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A quantum Monte Carlo approach, considering all the corrugation effects, wasused to calculate the complete phase diagram of the second $^3$He layeradsorbed on graphite. We found that a first-layer triangular solid was inequilibrium with a gas in the second layer. At a surface density $0.166 \pm0.001$ \AA$^{-2}$, this fluid changes into two first-layer registered phases:4/7 and 7/12 solids. The 7/12 arrangement transforms into an incommensuratetriangular structure of $\rho = 0.189 \pm 0.001$ \AA$^{-2}$ upon further heliumloading. A recently proposed hexatic phase was found to be unstable withrespect to those commensurate solids.

Fluid and registered phases in the second layer of 3He on graphite