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The phase field method is an established technique for investigation of microstructure evolution during materials processing. Large scale three-dimensional simulations including multiple phase fields and multiple components have high requirements for memory and computational power. In this paper we present a distributed-memory parallelization of the phase field library OpenPhase. We consider load imbalances that arise during phase field calculations and propose techniques to balance the computational load efficiently among the processors. We show benchmarks using thousands of processes and use the parallelized OpenPhase for a three-dimensional simulation, that was previously only viable in two dimensions.