Long-range order parameter in field model of solidification

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Abstract
The physical origin of the long-range order parameter in the computer simulation models of solidification is discussed. It is shown that the simplest kinetic model of the solidification is described by a multicomponent order parameter, the role of the component being played by structural amplitudes related to the star of the shortest reciprocal-lattice vectors of the crystalline phase. A general coarse-grain-free energy of the inhomogeneous state is formulated in terms of the Landau expansion with respect to the invariants of the components of the long-range order parameter. The kinetic equations for the multicomponent long-range order parameter in the solidification process are formulated. The way in which the nonlinear character of the kinetic coefficients can affect the growth kinetics is discussed. The physical conditions under which the existing single-component long-range order parameter field models could be applicable are demonstrated.