Infrared absorption spectroscopy has been applied to study interstitial oxygen (Oi) and oxygen precipitates in a series of multi-step annealed silicon samples. We have adopted Ham's theory of diffusion-limited precipitation. Then we have been able to determine concentration of the oxygen precipitates in the samples from decrease of Oi concentration during the high temperature annealing. We have also used triple-axis high-resolution x-ray diffraction to measure reciprocal space maps of these samples.