or 2 ruby spheres for both Raman and X-ray diffraction experiments. A small piece of 10-15 μm gold foil was also loaded in the sample chamber as a pressure marker for the synchrotron X-ray study. Pressure was monitored by the ruby fluorescence method 50 and/or equation of state of gold 51 .
Raman spectra were collected at the University of Western Ontario using a custom-built system. An argon-ion laser with a wavelength of 514.5 nm was used as an excitation source. The Raman signals were collected by a spectrometer with a 500-mm focal length and equipped with a liquid nitrogen-cooled CCD detector. The spectrometer was calibrated by a neon lamp and a silicon chip. The uncertainty in Raman shift measurements did not exceed 1 cm −1 . Two different in situ Raman measurements were carried out to 24.5 and 50 GPa, respectively. The pressure was measured by the shift of ruby R 1 emission peak before and after Raman measurements. The collection time of each spectrum was 240 seconds at lower pressure and then increased to 420 seconds at pressure above 24 GPa. The reported spectrum was the average of five spectra at each pressure step. Peakfit software (SPSS Inc., Chicago) was used for Raman peak curve-fitting.
In situ high-pressure angular-dispersive X-ray diffraction experiments were carried out at beamline 13-BM-C and 13-BM-D, sectors of GSECARS, Advanced Photon Source. At both beamlines LaB 6 was used for sample-to-detector distance calibration. The purity of the Mg 2 TiO 4 spinel phase was confirmed by X-ray diffraction before the high-pressure experiments. One run (Run 1) at pressure to 27.4 GPa was performed at 13-BM-D. The wavelength of the monochromatic X-ray beam at 13-BM-D was 0.3344 Å, and the beam size was focused to 3 × 7 µm. Two runs (Run 2 and 3) at pressures to 34 and 40.4 GPa were conducted at 13-BM-C. The wavelength of the monochromatic X-ray beam at 13-BM-C was 0.434 Å and beam size was focused to 12 ×18 µm. X-ray diffraction patterns were collected by two-dimensional MAR CCD at 13-BM-C and the exposure time of each pattern was 90-120 seconds with sample rotation angle from 80 to 100 degrees. The exposure time of a Perkin-Elmer area detector for each collection at 13-BM-D was 5 seconds without rotation and each diffraction image was the average of 20 patterns to enhance the signal-to-noise ratio. Two-dimensional images were integrated and reduced to one-dimensional patterns using Dioptas software 52 . The powder X-ray diffraction data were processed using the software PeakFit V4.12 (SPSS Inc.) and the unit cell parameters were calculated by the program UnitCell 53 . Experimental powder diffraction results are compared to theoretical values calculated using CRYSTALDIFFRACT software and Le Bail refinement by GSAS (Fig. 5c).