The carbonization process of a single domain 2X1-reconstructed Si(001) vicinal surface (5 degrees off axis from [001] in the [(1) over bar 10] direction) in acetylene has been studied by combining in situ surface science techniques (x-ray photoemission spectroscopy, x-ray photoelectron diffraction, reflection-electron energy loss spectroscopy, low-energy electron diffraction) and ex situ analytical techniques (C-12 and H-2 dosing by nuclear reaction analysis, scanning electron microscopy, and reflection high-energy electron diffraction). It is found that at a growth temperature of about 820 degrees C a variety of growth mechanisms can be observed, particularly during the first step of carbonization. An analysis of C 1s and Si 2p core-level shifts and of the respective intensities of them, combined with the examination of photoelectron diffraction curves, gives evidence for a penetration of C atoms into the silicon substrate, to form a nonstoichiometric compound. Contemporaneously 3C-SiC nuclei form, aligned with respect to the substrate. Then a quasicontinuous 3C-SiC film grows heteroepitaxially (''cube on cube'' unstrained growth) on the substrate up to a thickness of similar to 40 Angstrom. C 1s and Si 2p photoelectron diffraction patterns, compared with calculated ones, show that the single domain initial surface does not necessarily force a preferential alignment of one of the two inequivalent SiC{110} planes with respect to the (110) Si plane. Consequently, such vicinal Si(001) surfaces are not necessarily templates, as often reported in the literature. for the growth of crystalline films free of antiphase boundary domains. Finally, we have observed that an imperfect coalescence of 3C-SiC nuclei leaves easy paths for Si out migration from the substrate and SiC polycrystalline growth, even at a temperature as low as 820 degrees C. The current models of Si(001) carbonization are examined and compared to our experimental findings. Especially for the very beginning of carbide formation, a unified picture is lacking, as the role played by the steps and terraces of the initial surface remains unclear.