# [Pw_forum] hi,effect of temperature

Eduardo Ariel Menendez Proupin eariel99 at gmail.com
Wed Dec 8 17:51:15 CET 2010

```>I used Q.E to calculate the Youngs mudulud of Boron-Nitride nanotube and
h-Bn the result are >in agrement with previous calculation. At this stage i
want to calcualte the effect of temperature >on the Young mudulus of
Boron-Nitride structres. Can Q.E do such calcualtions?

Yes, you can calculate the temperature effects on the Young modulus. You
must also take into account the thermal dilation. For that, you may
calculate the phonon density of states and the free energy. Also, use finite
temperature DFT, with smearing='fermi-dirac'. The Young modulos is the
second derivative of the free energy with respect to the apropriate
deformation, divided by the unstressed unit cell volume (mimimum free energy
for a given temperature). Take a look at Phys. Rev. B 76, 054117 (2007)

I Guess that the QHA automates the proccess of the Free energy
calculations.

Using molecular dynamics you can also study the thermal effects, but not it
is not equivalent to the free energy calculation. Molecular dynamics is
classic for the motion of the atomic nuclei, hence you lose the quantum
effects that you obtain from a phonon calculation. Hence, for low
temperatures you should always do the phonon calculations and obtain the
free energies, and derive them to get the Young modulus. For high
temperatures, the anharmonic effects are more important than the quantum
effects, so, do molecular dynamics and obtain the Young moduli from average
stresses. I do not know what is "low" and "high" temperature, maybe
comparing with the Debye temperature.

I am not sure if the average stress in a molecular dynamics is all the
stress. I guess it is not. For example, the pressure reported by PWSCF is
the pressure due to the interatomic forces, it depends only on the
positions, but not on velocities. To obtain the total pressure at a given
temperature one must add the term NkT/V (ideal gas). The pressure is the
trace of the stress tensor, hence, the stress tensor must be corrected with
the ideal gas term, at least in the diagonal elements.

Best regards
Eduardo

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Eduardo Menendez
Departamento de Fisica