Element partitioning—at its most basic—is the distribution of an element of interest between two constituent phases as a function of some process. Major constituent elements generally affect the thermodynamic environment (chemical equilibrium) and therefore trace element partitioning is often considered, as trace elements are present in minute quantities and their equilibrium exchange reactions do not impart significant changes to the larger system. Trace elements are responsive to thermodynamic conditions, and thus they act as passive tracers of chemical reactions without appreciably influencing the bulk reactions themselves. In planetary sciences, the phase pairs typically considered are mineral-melt, metal-silicate, and sulfide-silicate, owing largely to the ubiquity of their coexistence in planetary materials across scales and context, from the micrometer-sized components of meteorites up to the size of planets (thousands of kilometers). It is common to speak of trace elements in terms of their tendency toward forming metallic, sulfidic, or oxide phases, and the terms “siderophile,” “chalcophile,” and “lithophile” (respectively) are used to define these tendencies under what is known as the Goldschmidt Classification scheme. The metric of an element’s tendency to concentrate into one phase relative to another is expressed as the ratio of its concentration (as a weight or molar fraction) in one phase over another, where convention dictates the reference frame as solid over liquid, and metal or sulfide over silicate; this mathematical term is the element’s partition coefficient, or distribution coefficient, between the two respective phases, D M Phase B Phase A (where M is the element of interest, most often reported as molar fraction), or simply D M . In general, trace elements obey Henry’s Law, where the element’s activity and concentration are linearly proportional. Practically speaking, this means that the element is sufficiently dilute in the system such that its atoms interact negligibly with one another compared to their interactions with major element phases, and thus the trace element’s partition coefficient in most settings is not appreciably affected by its concentration. The radius and charge of an element’s ionized species (its ionic radius and valence state)—in relation to either the major element ion for which it is substituting or the lattice site vacancy or interstitial space it is filling—generally determine the likelihood of trace element substitution or vacancy/interstitial fill (along with the net charge of the lattice space). The key energy consideration that underlies an element’s partitioning is the Gibbs free energy of reaction between the phases involved. Gibbs free energy is the change in internal energy associated with a chemical reaction (at a given temperature and pressure) that can be used to do work, and is denoted as Δ G rxn . Reactions with negative Δ G rxn values are spontaneous, and the magnitude of this negative value for a given phase, for example, a metal oxide, denotes the relative affinity of the metal toward forming oxides. That is to say, an element with a highly negative Δ G rxn for its oxide species at relevant pressure-temperature conditions will tend to be found in oxide and silicate minerals, that is, it will be lithophile (and vice versa for siderophile elements). Trace element partitioning systematics in mineral-melt and metal-/sulfide-silicate systems have boundless applications in planetary science. A growing collective understanding of the partition coefficients of elements has been built on decades of physical chemistry, deterministic theory, petrology, experimental petrology, and natural observations. Leveraging this immense intellectual, technical, and methodological foundation, modern trace element partitioning research is particularly aimed at constraining the evolution of plate tectonics on Earth (conditions and timing of onset), understanding the formation history of planetary materials such as chondrite meteorites and their constituents (e.g., chondrules), and de-convolving the multiply operating processes at play during the accretion and differentiation of Earth and other terrestrial planets.
Isotopic dating is the measurement of time using the decay of radioactive isotopes and accumulation of decay products at a known rate. With isotopic chronometers, we determine the time of the processes that fractionate parent and daughter elements. Modern isotopic dating can resolve time intervals of ~1 million years over the entire lifespan of the Earth and the Solar System, and has even higher time resolution for the earliest and the most recent geological history. Using isotopic dates, we can build a unified scale of time for the evolution of Earth, the Moon, Mars, and asteroids, and expand it as samples from other planets become available for study. Modern geochronology and cosmochronology rely on isotopic dating methods that are based on decay of very long-lived radionuclides: 238U, 235U, 40K, 87Rb, 147Sm, etc. to stable radiogenic nuclides 206Pb, 207Pb, 40K, 40Ca, 87Sr, 143Nd, and moderately long-lived radionuclides: 26Al, 53Mn, 146Sm, 182Hf, to stable nuclides 26Mg, 53Cr, 142Nd, 182W. The diversity of physical and chemical properties of parent (radioactive) and daughter (radiogenic) nuclides, their geochemical and cosmochemical affinities, and the resulting diversity of processes that fractionate parent and daughter elements, allows direct isotopic dating of a vast range of earth and planetary processes. These processes include, but are not limited to evaporation and condensation, precipitation and dissolution, magmatism, metamorphism, metasomatism, sedimentation and diagenesis, ore formation, formation of planetary cores, crystallisation of magma oceans, and the timing of major impact events. Processes that cannot be dated directly, such as planetary accretion, can be bracketed between two datable events.