The HostInc utility in EosFit7c performs calculations for anisotropic crystals in host-inclusion systems in a self-consistent manner. The utility also does calculations based on the isotropic model, details of which are described for the isomeke utility. Therefore this utility can do host-inclusion calculations for any combination of isotropic and anisotropic phases as host and inclusion.
If a phase is not cubic, then the cell parameter variations with P and T are calculated with the same methods as described for the cell utility, to ensure internal consistency.
EosFit cannot calculate elastic relaxation for anisotropic crystals. Therefore all calculations are done to/from the unrelaxed strains of the inclusion when the host is at the final conditions. To calculate relaxation you must use another program, for example EntraPT, or do your own calculation of the anisotropic relaxation. This normally requires finite-element modeling.
The principles behind the calculation of unrelaxed strains of an inclusion given the known entrapment conditions are explained in Mazzucchelli et al., (2019) for the example of anisotropic inclusions in isotropic host minerals, and in Gonzalez et al (2021) for fully anisotropic systems. In EosFit these strains are calculated via the deformation gradient tensor to avoid ambiguities arising from the definition of Cartesian axial systems when there are significant shear strains (e.g. Schlenker et al. 1978; Gonzalez et al 2021).
If the entrapment and final external conditions are specified, the deformation gradient tensor Fhost is calculated from the metric tensors of the host at entrapment and the final conditions, which are defined by the EoS of the unit-cell of the host. The deformation gradient tensor Finc,end>trap represents the deformation of a free inclusion crystal from the final conditions to entrapment, and is calculated from the metric tensors of the inclusion at entrapment and the final conditions, which are defined by its unit-cell EoS.
The deformation gradient tensor for the inclusion from a free crystal of the inclusion at the final external conditions to the unrelaxed trapped inclusion is then:
In which U is the matrix defining the relative orientation of the Cartesian axial system of the inclusion relative to the Cartesian axial system of the host. The unrelaxed strain of the inclusion is calculated as the infinitesimal Lagrangian strain from the deformation gradient tensor as shown in Schlenker et al. (1978) and Gonzalez et al (2021).
In order to calculate unique entrapment conditions of an anisotropic host-inclusion system, the user has to first perform the calculation of relaxation, and then provide the pttrap command with the infinitesimal Lagrangian strain of the unrelaxed inclusion, relative to a free crystal of the inclusion phase at room conditions. The pttrap command then calculates isomekes for three mutually perpendicular directions in the inclusion with the parallel directions in the host, and outputs a list of PT points for each of these three isomekes. It is left to the user to determine the crossing point of the three isomekes which would represent the entrapment conditions under external hydrostatic pressure. An example is given in Alvaro et al. (2020).
List of the Host-Inclusion commands
System and macro commands are the same as for the main program.
Eos Input, Output and Settings
Load |
Load the parameters from any previously saved EoS for the host or inclusion. If the file contains the EoS for several directions then they will all be loaded. If the direction information is not stored in the file, you will be asked to enter it. |
Clear |
Delete an EoS from the utility (does not delete the eos file). You can delete individual EoS, or all of the EoS for either the host or the inclusion. |
Params |
List the parameters for a chosen EoS. |
List |
List the loaded EoS |
|
|
Cryst |
Set the crystal systems for host and inclusion. These are used to calculate the lengths of symmetry-equivalent directions. See the Cell utility for the methods. |
Cart |
Set the Cartesian axial choice for both the host and inclusion crystals (it must be the same for both). Four choices covering all of the major published conventions are provided. |
Csym |
Set the Cartesian axial choice by symbol. Cartesian axial choices are defined by a two-letter code. The first defines the real cell axis parallel to a Cartesian axis. And the second defines the reciprocal axis parallel to a Cartesian axis. Thus 'CA' means c // Z and a* // X. Current allowed orientations are: CA BC BA CB |
Orient |
Set the relative orientation of the host and inclusion. This is specified as a rotation matrix which defines the orientation of the Cartesian axes of the inclusion cell with respect to the Cartesian axes of the host cell. The rows of the matrix are the direction cosines of the inclusion Cartesian axes with respect to the host Cartesian axes. |
Calculations for host-inclusion systems
|
Calculations using the isotropic model These commands apply the isotropic model for host-inclusion systems (Angel et al., 2017) and use only the volumes of the host and inclusion phases to calculate inclusion pressures. If the volume EoS for either the host and/or the inclusion has not been loaded, the volume variation with P and T is calculated from the variation in unit-cell parameters following the methods described here. The 'exact' model for relaxation is used if the shear modulus of the host is provided in its EoS. The results will be the same within calculation uncertainties with the results from EosFit-Pinc and the isomeke utility in EosFit-7c. |
Pinc |
Calculate the final inclusion pressure from the entrapment conditions for a host-inclusion system using the isotropic model and only the volume EoSs of the host and inclusion. |
Ptrap |
Calculate the entrapment isomeke from the final inclusion pressure Pinc for a host-inclusion system using the isotropic model and only the volume EoSs of the host and inclusion. |
GridP |
Calculate the final inclusion pressures for a grid of entrapment conditions in PT. Uses the isotropic model and only the volume EoSs of the host and inclusion. |
|
Calculations for anisotropic systems These commands can be used for any combination of crystal systems for the host and inclusion, including isotropic systems. Before doing any calculations you must:
Important: EosFit cannot calculate elastic relaxation for anisotropic crystals. Therefore all calculations are done to/from the unrelaxed strains of the inclusion when the host is at the final conditions. To calculate relaxation you must use another program, for example EntraPT, or do your own calculation of the anisotropic relaxation. This normally requires finite-element modeling. |
Equiv |
Calculate the equivalent direction in the host for a crystallographic direction in the inclusion, or vice-versa, using the relative orientation specified by the Orient command. |
Isomeke |
Calculate isomekes for a direction common to the host and inclusion crystal, as specified by the Orient command. Warning: Isomekes are calculated under the assumption that there is no relative rotation of the host and inclusion direction. This is not true when there is a significant difference in the elastic anisotropy of the host and inclusion.
|
EPth |
Calculate the unrelaxed strains of an inclusion (i.e. at Pthermo) from the cell parameter variations of the host and inclusion and the entrapment conditions. The results depend on the relative orientation of the host and inclusion crystals, which must be specified by the Orient command. The components of the strain tensor depend on the Cartesian convention (set by the Cart or Csym commands), and are the strains relative to a free crystal at the final external P and T applied to the host. The anisotropic relaxation cannot be calculated in EosFit. |
GridE |
Calculate the unrelaxed strains of an inclusion (i.e. at Pthermo) from the cell parameter variations of the host and inclusion and the entrapment conditions for a grid of entrapment conditions in PT. |
PTTrap |
Calculate the entrapment P and T for the inclusion from the unrelaxed final inclusion strains, using the cell parameter variations of the host and inclusion. The output is in the form of three entrapment isomekes for perpendicular directions over the T range chosen by the user. The unique entrapment conditions are at the P and T where the isomekes cross. If the isomekes do not all cross at one P,T point, then the system has suffered non-elastic modification. |
|
|
|
|