Good knowledge of the far-infrared and millimeter emission from
dust in the interstellar medium is important to get reliable
estimates of the dust mass, to trace and understand the evolution of
pre-stellar structures, and to accurately subtract the foreground
emission in the cosmological background anisotropy measurements. Up
to now the modeled dust emission profile in FIR and millimeter wavelength range is
deduced from the wings of some mid-infrared fundamental
lattice-resonances inside the silicate material, which is known to
be the dominant constituent of this dust component. However recent
astronomical observations have shown that the dust emission
profile could be significantly more complicated than expected. In
addition, spectroscopic studies in the laboratory on analogues of
amorphous interstellar grains have revealed that additional
processes can occur in that spectral range, which are strongly
temperature-dependent. We propose a new model for far-infrared and
millimeter dust emission which takes into account results from the
solid state physics, used to interpret these laboratory data. This
model explicitly incorporates the effect of the disorder in the
internal structure of the dust grain. We show that this model can
give a satisfactory interpretation for the astronomical
observations. It opens new perspectives to derive some new dust characteristics from the shape of
the dust emission spectrum.