  We construct supergravity backgrounds for the integrable eta-deformations of
the AdS2 x S2 x T6 and AdS5 x S5 superstring sigma models. The eta-deformation
is governed by an R-matrix that solves the non-split modified classical
Yang-Baxter equation on the superisometry algebra of the model. Such R-matrices
include those of Drinfel'd-Jimbo type, which are constructed from a Dynkin
diagram and the associated Cartan-Weyl basis. Drinfel'd-Jimbo R-matrices
associated with inequivalent bases will typically lead to different deformed
backgrounds. For the two models under consideration we find that the
unimodularity condition, implying that there is no Weyl anomaly, is satisfied
if and only if all the simple roots are fermionic. For AdS2 x S2 x T6 we
construct backgrounds corresponding to the three Dynkin diagrams. When all the
simple roots are fermionic we find a supergravity background previously
obtained by directly solving the supergravity equations. For AdS5 x S5 we
construct a supergravity background corresponding to the Dynkin diagram with
all fermionic simple roots.
