predict. Macroscopic continuum model Nowadays the best understanding for dendritic crystals comes in the form of the macroscopic continuum model which assumes that both the solid and the liquid parts of the system are continuous media and the interface is a surface. This model uses the microscopic structure of the material and uses the general understanding of nucleation to accurately predict how a dendrite will grow. Dendrite formation Dendrite formation starts with some nucleation, i.e. the first appearance of solid growth, in the supercooled liquid. This formation will at first grow spherically until this shape is no longer stable. This instability has two causes: anisotropy in the surface energy of the liquid-solid interface and the attachment kinetics of particles to crystallographic planes when they have formed. On the solid-liquid interface, we can define a surface energy which is the excess energy at the liquid-solid interface to accommodate the structural changes at the interface. For a spherical interface, the Gibbs-Thomson equation then gives a melting point depression compared to a flat interface , which has the relation where is the radius of the sphere. This curvature undercooling, the effective lowering of the melting point at the interface, sustains the spherical shape for small radii. However, anisotropy in the surface energy implies that the interface will deform to find the energetically most favourable shape. For cubic symmetry in 2D we can express this anisotropy int the surface energy as This gives rise to a surface stiffness where we note that this quantity is positive for all angles when . In this case we speak of "weak anisotropy". For larger values of , the "strong anisotropy" causes the surface stiffness to be negative for some . This means that these orientations cannot appear, leading to so-called 'faceted' crystals, i.e. the interface would be a crystallographic plane inhibiting growth along this part of the interface due to attachment kinetics. Wulff construction For both above and below the critical anisotropy the Wulff construction provides a method to determine the shape of the crystal. In principle, we can understand the deformation as an attempt by the system to minimise the area with the highest effective surface energy. Growth velocity Taking into account attachment kinetics, we can derive that both for spherical growth and for flat surface growth, the growth velocity decreases with time by . We do however find stable parabolic growth, where the length grows