  The existing theoretical analyses of solidification dynamics lack the
insights of historical relevance and transport processes in the whole system.
Through the phase-field model, this paper investigates the evolution in the
whole domain during entire directional solidification. First, the evolution of
characteristic parameters is obtained, including the solute concentration ahead
of interface and tip velocity, demonstrating the dissipative features of
solidification. Second, by adjusting the diffusion coefficient DL, the
dissipation at the interface can be altered. With different DL, different
stages during directional solidification are investigated, including planar
growth and instability, dendrite growth, and steady-state growth. The results
indicate the important role of solute diffusion in alloy solidification. From
the viewpoint of the whole domain, smaller DL corresponds to a higher degree of
dissipation, forming more interfaces during solidification. Moreover, the
competitive influences of tip curvature and velocity are also because of the
dissipation, resulting from the friction of atoms.
