Diffusion isotopic homogenization

If both chemical concentration gradients and isotopic ratio gradients are present (e.g., basaltic melt with Sr/ Sr ratio of 0.705 and andesitic melt with Sr/ Sr ratio of 0.720), the homogenization of isotopic ratio is referred to as isotopic diffusion (Lesher, 1990 Van Der Laan et al., 1994), although some prefer to call it isotopic homogenization. If there are concentration gradients in both major and trace elements, the diffusion of the trace elements is referred to as trace element diffusion (Baker, 1989). Isotopic diffusion and trace element diffusion are really part of multicomponent diffusion, which is complicated to handle. Isotopic diffusion should not be confused with self-diffusion, and trace element diffusion should not be confused with tracer diffusion. 

The cumulative effect of the instantaneous fractionations given by Equations (6)-(9) is easily calculated if it is further assumed that mass transport processes (e.g., chemical diffusion) are sufficiently fast to maintain chemical and isotopic homogeneity in both the gas and in the condensed phase. There are cases where diffusion in the residue or gas limits mass transport and these effects on isotopic and chemical fractionation have been explored by Richter et al. (2002). Let us consider first the isotopic fractionations associated with condensation in a supersaturated closed system. The change in the moles of isotope 1 of element k in the gas can be written as... 

The use of isotopes or tracers is a common means of studying diffusion. Tracer methods permit measurements of self-diffusion, that is, the diffusion of the crystal components in a crystal. Furthermore, they allow measurements of diffusion in homogenous materials, that is, without imposing chemical gradients (when one disregards the difference in atomic weight between atoms in the crystal and of the tracer). 

A common technique is to deposit a very thin film of radioactive isotopes on a plane surface of a sample, and, after subsequent diffusion anneal, determine the activity of diffusion species as a function of distance from the plane surface. If the thickness of the sample is very much larger than the penetration depth of the tracers, the solid can be considered semi-infinite. Furthermore, if the diffusion is homogenous (e.g. taking place by lattice diffusion), the concentration of the diffusing tracers normal to the plane is through solution of Fick s second law with appropriate boundary conditions given by... 

Most of the chemical reactions presented in this book have been studied in homogeneous solutions. This chapter presents a conceptual and theoretical framework for these processes. Some of the matters involve principles, such as diffusion-controlled rates and applications of TST to questions of solvent effects on reactivity. Others have practical components as well, especially those dealing with salt effects and kinetic isotope effects. 

Let us consider another situation where a force (or forces) is not compensated on a time average. Then the particles upon which the force is exerted become transported in the medium. This translocation phenomenon changes with time. Particle transport, of course, also occurs under equilibrium conditions in homogeneous media. Self-diffusion is a process that can be observed and its velocity can be measured, provided that a gradient of isotopically labelled species is formed in the system at constant composition. 

Galy et al. (2001) suggested that the mantle should have a homogeneous Mg isotope composition. Pearson et al. (2006), however, demonstrated that olivines from mantle xenoliths have a heterogeneous compositions with a 5 Mg range of about 4%c. These authors suggested that the differences are due to diffusion-related meta-somatic processes. 

In this equation, ,/ and mi/2 are the masses of the two isotopes making up RZ1, and the terms are condensation coefficients for the two isotopes, which are determined experimentally and are typically close to 1. Equation (7.2.1) is valid if a is independent of the evolving composition of the evaporating liquid, and the diffusive transport rate is fast enough to keep the liquid homogeneous. The last condition is violated in solids, where diffusion is very slow relative to the evaporation rate, so solids do not undergo Rayleigh distillation. 

During self-diffusion in a pure material, whether a gas, liquid, or solid, the components diffuse in a chemically homogeneous medium. The diffusion can be measured using radioactive tracer isotopes or marker atoms that have chemistry identical to that of their stable isotope. The tracer concentration is measured and the tracer diffusivity (self-diffusivity) is inferred from the evolution of the concentration profile. 

In Section 3.1.1, the self-diffusivity was obtained for a diffusion couple composed of a chemically pure material but with gradients of an isotope of that material. In this section we discuss self-diffusion of an isotopic species in a chemically homogeneous binary solution consisting of atoms of types 1 and 2 in the presence of a concentration gradient of the isotope. 

D is the self-diffusivity in a chemically homogeneous material comprised of only one species. It is usually determined by measuring the diffusion of a radioactive isotope that is chemically indistinguishable from the inert species. Because there is no mass flow, the C-frame is also a V-frame, and either may be used. 

Fick s first law, in the form given by Equation 5.12, allows us to define the tracer- and the self-diffusion coefficients. Diffusion of a tracer isotope is the case when a diffusing atom, which is marked by their radioactivity of by their isotopic mass (see Figure 5.1) [7], is introduced in an extremely dilute concentration in an otherwise homogeneous crystal with no driving force [4], In this case, the tracer gradient of concentration will give rise to a net flow of tracer atoms. Consequently,... 

There is evidence from chondrites that the solar nebula was well mixed between 0.1 and 10 AU during its first several million years of the evolution, as shown by the homogeneity in concentrations of many isotopes of refractory elements (Boss 2004 Chapter 9). This is likely caused by the evaporation and recondensation of solids in the very hot inner nebula, followed by outward transport due to turbulent diffusion and angular momentum removal. Materials out of which terrestrial planets and asteroids are built have been heated to temperatures above 1300 K and are thus depleted in volatile elements. The inner solar nebula, with some exceptions, does not retain memories of the pristine interstellar medium (ISM) chemical composition (Palme 2001 Trieloff Palme 2006). 

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