I am trying to compute the solid state phase diagram of the Ti-Nb alloy using ATAT. This system has two phases, the HCP-based alpha-phase and the BCC-based beta phase. The tar.gz attachment includes the cluster expansions for these phases. The attached pd.eps is a plot of the phase boundaries. Curve 1 in pd.eps is obtained by plotting the output phb.out (which is in /btinb/) from:
Here /atinb/ and /btinb/ are CE of alpha and beta phases respectively.
Curve 1 deviates from the experimental phase boundary. On the other hand, checkrelax in atinb/
prints a relaxation of more than 0.1 for a couple of structures, including structure 1, the pure
hcp Nb. The /test-atinb/ is the same alpha phase CE in which the structures with relatively
large relaxation, 1, 8 and 24 are excluded.
Curve 2 in pd.eps is obtained by plotting pb.out(which is in /btinb/) from:
While curve 2 is different from curve 1, still the two computed curves deviate from experimental
one. It is not clear what is basically causing the discrepancy between computed and measure
phase boundaries.
I have used the transferable force constants (TFC) scheme for the phonon free energy cluster
expansion using the fitsvsl & svsl programs. It is not clear to me how to assess the validity
of the transferability of the force constants. The TFC relations can be viewed by running
"gnuplot fitsvsl.gnu" in the CE folders. The TFC relations were computed in accordance with
section 3.1.2 of the paper Calpahd 33 (2009) 266. I did not do the relaxation described in
point (3) of section 3.1.1. I am not sure this is not required. Further, I have tried
different values for -dr (fitsvsl). No help. The option -op=2 also does not help.
Any advice to solve this problem within the ATAT framework is really helpful.
the transferable force constant scheme works well within a given lattice (e.g hcp or bcc) but not across two different lattices, which is what you are doing here. You should use the fitfc command (which fits does not rely on extrapolation, but of course that means you need to do ab initio calculations on more than a few structures). An relatively efficient way to combine the advantages of both approaches is to use fitfc for the endmembers (pure) to get an accurate inter-lattice free energy difference and use svsl within the lattice. This was done in
I can explain how to do this - but there is a more serious issue here:
2) Using fitfc on your existing data reveals that hcp Nb and bcc Ti may be mechanically unstable. First you should try with a larger supercell to be sure. If they are unstable, this means you should use fitfc for high Nb content for bcc an for high Ti content for hcp. First try 3 or 4 structures, fit a very short CE with that and see what happens. BTW don’t forget to disable the old fvib files, as in
Thank you for the advice on my Ti-Nb cluster expansion calculations. I tried with larger super cells for hcp Nb and bcc Ti (32 and 54 atom cells with EDIFF=1E-10/EDIFFG=-1E-03). But they remain unstable.
Please help me with the fitfc procedure. As I wrote earlier your participation would really help me complete the work.
First, in your hcp CE there seem to be many structures with very large relaxations (as seen with the checkrelax command). Restrict your composition range (-c0 and -c1 options) and move some of the structure far from pure Ti in some other subdirectories.
try just computing structure 0 and 1 (for bcc and hcp) with fitfc and fit a cluster expansion (empty and point cluster only) only to those structures. The command would be something like clusterexpand -s "1,1,0,0" fvib and then mkteci
(Make sure you rename old fvib files to avoid confusion). See if this works better with phb.
then (and only then_, you can try adding more structures calculated with fitfc (not too relaxed, close to ground state hull).
Thanks for the suggestions. The fitfc calculations of hcp and bcc Ti and Nb have been started.
Meanwhile, I read a paper on first principles investigations of Ti-Nb alloy, Phys. Rev. B 84, 054202 (2011). This paper also shows that harmonic phonon calculations predict unstable bcc Ti-Nb alloys. SCAILD self-consistent lattice dynamics calculation was used to obtain stable bcc Ti-Nb alloy.
While your suggestion to exclude structures far from pur Ti for hcp CE improves the (hcp-Ti) alpha-phase field (as well as transition temperature), the bcc-(Ti-Nb) is predicted to be stable down to 200K at the Nb-rich side of the phase diagram. I understand that suggestion 2 is towards fixing this issue. But, I am not sure fitfc will give a stable phonon spectrum for bcc Ti and hcp Nb.
Because of this, I would like to ask you whether it is worth considering to modifying fitfc to include self-consistent lattice dynamics calculation as well.
To me, the solution (for now) is simply to calculate phonon spectra
for bcc Nb and a few bcc structures at high Nb content.
for hcp Ti and a few hcp structures at high Ti content.
(phonons modes in bcc Ti are certainly unstable!)
I doubt the self-consistent lattice dynamics is a very general solution…
My group is working on a way to handle bcc Ti properly, I’ll keep everyone posted on this forum.
It’s a very difficult problem.
Thank you for the suggestions. I am trying with the phase boundary calculations with your suggestions: phonon spectra for bcc Nb and a few bcc structures at high Nb content. for hcp Ti and a few hcp structures at high Ti content.
I have not made any appreciable progress. The suggestions don’t seem to help.
Below is the phase boundary without phonon contribution. The Nb-rich side shows that the BCC (Ti,Nb) solution phase is stable down to below 200K. The corresponding experimental temperature is about 400K.
[attachment deleted]
We know that the phonon contribution to free energy typically lowers the transition temperatures. The same is observed in this case as well (Previous post). Therefore, I would like to consider that any improvement in obtaining the phonon free energy contribution could only make the BCC(Ti,Nb)/(HCP(Ti-Nb)+BCC(Ti,Nb)) transition temperature of the Nb-rich side to be lower than what is already obtained. It is not going to raise the current ~200K to ~400K.
It is likely that the Nb-rich BCC(Ti-Nb) solution phase is indeed stable down to about 200K rather than what is reported in the experimental-Calphad phase diagrams.
Please give your comments and suggestions. If I miss something, please correct me.
While it is true that phonon contributions often reduce transition temperatures, it is not always the case, see
Also, svsl is a fast but potentially inaccurate approach for difference in free energy between different lattices. So a full phonon analysis may give different results.
From you initial post, it seems that the problem is really on the Nb side.
Somehow the free energy cost of adding a small amount of Ti in Nb is underestimated in the calculations. Maybe try a single Ti impurity in Nb and use a simple dilute model, as in
You can model hcp Ti as pure Ti for this purpose - it won’t make much difference.
Thanks for the suggestions. Based on it, I computed the phonon spectrum of Nb with Ti impurities using VASP-DFPT-supercells method. Figures show the phonon spectrum of 2x2x2, 3x3x3, and 4x4x4 bcc Nb supercells with a impurity Ti. These calculations were carried out using PAW potentials with EDIFF=1E-10 and EDIFFG=-1E-04. A 3x3x3 k-mesh was used for the 4x4x4 supercell. It is evident however that a packet of imaginary phonon modes keeps appearing in the DOSs.
This appears to suggest that phonon spectrum of Nb with impurity Ti is anharmonic. Please give your comments and suggestions for improving the calculation of Ti-Nb phase boundaries.
I think I have found a general solution to these kinds of problem - bear with me, the work is almost completed, you’ll hear further suggestion in a few weeks. Sorry for the delay, but I think it will be worth it!