# Utilities¶

## 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

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

Usage:

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