The mechanism of diamond growth by hot-filament chemical vapor deposition (CVD) was investigated on the (100), (111), and (110) crystal faces of natural diamond by competition studies using carbon-13-labeled methane and carbon-12 acetylene. Homoepitaxial growth rates of 0.4, 0.5, and 1.3-mu-m/h were obtained for growth on the (100), (111), and (110) faces, respectively. The (100)- and (111)-oriented films were smooth initially, while films grown on (110) substrates quickly became rough. The (111) films had graphitic inclusions, as evidenced by the Raman spectrum, while the (100) and (110) films were graphite-free. The (111) films also exhibited substantial tensile stress, as indicated by a shift in the Raman peak and by spontaneous cracking in films grown thicker than 3.5-mu-m. The carbon-13 mole fraction of mixed C-13/C-12 diamond films grown on the diamond substrates was determined from the shift of the first-order Raman frequency, after correction for the shift due to stress. The carbon-13 mole fractions of methane, acetylene, and the methyl radical (derived indirectly from the mole fractions of H13C13CH and H12C13CH) in the gas phase were obtained by sampling the gas near the growth surface and subsequently determining its composition by matrix-isolation infrared spectroscopy. The carbon-13 mole fraction of the diamond film was equal to that of the methyl radical but differed significantly from that of acetylene for growth on all three crystal faces, indicating that the methyl radical is the dominant growth precursor under hot-filament CVD conditions regardless of the crystallographic orientation of the diamond substrate.