S and D Wave Mixing in High $T_c$ Superconductors

For a tight binding model with nearest neighbour attraction and a small orthorhombic distortion, we find a phase diagram for the gap at zero temperature which includes three distinct regions as a function of filling. In the first, the gap is a mixture of mainly $d$-wave with a smaller extended $s$-wave part. This is followed by a region in which there is a rapid increase in the $s$-wave part accompanied by a rapid increase in relative phase between $s$ and $d$ from 0 to $\pi$. Finally, there is a region of dominant $s$ with a mixture of $d$ and zero phase. In the mixed region with a finite phase, the $s$-wave part of the gap can show a sudden increase with decreasing temperature accompanied with a rapid increase in phase which shows many of the characteristics measured in the angular resolved photoemission experiments of Ma {\em et al.} in $\rm Bi_2Sr_2CaCu_2O_8$