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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Transcribed Image Text: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: o = V.|k| and their optical branches are assumed to obey to the
Einstein model o = ®g = Cst. Deduce the numerical values of their Debye and Einstein
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temperatures from their crystal structure and their common sound. velocity, vs = 18,000 m/s
with also vɛ (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, ke)
C, (%) x 3;2;1 Nkg unit
100 :
75
1D
50
2D
-3D
25
-T
T/0,
1
Heat capacity, C, as a function of T/6, for 1D, 2D, and 3D solids.
The vertical scale is in Nkg unit to multiply by 1, 2, or 3 as a
function of the degree of freedom for the atom vibrations.
Note the initial evolution in T, T², or T³ as a function of the
dimensionalitv of the solid.
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