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We study the interplay between surface roughening and phase separation duringthe growth of binary films. Renormalization group calculations are performed ona pair of equations coupling the interface height and order parameterfluctuations. We find a larger roughness exponent at the critical point of theorder parameter compared to the disordered phase, and an increase in the uppercritical dimension for the surface roughening transition from two to four.Numerical simulations performed on a solid-on-solid model with two types ofdeposited particles corroborate some of these findings. However, for a range ofparameters not accessible to perturbative analysis, we find non-universalbehavior with a continuously varying dynamic exponent.Comment: 10 pages, 8 figure

Interplay between phase ordering and roughening on growing films