I do not know the value, but it must be much higher than the bulk value; due to surface tension, these nano-ribbons are stiffer and harder than the boron nitride in the bulk.
Thank you dear Behnam. The point is that debye temperature is about 2300 and 322 K for bulk graphene and graphene nanoribbon, respectively. Typically debye temperature decreases by reducing the size.
You are welcome Sayyed Jalil. Regarding graphene, it depends on how many layers there are in each nanoribbon and how long such ribbon is. They must be very soft and flexible in the direction perpendicular to the surface of ribbon when they are thin (in the ideal case of one layer, no matter the material, atomic displacement in the direction perpendicular to the surface is less costly than otherwise would be the case). It is undoubtedly because of this softness and thinness of ribbons that graphene nanoribbons have a lower Debye temperature than the graphene in the bulk. Actually, I think graphene must be a special case, since it is especially extremely soft against sheer stress; that is why we make pencils out of them. But of course, as I mentioned earlier, I don't know the actual value and just made a guess on the basis of increased surface stress in the case of ribbons (and certainly I had not things like monolayer ribbons in mind).
Dear Behnam, I found out a method based on Debye approximation using molecular dynamics simulation to get debye temperature and i'm working on it. I'll let you know about it when it's done if you interested in of course.
Dear Sayyed Jalil, thank you. I am looking forward to hearing about the outcome of your calculations. Yes indeed, dispersion of phonon frequencies can be obtained from the time-Fourier transform of the position or velocity auto-correlation functions, which one can easily calculated in molecular-dynamics simulations. Additionally, for the calculation of the Debye temperature one needs only the dispersion of the low-energy acoustic phonons.
Thank you so much dear Behnam for your time and for your trend of helping me on this issue.
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