NMR studies of monolayer hydrogen films for both the expected root 3 x root
3 commensurate solid and the incommensurate solid (for full monolayer cove
rage) on hexagonal boron nitride (BN) are reported for ortho-H-2 concentrat
ions 0.30 less than or equal to X less than or equal to 0.74 and temperatur
es 0.08<T<4.2.K. Phase diagrams for these systems are mapped out in terms o
f X and T from clear structural changes of the NMR spectra, including the o
bservation of a 2D orientational quadrupolar glass ordering for X < X-crit
= 0.69, and long range orientational ordering for X > X-crit for commensura
te films.