  Thermotropic biaxial nematic phases seem to be rare, but biaxial smectic A
phases less so. Here we use molecular field theory to study a simple
two-parameter model, with one parameter promoting a biaxial phase and the
second promoting smecticity. The theory combines the biaxial Maier-Saupe and
McMillan models. We use alternatively the Sonnet-Virga-Durand (SVD) and
geometric mean approximations (GMA) to characterize molecular biaxiality by a
single parameter. For non-zero smecticity and biaxiality, the model always
predicts a ground state biaxial smectic A phase. For a low degree of smectic
order, the phase diagram is very rich, predicting uniaxial and biaxial nematic
and smectic phases, with in addition a variety of tricritical and tetracritical
points. For higher degrees of smecticity, the region of stability of the
biaxial nematic phase is restricted and eventually disappears, yielding to the
biaxial smectic phase. Phase diagrams from the two alternative approximations
for molecular biaxiality are similar, except inasmuch that SVD allows for a
first order isotropic-nematic biaxial transition, whereas GMA predicts a Landau
point separating isotropic and biaxial nematic phases. We speculate that the
rarity of thermotropic biaxial nematic phases is partly a consequence of the
presence of stabler analogous smectic phases.
