Entropy, Heat Capacity, and Vibrational Motion of Atoms in Crystals

Let us consider a diatomic molecule and assume that it behaves as a harmonic oscillator with two masses, nii and m2, connected by an ideal (constant-force) spring. At equilibrium, the two masses are at a distance Xq by extending or compressing the distance by an amount X, a force F will be generated between the two masses, described by Hooke s law (cf equation 1.14)  

The indefinite integration in dX of equation 3.1 gives the potential energy of the harmonic oscillator (cf equation 1.16)  

Force constant thus represents the curvature of the potential with respect to distance  

Most diatomic molecules have a force constant in the range 10 to 10 N m h A common tool for the calculation of Kp in diatomic molecules (often extended to couples of atoms in polyatomic molecules) is Badger s rule  

The frequency of the harmonic oscillator (cycles per unit of time) is given by 

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