A simple and generalised P–T–V EoS for continuous phase transitions, implemented in EosFit and applied to quartz

  • Ross J. AngelEmail author
  • Matteo Alvaro
  • Ronald Miletich
  • Fabrizio Nestola
Original Paper


Continuous phase transitions in minerals, such as the α–β transition in quartz, can give rise to very large non-linear variations in their volume and density with temperature and pressure. The extension of the Landau model in a fully self-consistent form to characterize the effects of pressure on phase transitions is challenging because of non-linear elasticity and associated finite strains, and the expected variation of coupling terms with pressure. Further difficulties arise because of the need to integrate the resulting elastic terms over pressure to achieve a description of the P–T–V equation of state. We present a fully self-consistent simplified description of the equation of state of minerals with continuous phase transitions based on a purely phenomenological adaptation of Landau theory. The resulting P–T–V EoS includes the description of the elastic softening occurring in both phases with the minimum number of parameters. By coupling the volume and elastic behaviour of the mineral, this approach allows the EoS parameters to be determined by using both volume and elastic data, and avoids the need to use data at simultaneous P and T. The transition model has been incorporated in to the EosFit7c program, which allows the parameters to be determined by simultaneous fitting of both volume and elastic data, and all types of equation of state calculations to be performed. Quartz is used as an example, and the parameters to describe the full P–T–V EoS of both α- and β-quartz are determined.


Quartz Continuous phase transition Equation of state Elasticity EosFit 



Software development for this project was supported by ERC starting grant 307322 to Fabrizio Nestola, and by the MIUR-SIR Grant “MILE DEEp” (RBSI140351) to Matteo Alvaro. We thank Andrea D’Alpaos and Mario Putti (University of Padova) for advice on least-squares minimisation, Tim Holland (Cambridge), Tom Duffy (Princeton) and Kyle Ashley (Texas) for discussions on various aspects of equations of state and phase transitions, Aaron Wolf (Ann Arbor) for a thorough and thought-provoking review, and Javier Gonzalez-Platas (La Laguna) for continuing collaboration on the development of the cfml library.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of GeosciencesUniversity of PadovaPadovaItaly
  2. 2.Department of Earth and Environmental SciencesUniversity of PaviaPaviaItaly
  3. 3.Institut für Mineralogie und KristallographieUniversität WienWienAustria

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