A Phase Field model is developed combining the Orientation Field approach to modeling solidification with the Kim, Kim, Suzuki method of modeling binary alloys. These combined methods produce a model capable of simulating randomly oriented second phase dendrites with discrete control of the solid-liquid interface energy and thickness. The example system of carbon in a liquid uranium (U) melt is used as a test for the model. The formation of uranium carbide within a liquid U melt is simulated for isothermal conditions and compares well with experiments.