3. Basic parameters of crystallization
At sufficiently high temperatures, the atoms in a poorly ordered dust material start to rearrange and to migrate into energetically more favorable positions, i.e. the dust material's structure gradually changes into the topology of a microcrystalline material. Even mass-dependent fractionation can occur. In systems that tend to decompose, chemical fractionation takes place.
Crystallization is a complicated process usually including nucleation and crystal growth. A comprehensive description of crystallization has to be based on a detailed kinetic theory (Vogel 1985; Gutzow & Schmelzer 1995).
We use an empirical approach for the description of this process that statistically includes both nucleation and crystal growth. In this approach, the overall crystallization is related to the spectroscopic behaviour of the samples. A characteristic annealing time can be defined as the time of the appearance of an ordered structure usually monitored by IR spectroscopy and X-ray diffraction (XRD) analyses. Its value can be expressed by
where is the effective activation energy empirically comprising nucleation and crystallization energy. The quantity is a constant that is proportional to the mean vibrational frequency of the silicate lattice (Lenzuni et al. 1995). For magnesium silicates, the mean vibrational frequency of the lattice is (Gail & Sedlmayr 1998). In the first place, we set to this value and keep in mind that the value of the activation energy derived from Eq. (1) depends on the value chosen for . Furthermore, we define a diffusion constant D and a unit of size l of already established crystalline order after a time t. They are related by the following equations (Gail & Sedlmayr 1998):
with a as the characteristic lattice length. In this paper, the activation energy is determined from annealing time measurements using Eq. (1).
As will be outlined in the following section, the overall crystallization of amorphous materials is associated with a significant drop in opacity in the far infrared (FIR) and a sharpening of absorption features in the mid infrared spectral range (MIR) (Henning et al. 1995). In the FIR, the dependence of the mass absorption coefficient on the wavelength can often be approximated by a power law
where is the spectral index and with . Eq. (4) has been applied to evaluate the FIR absorption of smoke-like and powder samples.
© European Southern Observatory (ESO) 2000
Online publication: December 15, 2000