3.12 what='scf_elastic_constants'

With this option the code calculates the elastic constants of the solid at the geometry given in the pw.x input. There are four different algorithms that at convergence should give the same results. In two of them, depending on the Laue class, the code calculates the nonzero components of the stress tensor for a set of strains and obtains the elastic constants from the numerical first derivative of the stress with respect to strain. The two algorithms standard and advanced differ only for the choice of the unit cell. In the standard method the code applies the strain to the primitive vectors of the unstrained solid and uses ibrav=0 and the strained vectors to compute the stress tensor. The advanced method, available only for selected Bravais lattices, tries to optimize the calculation by choosing strains for which the number of needed k-points is reduced. Moreover it identifies the Bravais lattice of the strained solid and recalculates the primitive vectors with the conventions of QUANTUM ESPRESSO. When available this should be the most efficient method. The other two algorithms are called energy_std and energy. Using the energy_std or energy algorithm the elastic constants are calculated from a polynomial fit of the total energy as a function of strain without computing stress. This option usually requires more independent strains. It can be used when stress calculation is not implemented in QUANTUM ESPRESSO. The difference between energy_std and energy is the same between the algorithms that use the stress. With energy_std the code applies the strain using ibrav=0, while with energy an optimized cell is used. As the advanced algorithm the energy algorithm is available only for selected Bravais lattices.
For all methods the number of strains is ngeo_strain for each independent strain. For each strain, the code relaxes the ions to their equilibrium positions if frozen_ions=.FALSE. or keeps them in the strained positions if frozen_ions=.TRUE.. Note that elastic constant calculations with frozen _ions=.FALSE. might require smaller force convergence threshold than standard calculations. The default value of forc_conv_thr must be changed in the pw.x input.

If you know in which direction the atoms relax and if there is only one atom that moves in each strain type, one can use frozen_ions=.TRUE., and compute the energy at several atomic positions choosing the one that minimizes the energy. This approach computes more energy configurations but does not relax them and should provide results identical to frozen_ions=.FALSE.. It can be used only with energy and energy_std algorithms, but should work also with the free energy in what=`elastic_constants_geo'.

At finite pressure all methods give the elastic constants that relate linearly stress and strain.
The input variables that control this option are:

frozen_ions: if .TRUE. the elastic constants are calculated 
             keeping the ions frozen in the strained positions. 
             Default: logical .FALSE.
ngeo_strain: the number of strained configurations used to 
             calculate each derivative. 
             Default: integer 4 ('standard' and 'advanced'), 
             6 ('energy')
elastic_algorithm: 'standard', 'advanced', 'energy_std' or 
             'energy'. See discussion above.
             Default: character 'standard' 
delta_epsilon: the interval of strain values between two 
             geometries. To avoid a zero strain geometry 
             that might have a different symmetry ngeo_strain 
             must be even.
             Default: real 0.005
epsilon_0:   a minimum strain. For small strains the ionic 
             relaxation routine requires a very small threshold 
             to give the correct internal relaxations and 
             sometimes fail to converge. In this case you 
             can increase delta_epsilon, but if delta_epsilon 
             becomes too large you can reach the nonlinear 
             regime. In this case you can use a small 
             delta_epsilon and a minimum strain (To be used 
             only for difficult systems).
             Default: real 0.0
poly_degree: degree of the polynomial used to interpolate 
             stress or energy. ngeo_strain must be larger 
             than poly_degree+1.
             Default: 3 ('standard', 'advanced', 2 
             if ngeo_strain < 6), 4 ('energy', 3 if 
             ngeo_strain < 6).
stype(1:strain_types): For each strain type for which this 
             variable is .TRUE. it is possible to compute 
             the energy by moving one atom in one direction 
             and minimizing the energy with respect to the
             ionic position. This option requires frozen_ions
             =.TRUE. and should give the same result of 
             frozen_ions=.FALSE. if the atom that moves and 
             its direction is chosen correctly.
             Default: logical .FALSE..
move_at(1:strain_types): The atom that moves in each strain type.
             Default: integer none (it must be set 
             if stype(istrain)=.TRUE.).
atom_dir(3,1:strain_types): The versor of the atomic movement in
             Cartesian coordinates (the vector can be given with 
             any module. It is normalized by the code).
             Default: real none (it must be set if 
             stype(istrain)=.TRUE.).
atom_step(1:strain_types): the step for each atomic displacement.
             Default : real 0.01 a.u..
nmove        Number of atomic positions sampled for minimizing 
             the energy at each strain type.
             Default: integer 5.
lcm_ec       If .TRUE. the center of mass of the cell is conserved 
             in the displacement introduced with previous variables.
             Default: logical .TRUE.
fl_el_cons:  the name of the file that contains the elastic 
             constants.
             Default: character(len=*) 'output_el_con.dat'

The three algorithms are equivalent only at convergence both with k-point sampling and with the kinetic energy cut-off, but large differences between the elastic constants obtained with the standard and advanced algorithms might point to insufficient k-point sampling. Large differences between the elastic constants obtained with the energy_std or energy algorithms with respect to the other two might point to insufficient kinetic energy cut-off.
Number of tasks for this option: ngeo_strain times the number of independent strains.

Using the elastic constants tensor the code can calculate and print a few auxiliary quantities: the bulk modulus, the poly-crystalline averages of the Young modulus, of the shear modulus, and of the Poisson ratio. Both the Voigt and the Reuss averages are printed together with the Hill average. The Voigt-Reuss-Hill average of the shear modulus and of the bulk modulus are used to compute average sound velocities. The average of the Poisson ratio and the bulk modulus allow the estimation of the Debye temperature. The Debye temperature is calculated also with the exact formula evaluating the average sound velocity from the angular average of the sound velocities calculated for each propagation direction solving the Christoffel wave equation. The exact Debye temperature is used within the Debye model to calculate the Debye's vibrational energy, free energy, entropy, and constant strain heat capacity. These quantities are plotted in a postscript file as a function of temperature.