We studied theoretically the deposition of Xe atoms on a sapphire substrate and the subsequent growth of ordered Xe phases via the low-temperature atom beam deposition method. This chemical synthesis method ͓D. Fischer and M. Jansen, J. Am. Chem. Soc. 41, 1755 ͑2002͔͒ is particularly suitable for synthesizing metastable solid compounds. The modeling procedure consisted of several steps, where we used empirical potentials to model the interactions within the substrate, the Xe-Xe interactions in the gas phase and the solid, and the interactions between the Xe atoms and the substrate. In a first step, we established that under the experimental conditions, no Xe clusters formed in the gas phase, and thus the deposition could be described by the adsorption of single Xe atoms on the substrate at low temperatures. Next, we simulated the Xe deposition process and we studied the growth mode depending on various synthesis parameters such as the deposition rate and the temperature of the substrate. Finally, the deposited Xe layers were tempered and the structure of the resulting compound was analyzed. We studied the establishment of locally ordered regions as a function of time, both during the deposition and the tempering. We observed that the final configuration was always crystalline, although defects such as stacking faults and dislocations were likely to form. The occurrence of different growth modes and the formation of defects were explained by studying diffusion and adsorption processes on the surface of both the substrate and the depositing phase.