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The heat capacity of graphite is high due to the high DOS in low frequencies than diamond

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e) This has to do with graphite sheet stretching and bending at low T and low frequency. At high T above 1000K sp2 in plane stretching and bending occurs in graphite but 3d sp3 bending occurs in diamond and there are more modes in 3d so diamond has a higher heat capacity at high temperature. Conduction electrons in graphite also contribute at low temperature.

We can conclude the observation by correlating the above pictures with what we learned above.1.At 100K, lower frequencies(<15)of graphite were activated, this is due to the conduction electrons. None of the frequencies were activated for diamond, this is due to the lack of conduction electrons.

2.Further at 300K, in graphite,a range of frequencies(0-55)were activated with highDOS when compared to diamond(0-40), this could be due to flexural vibrations and acoustic phonons. The lower frequencies of diamond are also activated due to acoustic phononsand could be due to low frequency vibrations of C-C bond in diamond. The heat capacity of graphite is high due to the high DOS in low frequencies than diamond. These low frequencies give graphite an edge over diamond on heat capacity.3.At 1000K, according to Tohei et al, the heat capacities of graphite and diamond are the same. Diamondshows highDOS at midfrequencies(20-40)when compared to diamond. This could be due to optical phonon modes (activated at high temperatures)supported by slower in planar low frequencylongitudinal vibrations in diamond due to weak C-C bond rather than a faster high frequency longitudinal vibrations due tostrong C=C bond in

graphite. The High DOS in higher frequencies (>40) in graphite is due to higher frequency vibrations of C=C bond which does notcontribute to thermal transport much. 4.Above 1000K, due to the absence of DOS in mid frequencies in graphite and high DOS in diamond in mid frequencies is the reason for the cross over at 1000K where diamond exceedsgraphite`sheat capacity.

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