The synthesis of Ti3SiC2 by pressureless reactive sintering of Ti/SiC/C mixtures under an Ar atmosphere has been studied using in situ neutron diffraction. The intermediate phases TiCx and Ti5Si3Cx (x less than or equal to 1) form first at similar to 800-1400 degreesC. These phases are consumed in the formation of Ti3SiC2, at similar to 1500 degreesC. After sintering, Ti5Si3Cx disappears but an amount of TiCx remains in the sample primarily as a surface layer. The studies appear to support a suggestion that the intermediate phases react to form Ti3SiC2 through a diffusion-controlled process. Prolonged stepwise heating under argon in some experiments resulted in decomposition of Ti3SiC2 above similar to 1400 degreesC and significant disproportionation of the sample.