Mixing two phases

The mechanism to mix the DOSs between two structures and then calculate the chemical potential is given below

  1. shift the DOS using Fermi energy as zero

\[ \begin{align}\begin{aligned}D_{AFM - b}^{'}\left( \varepsilon \right) = D_{AFM - b}\left( \varepsilon + \varepsilon_{F}^{AFM - b} \right)\\D_{AFM - a}^{'}\left( \varepsilon \right) = D_{AFM - a}\left( \varepsilon + \varepsilon_{F}^{AFM - a} \right)\end{aligned}\end{align} \]
  1. mix the DOSs

\[D_{\text{mix}}^{'}\left( \varepsilon \right) = (1 - x)*D_{AFM - b}^{'}\left( \varepsilon \right)+{x*D}_{AFM - a}^{'}\left( \varepsilon \right)\]
  1. calculate the chemical potential of electrons

\[\int_{- \infty}^{\infty}{\text{fD}_{\text{mix}}^{'}\left( \varepsilon \right)\text{dε}} = \int_{- \infty}^{0}{D_{\text{mix}}^{'}\left( \varepsilon \right)\text{dε}}\]

under Fermi distribution

\[\mathbf{f} = \frac{1}{e^{\frac{\varepsilon - \mu}{k_{B}T}} + 1}\]


python utilities/dosmixAPI.py -d0 dir0/ -d1 dir1/ -nC 11 -nT 101

The output to the text file thermo.out contains data as functions of phase compostion x and T. These data can be plotted following the section Example by Jupyter Notebook