Crystal growth, relaxation

The relaxation of a thermodynamic system to an equilibrium configuration can be conveniently described by a master equation [47]. The probability of finding a system in a specific state increases by the incoming jump from adjacent states, and decreases by the outgoing jump from this state to the others. From now on we shall be specific for the lattice-gas model of crystal growth, described in the previous section. At the time t the system will be found in the state. S/ with a probability density t), and its evolution... 

Kinetic phenomena can also be used to delimit the timescales of magmatic processes and, unlike radiometric ages, do not require absolute constraints on the timing of eruption. Two important kinetic controls on crystal properties are crystal growth and diffusional relaxation of compositional heterogeneities in minerals. Rates of crystal settling are not described here but have also been used to delimit crystal storage times (e.g., Anderson et al., 2000 Resmini and Marsh, 1995). 

In the case of two different materials, the agreement of lattice parameters becomes a key issue. For a disagreement of lattice parameter, which is too large, crystal growth is rendered impossible by the appearance of many defects like dislocations, which relax the mechanical constraints at the interface. The... 

Despite advanced methods of crystal growth, sohds still contain lattice defects at concentrations around lO -lO " cm, and typical concentrations of defects and impurities in commercial samples are around 10 cm . The latter concentration is usually much greater than the concentration of photogenerated free charge carriers in solids under moderate photoexcitation. Consequently, defects are expected to play an important role in photoexcitation and relaxation processes in heterogeneous systems. In fact, defects create a local distortion of the periodic potential in the solid s lattice. 

Kardar, M., Parisi, G., and Zhang, Y.-C., Dynamic scaling of growing interfaces, Phys. Rev. Lett, 56, 889, 1986 Villain, J., Continuum models of crystal growth from atomic beams with and without desorption, J. Phys. I France, 1, 19, 1991 Lai, Z.W. and Das Sarma, S., Kinetic growth with surface relaxation Continuum versus atomistic models, Phys. Rev. Lett, 66, 2348, 1991. 

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