Oxygen self-diffusion “fast-paths” in titanite single crystals and a general method for deconvolving self-diffusion profiles with “tails”

Abstract

Like most other minerals, titanite rarely if ever forms perfect crystals. In addition to the point defects that might affect lattice diffusion, there may be extended line- or planar defects along which fast diffusion could occur. During the course of an experimental study of oxygen lattice diffusion in titanite, we found that almost all of the 18O uptake profiles produced in natural titanite crystals departed from the complementary error function solution expected for simple lattice diffusion with a constant surface concentration. Instead, they exhibited “tails” extending deeper into the samples than expected for simple lattice diffusion. The purpose of this contribution is to report on these features—described as “fast-paths” for oxygen diffusion—and outline a method for coping with them in extracting information from diffusion profiles. For both dry and hydrothermal experiments in which the “fast paths” are observed, 18O was used as the diffusant. In dry experiments, the source material was 18O-enriched SiO 2 powder, while 18O-enriched water was used for the hydrothermal experiments. Diffusive uptake profiles of 18O were measured in all cases by nuclear reaction analysis (NRA) using the 18O (p,α) 15N reaction [see Zhang X. Y., Cherniak D. J., and Watson E. B. (2006) Oxygen diffusion in titanite: lattice and fast-path diffusion in single crystals. Chem. Geol. 235 105–123]. In our experiments, different sizes of “tails” (with varying 18O concentrations) were observed. Theoretically, under the same temperature and pressure conditions, the sizes of tails should be affected by two factors: the diffusion duration and the defect density. For the same experiment duration, the higher the defect density, the larger the “tail”; for the same defect densities, the longer the diffusion duration, the larger the “tail.” The diffusion “tails” could be a result of either planar defects or one-dimensional “pipe” diffusion. AFM imaging of HF etched titanite surfaces confirmed that the etched features might be caused by either parallel planar defects or parallel pipe defects, but could not differentiate between these possibilities. Through theoretical calculations simulating the tailed diffusion profiles using reasonable assumptions of lattice diffusivities and fast-path diffusivities, and comparing these with tail features measured in our samples, it can be concluded that the “tails” observed in our experiments are caused by planar defects rather than pipe defects. A new method was developed for separating the “fast-path” contribution from the overall composite diffusion profile consisting of both “fast-path” and lattice diffusion. Through this process, the lattice diffusion coefficient could be determined, which is required to analyze the tail. The oxygen diffusion rates in the fast-paths were obtained by traditional graphical analysis methods, using the Whipple–Le Claire equation (for 2-D defects) assuming that the width of the fast-path is 1 nm. Two Arrhenius relations were obtained for the fast-path diffusion phenomenon, one for experiments under dry conditions, and the other for hydrothermal conditions: D dry = 4.03 × 10 - 2 ( m 2 / s ) exp ( - 313 ± 22 ) ( kJ / mol ) / RT D wet = 3.48 × 10 - 7 ( m 2 / s ) exp ( - 219 ± 39 ) ( kJ / mol ) / RT Along with the lattice diffusivity, the presence and 3-D distribution of any fast-paths—and the diffusivities in these paths—are important to the bulk closure properties of single crystals. For titanites, AFM imaging showed that the fast-paths may not be interconnected at a length-scale comparable with the crystal dimension, so they may not have a significant effect on bulk closure properties.