Nucleation kinetics and crystal growth with fluctuating rates at the intermediate stage of phase transitions

Crystal growth kinetics accompanied by particle growth with fluctuating rates at the intermediate stage of phase transitions is analyzed theoretically. The integro-differential model of governing equations is solved analytically for size-independent growth rates and arbitrary dependences of the nucleation frequency on supercooling/supersaturation. Two important cases of Weber–Volmer–Frenkel–Zel'dovich and Mier nucleation kinetics are detailed. A Fokker–Plank type equation for the crystal-size density distribution function is solved explicitly. (paper)