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Diatomic elements are not rare — on the contrary! Nitrogen and oxygen, in their diatomic forms N 2 and O 2, make up 99 percent of the atmosphere on Earth. That's the opposite of rare.
Vibrations of monoatomic and diatomic linear chain. Acoustic and optical modes. Quantization of lattice vibrations (phonons). Lattice Thermal Properties: Density of states. Einstein and Debye models ...