“…The appearance of a smooth-cellular or jagged morphology from a planar interface, especially for binary alloys, depends on the material composition, C O (wt% or mole/m 3 ), velocity V (m/s) of the growing interface, and the temperature gradient G L (K/m) in the liquid and k, the non-dimensional solute partition coefficient. These variables at the point of morphological instability are commonly subscripted with the symbol (c) to indicate a transition [ 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 ]. Various theoretical models [ 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 ] have been offered to explain the transition, however, the two most widely employed models (prior to MEPR) that describe the interface instability from planar to non-planar are the constitutional undercooling (CUT) [ 19 , 20 , 21 , 22 , 27 ] and the linear stability theory model (LST) […”