Dynamics of partially faceted melt/crystal interfaces II: multiple step–source calculations

Dynamic three-dimensional simulation of facet formation and segregation in Bridgman crystal growth

“…Another numerical scheme, the kinetic model approach, is similar to the one proposed by Weinstein and Brandon [11][12][13]. It uses Eq.…”

“…This approach allows a small undercooling to be considered, so that growth mechanisms having a small undercooling could be easily incorporated without the restriction of the grid size. In fact, the facet formation through different mechanisms has been simulated successfully by Weinstein and Brandon [11][12][13]. Nevertheless, to precisely represent the facet, the cell size still needs to be large enough.…”

“…However, once the facet is formed, the fastest growth mode dominates in the facet, i.e., V n(facet) ¼ max[V n(DG) , V n(2DN) , V n(SM) ]. Therefore, the selection of the kinetic coefficient can be formulated as follows [11][12][13]:…”

“…The first attempt to simulate the faceting coupled with the heat transfer in oxide growth was made in Brandon's group [9,10] using a two-dimensional (2D) finite element approach. Recently, Weinstein and Brandon [11,12] also developed algorithms for faceting, taking into account the coupling of different kinetic mechanisms and extended them to 3D simulation as well [13]. Nevertheless, melt flow and segregation were not considered in their models because the faceting, except {1 1 1}, breaks axisymmetry and a 3D simulation is required.…”

“…Ma et al [15] also used a similar approach for the 2D growth of YAG crystals; however, dynamic formation of the facets was further considered. On the other hand, Weinstein and Brandon [11,12] used a kinetic model approach that moves the interface shape according to the local kinetic models related to crystallographic orientation and undercooling. Different mechanisms for facet growth could be considered.…”