3.31 what='mur_lc', what='mur_lc_t' and elastic constants

In order to plot the elastic constants as a function of temperature within the `quasi-harmonic' approximation, it is necessary to make a calculation with what='mur_lc_t' having on files in the directory anhar_files the elastic constants calculated for each geometry with the option what='elastic_cons- ants_geo'. In this case thermo_pw will be able to calculate the anharmonic properties using temperature dependent elastic constants and bulk moduli obtained by interpolating the ``fixed-geometry quasi-harmonic'' elastic constants computed by the option what='elastic_constants_geo' at the crystal parameters found at each temperature from the minimization of the free energy.

Note that the user must be careful to use the same value for the lel_free_ energy flag both in the calculation of the ``fixed-geometry quasi-harmonic'' elastic constants and in the present mur_lc_t calculation that interpolates the elastic constants.

A run of thermo_pw using what='mur_lc_t' having on files the T = 0 K elastic constants in the directory elastic_constants allows the calculation of the anharmonic properties using temperature dependent elastic constants and bulk moduli obtained by interpolating (within the ``quasi-static approximation") the T = 0 K elastic constants at the crystal parameters that, at each temperature, minimize the free energy. When both the T = 0 K and the temperature dependent elastic constants are on file in the directory elastic_constants and anhar_files respectively, the latter are used.

After computing the elastic constants at T = 0 K with the option what='ela- stic_constants_geo' one can also run another thermo_pw calculation with the option what='mur_lc' computing the crystal parameters for a range of pressures (using pmax and pmin input variables). If the elastic constants are found in the directory elastic_constants they are interpolated at the pressure dependent crystal parameters and plotted on output. A plot of the pressure dependent stress-strain elastic constants is produced.