Lead-free Mn-doped Na(0.5)K(0.5)NbO(3) (NKN) piezoelectric crystals were grown by a slow-cooling flux method where the cooling rates during crystal growth were fixed at 0.25 degrees C/min or at a fivefold increase of 1.25 degrees C/min, and the effects of the cooling rate on the domain structure were investigated. The domain observation using a polarizing microscope showed that the numbers of the 60 degrees domain walls in the crystals grown at 0.25 degrees C/min were larger than that in the crystals grown at 1.25 degrees C/min. The Raman spectroscopy measurement confirmed that the stretching mode of nu(2) (E(g)) and separated bending mode of nu(5) (F(2g)), which is the vibrational mode of NbO(6) units in the NKN perovskite-type structure, were detected in the crystals grown at 0.25 degrees C/min even though these modes were not detected in the crystals grown at 1.25 degrees C/min. Therefore, the nu(2) and separated nu(5) modes in Raman spectra appears to be attributed to the presence of the 60 degrees domain structure. In addition, the internal stress, which is caused by the phase transitions during crystal growth, was affected by the presence of 60 degrees domains because the vibrational modes were changed. The crystals grown at 0.25 degrees C/min exhibited a rectangular P-E hysteresis loop compared with that of the crystals grown at 1.25 degrees C/min. From these results, it was found that the ferroelectric domain structures in the NKN crystals depended on the cooling rates during crystal growth, and the polarization property was affected by the domain structure, which was determined by the cooling rates.