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[References: 55 tit.]

The specific heat of multi-walled carbon nanotubes (MWCNTs) with a low defectiveness and with a low content of inorganic impurities has been measured in the temperature range from 1.8 to 275 K by the thermal relaxation method. The elemental composition and morphology of the MWCNTs were determined using scanning electron microscopy analysis and energy dispersion x-ray spectroscopy. The MWCNTs were prepared by chemical catalytic vapor deposition and have mean diameters from 7 nm up to 18 nm and lengths in some tens of microns. MWCNTs purity is over 99.4 at.%. The mass of the samples ranged from 2-4 mg. It was found that the temperature dependence of the specific heat of the MWCNTs differs significantly from other carbon materials (graphene, bundles of SWCNTs, graphite, diamond) at low temperatures. The specific heat of MWCNTs systematically decreases with increasing diameter of the tubes at low temperatures. The character of the temperature dependence of the specific heat of the MWCNTs with different diameters demonstrates the manifestation of different dimensions from 1D to 3D, depending on the temperature regions. The crossover temperatures are about 6 and 40 K. In the vicinity of these temperatures, a hysteresis is observed.