Kinetics of Al-Si exchange in low and high quartz: calculation of Al diffusion coefficients

Abstract

Non-uniform distribution of Al between the three symmetrically equivalent Si sites in low quartz is converted to a random distribution by dry or hydrothermal annealing above 400°C due to Al-Si exchange, as shown previously by EPR measurements. Rate equations for the Al-Si exchange are derived from the experimental results presented here. We show that the kinetics of the Al-Si exchange reaction are strongly influenced by the type of Si substitution, whether by Al+Na ([AlO 4 Na] 4− ) or Al+Li ([AlO 4 /Li] 4− ). Rate constants k and activation energies E of the Al-Si exchange differ significantly under identical run conditions according to the [AlO 4 /Na] 4− and [AlO 4 /Li] 4− defects. Thus, it is concluded that Na and Li are involved in the rate determining step of the Al-Si exchange reaction. The role of Na and Li is discussed from the electrostatic and structural viewpoints. In the case of [AlO 4 /Na] 4− defects, no significant effect of water pressure on the activation energy E of the Al-Si exchange is observed, while the rate constant k decreases with increasing water pressure. In the case of [AlO 4 /Li] 4− defects, the activation energy of the Al-Si exchange in low quartz increases from 278 ± 20 KJ/mole (dry, in air) to 400 ± 25 KJ/mole at 100 MPa water pressure, while k decreases. For high quartz, no effect of water pressure is observed with respect to E and k, and the activation energy E is drastically reduced compared with low quartz. From the experimental results obtained on samples from different growth sectors of the same crystal, it is concluded that a vacancy mechanism is responsible for the Al-Si exchange. Based on the «random walk» theory, equations are derived which allow calculation of the diffusion coefficients (D∥ c and D⊥ c ) of Al from rate constants (k) of the Al-Si exchange reaction. The calculated diffusion coefficients are in the range 10 −24 to 10 −27 m 2 s −1 . With the method described here, diffusion coefficients can be estimated temperature ranges where conventional methods fail (e.g. diffusion of radioactive tracers or measurements of electrical conductivity)