Using molecular dynamics simulations, we study the crystallization process in Ag6Cu4 and CuAu alloys. By changing the amount of supercooling, we are able to identify the role played by icosahedral order in the crystal growth kinetics. Specifically, the Ag6Cu4 alloy exhibits a slowing down of the growth rate when temperature decreases, as a result of the greater amount of icosahedral order in the liquid. On the other hand, there is much less icosahedral order in the CuAu alloy and, as a result, this system displays the expected behavior of increased growth rates for greater supercooling. Furthermore, by varying the metal used as a substrate for the crystal growth process, we are able to show the major role played by the size mismatch between the atoms of the substrate and the alloy during the polymorph selection process. (C) 2017 Elsevier B.V. All rights reserved.