EosFit7-Pinc does the same calculations as the Isomeke sub-program in EosFit7c, but with a GUI interface. It is only available for windows operating systems.
EosFit7-Pinc includes the utilities to calculate isomekes and to perform the calculations of remnant and formation pressures for spherical inclusions of single phases trapped in host materials. If you need to do calculations for inclusions containing more than one phase, use the host-inclusion utility of EosFit7c.
All calculations in EosFit-Pinc are performed in two parts:
- The thermodynamic part: this is purely based on the two EoS's of the two phases. No interaction between them is considered. Neither is anisotropy considered. Such calculations can be applied to any system of two phases with different properties, and with any physical geometry.
- The interaction part: the mutual elastic relaxation of two physically-connected phases after a change in pressure and/or temperature strongly depends on several factors including the geometry of the system (how the two phases are connected together) and the elastic anisotropy. The general problem is not soluble algebraically. Further, until Angel et al (2014, Am Min), the relaxation of the simple system of a spherical inclusion within an infinite host, both elastically isotropic, had only been solved for linear elasticity, and not for EoS and significant changes in P and/or T. EosFit7-Pinc implements the non-linear solution for spherical inclusions given in Angel et al (2014, Am Min), the linear solution given by Zhang (1998), and a new exact solution based on the hollow-sphere problem adapted to non-linear elasticity (Angel et al., 2017, Am Min).
Before using EosFit7-Pinc we advise you to:
- Read the recent literature on isomekes and relaxation of simple isotropic spherically-symmetric host-inclusion systems (Zhang, 1998; Angel et al., 2014, Am Min; Angel et al., 2017, Am Min) and the references in those papers.
- Understand the assumptions behind the calculations of the elastic interactions and how they might limit the applicability of the results to more complex systems, including those with anisotropic elasticity. Remember that even cubic crystals are elastically anisotropic; only amorphous materials and true liquids are elastically isotropic!
Some definitions:
- Isomeke: A line in P,T space along which the volumes of two phases change by the same relative amount. It therefore represents a path along which the fractional volume changes of the host and inclusion are the same. It's instantaneous slope is determined by the ratio of the differences in volume thermal expansion coefficients and compressibilities of the two phases.
- Entrapment conditions: It is assumed that when the inclusion is trapped within the host and elastically isolated from the outside, the P and T of the host and inclusion are the same, and that the inclusion fits perfectly within the host without stress or strain gradients.
- Pthermo: The pressure that the inclusion would have if there was no elastic relaxation. The Pthermo is calculated as the thermodynamic part (see above) from the EoS of the host and inclusion.
- Remnant pressure: Called Pinc. The pressure in an inclusion that is different from the external pressure. It arises from a change in P and T, and because the host and inclusion phases have different EoS. It includes the mutual elastic relaxation of the system after the change in P and T. When the host/inclusion system is moved along an isomeke through the original entrapment conditions the Pinc and Pthermo are equal to the external P.
Important: shear moduli
If you have an EoS for the host without a value for the shear modulus (G), then the mutual elastic relaxation will be calculated as zero.
- Since the 2017 release .eos files can store the value of the shear modulus at the reference conditions (G0), and its variation with P and T, as derivatives dG/dP and dG/dT etc. Use the input utility in EosFit7c to input these values and then save the .eos file before using it in EosFit-Pinc.
- If you have an old .eos file (from before May 2017), it will not contain shear moduli. Load the .eos file into EosFit7c and use the input utility to add the value of the shear modulus at the reference conditions (G0). If you want to calculate remnant inclusion pressures at non-ambient P and T, you must also input dG/dP and dG/dT. Save the .eos file and read it into EosFit-Pinc.
- If you import an EoS from the Thermocalc database directly into Eosfit-Pinc, the import dialogue also allows you to set the shear modulus (G0) for the host crystal at room P and T
The EosFit7-Pinc GUI is made up of several tabs that are devoted to different functions. Calculation tabs only become available after you have loaded the EoS of both the host and the inclusion.
