The rate of nucleation and the rate of growth of crystallites in amorphous Si50Ge50 thin films was determined using transmission electron microscopy. With the data on nucleation and growth kinetics, the temperature dependence of the nucleation free energy barrier W* was obtained using a recently developed method. Within the temperature range of 525 similar to 575 degrees C, the nucleation free energy barrier shows a linear increase with temperature and the mean value of W* is 1.92 eV. The theoretical relationship, developed by the authors, between the nucleation free energy barrier and the average grain size in the fully crystallized Si50Ge50 thin films was examined in the light of the present data.