Test of the vibrational modelling for the ?-type transitions: Application to the ?-? quartz transition

Abstract

Abstract.Vibrational modelling is at the present time the only known way to predict the heat capacities of the Earth's mantle minerals at high-pressure and high-temperature. To test the validity of this method for 2-type transitions, we have applied it to the c~-fl quartz transition (T o = 846 +_ 1 K). Raman spectra of quartz were recorded up to 900 K. Measured frequency shifts of the c~-quartz Raman modes were then used in conjunction with available high-pressure Raman data to calculate intrinsic mode anharmonicity, through the parameter a i = (c~LnvJ c~T)v. Vibrational modelling of the heat capacity at constant volume, Cv, and at constant pressure, Cp, including anharmonic corrections deduced from the a~ parameters, are compared to experimental data. Taking into account the soft-mode associated to the ~-fl quartz transition, the model reproduces the excess of Cp related to the transition. Then, this study confirms that detecting a soft-mode from vibrational data allows one to predict 2-type transitions. However, when modelling the thermodynamic properties, the contribution of a soft-mode cannot be established from spectroscopic data. Therefore, one needs first to determine this contribution in order to predict the heat capacities of Earth's mantle minerals displaying 2-type transitions. In c~-quartz, this contribution has been determined as 0.007% of the total number of the optic modes in the model of the density of states.

Analysis of temperature‐dependent Raman spectra of minerals: Statistical approaches

“…In the region >600 cm −1 , modes are associated with stretching vibrations, [63] in the region 355-509 cm −1 with bending vibrations of SiO 4 tetrahedra, [64] whereas in the region 129-265 cm −1 , they are associated with bending and/or rotational vibrations of SiO 4 tetrahedra. [32] α-β displacive phase transition with a symmetry change from space group P3 2 21 to P6 2 22 takes place in quartz at 846 K. [31,33,40] Limited by 873 K, the studied temperature range makes a clear determination of the phase transition based on our data problematic; however, spectral changes in the pretransition region contain the signs of a phase transition and are consistent with those obtained previously. [32,41,65] A broadening and shift of most modes to the low-energy spectral region is observed with increasing temperature (Figures 2e and 4a), which is most pronounced for low-energy modes of 128 and 209 cm −1 , as well as a change in the relative intensity of individual spectral bands-in particular, a gradual decrease in A 1 mode intensity at 355 cm −1 (Figure 2b).…”

“…[32] α-β displacive phase transition with a symmetry change from space group P3 2 21 to P6 2 22 takes place in quartz at 846 K. [31,33,40] Limited by 873 K, the studied temperature range makes a clear determination of the phase transition based on our data problematic; however, spectral changes in the pretransition region contain the signs of a phase transition and are consistent with those obtained previously. [32,41,65] A broadening and shift of most modes to the low-energy spectral region is observed with increasing temperature (Figures 2e and 4a), which is most pronounced for low-energy modes of 128 and 209 cm −1 , as well as a change in the relative intensity of individual spectral bands-in particular, a gradual decrease in A 1 mode intensity at 355 cm −1 (Figure 2b). The A 1 mode at 209 cm −1 , which is usually regarded as soft mode related to the phase transition, [32,41,64] can be attributed to the rotational vibrations of the tetrahedra as a whole and consequently responsible for the displacive phase transition.…”

“…[32,41,65] A broadening and shift of most modes to the low-energy spectral region is observed with increasing temperature (Figures 2e and 4a), which is most pronounced for low-energy modes of 128 and 209 cm −1 , as well as a change in the relative intensity of individual spectral bands-in particular, a gradual decrease in A 1 mode intensity at 355 cm −1 (Figure 2b). The A 1 mode at 209 cm −1 , which is usually regarded as soft mode related to the phase transition, [32,41,64] can be attributed to the rotational vibrations of the tetrahedra as a whole and consequently responsible for the displacive phase transition. [66,67] In this regard, the use of the proposed algorithms for the analysis of quartz spectra was aimed at testing them in order to study the effects of dynamic disordering with strong bias and broadening of the soft mode in the vicinity of the phase transition.…”

“…From the example of synthetic (model) and experimental spectral arrays, it can be seen that statistical analysis of I(ν,T) data allow an objective, express (without peak fitting) diagnosis of spectrum changes to be carried out, revealing the similarity/difference between the functional dependencies of the spectral statistical parameters on T in different temperature or spectral ranges at a qualitative level and determining the critical temperature values, including the temperature of phase transitions. On the example of zircon, which does not have phase transitions in the indicated temperature range at atmospheric pressure, [28,29] we illustrate the manifestation of anisotropic thermal expansion of the lattice and phonon-phonon interaction in the dependencies of statistical parameters on T. On the example of quartz undergoing a two-stage α-β displacive phase transition involving an intermediate incommensurate phase from the side of the β phase at 848 K, [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45] we show the effect of changes in the spectral profile in the regions of soft and hard modes on the temperature dependencies of statistical parameters in the T region preceding the phase transition. Hardware temperature limitations (870 K) prevented the reliable recording of β-phase spectra.…”

New experimental developments in Raman spectroscopy at high pressures and temperatures on crystalline and amorphous phases

“…: : : have a linear temperature dependency up to the transition toward the &phase at 847K (see for instance Gillet et al, 1990;Castex and Madon, 1995). They have also a linear pressure dependency up to at least i G P a (Hemley, 1987).…”