I’m calculating psuedo-binary phase diagram of (Cr,Ti)2AlC using phb. The code returns a phase diagram which I believe to be a reasonable metastable' psuedo-binary phase diagram. The reason for the metastable’ is that in a certain range of composition near Ti2AlC side while many binary intermetallic compounds were experimentally observed they were not considered in the CE-phb calculations.
I wonder if there was a way to tell phb/emc2 to bring to account the binary intermetallic compounds, e.g. Ti3Al, in the calculations of the psuedo-binary phase diagram of (Cr,Ti)2AlC?
with emc2, you could calculate the free energy as a function of composition. If the intermetallic are stoichiometric, then you can just compare their energies with the above free energy curve and do a common tangent construction. If they are not stoichiometric, then you need a separate CE for each: you can overlay the free energies and do common tangents between the curves. See https://arxiv.org/abs/cond-mat/0201473 for more info.
with phb, you can create equilibria between phases on different lattices (use the -d1=… and -d2=… options). If the intermetallics are stoichiometric, you can make a "fake" CE that just penalize enormously any deviation from stoichiometry.
Use sqs2tdb . This is a new and very different way to proceed, but it does not use what you have calculated so far.
Read a little bit the -h output for each of the commands to see a little more about how it’s done.
What does "stoichiometric" mean in this case? Is Ti3Al stoichiometric to (Ti,Cr)2AlC? Will they be singular points in the energy surface construction?
1.5. Is there a reliable and fast way to construct common tangent (code or paper)? I found some resources on common tangent construction of circles and polygons, but not two functions. It appears to be a very standard job and maybe there is no need to reinvent the wheel.
How can one make a "fake" CE within the toolbox of ATAT?
sqs2tdb seems to be new and deals with random structures. Why is this applicable to this case?
Stoichiometric means all sublattices are entirely occupied each with a single kind of atom.
Now, Ti3Al has not C in it - this is a strange equilibrium. You’re sure it’s not a 3-phase equilibrium?
CALPHAD codes (OpenCalphad, pandat, thermocalc, or etc.) can do this.
I think this problem is really multicomponent, so phb can’t handle it, although other codes in ATAT, such as memc2 could.
But before you we go this way, you really need to check exactly what the phases in equilibrium are.
Yes: It can deal with stoichiometric and random structures. But it does need a CALPHAD-type code, as the last step, to plot the phase diagram.
Since I’m not the original poster, I don’t get to answer that…
The system of my concern is somewhat similar. It is a mixture of (AB)N and (AB)N2. My thought was to get a CE for each of them, and select the ground states of each and use emc2 to get the free energy curves. Since there is an extra nitrogen released as gas:
(AB)N2 –> (AB)N + 1/2 N2
the gas thermodynamics will be considered from a standard reference table. It will be considered as some kind of compensation.
Can this work?
I guess my question is, shouldn’t the poster want simulations for a continuous temperature range, rather than just the high temperature random phase?
you need the DFT energy of N2 to convert the energy reference of the calculations into the experimental energy reference.
the DFT error in molecules and in solids are rather different, so there may need to be an adjustable shift in the energy to get a good accuracy. This is rather system-independent however (for a given gaseous specie). I know this has been done many times for O2. Perhaps N2 has been considered previously too.
I’m aware of a few papers fixing the overbinding of O2, as a means to obtain the "better" +U values of GGA+U approach, which was then applied to the materialsproject.org. Just as a reference:
L. Wang, T. Maxisch, and G. Ceder, Phys. Rev. B 73 (2006).
A. Jain, G. Hautier, S. P. Ong, C. J. Moore, C. C. Fischer, K. A. Persson, and G. Ceder, Phys. Rev. B 84 (2011).
Not sure how bad it’ll be for N2 though.
Like you mentioned in https://doi.org/10.1088/0965-0393/10/5/304, the semi-grand-canonical potential phi does not need a common tangent construction, but just an equality condition. I guess I can just adjust the Gibbs energy of N2: phi(N2) = G(N2) + mu * x to take advantage of this nice property?
Is there a good reference for a detailed proof?
I looked into those three (well… first two). I’m not sure how to wade through the learning curve and find the right interface/function/code that can be directly used. Could you give some directions?