first, try  to look at P-T diagram of the material (maybe is's known for a long time). 

Dr. Brylev,  gives us practical way how to find the transformation temperature for a given pressure or visa verse using the experimentally drawn P-T  diagram!!!

Thermodynamics has only one useful relationship known as Clapeyron' s relationship, which can be also applied to two condensed phases.  That gives you the slope of dP/dT  of the P-T  diagram in terms of the ratio of molar enthalpy and volume differences.  dP/dT=  DH/TDV    or   = DS/DV,   where  D is the finite difference operator:  DH= Ha -Hb    DV= Va-Vb,  etc,

The main point is;  for condensed phases, both Va and Vb  are very small, and their difference is much smaller.  Usually a pressure of some hundred atmospheres is required to change the freezing point by a single degree.  For example for water: dPT/dT is about - 1.8 x 102  atm/deg. 

Thank you for your answer !

For complex materials, this can be hard to calculate analytically.

However, you can obtain the phase transition pressure from computational modelling. The research group that I work in has long used atomistic simulations (performed with the GULP code) to find the transition pressure for many materials and this technique has been proven to be successful. Maybe you also can try to use this tool for the material that you are studying.

Here goes some papers that illustrate the technique, in case you want to try.

Article Computer simulation of Na2ThF6 single crystals: Prediction o...

Article Behavior of the elastic and mechanical properties of Ba2BiTa...

Article About the mechanism of the reconstructive structural phase t...

Article Structural phase transitions under pressure in rare earth tr...

I check your two papers immediately. You calculate the enthalpy differences between  two known structures as a function of pressure for given temperature. To do that  you have to know how specific volume difference change with pressure. You need that data as a function of temperature and pressure. Actually if you have that data all you have to see at what pressure that difference shows sudden change or discontinuity/ 

BUT I WILL CHECK MORE TO SEE WHY IT WORKS SO GOOD!!!

@Tarik Ömer Oğurtani

Exactly. Using this program (GULP), you can obtain all the theoretical data needed to compare the two structures.

It gives you not only enthalpy, but also a number of other properties as a function of external pressure: lattice parameters, ions fractional coordinates, unit cell volume, dielectric constant matrix, elastic constant matrix, piezoelectric constant matrix, etc. The behavior of some these observables change in a very characteristic way (some matrix elements become null or equal to other elements, etc) when a specific structural phase transition takes place and this gives you less subtle parameters to rely on.

In the case of Na2ThF6, the transition was driven by the change in the Na z coordinate, so it wasn't necessary to compare two different phases. All that was needed was to observe the dependence of this coordinate on pressure. If this is the case, the analysis is somewhat simpler and more direct then observing enthalpy differences.

Dear Dr. Mouta; unfortunately theywere using the  black boxes (GULP) , like  the most people doing optimization,  without knowing what was the penalty function  to be optimized in that box.  Mostly they were calculating  the interaction energy of a   configuration which varies around the well known structure used as a template. Then they tried  to justify their  findings  relying  on the elastic constants whether they are matching well to the experimentally observed values or not!

 If one is using  temperature ,  pressure or stress tensor  plus the position of the individual particles as independent free variables then one has to  employ generallzed Gibbs Free energy function [ G=U+PV -TS]  or   its paffian differential form    [ dG= -SdT+ V dP  + SUMİJ ( FİJdxİJ) ]  to be optimized to  get the stable state of a thermodynamic system, which is  enclosed by flexible walls under the external tractions and body forces. If  one takes an  isothermal hypersurface, which they  do in their calculation then one doesn't have to worry about  the entropy.  To use  Enthapy as a penalty function in the optimization is bad choice  The  variation of which is denoted by   dH= TdS+ V dP + SUMİJ ( FİJdxİJ)  that shows that not only  interaction energy but also the configuration entropy should be calculated.  That was not done. This means they were operating at absolute degrees of Kelvin?  My suggesting is that moleculer dynamic calculations are necessary in  a way that quasi-thermostatics   arguments should be respected as much as possible in the optimization. Best Regards

Dear Dr. Oğurtani, I agree with you about the entropy. It really should be taken into account. The usual procedure in both ab initio and atomistic simulations is to minimize the enthalpy, instead of Gibbs energy. It is a globally accepted procedure, but I agree it's not the most adequate one. The quantity to be compared should be Gibbs energy. There are two ways of doing it using GULP.

The first one is minimizing H, but asking the program to calculate the phonon properties (give the temperature and use the "phonon" keyword). The output file will then display some vibrational properties calculated from the partition function due to the phonons, as: zero point energy (ZPE), entropy, specific heat, etc. Thus you can calculate G:

                                        G = ZPE + H - TS 

The term ZPE must be included explicitly, as it is not taken into account in the optimized enthalpy.

The second way is optimizing G itself. Although this is clearly more adequate and the comparisons are much more straightforward, Gibbs energy calculations are more expensive, computationally speaking. The potential parameters should be very good, otherwise the optimization tends to fail. The attached paper gives an idea of the methodology to optimize Gibbs energy and to find good potential parameters. If you have any doubt, I'm glad to help.

Article Concentration of Charge Carriers, Migration, and Stability i...