We have studied the process and kinetics of the order-order phase transition (OOT) from spheres in a body-centered-cubic lattice (bccsphere) to hexagonally packed cylindrical microdomains (hex-cylinder) for a poly styrene-block-polyisoprene-block-polystyrene triblock copolymer, induced by abrupt temperature drops. In this study, time-resolved small-angle X-ray scattering (SAXS) measurements are conducted to investigate the OOT processes in situ and at real time. Transmission electron microscopy observations for specimens rapidly frozen below the glass transition temperature at particular times in the OOT processes are also conducted to visualize the transient structures developed during the OOT. We elucidated the following pieces of evidence. (I) The OOT proceeds via the nucleation and growth process as follows: After quenching the specimen, the system stays at a bcc-sphere state in the incubation period, t(i). After this period, (II) anisotropic grains of hex-cylinder are nucleated at the vicinity of grain boundaries of bee sphere. (III) The growth of the grains appears to be faster along the cylindrical axis than along the direction perpendicular to it, on the contrary to the growth of hex-cylinder from the disordered phase. The OOT involves deformation of spherical domains toward a [111] direction of a bee lattice, followed by coalescence and connection of them to cylindrical microdomains. (IV) The rate of OOT as observed by time-resolved SAXS was found to depend on quench depth, Delta T (equivalent to T-OOT - T-cyl)=4-10 K, or thermodynamic driving force for the OOT, epsilon(equivalent to Delta T/T-OOT) =0.0087-0.0217, where TOOT is the OOT temperature between hex-cylinder and bcc-sphere: The larger AT or - is, the shorter t(i) is and the faster the transformation rate, R-T, is after the incubation time. (V) Consequently, the time change of a characteristic parameter as observed by SAXS at various Delta Ts fall on to a master curve when real time is reduced with ti, revealing that the following two intriguing conclusions: (i) t(i) and R-T(-1) have the same temperature dependence, and hence the system has only single time scale, and (ii) the transformation after the incubation period starts only when the characteristic parameter reaches a temperature independent critical value. (c) 2005 Elsevier Ltd. All rights reserved.