Structure-property relationships of fast copper ion conductor cubic gamma-CuI (300 K) and alpha-CuI (773 K) has been investigated using the time-of-flight (TOF) neutro powder diffraction over the Q-range up to 30 angstrom(-1). Crystal structure of the both gamma- and alpha-phases were refined using the conventional Rietveld methods combined with the maximum-entropy-method (MEM), whilst the local structures were analyzed by means of the pair distribution function (PDF) combined with the reverse Monte Carlo (RMC) simulation. The crystal structure analysis revealed temperature dependence of large thermal displacement of copper ions along < 111 > directions, with average copper ions density mostly distributed at the 8c center of tetrahedrally-coordinated by 1 ions. The PDF analysis estimated the new peak position of Cu-Cu pairs shifted from 4.27 A in the gamma-phase to 2.49 A in the alpha-phase and estimation of coordination number decreases from 12.1 to 5.8, respectively. The local structure analysis found the new split peaks of g(Cu-Cu)(r) at r about 2.47 angstrom and 2.72 angstrom in the alpha-phase that roughly correspond to the Cu-Cu diagonally distance between nearest neighboring tetrahedral corner 32f-32f sites and between tetrahedral center 8c-32f sites such as represented by the splitting Cu site model of Fm-3m. (C) 2008 Elsevier B.V. All rights reserved.