The Einstein Heat Capacity Equation

Einstein9 was the first to propose a theory for describing the heat capacity curve. He assumed that the atoms in the crystal were three-dimensional harmonic oscillators. That is, the motion of the atom at the lattice site could be resolved into harmonic oscillations, with the atom vibrating with a frequency in each of the three perpendicular directions. If this is so, then the energy in each direction is given by the harmonic oscillator term in Table 10.4 

The quantity (hcCb/k) has the units of temperature. It is often written as the Einstein temperature, in which case 

Equation (10.148) correctly predicts the qualitative dependence of Cv m on T. It is easy to show the following limiting values 

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Figure 10.12 Comparison for diamond of the experimental Cr.m (circles) and the prediction of the Einstein heat capacity equation with = 1400 K (solid line). The experimental results below T = 300 K are closely spaced in temperature, and not all are shown in the figure.

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