Boson peaks and floppy modes: some relations between constraint and excitation phenomenology, and interpretation, of glasses and the glass transition

We make here an effort to find commonality between the athermal constraint approach to glassiness due to Phillips and Thorpe, in which composition is the key variable, and the more conventional temperature-induced softening approaches to the glass transition at constant composition. A starting point for our discussion is the parallel in behaviour of the boson peak, derived from the vibrational density of states, which is enhanced both by increasing glass fictive temperature (potential energy), and by decreasing glass coordination number (through a rigidity threshold), e.g. in chalcogenide glasses. We relate the potential energy of the glass to a topological defect concentration, and see defect formation as a means of lifting constraints, and hence promoting flow in formally overconstrained glasses. This viewpoint is supported by observations on irradiation of glasses, in which the athermal introduction of defects, or lifting of barriers, may induce flow, or relaxation/annealing. These considerations emphasize the importance of taking temperature, and fictive ('structural') temperature, considerations' into account in evaluating the properties of laboratory glasses for comparison with constraint theory predictions.