Crystallization crystal-melt interface

An intrinsic surface is built up between both phases in coexistence at a first-order phase transition. For the hard sphere crystal-melt interface [51] density, pressure and stress profiles were calculated, showing that the transition from crystal to fluid occurs over a narrow range of only two to three crystal layers. Crystal growth rate constants of a Lennard-Jones (100) surface [52] were calculated from the fluctuations of interfaces. There is evidence for bcc ordering at the surface of a critical fee nucleus [53]. 

Steady-state crystallization rates were measured for a range of temperatures below the melting point by Broughton et al (13). A face-centered cubic (100) crystal-melt interface was equilibrated in a box elongated in the... 

Fig. 7 Molecular dynamics calculations, open circles, for the velocity of the crystal-melt interface versus the temperature of the interface. The solid curve corresponds to eq. (1) and the dashed curve to eq. (3).

Keywords Chain folding Computer modeling Crystal growth Crystal-melt interfaces Molecular dynamics Polymer crystallization... 

Yamamoto, T. Molecular Dynamics Modeling of the Crystal-Melt Interfaces and the Growth of Chain Folded Lamellae. Vol. 191, pp. 37-85. 

Chromite crystallization from a melt, or its re-equilibration with a melt, creates an even more reduced boundary layer at the crystal-melt interface as a consequence of the incorporation of Cr " and Fe " relative to divalent ions. The reduced conditions trigger the precipitation of IPGE minerals on the surface of crystallizing chromite that can be later on entrapped during chromite growth (Finnigan etal. 2008). 

To solve the above problem, the usual method is to eliminate the moving boundary by adopting a reference frame that is fixed to the crystal-melt interface. That is, in the new reference frame and new coordinates y, the interface position is always at y=0. Hence, we let... 

No matter which reference frame we start with, when transformed into the same interface-fixed reference frame, the results should be the same. Hence, starting from Equation 4-86b, we should also arrive at Equation 3-114a. Let y be the coordinate fixed at the crystal-melt interface then... 

In a spherical nucleus, AG is associated to the supercooling, T, and the surface free energy at the crystal/ melt interface, o, through the Gibbs-Thompson equation (Eq.2) ... 

Figure 2. Evolution of order parameters Hx(z) (left axisX ( ) (right axis) through bcc 100 crystal-melt interface. Distance z is measured in reduced units of crystal cubic unit cell side length. (From Haymet and Oxtoby. )... 

Coefficient tensor of the interface gradient of the rjr field r Mobihty related to propagation of crystal-melt interface of the xir field... 

To determine the factors that affect the growth rate of the crystal we need to consider the heat flow in the system. The heat input, (jin, to the crystal across the crystal/melt interface is given by the sum of the heat associated with crystallization, (Jl, and the heat flow from the melt, qu-... 

The main difference between the methods of Kyropoulos (see Figure 7.19a) and Czochralski (see Figure 7.19b) is that in the former the seed is permitted to grow into the melt, while in the latter the seed is withdrawn at a rate that keeps the solid-liquid interface more or less in a constant position. Pull rates depend on the temperature gradient at the crystal-melt interface and can vary from 1 to 40mmh . The steeper the gradient the faster the growth rate and, hence, the faster the permissible rate of withdrawal. 

The second process is crystal growth, which essentially depends on the diffusion of segments from the melt to the crystal-melt interface. At temperatures well below the melting point, the growth rate of the nuclei, rather than their rate of formation, determines the kinetics of crystallization. This growth rate is normal in that it diminishes with falling temperature. As a result, the rate of crystallization does not increase indefinitely as the temperature is lowered but rather passes through a maximum. 

---