High-resolution (+/-1 degrees) x-ray photoelectron diffraction (XPD) patterns were obtained along high symmetry azimuths of the (3X3) and (root 3X root 3) R30 degrees reconstructed (0001)(Si) 6H-SiC surfaces. The data were compared to XPD patterns obtained from (7X7) Si (111) as well as to models proposed for the (3X3) and (root 3X root 3) R30 degrees 6H-SiC reconstructions. Forward scattering features similar to those observed from the (7X7) Si (111) were also observed from the (root 3X root 3) R30 degrees 6H-SiC (0001)(Si) surface. Additional structures were found and attributed to the substitution of carbon atoms for silicon. Unlike (1X1) and (7X7) Si (111) surfaces, the XPD patterns of (3X3) and (root 3X root 3) R30 degrees SiC (0001) Si surfaces are different which is due to the presence of an incomplete bilayer of Si on the (3X3) surface. The most significant difference with the Si system is the equivalence of the [10 (1) over bar 0] and [01 (1) over bar 0] azimuths in the (3X3) structure. These results are consistent with a faulted Si bilayer stacking sequence which was proposed based on scanning tunneling microscopy observations. (C) 1998 American Institute of Physics. [S0021-8979(98)01423-6].