Experience shows that for many materials Hooke's Law holds only over a very small range. A steel bar for instance can only be extended by about 1% by an applied force before it fractures. Translate into the microscopic picture this means that the distance between the molecules changes only by about 1% before dissociation is achieved and the molecular bond breaks. Now the potential curve of molecular bonds typically varies over a range of 1 Angstrom ( i.e. the average distance between the molecular nuclei; see http://www.chem.vt.edu/chem-ed/quantum/harmonic-oscillator.html [Broken]). This however would mean that one would roughly need to double the distance between the nuclei before dissociation is achieved, in contradiction to experience. What is the explanation for this discrepancy ? Is the potential curve in metals only 10^-2 Angstrom wide (and the dissociation energy reduced by a corresponding amount) and if yes why?
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