Molecular dynamics simulations adopting the Born-Mayer-Huggins potential function are performed on (KBr)108, (KBr)256, (KBr)500 and (KBr)864 clusters to analyze structural, energetic, and kinetic aspects of phase changes. Melting and freezing are reproducible when clusters are heated and cooled. Various diagnostic methods, including the total energy curves, the Lindemann indices, and pair-correlation functions, are used to characterize phase changes during heating and cooling stages. Results demonstrate that the melted clusters are not spherical in shape. On the other hand, the melting temperatures and heats of fusion decrease approximately linearly with the reciprocals of cluster radii. The melting point and heat of fusion for bulk KBr obtained by extrapolation are close to the experimental values.