We introduce a method for examining the boundaries between periodic block copolymer morphologies using self-consistent field theory (SCFT). The technique is illustrated on kink grain boundaries in the AB diblock copolymer lamellar phase. In agreement with experiment, the A and B domains evolve from a simple ''chevron'' shape to a complex ''omega'' shape as the kink angle theta increases beyond about 90 degrees, The transformation begins with the formation of an ''intermediate'' shape where protrusions develop symmetrically from the A and B domains at the center of the grain boundary. Following that, a continuous symmetry-breaking transition occurs forming the omega boundary where protrusions extend only from either the A or B domains. At low angles, in the chevron region, the grain boundary tension Gamma(K) obeys the scaling relation Gamma(K) similar to theta(3), and at high angles, in the omega region, the tension peaks and then decreases with increasing angle. Raising the segregation in the melt causes a monotonic increase in the grain boundary tension; at strong segregations, the tension should scale as Gamma(K) similar to chi(1/2), where chi is the Flory-Huggins interaction parameter. Both compositional and conformational asymmetries in the diblock molecule produce a decrease in Gamma(K). (C) 1997 American Institute of Physics.