We find that the phonons of certain frequencies are scattered by the boundary of the nanocrystal so that the specific heat depends on the size of the particles. At low temperatures, the Debye's T 3 law, which is known for a large number of particles, is completely broken and exponential behavior may be observed. In the case of a magnetically ordered ferromagnet, we find that the specific heat depends on the size of the nanocrystals because of the scattering of spin waves from the surface of the nanoferromagnets.
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Keshav Narain Shrivastava (2001) studied this question.
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