How to accelerate phb calculation?

Alloy Theoretic Automated Toolkit (ATAT)
1

Dear Alex,

I use the ECI of ZnO1-xSx obtained by maps to do calculate x-T phase diagram by using phb -gs1=0 -gs2=1 -dT=25 -dx=1e-3 -er=50 -ltep=5e-3 -keV -o=ph01.out. It took 10 days to reach 3700 K and still continues because the critical temperature doesn’t reach until now. It seems to take long time in high temperature. How can I accelerate the calculation? By increasing -er or by using -dn?

Mingkai Li

2

It is well-known that Monte Carlo becomes slow to converge near a critical point.
You could run at constant speed (but with decreasing precision, using -eq and -n instead of -dx).
Now, this phase diagram looks pretty good to me! If you just join the two ends manually you are done, within the accuracy of the plot!
You can explore the critical region "manually" with emc2 if you want. But fluctuation will be slow to average out there too.
It is also possible that the two phases have merge at the next T step, so the code searches for the phase transition, which does not exist (it usually detects this and stops, but it may sometime fail to do so).

3

Thank you for helping me out.

I want to know whether ATAT can give spinodal curve, which indicate the meta stability?

4

Getting the spinodal is difficult with Monte Carlo, because you are at the onset of an unavoidable instability. In fact even the region between the phase boundary and the spinodal can spontaneously snap to the other phase boundary.
In the completely random approximation, you could use SQS to get the formation enthalpies and add an ideal entropy term (x*ln x + (1-x)*ln(1-x))*kT to get the free energy. You could get the spinodal analytically. It is approximate, however.

5

You mentioned to use SQS to get formation enthalpies and add an ideal entropy term (x*ln x + (1-x)*ln(1-x))*kT to get the free energy. My question is whether I have to use SQS to get formation enthalpies. However SQS structures usually do not have mimum energies for each content. Is it reasonable to use the the lowest fitting energies for each content from maps as the formation enthalpies? In my opinion, the system always falls down to the minimum energy state. So it shoulbd be right to choose the mimimum energies to construct the free energy.

6

A random construction usually has a higher total energy than the ground state total energy at that composition, because it has to meet the constraint of being "random".

My experience (two systems…) with ab initio calculation of SQS cells and cluster expansion fitting of random cells is that with full relaxation, ab initio SQS gives even lower total energy values.

With corrdump -rnd, one can get the cluster expanded random cell total energy. This can be combined with random mixing entropy to get free energy of the high T random phase.

7

Thermodynamic fact:
The system only goes to the minimum energy at T=0K.
At higher temperature, it goes to the minimum free energy, which also includes an entropy term. This is actually why system for solid solutions at high T!

8

In the region between the phase boundary, does the free energy have a physical meaning (since it’s unstable)?

I tried to use the canonical mode to get there, but the free energy is always constant.

                       lro          E        G  var(E)
x         T
-0.900463 2000.0  0.950231  44.567978  0.15058     0.0
-0.800926 2000.0  0.900463  44.407847  0.15058     0.0
-0.700231 2000.0  0.850116  44.352941  0.15058     0.0
-0.600694 2000.0  0.800347  44.390807  0.15058     0.0
-0.400463 2000.0  0.700231  44.697698  0.15058     0.0
-0.300926 2000.0  0.650463  44.949476  0.15058     0.0
-0.200231 2000.0  0.600116  45.260388  0.15058     0.0
-0.100694 2000.0  0.550347  45.619404  0.15058     0.0
 0.099537 2000.0  0.450231  46.464873  0.15058     0.0
 0.199074 2000.0  0.400463  46.927753  0.15058     0.0
 0.299769 2000.0  0.350116  47.407939  0.15058     0.0
 0.399306 2000.0  0.300347  47.882723  0.15058     0.0
 0.599537 2000.0  0.200231  48.786425  0.15058     0.0
 0.699074 2000.0  0.150463  49.186573  0.15058     0.0
 0.799769 2000.0  0.100116  49.549282  0.15058     0.0
 0.899306 2000.0  0.050347  49.866345  0.15058     0.0

I’m a bit curious, how were the enthalpy, entropy and free energy smooth curves drawn in this: https://www.sciencedirect.com/science/ar … 3706021909

9

Which "canonical mode" -cm or -g2c ?
With -cm, the code cannot integrate the free energy as you scan over composition.
I am not sure which column of the output your are reporting. Perhaps you are not using the right free energy?
It should be possible to get the free energy in the metastable region between the spinodal and the phase boundary.