Incoherent phase transitions are far more difficult to treat than thei
r coherent counterparts. The interface, which appears as a single surf
ace in the deformed configuration, is represented in its undeformed st
ate by a separate surface in each phase. This leads to a rich but deta
iled kinematics, one in which defects such as vacancies and dislocatio
ns are generated by the moving interface. We introduce an incoherency
tensor that measures the stretching and twisting of one phase relative
to the other. We show that incoherency is completely characterized by
the incoherency tensor, the vacancy production, and the slip between
phases.