Is there an equation linking phase relation and properties in mantle?

[Atr cheema]

I have information about temperature, pressure, normal and shear stresses, viscosity, conductivity, density, heat capacity and adiabatic heating for a particular area of mantle in the form of 2D matrices. I want to show phase relation for this region of mantle. Is there an equation (group of equations) which relates phase relation for mantle with these properties?

 

[stefan r]

My geology background is weak. I have more background in inorganic chem.

Are you looking for phase diagrams? Composition was not in the list of information you said you have. My impression was that composition phase diagrams were found by experiment. You can calculate equations for pressure-temperature phase transitions.

Here is one for silica:

This power point has several phase diagrams:

 

[billiards]

You would also need to know the composition.

Often a pyrolite composition is assumed for the Earth's whole mantle.

You might want to look at some equations of state the Birch-Murnaghan equation of state is often used in geophysics.

You may want to see how some open-source software can help you. For example Burnman contains mineralogical databases and some potentially useful functions which could be very useful.