Spatial dimension of atoms arrangement as a function of temperature: A fractons' functional

The mechanisms related to the structure of compounds as a function of temperature are partially elucidated. Experiments in the area are explicitly declared and compared to this proposal. The parameters of structural equilibrium determine the response of the arrangements and define their fractional dimension. When the temperature decreases there are three cases depending on the parameters: (a) the arrangement of atoms, in dimension three, passes continuously to layers simulating dimension two, (b) the arrangement takes up its original dimension (three) but gets new symmetries and (c) the critical case with linear variations of the fractional dimension with temperature. Thermodynamically, the specific heat of the arrangements as a function of temperature is envisaged and, in some regions of parameters, an exergonic behavior is inferred.