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Frederick Lindemann related characteristic atomic oscillations to heat capacity and melting. His 1910 treatment estimated molecular eigenfrequencies and compared them with frequencies inferred from thermal and optical observations. The associated Lindemann melting criterion treats sufficiently large thermal atomic displacements relative to atomic spacing as a sign that a crystal becomes unstable. It is an approximate physical model: comparisons between independently inferred frequencies test the model, while a universal exact displacement threshold is not implied.^[ref]