Relation Between Bulk and Interface Descriptions of Alloy Solidification
  From a simple bulk model for the one-dimensional steady-state solidification of a dilute binary alloy we derive an interface description, allowing arbitrary values of the growth velocity. Our derivation leads to exact expressions for the fluxes and forces at the interface and for the set of Onsager coefficients. We, moreover, discover a continuous symmetry, which appears in the low-velocity regime, and there deletes the Onsager sign and symmetry properties. An example is the generation of the sometimes negative friction coefficient in the crystallization flux-force relation. 
Alexander L. Korzhenevskii, Richard Bausch and Rudi Schmitz
cond-mat.mtrl-sci cond-mat.stat-mech