Phase field technique is an extremely versatile method capable to simulate intricate changes related to quenching of polycrystalline microstructures and the scope of its application has expanded to encompass a broad spectrum such as laser-based additive manufacturing, solidification, fracture, and more. In this study, we investigate the influence of gradient energy coefficients (k = 0.01 and k = 0.1) on the average grain size of a nanoscale polycrystalline microstructure using the multi-phase field method and finite-element technique for simulation.