Cell utility

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The Cell utility in EosFit7c calculates cell parameters and their properties in a internally consistent way. It does not perform any fitting of EoS for either volumes or cell parameters.

 


Motivation: If you fit the unit-cell parameters and the unit-cell volume to obtain axial and volume EoS, the results will not be 100% consistent except when the crystal is cubic. Instead, you will find that the calculated cell parameters from the axial EoS will predict a volume that is not exactly the same as that predicted by the EoS of the volume. The same will be found for properties such as the elastic moduli. Normally the discrepancies are within the esd's and for most applications are not significant. However, for calculation of strain tensors and some host-inclusion calculations it is useful to do the calculations in a way that ensures 100% consistency between the cell parameters and the volume.


Method: 



which we can write as V = abc.A where A represents the entire square-root expression, which involves just the unit-cell angles. the relationship between the compressibilities of the unit-cell axes, the angles and the volume is given by:

and a similar equivalent expression for the thermal expansion coefficients. A second differentiation defines the relationships between the derivatives of these compressibilities:

These expressions can be written in terms of bulk and linear moduli as:


In crystal systems in which the unit-cell angles are constrained by symmetry, these last two expressions can be simplified to: 

For Reuss moduli:

And their pressure derivatives:


For other, general, directions in the unit cell the cell parameters are first calculated from the loaded EoS, and the metric tensor is constructed, from which the length of the chosen vector is calculated. Properties such as the linear modulus or thermal expansivity are calculated numerically from a spline to a series of length calculations over a small range of P or T, as appropriate. This numerical approach means that the calculated properties of general directions have lower precision than those calculated for unit-cell axes for which EoS are available, and the precision decreases as the order of the volume derivative increases; calculated values of the linear modulus M are more reliable than the derivatives M´ or dM/dT.




EoS


The user can load any combination of EoS for the cell parameters, volume and angles that provides all but one of the required quantities: 







When you create linear EoS for cell calculations we recommend that you use the dlabel command in the input utility to label each EoS with its direction before saving them to .eos files. The cell utility will then read the linear EoS from the .eos files without asking the user for the direction information.


Once you have loaded all of the individual .eos files for a crystal into the cell utility, you can save them to one single .eos file with the save command. This file with all of the information can be loaded back in to the cell utility, or into the hostinc utility. If you load an .eos file without multiple EoS into other utilities or the main level of the program, it is not a problem: the program will ask which of the EoS you want to load.



Correct results will only be obtained if:



List of the Cell commands 


System and macro commands are the same as for the main program.


Note: In this list of commands V means volume, L means an axial length and V/L means one of these two.


Eos Input and Output

Input

Start the input subroutine that allows you to load/save and modify the parameters of one EoS

Load

Load the parameters from any previously saved EoS. 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.

Save

At the command-line prompt, type save to save the parameters for one of the EoS currently in use. 

Save all

Use this command with 'all' to save all of the EoS to a single file.

Import

Import EoS parameters and EoS data from files in other formats. 

Clear

Delete an EoS from the utility (does not delete the eos file). Clear All will delete all of the EoS from the utility

Cryst

Set the crystal system

Params

List the parameters for a chosen EoS.

Document

Load or delete comments for an EoS

List

List the loaded EoS




Calculations

Props

Calculate the properties of one direction or the volume at one P and T. 

Pcalc

Calculate the pressure of one direction or the volume at one V/L and T

PVcal

Output an iosthermal P-V or P-L  list for one direction or the volume to a file (useful for plotting in external programs)

TVcal

Output an isobaric T-V or T-L  list for one direction or the volume to a file (useful for plotting in external programs)

Isochor

Calculate an 'isochor' for one direction or the volume - a line of P,T points along which the axis or volume is constant.

Isoratio

Calculate a line of P,T points along which the ratio of two directions is constant.

Calc

Calculate all cell parameters (no properties) at one P and T.

Cellcal

Calculate a list of cell parameters and the property tensors

Tensor

List the calculated cell parameters and property tensors

Strain

Calculate the strain tensor between the cells at two PT points

Equi

Calculate the equivalent descriptions of a direction as (hkl), [UVW], or Cartesian vector from any one of them, at a given P and T.




The following example shows you how to use some of these commands to calculate the cell and volume properties of rutile in a self-consistent way from the EoS for the a-axis and the volume stored in the file rutile_aV.eos that is included in the distribution. The EoS were determined by Zaffiro et al.,  (2019) Constraints on the Equations of State of stiff anisotropic minerals: rutile, and the implications for rutile elastic barometry. Mineralogical Magazine, doi: 10.1180/mgm.2019.24


Cryst command:


Start the Cell utility with the command cell in the main program.


Before loading a set of EoS for a phase it is important to set the crystal system with the cryst command, because if you load the EoS first and then type cryst, some of the cell parameter eos may get changed from what you input.


When the program starts the default crystal system is set to orthorhombic. 


In this example we are using rutile, which is tetragonal. Therefore, after entering cryst, give tetra (or longer, like tetragonal) as the crystal system.







Load command:


The load command reads EoS from .eos files. 


If there is more than one eos in the file, the program will ask you which EoS you want to load, as in this example. It is more convenient to store all of the EoS for one phase in one .eos file. In this example, the file rutile_av.eos contains the axial EoS for the a-axis and the volume.


Type load and use the file browser to select and open the file rutile_av.eos that is in the example files folder.


The program tells you that there are 2 EoS in the file. 


For each EoS the program tells you the title, and asks the parameter to which the EoS applies. In this case the choice for tetragonal is a,b, c, or V. In the example file, the first EoS is for a, so enter a.


The second EoS is for V, so enter V.


Note that if you do not want to load an EoS, enter x


At the end of the input questions, the program tells you which EoS are available, and whether they are PV, VT or PVT


Note that in this example, it tells you that the b-axis is set by symmetry (from the a-axis) and the c-axis will be calculated from the other EoS. In this case, c=V/a2



Calculations of Properties:


If you want to do a calculation on a loaded EoS, for example with pvcal, props, etc., the Cell utility works in just the same way as the main program, except that it will ask you for which EoS to use.


If you choose an EoS that is set by symmetry to be equivalent to another axis (eg b = a in tetragonal) the same calculations will be performed, but with the symmetry-equivalent EoS.


If you choose an axis (or the volume) which is set to be calculated from the other cell parameters, you will see a different output, as shown here:


  • There is no listing of EoS parameters, because there are none
  • There is a message that the properties will be calculated from other axes and volumes.
  • The program then prompts you to input P and T (if you have PVT EoS loaded).
  • The program calculates the properties at this P and T from the EoS of the other axes. Only the basic porperties are output.




Calc command:


The calc command tells you all of the unit-cell parameters at one individual P and T



The isochor command allows you to calculate and save a line in P-T space along which one of the cell parameters does not change.


The isoratio command allows you to calculate and save a line in P-T space along which the ratio of one cell parameter to another does not change.