The Isomeke utility in EosFit7c calculates isomekes and performs the calculations of remnant and formation pressures for spherical single phase inclusions trapped in host materials. It uses the isotropic model only, and therefore only the volume EoS of the host and inclusion phases.
In the Isomeke utility calculations are performed in two parts:
Before using the isomeke sub-program in EosFit7c we advise you to:
Some definitions:
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.
List of the Isomeke commands
System and macro commands are the same as for the main program.
Eos Input and Output
Input |
Load or input or change the EoS type and parameters for the two phases. Uses the INPUT utility. |
Load |
Load the EoS parameters of the two phases from .eos files. All .eos files for these datasets can be downloaded from the data library at www.rossangel.com, along with files for many other EoS. |
Save |
Save the EoS parameters of the two phases to .eos files. All the Equation of State files are exchangeable between EosFit7c and EosFit7 GUI (i.e you can save it in EosFit7c and read it EosFit7 GUI and vice-versa) |
Import |
Import EoS parameters from other file formats |
Params |
List the EoS parameters for both phases |
Notes: 1: These commands operate in the same way as in the main program, and are not described in detail here. 2: For isomeke calculations the value of V0 is not needed in the EoS of the two phases, because what is important is the relative changes of volume of the two phases over a given P and T range. Therefore, you will not be asked for V0, and you may see it change as calculations proceed because the program resets it to convenient values at various points in the calculations. 3: If you use the same .eos files again and again, you might record the commands that you use to start the calculation with the macro command. Then you can later load all of the files and numbers with a single command to run the recorded macro! |
Calculations
Isocal |
Calculate one or more isomekes for two EoS. This is a purely thermodynamic calculation. |
Pinc |
Calculate the remnant pressure on a spherical inclusion in a host, after a change in P and T. Provides results in two parts; first the purely thermodynamic calculation with no elastic relaxation, second including the elastic relaxation calculated from several models. See example below. |
Ptrap |
Calculate the possible entrapment conditions for an inclusion from the EoS of the two phase and the remnant pressure on the inclusion. A spherical inclusion in an isotropic host is assumed. The isomeke of entrapment is calculated for each of the relaxation models. |
Gridp |
Calculates the inclusion pressure over a grid of P,T points, using the EoS of the two phases and the entrapment conditions. |
Delv |
Calculates the difference in the free volumes of the two phases at any P,T from the EoS of the two phases. Note that this is not a host/inclusion calculation as it does not consider the mutual elastic interaction of a host and inclsuion. It just calculates the deltaV! |
The following examples of calculations assume that you have already loaded in the EoS parameters for two phases. Here we use diamond as a host, and Fo92 olivine as an inclusion. The .eos files are available by download from the data archive at www.rossangel.net.
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The isocal command works in two modes. If you input Y to the first question, you can calculate a family of isomeke lines (as then listed). An isomeke is calculated at each requested pressure starting at the minimum temperature. The output lists the P and T where the volumes of the two phases have changed by the same amount from the starting conditions. The output includes the calculated V of both phases at the P,T points, so that you can confirm the precision of the calculations. At the end you have the option to save the output to a .cal file for plotting in external programs. |
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If you input N to the first question, you can calculate a single isomeke line starting from the P and T that you input. The output lists the P and T where the volumes of the two phases have changed by the same amount from the starting conditions. The output includes the calculated V of both phases at the P,T points, so that you can confirm the precision of the calculations. At the end you have the option to save the output to a .cal file for plotting in external programs |
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The pinc command calculates the remnant pressure on an inclusion at your chosen P,T, given the entrapment conditions. After listing the EoS parameters and asking if you want to change them, the program asks for two items of information: 1: Input entrapment P & T: Enter the entrapment conditions 2: Final P & T: The calculation can be performed for any P & T, but if you want the reference conditions of the EoS (often room P and T) you can just hit enter <CR>. |
The output lists results for five models of relaxation: 0: No relaxation - the pure thermodynamic calculation. 1: Pure Zhang (1998). This is the linear relaxation, with elastic parameters for relaxation always at room conditions. 2: Linear Elastic. This the linear relaxation, but with the elastic parameters for relaxation calculated at the final conditions of P and T. 3: Full Iso P*. This is the non-linear relaxation of Angel et al (2014), calculated with a value of K21 from the elastic parameters at P*, Tend. It is intended to indicate, by comparison with #4, the uncertainties arising from the assumption of constant K21. 4: Full Iso Pend. This is the non-linear relaxation of Angel et al (2014), calculated with a value of K21 from the elastic parameters at Pend, Tend. 5: An exact solution to the relaxation problem based on the elastic hollow sphere solution (Angel et al., 2017c). The final Pinc from this model should lie between that of models 3 and 4, and should be the correct Pinc. |
The results are provided in a Table: Pinc is the final remnant P on the inclusion. Pthermo is the remnant P without relaxation, a purely thermodynamic calculation. delPrelax is the relaxation of P in the inclusion, equal to Pinc-Pthermo The Vnow columns give the relative volume of the inclusion relative to entrapment and to reference P,T Kinc and Ghost give the bulk modulus of the inclusion and the G of the host used to calculate the delPrelax. They are the values at P(props). Further calculations can be performed by entering new entrapment conditions at the prompt that appears. |
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The Ptrap command calculates entrapment conditions given a remnant pressure. The entrapment conditions are not unique: they are points on an isomeke passing through the final T and a pressure Pfoot. After listing the EoS parameters and asking if you want to change them, the program asks for two items of information: 1: The remnant pressure on the inclusion. 2: Final P & T: The calculation can be performed for any P & T, but if you want the reference conditions of the EoS (often room P and T) you can just hit enter <CR>. |
The output lists results for five models of relaxation, as described above. There are two steps to the calculation and results listing: Step 1: The determination of a pressure at the final T at which there is no stress gradient in the system. This is termed Pfoot. It depends on the relaxation model. The other items in the results table match those from the Pinc command (see above). Step 2: The user inputs the range of temperatures for calculating the isomeke that passes through Pfoot, Tend, and which thus represents possible entrapment conditions. The output lists the isomekes for the five relaxation models.
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Further calculations can be performed by entering new entrapment conditions at the prompt that appears. |