The alpha-AgI-frozen composite with the composition of 82AgI . 13.5Ag(2)O . 4.5B(2)O(3) (in mol%) prepared by rapid quenching showed a typical morphology of dispersed-type composites; fine particles of alpha-AgI were stabilized in a glass matrix at room temperature. On the other hand, the rapidly quenched 90AgI . 7.5Ag(2)O . 2.5B(2)O(3) sample showed a morphology with large particles of beta-AgI precipitated in a glass matrix. The exothermic peak due to the alpha --> beta phase transformation of AgI in the cooling curve of DSC for the alpha-AgI-frozen 82AgI . 13.5Ag(2)O . 4.5B(2)O(3) composite was observed at much lower temperatures than those for the 90AgI . 7.5Ag(2)O . 2.5B(2)O(3) sample with the large beta-AgI particles. The fine particles of alpha-AgI stabilized in the 82AgI . 13.5Ag(2)O . 4.5B(2)O(3) composite were thought to have a larger nucleation barrier for the or alpha --> beta transformation than the larger particles of beta-AgI in the 90AgI . 7.5Ag(2)O . 2.5B(2)O(3) sample had. Such a larger nucleation barrier, which lowered the rate of or alpha --> beta transformation of AgI in the 82AgI . 13.5Ag(2)O . 4.5B(2)O(3) composite, must be generated by the large strain energy caused by the transformation of the fine alpha-AgI particles to the beta-phase and by the fact that the concentration of defects which induce the nucleation of beta-phase is very small in the fine alpha-AgI particles.