  Mechanical properties of engineering alloys are strongly correlated to their
microstructural length scale. Diffusive insta- bilities of the Mullins-Sekerka
type is one of the principal mechanisms through which the scale of the
microstructural features are determined during solidification. In contrast to
binary systems, in multicomponent alloys with arbitrary interdiffusivities, the
growth rate as well as the maximally growing wavelengths characterizing these
instabilities depend on the the dynamically selected equilibrium tie-lines and
the steady state growth velocity. In this study, we derive analytical
expressions to characterize the dispersion behavior in isothermally solidified
multicomponent (quaternary) alloys for different choices of the
inter-diffusivity matrices and confirm our calculations using phase-field
simulations. Thereafter, we perform controlled studies to capture and isolate
the dependence of instability length scales on solute diffusivities and steady
state planar front velocities, which leads to an understanding of the process
of length scale selection during the onset of instability for any alloy
composition with arbitrary diffusivities, comprising of both independent and
coupled diffusion of solutes.
