Abstract: In order to prevent impurities, in particular a chlorine impurity, present in the wall of the vessel from diffusing into the interior of the vessel and there disturb the growth process of the crystal, a hollow member, in particular a tube (1), of quartz is provided on its inside with a coating of silicon dioxide, while argon, gaseous silane and a gaseous oxidant, for example, dinitrogen oxide and/or carbon dioxide are introduced into the hollow member heated at 250.degree. to 350.degree. C. and are converted by means of a microwave resonator (2) into a porous coating of silicon dioxide at a pressure between 20 and 30 mbar, which coating is sintered to form a coating which is preferably at least 50 .mu.m thick.