[Pw_forum] Young's Modulus

[mohsen modaresi]

Dear Eduardo Ariel Menendez Proupin,
Thanks for your useful comments.
Mohsen

On Thu, Sep 23, 2010 at 12:56 PM, Eduardo Ariel Menendez Proupin <
eariel99 at gmail.com> wrote:

> Dear Mohsen
>
> Let me comment on your procedure
>
> >At first i relaxed nano-tube and obtain the position of carbon atoms in
> the >ground state. Then i decrease the tube length. A in the relation is the
> area of >nano-tube (A=pi*R*R which R is the radius of tube). F is the atomic
> force in >the Z axis which can be calculated by using Q.E.
> >I think it is better to calculate total energy in some configuration and
> use >(F=dE/dz, where E is the total energy in different configuration).
> >Is there any problem in this procedure?
>
> First, are you calculating the Young modulus of an isolated nanotube, or of
> a material composed of (3,3) nanotubes perfectly oriented and with a well
> defined density ?
>
> The Young modulus is a concept that is well suited for a homogeneous
> material, e.g., a bulk of nanotubes. It will depend on the density and
> orientations of the nanotubes, but will be indendent of the transverse area
> (the force and the energy of deformation is prportional to the area). In a
> bulk of nanotubes perfectly oriented, the relevant area A would be the
> transverse area of the unit cell, and the size and shape of the  unit cell
> depends on the density of nanotubes, or must be optimized by a mimimum
> energy criterium. If you are studying the Young modulus of a single isolated
> nanotube, then note that the Young modulus is well defined only if everybody
> use the same definition of A. Hence, be sure of considering the same
> definition as the other results that you compare. Second, be sure to use a
> unit cell sufficiently wide,  so that the preriodic replicas of the nanotube
> are far enough and  the results do not depend on the transversal dimensions
> of the unit cell.
>
>
> >If we relaxed the tube after compression there is no net force on carbon
> >atoms so I did not relax the system after compression.
> *>Have you used a finite nanotube and computed the forces upon the >atoms
> of the edge?*.....> A finite nano-tube? I consider a unit cell (which can
> >make an infinite tube ) and calculate force between atoms.
> >Is there any problem?
> Yes. The state with the atoms not relaxed is not a state of equilibrium,
> and according to Boltzmann law, if its energy difference with the relaxed
> state is larger than kT (0.026 eV at 300 K), this state may happen only once
> in the lifetime of the universe. Then, the property you calculate may have
> nothing to do with a real situation. Hence, relax the atoms.
>
> If you relax, of course  there will be no net force upon the atoms, but the
> tube have stress. Use tstress=.true. and use the appropriate  component of
> the stress tensor as F/A. Remember to do it for various transverse sizes of
> the simulation cell and be sure that the stress is independent of the cell
> size, or extrapolate. Of course, also must be independent of the cutoffs and
> smearing parameters (degauss). Alternatively, you may use the second
> derivative of the total energy to obtain the Young modulus. It is healthy to
> use both methods to check that the results are fine. The numbers will not be
> exactly equal due to numerical reasons, and you can systematically improve
> the agreement increasing the cutoffs and the number of kpoints.
>
>
> When I asked about a finite nanotube, I was thinking in an alternative way
> to do it. Use a large cubic cell, with a finite nanotube inside, made a
> constrained relaxation fixing the z coordinate (I assume that z is the
> nanotube axis) of the edge atoms, relax the other atoms, and sum the forces
> acting upon the atoms at one edge (that must be the negative of the total
> force upon the other edge). With that you can obtain the Young modulus of a
> finite nanotube. If you want it for the infinite nanotube you must do it
> with several lengths and extrapolate to infinite length. Of course this is
> much more  expensive (really brute force) if your goal is the infinite
> nanotube, but is is what you should do if your interest is in short
> nanotubes.
>
> Best regards
> Eduardo
>
> --
>
>
> Eduardo Menendez
> Departamento de Fisica
> Facultad de Ciencias
> Universidad de Chile
> Phone: (56)(2)9787439
> URL: http://fisica.ciencias.uchile.cl/~emenendez<http://fisica.ciencias.uchile.cl/%7Eemenendez>
>
> Let's pray for the 33 trapped miners! Four months to rescue.
>
>
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>


-- 
Mohsen Modarresi,
PhD student of Solid State Physics, Ferdowsi University of Mashhad, Iran.
Phone +98-9133452131
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