Time-resolved small-angle x-ray scattering has been used to study the phase transformation kinetics of a thermally quenched, asymmetric, diblock copolymer. The roles played by homogeneous and heterogeneous nucleation in the microdomain ordering process are considered through comparison of results from pure samples and samples doped with impurities. This crystallization process is unique in that it involves constituent particles (microdomains) that are hundreds of angstroms in size ordering onto a lattice with spacings on a similar length scale. Models derived from classical nucleation and growth theories are used to analyze results from pure and doped samples. Clear experimental evidence of a heterogeneous nucleation process occurring in the doped samples suggests that impurity effects cannot be ignored in these materials. In addition, it is proposed that the late-time coexistence of crystalline and amorphous microdomain structures is due to strain energy effects induced by the volume constraints of the sample cell.