Growth of different faces in a body centered cubic lattice: A case of the phase-field-crystal modeling

Abstract

Interface energy and kinetic coefficient of crystal growth strongly depend on the face of the crystalline lattice. To investigate the kinetic anisotropy and velocity of different crystallographic faces we use the hyperbolic (modified) phase field crystal model which takes into account atomic density (as a slow thermodynamic variable) and atomic flux (as a fast thermodynamic variable). Such model covers slow and rapid regimes of interfaces propagation at small and large driving forces during solidification. In example of BCC crystal lattice invading the homogeneous liquid, dynamical regimes of advancing front propagating along the selected crystallographic directions are studied. The obtained velocity and the velocity sequences for different faces are compared with known results.

About one unified description of the first‐ and second‐order phase transitions in the phase‐field crystal model

“…The resulting phenomenological coefficients B x 0 , ΔB 0 , a, v in general can be calculated for different metals by fitting the density and energy gap between liquid and crystalline phases and parameters of liquid structure factor. 18,30,31 Here, we would use the model parameters preserving the realistic relation between coefficients, which lead to the existence of stable BCC-crystal.…”

“…Let one introduce new variables P and to split dynamical Equation ( 6) effectively reducing the spatial derivative's order: 10,31 ⎧ ⎪ ⎨ ⎪ ⎩…”

“…where is the driving force and is a field variable of Swift-Hohenberg free energy and ≠ 0 was considered in all cases designating the intermediate relaxation time for the atomic flux in this model. 31,36 The numerical simulations of two types of the PFC models Equations ( 6) and ( 15) for crystallization from the undercooled liquid to the BCC-crystal was performed for the three different domains of size…”

“…The system in the smallest domain 27 × 27 × 27 obeys a two-stage crystallization and starts to crystallize almost instantly to the intermediate rods-like structure (see F curve in Figure 4 and A and B in Figure 5). Such metastable structures can be formed on the phase front with high velocities, 31 if the flow relaxation rate is insufficient. However, for the symmetrical domains such structures can be generated by the confinement-induced standing waves.…”

Distance-Based Skeletonization on the BCC Grid

“…An alternative structure, the body-centered cubic (BCC) grid tessellates the space into truncated octahedra, which results in a less ambigous connectivity structure compared to the cubic grid [21]. The importance of BCC grid shows an upward tendency in the analysis of 3D digital images [1,13,14,15,24].…”