The growth of vertically aligned arrays of single-walled carbon nanotubes (SWNT) has provided an efficient route toward production of highly aligned SWNT that can be grown ultra-long. Here, the growth of such aligned SWNTs is demonstrated from a thin e-beam deposited catalyst layer composed of Fe-Mo with ratio (5:1) respectively, supported by Al2O3. Using C2H2 decomposition in a hot filament chemical vapor deposition apparatus, experiments indicate that the order of deposition of the respective Fe and Mo catalyst components significantly affects growth characteristics, especially evident during growth at elevated reaction pressures under high carbon flux. The role of temperature and pressure on features of the nanotube arrays, such as height, alignment, quality, volumetric density, and diameter distribution are compared for each case of Fe/Mo and Mo/Fe considered. In order to better understand this effect, atomistic modeling using the Bozzolo-Ferrante-Smith (BFS) method for alloys is employed along with the Monte Carlo-Metropolis method. The dependence of the growth on the order of co-catalyst deposition is observed to be a structural effect that can be explained in a straight-forward interpretation of the BFS strain and chemical energy contributions toward the formation of Fe-Mo catalyst prior to growth. The competition between the formation of metastable inner Mo cores and clusters of surface-segregated Mo atoms in Fe-Mo catalyst particles influences catalyst formation, and the role of Mo concentration and catalyst particle size is found to also be a factor influencing this formation process. Finally, this modeling procedure is demonstrated as a general technique that can be employed to study the structural stability and formation of binary catalyst particles in a reducing environment-providing a potentially cheap and efficient method for catalyst design.