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. > > > _______________________________________________ > Pw_forum mailing list > Pw_forum at pwscf.org > http://www.democritos.it/mailman/listinfo/pw_forum > > -- Mohsen Modarresi, PhD student of Solid State Physics, Ferdowsi University of Mashhad, Iran. Phone +98-9133452131 -------------- next part -------------- An HTML attachment was scrubbed... URL: http://www.democritos.it/pipermail/pw_forum/attachments/20100924/9a44948a/attachment.htm
