Further Study of Intersectorial Isotope Fractionation in Quartz

During the growth of crystals, different amounts of isotopes are incorporated at the crystallographically differing crystal faces [1-5]. If the temperature and the isotopic composition of the mother solution are constant in time (as could and should be achieved in artificial crystal growth), this interfacial isotope effect and its dependence on temperature can easily be measured. During natural growth, however, the temperature and isotopic composition of the mother solution may vary with time. This causes isotopic mantle zoning in the crystal, which interferes with the interfacial isotope effect. The depth of a mantle zone is different under the different faces because of the different growth rates of the faces, the depth being proportional to the growth rate of the corresponding crystal face. The regions in a crystal that have grown from its different faces are called sector zones. If two neighbouring sector zones have grown with a constant ratio of their growth velocities, the two-dimensional boundary between the two sector zones is plane; if not, it is curved. In our paper on the 1 8 0 / 1 6 0 ratio in smoky quartz [4] we had mentioned that the sectorial boundary through the mantle zone from which the samples for the isotope analysis are taken should be plane. In this paper we present a calculation for the case where, due to a sudden change in the ratio of the growth velocities, this boundary is not plane. We also report on isotope analyses performed on the same smoky quartz crystal as used in [4] but with