Good knowledge of the far-infrared and millimeter emission fromdust in the interstellar medium is important to get reliableestimates of the dust mass, to trace and understand the evolution ofpre-stellar structures, and to accurately subtract the foregroundemission in the cosmological background anisotropy measurements. Upto now the modeled dust emission profile in FIR and millimeter wavelength range isdeduced from the wings of some mid-infrared fundamentallattice-resonances inside the silicate material, which is known tobe the dominant constituent of this dust component. However recentastronomical observations have shown that the dust emissionprofile could be significantly more complicated than expected. Inaddition, spectroscopic studies in the laboratory on analogues ofamorphous interstellar grains have revealed that additionalprocesses can occur in that spectral range, which are stronglytemperature-dependent. We propose a new model for far-infrared andmillimeter dust emission which takes into account results from thesolid state physics, used to interpret these laboratory data. Thismodel explicitly incorporates the effect of the disorder in theinternal structure of the dust grain. We show that this model cangive a satisfactory interpretation for the astronomicalobservations. It opens new perspectives to derive some new dust characteristics from the shape ofthe dust emission spectrum.