  Rayleigh-B\'{e}nard convection in horizontal layers of binary fluid mixtures
heated from below with realistic horizontal boundary conditions is studied
theoretically using multi-mode Galerkin expansions. For positive separation
ratios the main difference between the mixtures and pure fluids lies in the
existence of stable three dimensional patterns near onset in a wide range of
the parameter space. We evaluated the stationary solutions of roll, crossroll,
and square convection and we determined the location of the stability
boundaries for many parameter combinations thereby obtaining the Busse balloon
for roll and square patterns.
