X-ray diffraction measurements were carried out at temperatures from 86 to 298 K for the rapidly quenched 82AgI.13.5Ag(2)O.4.5B(2)O(3) composite in which the superionic phase of alpha-AgI was frozen at room temperature in a glass matrix. A broadening of the diffraction peaks of alpha-AgI was observed with decreasing temperature and the broadened peaks became sharper again at around 270 K with increasing temperature. This broadening of the alpha-AgI peaks at low temperatures was attributable to a larger lattice strain (ununiform deformation) of frozen alpha-AgI microcrystals. The electrical conductivities were also measured at low temperatures for the composite; the activation energies for conduction E, were steeply decreased at around 270 K on heating process. The larger E(a) values at lower temperatures were attributable to a positional ordering of Ag+ ions in the frozen alpha-AgI in the composite. Such an ordering of Ag+ ions must be associated with an increase in the lattice strain of the alpha-AgI microcrystals.