Elastic neutron diffraction has been used to study the structure of N2 films adsorbed on the (0001) surfaces of an exfoliated graphite substrate at coverages 0 between 1.0 and 1.67 layers and at temperatures below 11 K. For 0=1.0, the diffraction patterns can be fit by the in-plane rectangular V 3 X 3 herringbone structure denoted C (commensurate), previously inferred from low-energy electron diffraction (LEED) experiments. Analysis of the relative Bragg-peak intensities in the neutron diffraction pattern of the C phase extends the LEED results by yielding a value of /=45'+5 for the angle between the N -N bond and the short axis of the unit cell. Also, we find a substantially smaller Debye-Wailer factor for this phase than previously inferred from x-ray experiments. At coverages 8=1.13 and 1.27, the diffraction patterns are consistent with the uniaxial incommensurate (UI) phase seen by LEED. The patterns can be fit with the same molecular orientational parameters as for the C phase. We find the compression of the monolayer to be complete at 6=1.67 where the film density is -10% greater than for the C phase. Fits to the diffraction pattern at this coverage indicate a slight oblique distortion of the unit cell from hexagonal symmetry. For this nearly triangular incommensurate (TI) phase, we obtain orientational parameters in the ranges 30' & P &45' and 10 & P & 20 where l3 is the tilt angle of the N -N bond with respect to the surface.At coverages between 6=1.27 and 1.40, there is evidence of coexistence of the UI and TI phases.
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