  A specialization of a K3 surface with Picard rank one to a K3 with rank two
defines a vanishing class of order two in the Brauer group of the general K3
surface. We give the B-field invariants of this class. We apply this to the K3
double plane defined by a cubic fourfold with a plane. The specialization of
such a cubic fourfold whose group of codimension two cycles has rank two to one
which has rank three induces such a specialization of the double planes. We
determine the Picard lattice of the specialized double plane as well as the
vanishing Brauer class and its relation to the natural "Clifford" Brauer class.
This provides more insight in the specializations. It allows us to explicitly
determine the K3 surfaces associated to infinitely many of the conjecturally
rational cubic fourfolds obtained as such specializations.
