  A U(3) model proposed by Iachello for superconductivity in cuprate materials
is analyzed. The model consists of s and d pairs (approximated as bosons) in a
two-dimensional Fermi system with a surface. The transition occurs between a
phase in which the system is a condensate of one of the bosons, and a phase
which is a mixture of two types of bosons. In the current work we have
investigated the validity of the Bogoliubov approximation, and we used a
reduced Hamiltonian to determine a phase diagram, the symmetry of the phases
and the temperature dependence of the heat capacity.
