The conditions governing the growth of indium antimonide (InSb) nanowires by antimonidization of indium (In) droplets in a Chemical Vapor Deposition (CVD) system are examined. We report on factors that affect the InSb nanowire morphology and stoichiometry when growth is catalyzed by a low surface energy metal like In. Using thermodynamics and kinematics of nanowire growth, theoretical predictions are compared to experimental data. Results detailing the dependence of morphology and composition of these nanowires on temperature and diameter of the alloyed droplet are analyzed to show the dependence of these parameters on the chemical potential between vapor, liquid and solid phases. The Gibbs-Thomson (GT) effect is used to explain lower effective supersaturation and slower nucleation in small sized droplets, resulting in nanowires with diameters below a critical diameter range to be comprised of pure In.