Those of us who were fortunate enough to study under Don, either at UC Berkeley or UCLA, were keenly aware of Don’s fascination with simple models of the Earth at all scales – from models of the crust and mantle to models of ocean chemistry and biogeochemical cycles, and from sediments and pore waters and their mutual interaction to nucleation and growth kinetics of individual calcite crystals. Don pushed all of us to tackle complicated questions using simple tools and clever measurements, reminding us that there was almost no aspect of Earth science that could not benefit from fresh scrutiny.
In his seventieth year, this monograph honors the contributions Don has made as one of the foremost thinkers in the geological sciences. Don’s eclectic scientific interests have not only inspired future generations of scholars but also promoted a new way of attacking the mysteries of the Earth system. We all call ourselves isotope geochemists – but Don expanded the definition of what that means to touch nearly every corner of Earth science and explore the full range of geologic time. Many of us would hardly recognize each other’s work at conferences, but we all share a common background and a common approach cultivated by Don, which is now being passed on to successive generations.
For all of us students, Don has inspired and transformed our lives. Through Don, we learned to think more critically and to find value in quiet contemplation. His unwavering vision of his own scientific career helped us to define our own paths. His unconcealable enthusiasm for a problem well‐posed taught us that science is both important and fun. But perhaps most importantly, through Don’s belief in each of us, we learned to believe in ourselves. And it is for that gift that we will be forever appreciative.
Kenneth W. W. Sims, Kate Maher, and Daniel P. Schrag
1 High‐Temperature Kinetic Isotope Fractionation of Silicate Materials
Frank M. Richter
Department of the Geophysical Sciences, The University of Chicago, Chicago, Illinois, USA
ABSTRACT
Laboratory experiments were used to document kinetic isotope fractionation by mass transport in high‐temperature silicate materials. Large kinetic isotope fractionations were found in experiments in which basalt and rhyolite were juxtaposed and annealed in a piston cylinder assembly, and in experiments where the piston cylinder assembly was displaced from the furnace hot spot so that mass transport was also driven by differences in temperature (i.e., Soret diffusion). Another set of laboratory experiments showed, somewhat surprisingly, that diffusion in silicate minerals can be more effective at fractionating isotopes than diffusion in silicate melts. Isotope fractionations by diffusion in minerals are especially important in that they provide a new way of determining the degree to which diffusion was responsible for all, some, or none of the zoning of minerals from natural settings. Evaporation of silicate materials was an important process in the protoplanetary nebula. This motivated vacuum evaporation experiments that quantified the isotope fractionation associated with the amount of a parent element volatilized, allowing one to interpret the isotopic fractionation of early solar system materials in terms of mass loss by evaporation. A closing section gives some thoughts regarding future directions for research on high‐temperature kinetic isotope.
1.1. INTRODUCTION
It has long been known from the kinetic theory of gases that the relative mobility of isotopes in a gas depends on their mass. In the limit of a rarefied gas with isotopes of mass mi and mj the ratio of their diffusion coefficients is given by Di/Dj = (mj/mi)0.5. In the case of a trace gas diffusing in a gas of molecular mass M the ratio of the isotope diffusion coefficients depends on the inverse square root of their reduced mass so that Di/Dj = ( μ j/ μ i)0.5 where
The following sections discuss high‐temperature laboratory diffusion experiments that quantified kinetic isotopic fractionations associated with diffusion in silicate liquids and minerals. The results of these experiments are used to identify the processes responsible for chemical gradients in silicate materials from natural settings. Experiments quantifying kinetic isotope fractionation by evaporation from silicate liquids of interest to cosmochemistry are discussed in a final section. The experimental and analytical methods are only briefly described, and the interested reader will find them discussed in detail in the various papers referenced in connection with kinetic isotope fractionation in laboratory and natural samples.
1.2. DIFFUSION IN MULTI‐COMPONENT CONDENSED SYSTEMS: THEORY AND DEFINITIONS
1.2.1. Fick’s Laws and the Diffusion Matrix
Fick’s first law of diffusion
is often used to characterize the particle or molar flux Ji (i.e., particles or moles of i per cm2 per second) in terms of the gradient in particle or molar density ρ i (particles or moles of i per cm3) and a proportionality constant called the diffusion coefficient Di with units of length square per unit of time. Fick proposed this simple flux law in 1855 for physical particles by analogy to Fourier’s law of heat conduction. With this representation of the flux, the one‐dimensional conservation equation of ρ i, often referred to as Fick’s second law, is
However, Fick’s law is known to be inadequate for representing the flux due to chemical diffusion in a multi‐component, non‐ideal system such as a silicate liquid. It cannot explain, for example, uphill diffusion, such as that shown later for Al2O3 in Fig. 1.3, or that the rate of diffusion of a component in a multi‐component