Test of the vibrational modelling for the λ-type transitions: Application to the α-β quartz transition |
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| Authors: | Joëlle Castex Michel Madon |
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| Institution: | 1. Département des Géomatériaux, Institut de Physique du Globe de Paris, 4, place Jussieu, 05, Paris Cedex, France
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| 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 λ-type transitions, we have applied it to the α-β quartz transition (T 0=846±1 K). Raman spectra of quartz were recorded up to 900 K. Measured frequency shifts of the α-quartz Raman modes were then used in conjunction with available high-pressure Raman data to calculate intrinsic mode anharmonicity, through the parameter a i=(?Lnvi/?T)v. Vibrational modelling of the heat capacity at constant volume, Cv, and at constant pressure, Cp, including anharmonic corrections deduced from the a i parameters, are compared to experimental data. Taking into account the soft-mode associated to the α-β 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 λ-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 λ-type transitions. In α-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. |
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