In the tetragonal rutile structure (space group: P42/mnm), the Ti4+ cations are coordinated with 6 O2- anions, forming TiO6 octahedra stacked parallel to the c-axis (Swope et al., 1995; Howard et al., 1991). The refined unit-cell parameters for the Fe-bearing natural rutile sample are a=4.604 6(2) Å, c=2.963 9(2) Å and V=62.842(7) Å3, and the atomic position coordinates are: x=y=0.304 9(4) (z=0) for O2- with Ti4+ fixed at the inversion center (0, 0, 0). The Ti-O bond lengths and O…O distances are calculated using the software package Xtaldraw (Downs et al., 1993), and sketched in Fig. 1. In this natural sample, 1.4 mol.% of Ti4+ cations are dominantly substituted by Fe3+, which enlarges both the unit-cell and octahedral TiO6 volumes by 0.7%–0.8%, as compared with the Ti-pure rutile samples (Swope et al., 1995; Howard et al., 1991; Sugiyama and Takéuchi, 1991; Meagher and Lager, 1979). On the other hand, the incorporated protons (H+) coupled with Fe3+ substitution could be detected by infrared spectrum (Lucassen et al., 2012; Bromiley and Hilairet, 2005; Vlassopoulos et al., 1993).
Figure 1. The crystal structure of TiO2 rutile. The Ti-O bond lengths and O…O edge distances are calculated from the structure refinement in this study.
Two IR-active OH-stretching bands are observed for this rutile sample at ambient condition (Fig. 2), and the intensity of Band 1 (at 3 279 cm-1) is higher than that for Band 2 (at 3 297 cm-1), which is consistent with the previous measurements for hydrous Fe-bearing rutile samples (Yang et al., 2011; Bromiley and Hilairet, 2005; Bromiley et al., 2004). The band at 3 279 cm-1 is associated with the reduction of Ti4+ (Ti4+=Ti3++H+) and decoupled with any compositional defects or trivalent cation substitution (Bromiley and Shirvaev, 2006; Hammer and Beran, 1991; Johnson et al., 1973, 1968), while the one at 3 297 cm-1 is coupled with Fe3+ incorporation. Many of the reported studies attributed the OH modes to protonation near the position of (1/2, 1/2, 0), which is along the shared O…O edge of the octahedron in the (001) plane (Bromiley and Shiryaev, 2006; Bromiley and Hilairet, 2005; Swope et al., 1995; Vlassopoulos et al., 1993). In addition, another position at (1/2, 0, 0) is also proposed as a favorable site for protonation in the rutile structure (Koudriachova et al., 2004; Johnson et al., 1968), which is at the channel center outside TiO6 octahedra.
Figure 2. Representative IR spectra for this hydrous rutile at ambient condition, with the position of bands 1 and 2 labelled.
The water concentration in rutile was calculated on the basis of Lambert-Beer Law (Eq. 1)
where ε is the absorption coefficient, γ is the parameter for the orientation factor, while d is thickness of the sample. I0(v) and I(v) are the intensities of the incoming and transmitted radiation at the frequency v, respectively. Here, we adopt the absorption coefficients from Maldener et al. (2001) (38 000 L·mol-1·cm-2) and Johnson et al. (1973) (30 200 L·mol-1·cm-2), and set the orientation factor to be 1/3 for unpolarized FTIR spectra. The IR absorbance is integrated in the frequency range of 3 200–3 400 cm-1 for each measured point. The 3 to 5 points were measured at different locations on each of these 6 crystal pieces, and the averaged water content (over 20 measurements) with standard deviation of 4 350±670 H/106 Ti (CH2O=490±75 ppmw.) by the calibration from Maldener et al. (2001), while 5 470±840 H/106 Ti (CH2O=620±95 ppmw.) from Johnson et al. (1973). The EPMA analysis gives a Fe content of 1.4 mol.% (14 000 Fe/106 Ti), which is more than 20 times of the H atomic concentration in this rutile sample and accounts for 86.5 mol.% of the incorporated trivalent cations (M3+) in this rutile sample. Hence, there should be two ways for M3+ (mainly Fe3+) incorporation: the electrostatically coupled substitution (Ti4+=Fe3++H+) and the substitution causing oxygen vacancies (2Ti4+=2Fe3++OV), while the latter one might be dominant in this natural rutile. Such trivalent cation substitution mechanism is similar to that in Al-bearing SiO2 stishovite (Si4+=Al3++H+ together with 2Si4+= 2Al3++OV) (e.g., Litasov et al., 2007; Pawley et al., 1993).
The powder XRD pattern at T=300 K (Fig. 3) was obtained when quenched from 923 K after significant dehydration, and then the sample powder was gradually heated up to 1 500 K. The unit-cell parameters at various temperatures were refined by at least 7 reflection lines out of (110), (100), (200), (111), (210), (211), (220), (002), (310), (301) and (112) (Table S3). At ambient condition, the unit-cell parameters (a, c and V) quenched from 923 K (by powder XRD) agree with the ones before any heating (by single-crystal XRD), within the experimental uncertainty. Hence, we speculate that such a water concentration (CH2O < 700 ppmw.) should have little impact on the unit cell. Another XRD pattern was also measured at room temperature (noted as 'quench' pattern in Fig. 3) when quenched from 1 500 K, and the reflection pattern is quite consistent with that quenched from 923 K, implying that rutile was stable without any phase transition at high temperatures up to 1 500 K at ambient pressure.
Figure 3. XRD patterns obtained at 300 K (middle) and 1 500 K (top), as well as quenched from 1 500 K (bottom). The Bragg's peaks for rutile are indexed, and some of the Pt reflection lines are marked for the pattern measured at 300 K.
Variations of the a and c axes with temperature are plotted in Fig. 4a, which have been normalized to the ones at 300 K. The averaged axial thermal expansion coefficients are 9.25(8)× 10-6 K-1 (R2=0.994 7) and 11.98(8)×10-6 K-1 (R2=0.999 4) for the a and c axes, respectively, which are quite consistent with the previous measurements (Hummer et al., 2007; Sugiyama and Takéuchi, 1991). The c axis shows larger thermal expansion coefficient as compared with the a-axis due to the increased TiO6 octahedral distortion at elevated temperatures. Hummer et al. (2007) conducted high-temperature synchrotron powder XRD measurement up to 575 K. Sugiyama and Takéuchi (1991) carried out single-crystal XRD experiment up to 1 873 K but with larger temperature intervals (fewer data points) as compared with this study, and part of their dataset (within 1 500 K) was shown in Fig. 4a. In addition, both the studies took measurements on synthetic Ti-pure rutile sample, while we adopted the natural sample with 1.4 mol.% Fe in this study. Good agreement among these three datasets suggests that such Fe concentration should not have significant effect on the thermal expansivity for rutile.
Figure 4. (a) Variations of the a and c axes with temperature, which are normalized to the ones at 300 K. Comparison is also made with the literatures (Hummer et al., 2007; Sugiyama and Takéuchi, 1991). (b) The unit-cell volume as a function of temperature with the fitting curves by Suzuki (Eq. 4) and Kumar (Eq. 5) equations. The inset shows the fit residue for the volumes.
The thermal expansion coefficient (α), which describes the variation of volume as a function of temperature, is defined as
Various function forms have been proposed for α as a function of T at P=0 GPa, and a famous one is proposed by Fei (1995) as below
The fitted Fei Equation on this dataset yields: α0= 25.40(7)×10-6 K-1, α1=6.93(8)×10-9 K-2 and α2= -0.668(8)×10-6 K. Besides, Suzuki (1975), Suzuki et al. (1979) and Kumar(2003, 1996, 1995) established the correlation between the volume and temperature on the basis of the Mie-Grüneisen- Debye Equation of state, which are believed to be more accurate at high temperatures well above the Debye temperature. The Suzuki and Kumar equations are expressed as in Eqs. (4) and (5), respectively
In the above equations, Q0=V0(0)·KT0(0)/γMGD, and k= (KT'–1)/2. V0(0) and KT0(0) are the volume and isothermal bulk modulus at P=0 GPa and T=0 K, and the pressure derivative of the isothermal bulk modulus KT'=6.5 (Arlt et al., 2000). The thermal energy Eth(T) is constructed on the Debye model
where R is the gas constant, n is the number of atoms in the formula (3 for rutile), while ΘD is the Debye temperature, which could be derived in the acoustic mode
where h, k and N are the Boltzmann, Plank and Avogadro's constants, respectively. The molar mass M=79.9 g/mol and the density ρ=4.233 g/cm3 for rutile, and the mean seismic velocity Vm can be calculated as in Eq. (8)
Isaak et al. (1998) reported the seismic velocities for rutile at ambient condition: VP=9.24(7) km/s and VP=5.16(8) km/s, and we can derive the mean velocity Vm=4.67(9) km/s and the acoustic ΘD=636(17) K. Our V-T dataset was fitted by Suzuki and Kumar equations (Fig. 4b), and the differences between the fitted and measured volumes at high temperatures are generally within ±0.02 Å3, which are significantly smaller than the uncertainties of measurement. The fitted unit-cell volume and Q0 parameter at T=0 K are: V0(0)=62.50(12) Å3 (18.812(4) cm3/mol) and Q0=2.63(1)×106 J·mol-1·K-1 for Kumar Equation, while V0(0)=62.48(14) Å3 (18.806(4) cm3/mol) and Q0= 2.72(1)×106 J·mol-1·K-1 for Suzuki Equation. On the basis of the measured KT0(300 K)=210.3 GPa and ∂KT/∂T= -0.05 GPa/K (Isaak et al., 1998), it could be obtained that KT0 (0 K)=225.3 GPa, as well as the Grüneisen parameter γMGD=1.56 for Kumar Equation, while 1.61 for Suzuki Equation.
The volumetric thermal expansion coefficients (αV), fitted from Fei, Suzuki and Kumar equations, are plotted as a function of temperature in Fig. 5, and they agree well with each other within a discrepancy of ±3% when extrapolated to 2 000 K. Our results are also compared with the data in the literatures (Henderson et al., 2009; Hummer et al., 2007; Saxena et al., 1993; Sugiyama and Takéuchi, 1991; Touloukian and Kirby, 1977; Rao et al., 1970). According to the Debye model, the thermal expansion coefficients for materials generally increase with temperature increasing, while the αV profiles from this study are located between those from Touloukian and Kirby (1977) and Saxena et al. (1993) at high temperatures above 800 K. On the other hand, the averaged thermal expansion coefficient (α0) from this study is 30.48(5)×10-6 K-1, which is 5%–30% larger as compared with the previous studies (Henderson et al., 2009; Hummer et al., 2007; Sugiyama and Takéuchi, 1991; Rao et al., 1970).
Figure 5. The volumetric thermal expansion coefficient (αV) as a function of temperature. Comparison is made between this study (bolded curves) and the previous studies (normal dotted curves; a. Rao et al., 1970; b. Henderson et al., 2009; c. Hummer et al., 2007; d. Sugiyama and Takéuchi, 1991; e. Touloukian and Kirby, 1977; f. Saxena et al., 1993).
There are 15 optical vibrational modes in rutile with irreducible representation in total: 1A1g(R)+1A2g (inactive)+1A2u(I)+ 1B1g(R)+1B2g(R)+2B1u(I)+1Eg(R)+3Eu(I) (R: Raman-active; I: infrared-active) (Lan et al., 2012; Hemley et al., 1986; Mammone et al., 1980; Porto et al., 1967). The selected Raman spectra for the lattice vibrations (below 1 000 cm-1) at low and high temperatures are shown in Fig. 6. The Eg (O-Ti-O bending) and A1g (asymmetric Ti-O stretching) modes are observed around 440 and 610 cm-1, respectively, with quite strong intensities and similar half-height widths. The B1g band (TiO6 octahedron rotation around the c axis) is detected to have a sharp peak around 140 cm-1 with much lower intensity, while B2g (symmetric Ti-O stretching) appears as a weak and broad band above 810 cm-1, which could only be observed at the temperatures below 400 K. In addition, the multi-phonon process is observed as a broad 'hump' around 230 cm-1, which is caused by the anharmonic feature as well as disorder in the rutile structure (Lan et al., 2012; Balachandran and Eror, 1982; Hara and Nicol, 1979).
Figure 6. Representative Raman spectra for the lattice vibrations (including the multi-phonon process) at low and high temperatures. The vertical dashed lines stand for the peak positions of the modes at room temperature (RT), and the backgrounds of the black-body radiation have been subtracted.
The black-body radiation got stronger with temperature increasing, while the intensities of the vibrational bands (including the multi-phonon process) systematically become weaker at elevated temperature. Variations of these modes with temperature are plotted in Fig. 7, and the slopes ((∂vi/∂T), cm-1·K-1) from the linear regressions are compared with the data in the literatures (Lan et al., 2012; Samara and Peercy, 1973) in Table 1. The internal Ti-O stretching (A1g, B2g) and O-Ti-O bending (Eg) modes systematically shift to lower frequencies at elevated temperature, since the covalent Ti-O bonds get elongated during the thermal expansion procedure (Sugiyama and Takéuchi, 1991). The B1g mode is nearly temperature independent, implying that temperature has little impact on the rotation of the TiO6 octahedron. On the other hand, the multi-phonon process exhibits 'blue-shift' at higher temperature, which is in accordance with the fact that the anharmonic features, as well as disorder in the crystal structure, increases with temperature increasing.
Figure 7. Evolution of the Raman shifts for the lattice modes (including the multi-phonon process) with temperature increasing.
Assignment vi (cm-1) (∂vi/∂T)P (cm-1·K-1) Lattice vibrations This study Lan et al. (2012) Samara and Peercy (1973) B1g 142 0.002(3) 0.001 0.000 9(6) Multi-phonon 232 0.040(6) -- -- Eg 439 -0.032(5) -0.049 -0.028(2) A1g 608 -0.011(4) -0.009 0.003 7(2) B2g 810 -0.044(8) -- -- OH-stretching This study (IR-active) This study (Raman-active) Yang et al. (2011) Guo (2017) Band 1 3 279 -0.056(2) -0.059(4) -0.021(3) -0.083 Band 2 3 297 -0.082(3) -0.056(3) -0.049(3) -- Merged band 3 245a -0.048(2) -0.069(2) -- -- a. Measured at 923 K by FTIR spectrum.
Table 1. The temperature-dependence (∂vi/∂T) P of the frequencies for both the lattice and OH-stretching vibrations
In addition, the microscopic isobaric Grüneisen parameter (γiP), describing the evolution of the mode frequency with temperature at fixed pressure, is defined below
Taking the average thermal expansion coefficient from this study (α0=30.48(5)×10-6 K-1), we derived the γiP parameters for the lattice vibrational modes: -0.5(7) for B1g, +2.4(3) for Eg, +0.6(2) for A1g, and +1.8(3) for B2g.
The OH-stretching bands 1 and 2 are also detected by Raman spectra at 3 283 and 3 293 cm-1 (at 300 K in Fig. 8a), which agree well with the IR-active ones (Fig. 8b). The shifts of these OH-stretching bands are recorded by high-temperature FTIR and Raman spectra up to 1 273 K, as well as low-T Raman spectra down to 123 K. Around a temperature of 873 K, bands 1 and 2 (for both Raman-active and IR-active modes) merge completely into a single band. While the OH-stretching bands are still deconvoluted into two bands at the temperatures below 873 K, so as to better describe the thermal behaviors for bands 1 and 2. The Raman-active OH-stretching band cannot be detected above 1 073 K due to strong black-body radiation, but can still be recovered when quenched from 1 273 K (Fig. 8c).
Figure 8. Selected Raman (a) and FTIR (b) spectra for the OH-stretching bands measured at various temperatures. The signals for the Raman (at 1 073 K) and FTIR (at 1 273 K) spectra are magnified for clarity. The Raman (c) and FTIR (d) spectra, obtained when quenched from high temperatures, are compared with the one before heating. Background has been subtracted for each spectrum.
Both the Raman-active and IR-active OH-stretching modes systematically shift to lower frequencies at higher temperature (Fig. 9), with the decreasing rates ((∂vi/∂T), cm-1·K-1) listed in Table 1. Similar phenomenon for the 'red-shift' of OH-stretching bands is also observed by other FTIR measurements (Guo, 2017; Yang et al., 2011). According to the empirical correlation between the hydrogen bond length (dO…H) and the frequency (vi) of OH-stretching mode (Libowitzky, 1999), the OH bands in rutile should correspond to an O…H bond length about 1.85 Å as well as an O…O distance of 2.75 Å. While the shared O…O edge for protonation is much shorter as measured by single-crystal XRD (dO…O=2.542 Å in Fig. 1). Therefore, the O-H…O bond must be nonlinear, and the shift of the OH-stretching frequency might be dominantly determined by the elongation of the covalent O-H band itself at high temperature (Mookherjee et al., 2001). In addition, the IR-active band at 3 279 cm-1 (decoupled with Fe3+ substitution) shows the temperature-dependence in a larger magnitude as compared with the one at 3 297 cm-1 (coupled with Fe3+ substitution), and similar phenomenon was also reported by Yang et al. (2011), which was attributed to the fact that the electronegativity of Ti4+ is larger than that for Fe3+ (Li and Xue, 2006).
Figure 9. The frequencies of IR-active (solid symbols) and Raman-active (open symbols) OH-stretching modes as a function of temperature. The vertical line represents T=900 K, around which bands 1 (five-star) and 2 (circles) completely merge into one single band (triangle). The vertical error bars for the full-width of half maximum are presented if larger than the sizes of the symbols.
The integral IR absorbance and Raman signal intensity for the whole OH-stretching bands are plotted as a function of temperature in Fig. 10a. To make a consistent comparison, the Raman spectra at different temperatures were collected at the constant experimental condition (including the incident laser power, beam spot size as well as the exposure duration). The intensities for both Raman and IR signals decrease abruptly at a temperature of around 873 K, due to the factors of both dehydration and smaller absorption coefficient (ε) at higher temperatures. For most hydrous minerals, the absorbance (logarithm for the ratio between I0(v) and I(v) as the numerator in Eq. (1)) generally becomes smaller at elevated temperatures even without dehydration (CH2O remains constant), suggesting negative dependence between the absorption coefficient (in the denominator of Eq. (1)) and temperature. On the other hand, the Raman signal intensity decreases to 58% and 16%, when quenched from 873 and 1 273 K, individually, with respect to that before heating (Fig. 8c). While the integral IR absorbance decreases to 56% and 15% (Fig. 8d), when quenched from 823 and 1 273 K, respectively, hence, we speculate about 43% dehydration by 850 K, and 85% dehydration by 1 273 K, according to the quenched spectra. We also checked the variations of bands 1 and 2, separately, in the temperature range up to 873 K (Fig. 10b), and the intensities for each band have been normalized to the one at 300 K. Both the Raman and FTIR results support the general trend that the intensities of OH-stretching bands decrease with temperature increasing, and partial dehydration may happen at both the decoupled and coupled H sites in this rutile structure. It should be also noted that at each time, the sample was quenched immediately with power off, and the temperature was cooled down below 500 K within half a minute.
Figure 10. (a) The integral IR absorbance and Raman intensity for the OH-stretching bands as a function of temperature. (b) Variations of the intensities for bands 1 and 2 with temperature below 900 K (solid symbols: IR-active; open symbols: Raman-active). The intensities have been normalized to the ones at 300 K for IR-active and Raman-active signals, respectively.