Hi, @shyamd,

I’m going to find out how to calculate critical potentials in principle. In my opinion, critical potentials are calculated from each of equilibria in Gibbs phase diagrams in the pymatgen with a principle below, with a reference of the method *_get_facet_chempots()* in class *PhaseDiagram*, (https://github.com/materialsproject/pymatgen/blob/676e33da0be7c099af4ecb59d963592d4d56c813/pymatgen/analysis/phase_diagram.py#L702).

In the equilibrium Li-Be-BeO of the Li-Be-O system, we can get \mu_{Li} = -1.909 eV/atom from the equation set,

\mu_{Li}∗x_{Li}^{Li_{BCC}}+\mu_{Be}∗x_{Be}^{Li_{BCC}}+\mu_{O}∗x_{O}^{Li_{BCC}}=E_{Li_{BCC}}

\mu_{Li}∗x_{Li}^{BeO}+\mu_{Be}∗x_{Be}^{BeO}+\mu_{O}∗x_{O}^{BeO}=E_{BeO}

\mu_{Li}∗x_{Li}^{Be_{HCP}}+\mu_{Be}∗x_{Be}^{Be_{HCP}}+\mu_{O}∗x_{O}^{Be_{HCP}}=E_{Be_{HCP}}

x_{Be}^{BeO} is the atomic fraction of element Be in phase BeO, that is 0.5

E is the Gibbs free energy per atom (also is the corrected final energy per atom)

In this way, we can get \mu_{Li} for all equilibria of the phase diagram

equilibrium |
\mu_{Li} eV/atom |

Li-BeO-Be |
-1.909 |

LiO8-BeO-O2 |
-5.559 |

Li2O-Li-BeO |
-1.909 |

Li2O2-LiO8-BeO |
-5.161 |

Li2O2-Li2O-BeO |
-4.807 |

After sorting, critical chemical potentials and corresponding ranges are [-1.909, -4.807, -5.161, -5.559], as the same as the webapp displayed.

What puzzles me is why chemical potential ranges calculated from the Gibbs phase diagrams are used to construct the grand potential phase diagrams.

Now I realize that two kind of phase diagrams should have the same set of critical chemical potentials. Actually, chemical potentials are hidden info of equilibrium in both the Gibbs phase diagrams and the grand phase diagrams. Different equilibria in the Gibbs phase diagrams may have different chemical potentials, and different the grand phase diagrams contains different chemical potentials. The critical chemical potentials should be able to obtained from both the Gibbs phase diagrams and the grand phase diagrams, but how to calculate critical chemical potentials directly from the grand phase diagrams may still be a problem. Just correct me if anything wrong.

Thanks,

Kai