You can perform any type of calculation using any of the EoS formalisms available in the program without an actual dataset but only starting from known EoS coefficients.No data is actually required. You can calculate volumes, bulk modulus and its derivatives, alphas and Ff values at any pressure and/or temperature just by typing in the EoS parameters to the program!
If you have the full esd's and covariances of the EoS parameters (either directly from fitting, or because they were in the .eos file that you loaded) then the esd's of the results will be calculated from the variance-covariance matrix of the refined EoS parameters. Details in Angel (2000a).
Moreover, EosFit7c includes commands that help you plot data and equations of state in external graphics programs. All of these commands produce text files with the output values in fixed columns (and no delimiters).
List of the commands for 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. |
Conf |
Calculate and output to a file the coordinates for plotting confidence ellipses of parameters. |
Isochor |
Calculates a series of isochors (PT points of equal V) from the EoS. |
Tcal |
Calculates the temperature from the EoS at any given V (and P) |
Vcal |
Calculates the volume from the EoS at any given T and P |
PVFile |
Calculates the volume from the EoS at any given T and P listed in a text file, and outputs to a cal file. |
VdP |
Calculates the integral of VdP from P=0 to a chosen P at the chosen temperature, for contribution to Gibbs free energy. Only works correctly if the pscale and vscale of the EoS are set correctly |
PTGrid |
Calculate one property of the EoS over a grid of PT points |
Pthermal |
Calculate the thermal pressure at any PT point |
|
|
A complete list of file extensions used by EosFit7c is here.
These commands are described in more detail:
|
|
|
At the command-line prompt, type props and the program will prompt for the pressure value at which the calculation will be performed. If you have a P-V-T EoS, then you will be asked for the P and T. Type in the values and the program will output:
Important: If you have a thermal-pressure EoS, the thermal pressure reported as Pth is the thermal pressure difference from the reference temperature Tref. If you type a new value a new calculation is performed, hit return (<CR>) to exit the current calculation. |
|
|
|
At the command-line prompt, type pcal and the program will prompt for the volume value at with the calculation will be performed. If you have a P-V-T EoS, then you will be asked for the T and V. For each volume value input, the program will output the corresponding value of pressure. If you type a new value a new calculation is performed, hit return (<CR>) to exit the current calculation. Tcal works exactly in the same way, but calculates T from the input V. If you have a P-V-T EoS, then you will be asked for the P and V. |
|
|
|
Lists P-V (or P-linear) and all properties calculated from the current EoS parameters in an output file with default extension *.cal unless a different extension is specified. Once all the required EoS parameters have been loaded correctly (i.e. quartz in the example) by typing pvcal the program prompts for the pressure limits and step to use. You will need to type in the range of pressure where you want the calculation to be performed and the pressure step size for each calculation, as in this example calculation will be performed between 0 and 15 GPa every 0.5 GPa. |
|
The output file is by default given the extension .cal After the header information, and the EoS parameters, the properties of the EoS are listed for the selected pressure ranges. If the parameters were determined by least-squares fit to data, then the estimated uncertainties of each parameter are also calculated at each pressure step. (This is done by transformation of the variance-covariance matrix). All values are given in fixed format, delimited by commas The columns labeled 'f' and 'F' are the finite strain and normalised pressure for the selected kind of EoS. If you have a linear EoS, then the column labels are adjusted as appropriate, and the values of moduli are as defined in the theory section. |
|
|
|
Lists T-V (or T-linear) and all properties calculated from the current EoS parameters in an output file with default extension *.cal unless a different extension is specified. If you have a P-V-T EoS, then the properties are calculated for a range of T at a series of P selected by the user. |
|
Here is an example of the output file created by the program (this output file is related to the dataset T_lawsonite.dat) After the header information, and the EoS parameters, the properties of the EoS are listed for the selected temperature ranges. If the parameters were determined by least-squares fit to data, then the estimated uncertainties of each parameter are also calculated at each pressure step. (This is done by transformation of the variance-covariance matrix). All values are given in fixed format, delimited by commas This file was created from a thermal expansion equation only. Therefore all moduli have 'dummy' values, and only the V and alpha are meaningful. If you have a P-V-T EoS, then all columns would be filled with values. If you have a linear EoS, then the column labels are adjusted as appropriate, and the values of moduli are as defined in the theory section. |
|
|
|
Only works for P-V-T EoS !!! Lists a series of isochors (PT points of equal V) calculated from the current EoS parameters in an output file with default extension *.cal unless a different extension is specified. After opening a file for the output, you will be asked for the ranges of P and T over which to do the calculations. The output file contains the same header information as other .cal files. Then there is a listing of P and T points with their V. Each group of points with the same V is one isochor. |
|
|
Conf |
|
|
The refined values of EoS parameters are usually highly-correlated, often to 90% or more. Therefore, in interpreting the parameter values it is important not to just consider the parameter esd's (from their variance), but also the consider their co-variance. The covariance (or correlation) of refined parameters is best illustrated by plotting confidence ellipses, which are can be calculated from the variance-covariance matrix of the refinement. The complete method is described in Angel (2000a). After you have completed a refinement of EoS parameters, run the conf command. The program prompts you for:
After the calculation is complete, you can enter another sigma level. No input allows you to exit from the utility, as shown. |
|
Here is an example of the output file from conf. At the top of the file is the header information about the program, followed by a list of the EoS parameters and type. Then there is:
Then the columns labeled X, Y1, Y2 provide the coordinates of the confidence ellipse in the parameter space. The ellipse is centred on the refined values. The points to be plotted are with coordinates (X,Y1) and (X,Y2). If you join up the two series of points with lines you will get the ellipse! |
PVFile |
|
|
This command allows you to calculate the Volume and other EoS parameters from values of P and T listed in a text file. The text file must contain one pair of values of P and T on each line. It can be P,T or T,P: Eosfit7c will ask you what you have in the file. The temperatures can be in C or K: again EosFit7c will ask you The calculated volumes, bulk moduli etc., are written out to a text file, whose name you can input. |
VdP |
|
|
This command calculates the elastic strain energy and the integral of VdP (for free energy calculations). All of the results of this command depend on the units used for the V and the P in the EoS. Make sure that you have set the pscale and vscale correctly, otherwise the results will be meaningless! EosFit7c looks at pscale and vscale and will tell you the units of energy for the results. If pscale = GPa, and vscale = cm3/mol, the energies will be given in kJ/mol. The elastic strain energy is the volume and hydrostatic pressure equivalent of the anisotropic strain energy written in terms of the elastic moduli and strains as
For hydrostatic pressure the principal stresses are equal to the pressure, and the sum of the principal strains is the volume strain, so for a small increase in hydrostatic pressure, the first and last versions of the strain energy become respectively:
This is given both as a 'Linear approximation', and by numerical integration with small steps in P. It is the strain energy for the increase in pressure from P=0 to P at the chosen temperature. The integral of VdP from P=0 to P at the chosen temperature gives the contribution of compression to the Gibbs free energy. The integral is performed analytically with the given EoS parameters put into a Murnaghan EoS, and this result should be similar to the numerical integration with the same parameters in the chosen EoS model. |