Abstract
The simple chemistry and structure of quartz together with its abundance in nature and its piezoelectric properties make convenient its employment for several applications, from engineering to Earth sciences. For these purposes, the quartz equations of state, thermoelastic and thermodynamic properties have been studied since decades. Alpha quartz is stable up to 2.5 GPa at room temperature where it converts to coesite, and at ambient pressure up to 847 K where it transforms to the beta phase. In particular, the displacive phase transition at 847 K at ambient pressure is driven by intrinsic anharmonicity effects (soft-mode phase transition) and its precise mechanism is difficult to be investigated experimentally. Therefore, we studied these anharmonic effects by means of ab initio calculations in the framework of the statistical thermodynamics approach. We determined the principal thermodynamic quantities accounting for the intrinsic anharmonicity and compared them against experimental data. Our results up to 700 K show a very good agreement with experiments. The same procedures and algorithms illustrated here can also be applied to determine the thermodynamic properties of other crystalline phases possibly affected by intrinsic anharmonic effects, that could partially invalidate the standard quasi-harmonic approach.
Highlights
Alpha quartz is a very common mineral in everyday life
On the other hand, when the anharmonicity is not taken into account either by using the harmonic approximation or by excluding the anharmonic modes from the calculation, the bulk modulus decreases much more slowly with respect to the trend obtained in case (1), and with respect to the experiment [8]; the α → β quartz phase transition is not predicted
The anharmonicity is the key for the correct reproduction of the bulk modulus behavior beyond 750 K, even if the phase transition is predicted to occur at a higher temperature than the experimental one
Summary
Alpha quartz is a very common mineral in everyday life. its piezoelectric properties make it suitable for engineering applications as oscillator and sensor in electronic devices (e.g., [1,2]) and it is one of the main constituents in the Earth’s crust. Since the abundance of quartz in a variety of geological environments and its multiple applications in material sciences, high-pressure and high-temperature experiments have been carried out to determine and constrain its thermoelastic properties (e.g., [3,4,5,6,7,8]) It has been recently studied in the framework of Raman elastic geobarometry applications (e.g., [9,10,11,12,13]) to calculate the entrapment conditions (i.e., pressure and temperature) of host-inclusion systems found in metamorphic rocks (e.g., [14,15,16]). In temperature (at ambient pressure) quartz shows a displacive phase transition at about
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