The mphase (=multiphase) utility provides several different calculations for mixtures of isotropic phases under hydrostatic stress. This means that all calculations are performed with the volume EoS of the phases, all anisotropy in both the individual phases and in the microstructure is ignored, and all calculations are performed at the Reuss bound with all of the phases under the same hydrostatic pressure (except for host-inclusion calculations). In this utility you can:
Methods
IMPORTANT: The calculations of the elastic properties of mixtures only works if:
The total volume of a mixture of several phases is given by the sum of the volumes of the individual phases, the molar volume of each multiplied by the number of moles of that phase in the mixture:
and the volume fraction fi of a phase in the mixture is given by:
If all of the phases are under the same pressure, the compressibility of the mixture is obtained by taking derivatives of the above with respect to pressure:
An equivalent expression holds for the volume thermal expansion coefficient of the mixture.
The bulk modulus is:
The pressure derivative of the compressibility is:
And the bulk modulus of the mixture is:
Solutions: There are times when the user wants to set or calculate the stoichiometries of phases or groups of phases corresponding to volume fractions of phases. EosFit uses solutions for these calculations. A solution is a phase or a group of phases whose relative molar stoichiometries remains constant. A solution has constant molar fractions within it at all P and T. One example would be a pure phase, where the solution contains 100mol% of the phase. A second example would be a solid solution such as olivine, where one can set it as having 90mol% forsterite and 10mol% fayalite. The solutions are not used any further in calculations, they are only used as a way of calculating stoichiometry factors, and sometimes for calculating volume fractions of solutions.
Solutions only work when all of the EoS loaded in mphase have volumes in the same units. If volume scales that are not molar volumes are used (but are Å3/cell for example) then the results of the calculations presented as volumes or volume fractions are often confusing, especially if you are mixing different types of structures. You can still calculate the properties of mixtures of phases in this case, but be careful in reading the output; the properties are those for the listed volume fractions defined in terms of the Vscales of the EoS.
Solutions are set up with the soln command, in which you state the stoichiometric fractions of each component EoS that belongs to the solution. If your EoS are in molar volumes, these fractions are the molar fractions. If the input fractions do not sum to 1.0, the program will renormalise them so that they do, maintaining the stoichiometric ratios between components.
Once you have defined solutions, the setvf command allows one to set the stoichiometries of the phases to correspond to a chosen set of volume fractions at a specified P and T. But you can also do calculations of properties of the mixtures of phases without using the setvf command.
List of the Mphase commands
System and macro commands are the same as for the main program.
Eos Input and Output
All of these commands can take the list number of an EoS as an argument, so that you can work directly with that EoS. for example, save 2 will save the 2nd Eos in the list. if you do not give a number, you will be asked for one.
List |
List the EoS that have been loaded |
Input |
Load or input or change the EoS type and parameters for the two phases. Uses the INPUT utility. |
Load |
Load the parameters of an EoS |
Save |
Save the parameters of an EoS to an .eos file. |
Import |
Import EoS parameters from other file formats |
Clear |
Clear an EoS from the list. This does not delete the .eos file |
Params |
List the EoS parameters for both phases |
Document |
Load or clear comments for an EoS. |
Calculations with one EoS.
All of these commands can take the list number of an EoS as an argument, so that you can work directly with that EoS. for example, props 2 will start the properties calculation for the 2nd Eos in the list. if you do not give a number, you will be asked for one.
These commands are identical to the ones listed under EoS calculations.
Props |
Lists the properties of the EoS at any given P (and T) |
Pcal |
Calculates the pressure from the EoS at any given V (and T) |
Pvcal |
Calculates a series of PV data points, with all properties of the EoS. |
Tvcal |
Calculates a series of TV data points, with all properties of the EoS. |
Isochor |
Calculates a series of isochors (PT points of equal V) from the EoS. |
Calculations with multiple EoS.
All calculations are performed under the assumption that all of the phases are at the same pressure. Therefore properties are calculated at the Reuss bound.
Check |
Check the consistency of units etc between the EoS of different phases |
Stoich |
Set the stoichiometry factor for EoS |
Soln |
Assign EoS to solutions |
Setvf |
Set the volume fractions of solutions in a mixture |
Mixprops |
Calculate elastic properties of a mixture of solutions at a chosen input P and T. This can be run for a range of volume fractions, or for the volume fractions already set with the setvf command. The output also lists the volume fractions and molar fractions of phases in the mixture. |
MixVcal |
Calculate elastic properties of a mixture of solutions over a grid of P and T points, at the the fixed stoichiometries of the phases, set with the stoich or setvf commands. The output also lists the volume fractions and molar fractions of phases in the mixture. |
DelV |
Calculate the volume change of a reaction as specified by the stoichiometries of the phases. Reactants must be given negative stoichiometries, the products positive stoichiometries. |
DVcal |
Calculate the volume change of a reaction as specified by the stoichiometries of the phases over a grid of PT points. Reactants must be given negative stoichiometries, the products positive stoichiometries. |
Pmix |
Calculate the P of a mixture of solutions at a given V and T. |
Mixchor |
Calculate an isochor of a mixture |
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Calculations for host-inclusion systems.
These allow host-inclusion calculations to be made for mixed-phase inclusions inside a single-phase host. It is assumed that all of the phases in the inclusion are at the same pressure, and that the inclusion is closed so that the molar proportions of the phases in the inclusion do not change. The isotropic model for host-inclusion systems is used.
Host |
Set EoS to use as a host. The EoS must be loaded into the list of EoS |
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 phases with the stoichiometries of the phases in the list of EoS. |
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 phases with the stoichiometries of the phases in the list of EoS. |
Mixmeke |
Calculate the isomekes between the host and a mixture of phases in the inclusion. |