4) The crystal basis of graphene and of diamond is composed of two carbon atoms in nonequivalent position. Thus, their dispersion curves are composed of acoustical branches and optical branches and their acoustical branches are assumed to obey to the Debye approximation: = vs|k| and their optical branches are assumed to obey to the Einstein model <> = E= Cst. Deduce the numerical values of their Debye and Einstein temperatures from their crystal structure and their common sound. velocity, v₁ = 18,000 m/s with also VE (Einstein frequency) at about 4 *1013 Hz. From the C, graph shown in below, evaluate the specific heat of diamond at room temperature, 290 K. (h, kB)
4) The crystal basis of graphene and of diamond is composed of two carbon atoms in nonequivalent position. Thus, their dispersion curves are composed of acoustical branches and optical branches and their acoustical branches are assumed to obey to the Debye approximation: = vs|k| and their optical branches are assumed to obey to the Einstein model <> = E= Cst. Deduce the numerical values of their Debye and Einstein temperatures from their crystal structure and their common sound. velocity, v₁ = 18,000 m/s with also VE (Einstein frequency) at about 4 *1013 Hz. From the C, graph shown in below, evaluate the specific heat of diamond at room temperature, 290 K. (h, kB)
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