We propose a new description of astronomical dust emission in the spectral region from the Far-Infrared to millimeter wavelengths. Unlike previous classical models, this description explicitly incorporates the effect of the disordered internal structure of amorphous dust grains. The model is based on results from solid state physics, used to interpret laboratory data. The model takes into account the effect of absorption by Disordered Charge Distribution, as well as the effect of absorption by localized Two Level Systems. We review constraints on the various free parameters of the model from theory and laboratory experimental data. We show that, for realistic values of the free parameters, the shape of the emission spectrum will exhibit very broad structures which shape will change with the temperature of dust grains in a non trivial way. The spectral shape also depends upon the parameters describing the internal structure of the grains. This opens new perspectives as to identifying the nature of astronomical dust from the observed shape of the FIR/mm emission spectrum. A companion paper will provide an explicit comparison of the model with astronomical data.
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