The problem of Cp from phonon calculations

Alloy Theoretic Automated Toolkit (ATAT)
1

Recently I carried out the phonon calculation of pure Ni, Cr, Nb, Zr and Laves_Cr2Nb(C14 and C15), compared with the result with published by S L Shang, I found the Cp of Ni differs at low temperature. Other four calculations exists the same questions. The Cp at low temperature is larger than experimental result(or SGTE data).At the same time, the Cp of Cr and Zr deviate from the experimental results(lower at high temperature). I do not know the reason for the deviation. Could you tell me the possible wrong thing? I hope to hear from you. Thank you very much!

The parameter I used is 48-atoms. 666 Gamma K-point.[/img][/img][/img][/img]

2

There could be many reasons:

  • thermal expansion (did you use more than 1 volume , i.e.e, vol_? directories)?
  • numerical convergence (number of force constants, energy cutoff etc.)
  • point defects (even for pure phases, vacancies can form)
  • anharmonicity
  • magnetism (Ni and Cr are magnetic; both have complex spin states, especially Cr)

the first three are easy to handle
the last two not so much…

3

Nine volumesM-oM-<M-^L -er=9 -ms=±0.04 -ns=5 -dr=0.1. After calculation, the cutoff range is 4A, I tried different -fr value and found it affected the Cp a little? How can we deal with the point defects in ATAT to get a more accurate results?
The Cp of hcp-Zr is wrong, is hcp structure hard to get a right Cp?

4

The Cp of Nb basically agrees with experimental result, except low temperature(larger),but the same method applied in calculation of hcp-Zr could get wrong result, With 2 volumes and proper -fr value the fvib can be obtained (wrong Cp). If 9 volumes ,the fvib will show the same value(the vibrational energies is zero),why is this so?

5

One more possible issue is that in hcp the c/a ratio can change with temperature.
1st approximation: make sure you relax the cell shape but not volume in each vol_?/ directory (but not in vol_?/* directories). (This neglects changes in c/a ratio due to entropy.)
A better way would be would be to calculate F_vib as a function of cell shape and volume and optimize over both at each T (this is not implemented, so you would have to do that outside of fitfc, using fitfc to get fvib at a fixed cell shape and volume). But don’t go there unless you have to.

An unrelated numerical issue is that if you use many volumes (e.g. 9) or use a maximum strain that is too large, the code may try to fit a too-high order polynomial to the F vs volume curve and you get oscillations in the equation of state, so the optimizer gets stuck in an unphysical wiggle.
Inspect all output files, in particular eos0.gnu and eos0.out to debug this.

6

Thank you for your answeringM-oM-<M-^LCan I know how to deal with the point defects in ATAT? Just change something in the POSCAR for perturbation?

7

If point defects are dilute, see, e.g.,
@article{ozolins:alsc,
author="V. Ozoli{\c{n}}{\v{s}} and M. Asta",
title="Large Vibrational Effects upon Calculated Phase Boundaries in {Al-Sc}",
journal="Phys. Rev. Lett.",
volume=86,
pages=448,
year=2001
}
Otherwise, see the references listed on the main ATAT page.