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date: 24 July 2021

# Isotopic Dating

• Yuri AmelinYuri AmelinResearch School of Earth Science, Australian National University

### Summary

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.

### Subjects

• Observational and Experimental Techniques
• Planetary Surfaces
• Planet Formation

### Introduction

#### Terminology and Definitions

When we determine isotope abundances in a rock or mineral, we get a measure of time called “date.” The “date” is the time calculated from the ratio of a radioactive isotope and its daughter isotope using the law of radioactive decay. The time values calculated from a linear regression in an isochron diagram, or from analysis of a single rock or mineral, are called “isochron date” and “model date,” respectively (Amelin, 2006; Faure, 1986). If there is sufficient proof that the conditions of the isochron approach and/or model (single-point) approach are satisfied, then the date may be interpreted as the age of the rock or mineral—the time between a geological (or any other natural) event and the present. The usage of the term “age” in place of “date” should be avoided, because it creates a false impression that any measure of time calculated from the isotopic relationships has a geological significance.

#### The Principles of Isotopic Dating

Isotopic dating is based on the decay of natural radioactive (parent) isotopes and the accumulation of their decay products (radiogenic or daughter isotopes) that occur with a constant and known rate (Dickin, 2005; Faure, 1986). The number of decays of the parent isotope (dP) per unit of time (dt) is proportional to the number of atoms of the parent isotope (P):

$Display mathematics$(eq.1)

The proportionality constant λ‎, which is called “decay constant,” has a unique numeric value for the particular radioisotope. Integrating and rearranging eq. 1, we get the number of radioactive parent atoms that remain from the original number of atoms $(P0)$ that were present when $(t=0)$:

$Display mathematics$(eq.2)

The number of daughter atoms produced by radioactive decay $D*=P0-P$ over time t is:

$Display mathematics$(eq.3)

Some atoms identical to the atoms of the daughter isotope are often present in the rock or mineral initially $(D0)$, so the total number of atoms of the isotope D is:

$Display mathematics$(eq.4)

Solving eq. 4 for time t, we get the basic equation of isotopic dating:

$Display mathematics$(eq.5)

This equation is used, directly or indirectly, in all age determinations based on radioactive decay and accumulation of radiogenic decay products.

#### The Place of Isotopic Dating in Earth and Planetary Research

Isotopic chronometers measure the time of the processes that fractionate parent and daughter elements. Fractionation of chemical elements that is datable with isotopic clocks occurs in many processes including, but not limited to, melting, melt crystallization, metamorphism, metasomatism, condensation, evaporation, and metal–silicate segregation that happen, or have happened in the past, in Earth and other planets, asteroids, and their precursor materials, throughout the history of the Solar System. Furthermore, the rate of radioactive decay is constant under physical conditions in the Solar System (it changes significantly only under extreme pressures and temperatures such as are found in the cores of massive stars). This makes isotopic dating a unique tool that allows us to place various terrestrial and extraterrestrial rocks, and their parent planetary bodies, into a unified scale of time.

### The Origin and Progress of Isotope Geochronology and Cosmochronology

#### The Beginning

From its beginning, isotopic dating was, and still remains, a discipline at the crossroads of physics, chemistry, geology, and planetary sciences, being empowered by developments in these disciplines, and contributing to their progress in turn. Isotopic dating was born around 1900, as a spin-off of the discovery of radioactivity by Henri Becquerel, the discovery of radioactive elements and the methods for their separation by Pierre and Marie Curie, and the formulation of the law of radioactive decay by Ernest Rutherford and Frederick Soddy (Rutherford & Soddy, 1902). Shortly after these discoveries, Bertram Boltwood, following a suggestion by Rutherford, established that Pb was the final decay product of U, and determined the ages of several specimens of the mineral uraninite (UO2) of 400 to 2200 million years (Ma) from their chemical Pb/U ratios (Boltwood, 1907). In the following four to five years, Arthur Holmes expanded application of chemical Pb/U dating from U-rich ore minerals to more common minerals such as zircon with much lower content of U. In his book The Age of the Earth (Holmes, 1913) he used his dating results to infer that the Earth is older than 1600 Ma. This estimate, confirmed and refined by subsequent geochronological studies, was a major breakthrough, compared with numerous estimates of the age of our planet based on cooling models, orbital physics, Na accumulation in the oceans, and sediment accumulation that yielded a hugely discrepant set of values ranging from ~5 Ma to ~15,000 Ma (Dalrymple, 2001).

#### Isotopes, Mass Spectrometry, Ion Exchange Resins, and Isotopic Tracers

Since its origin, geochronology has come a long way. It was shaped by benchmark discoveries and developments. The first of these was the discovery of isotopes—the varieties of atoms of the same chemical element with different masses. The existence of isotopes was suggested by F. Soddy in 1913 on the basis of his study of the radioactive decay chains. In the same year, J. J. Thomson discovered that the positive ions of Ne can be separated by magnetic and electrical fields into two streams corresponding to the atomic masses of 20 and 22. This finding demonstrated that stable (non-radioactive) elements can also contain multiple isotopes, and marked the birth of mass spectrography—a technique for recording a spectrum of ions with different masses on a photographic plate. The advancements of techniques for isotope detection by Francis Aston, Arthur Dempster, and Alfred Nier converted the mass spectrograph into a mass spectrometer—an instrument for precise measurement of relative abundances of ions with different mass by collection and amplification of small electrical currents produced by the ion beams of individual isotopes. Modern mass spectrometers, although immensely more complex and technologically refined, are still built on the same principles and comprise the same modules (ion source, mass analyzer, ion detector(s), and supporting vacuum system) as Nier’s instruments of the 1930s and 1940s. The inventors of the early mass spectrometers used these instruments to identify many new isotopes of various elements, including the existence of two long-lived isotopes of uranium, 238U and 235U. The observation that two isotopes of U decay to two isotopes of Pb made it possible to perform independent age determinations with the two parent–daughter isotopic pairs, 238U-206Pb and 235U-207Pb, a technique that was pioneered by Nier (1939).

The discovery of isotopes, the development of mass spectrometry, and the understanding of isotopes as varieties of atoms with nuclei containing identical numbers of protons but different numbers of neutrons (following discovery of the neutron by James Chadwick in 1932) transformed “chemical” U-Pb dating based on the determination of bulk quantities of parent and daughter elements into isotopic dating based on determination of the abundance ratios of individual parent and daughter isotopes—a quantitative research tool for measuring geological time. Two additional analytical developments significantly contributed to the progress of isotopic dating: ion exchange resins and element separation procedures, and production (with eventual commercial availability) of enriched isotope materials, were performed as part of the “Manhattan Project,” the first U.S. nuclear weapons development project of the 1940s. These developments provided means for fast and efficient separation of parent and daughter elements from rocks and minerals, and enabled precise determination of trace element concentrations and abundance ratios by addition of these enriched isotope materials as tracers using the method of isotope dilution.

#### 1950s to 1970s: Meteorites, Lunar Rocks, and Early Archaean

By the mid-1950s, the dating methods were sufficiently mature to be transformed from a small number of highly laborious projects to a mainstream research tool in earth sciences, and to encourage researchers to undertake the first dating of extraterrestrial materials. The birth of cosmochronology is marked by the papers of Patterson (1955) and Wasserburg and Hayden (1955), who determined the ages of meteorites now known as equilibrated ordinary chondrites, eucrites, and IAB and IIIAB irons, with the 207Pb-206Pb and 40Ar-40K methods. The Pb-Pb isochron of Patterson (1955, 1956) yielded an age for the Solar System of 4550 ± 70 Ma that agrees, within uncertainty, with the current best estimate. Isochron recalculation of Patterson’s Pb isotopic data with the current best value of the Solar System 238U/235U ratio (Goldmann, Brennecka, Noordmann, Weyer, & Wadhwa, 2015), U isotope decay constants (Villa, Bonardi, De Bièvre, Holden, & Renne, 2016), and modern procedures for linear regression yields 4476 ± 110 Ma, which is still in agreement with the current value.

Along with improving analytical techniques, geochronologists were searching for more potent methods for calculating ages of rocks and minerals that contain some initial (non-radiogenic) amount of the daughter elements, or were disturbed by migration of parent and/or daughter elements after crystallization. Wetherill (1956a, 1956b) proposed plotting U-Pb data in a concordia diagram (Figure 1a,b)—a graph showing 207Pb*/235U and 206Pb*/238U ratios on opposite axes (asterisk denotes radiogenic only atoms after subtraction of initial Pb). Data sets that form straight lines in a concordia diagram can yield both the time of crystallization and the time of metamorphism. An alternative form of the concordia diagram (Figure 1c,d) was developed by Tera and Wasserburg (1972a) for plotting U-Th-Pb data for lunar rocks. The Pb-Pb isochron plot (Figure 2a) proposed by Holmes (1946) and Houtermans (1946), was used by Patterson (1955, 1956) in his pioneering work on meteorite chronology. An alternative form of the Pb-Pb isochron plot (Figure 2b) was developed by Tera and Wasserburg (1972b) for dating lunar rocks, and is currently widely used in meteorite chronology. Nicolaysen (1961) developed the isochron diagram (Figure 2c) that allows calculation of an age from analyses of a set of cogenetic rocks or minerals with variable parent–daughter ratios that contain mixtures of radiogenic and initial components. This isochron diagram can be used for various isotopic systems and can in many cases produce accurate ages even for the rocks and minerals with high abundance of the initial component. All these forms of graphical presentation, age calculation, and interpretation remain most popular in geochronology to this date. These developments were supplemented by new mathematical procedures for linear regression of geochronological data (York, 1969) that account for uncertainties of individual analyses and their correlations, and are applicable to various forms of isochron and concordia plots.

In the 1960s geochemists made further advances in the methods of isotopic dating. Mass spectrometers with full digital control that enabled isotopic analyses of unprecedented precision and accuracy were designed (e.g. Wasserburg, Papanastassiou, Nenow, & Bauman, 1969), better clean labs for sample processing with minimal contamination were constructed, and refined protocols for isotope analysis were developed. Analysis of rocks at these advanced facilities allowed for the extraction of comprehensive information from materials available in limited quantities. These developments were crucial for getting comprehensive information from lunar rocks that were returned to the Earth shortly thereafter by five manned Apollo missions in 1969–1972, and three robotic Luna missions in 1970–1976.

1969 was a remarkable year for planetary chronology, and planetary science in general, as it was the year of the first delivery of lunar rocks by the Apollo 11 space mission. It was also the year when two exceptional meteorites fell and were rapidly recovered: CV carbonaceous chondrite Allende, and CM carbonaceous chondrite Murchison. These meteorites are large (ca. 2000 kilograms and 100 kg, respectively) and were collected shortly after their observed fall, so they are almost free from terrestrial overprint. Both Allende and Murchison contain refractory crystals (e.g., hibonite) and mineral aggregates (Ca-Al-rich refractory inclusions, usually abbreviated as CAIs) that probably formed during the most energetic early phase of evolution of the protosolar disk (Scott & Krot, 2014). These inclusions provided researchers with an opportunity to study, for the first time, the processes in the Solar System before planetary formation.

Meanwhile, terrestrial geochronology had its own challenges and breakthroughs. In the early 1970s, very old rocks (Amîtsoq gneisses and Isua supracrustal belt, now collectively known as Itsaq gneiss complex) were discovered in West Greenland. To decipher their prolonged and complex geological history, researchers required a geochronological “toolbox” that would include dating methods that can “see through” metamorphic overprint and yield the age of the protolith, as well as methods that yield the timing of one or more cycles of metamorphism. The age of the igneous protolith was determined with whole rock Rb-Sr and Pb-Pb isochron methods, on the basis of the idea that migration of parent and daughter elements during metamorphism occurs on a limited scale, so if the samples are larger than the scale of migration induced by metamorphism, then the whole rock isochron would yield the age of primary magmatic differentiation of the protolith. These studies convincingly demonstrated exceptionally old ages over 3.6 billion years (Ga) for the Amîtsoq gneisses (Black, Gale, Moorbath, Pankhurst, & McGregor, 1971) and Isua metavolcanic rocks (Moorbath, O’Nions, & Pankhurst, 1973), and opened up more than 80% of the Earth’s history to geological and geochronological inquiry. However, because of relatively large age uncertainties of ca. 50–100 Ma, the stages of geological evolution close in time could not be resolved with these methods, and the search for more precise dating techniques continued.

#### Zircon U-Pb Dating: Towards Micro-Scale Sampling and Analysis of Closed Isotopic Systems

Zircon (ZrSiO4) was used for U-Pb dating since the early work by Holmes (1913), and its use as a geochronometer continued to expand since then. It is a common mineral in a wide variety of terrestrial rocks, and is present in some lunar rocks and meteorites. It is rich in U (typically between 10–1000 micrograms per gram) and, as long as its crystal structure is intact, contains practically no non-radiogenic Pb and remains closed to migration of U and radiogenic Pb. It is resistant to weathering and can survive metamorphism. These qualities make zircon the prime mineral for U-Pb dating.

If zircon (or another U-Pb geochronometer mineral such as monazite (Ce,Th)(PO4), baddeleyite (ZrO2), or uraninite (UO2)) is closed to migration of U and radiogenic Pb since its formation, its 238U-206Pb and 235U-207Pb dates are identical. In the concordia diagram the analyses of such minerals plot, within analytical uncertainties, on the concordia curve, and their interpretation is straightforward: either the 238U-206Pb, 235U-207Pb or 207Pb/206Pb date (usually the date with the smallest uncertainty) can be interpreted as the time of zircon crystallization and, by inference, the age of the rock (see Ludwig (1998) for an in-depth discussion of concordant U-Pb ages). However, since the publication of the first U-Pb ages (Nier, 1939), the 238U-206Pb and 235U-207Pb dates in most U-bearing minerals, including zircon, are commonly discrepant (discordant) rather than consistent (concordant), indicating open system behavior, and preventing determination of a reliable age. A number of models were proposed to explain discordance of U-Pb dates. Wetherill (1956b) interpreted linear arrays (discordia lines) in concordia diagrams as pointing to two events (Figure 3): the upper concordia–discordia intercept yielding the time of zircon formation, and the lower intercept marking the time of episodic loss of radiogenic Pb, or a second zircon growth episode (either new crystals, or a younger zircon phase overgrowing older cores). Tilton (1960) proposed that discordance, and linear arrays in a concordia diagram, can be caused by continuous loss of radiogenic Pb due to volume diffusion. Attempts at interpretation of linear and non-linear data arrays in concordia diagrams brought about a number of models of increasing complexity (e.g., Allègre et al., 1974; Silver & Deutsch, 1963; Steiger & Wasserburg, 1966) that shared one fundamental problem: the accuracy of the ages derived from intercepts between concordia and the model lines is only as good as the match between the model and the real geochemical processes that it intends to reproduce, but this match is very hard, if at all possible, to verify.

Two lines of development transformed this early, inherently unreliable U-Pb geochronology based on a model-dependent interpretation of discordant data into modern U-Pb dating with high precision and accuracy based on extraction and analysis of concordant domains from zircon grains. The first is a set of methods for high precision dating of individual grains of zircon (and other U-bearing minerals) by isotope dilution thermal ionization mass spectrometry (ID-TIMS). Zircon decomposition in hydrofluoric acid at high temperature and subsequent extraction of U and Pb using anion exchange resin packed in small columns (Krogh, 1973) reduced processing contamination to 0.5–5 x10-9 grams Pb from 200–1000 x10-9 grams typical for the previously used borax fusion technique. The new low contamination procedure allowed geochronologists to reduce to sample sizes from milligram fractions containing thousands of zircon grains to microgram fractions consisting of a few grains, or single grains. Subsequent refinements of techniques over the following 45 years (miniaturization, changes in the bomb design, better bomb cleaning protocols, better methods for acid purification, and, importantly, drastic reduction of the environmental content of Pb due to elimination of automotive fuels doped with tetraethyl lead) reduced the blanks by another three orders of magnitude to its current level of 0.2–1.0 x10-12 grams Pb (U blank is still lower and is relatively insignificant in U-Pb zircon dating). With this blank level, it is now possible to date individual zircon grains of any size, age, and U content, containing as little as 10–100 x10-12 grams of radiogenic Pb.

The ability to date single zircon grains stimulated development of techniques for separating crystalline zircon with a concordant U-Pb system from metamict zircon with the crystal lattice damaged by radiation and fluid-rock interactions that has a disturbed U-Pb system. The methods based on magnetic susceptibility (Krogh, 1982a) and removal of the outermost parts of the crystals by air abrasion (Krogh, 1982b) work well for elimination of the most discordant part of a zircon population and allow for effective elimination of the near-surface damage, but are less efficient if metamict zones are located inside zircon crystals and are shielded by crystalline outer domains. The latter problem has been resolved with the development of chemical abrasion (Mattinson, 2005) whereby zircon grains are annealed at 800–1100 °C to restore the crystal structure in domains slightly to moderately damaged by radiation, and then leached in hydrofluoric acid to dissolve and remove domains with heavily damaged metamict crystal lattice that cannot be repaired by annealing. Chemical abrasion effectively eliminates discordant material located anywhere in zircon crystals, and is currently a universally adopted procedure for zircon treatment in U-Pb ID-TIMS geochronology. The best current procedures using chemical abrasion and ID-TIMS allow single zircon grain age determinations with relative uncertainty of 0.03–0.1%.

The second line of advance in zircon dating was the development of procedures for sampling small domains within individual zircon grains with focused primary ion beam in secondary ion mass spectrometers (SIMS), also known as ion microprobes. The primary beam of oxygen ions is focused to a spot of 20–30 microns or smaller, allowing us to get ages of multiple domains within a zircon grain. Early attempts at using ion microprobe were plagued with low sensitivity and insufficient mass resolution to quantitatively separate the beams of molecular ions interfering with Pb isotopes. These problems were overcome with the development of a Sensitive High Resolution Ion Micro Probe (SHRIMP) with a large mass analyzer magnet with one meter radius that provided high mass resolution without loss of sensitivity (see Compston (1996) for the history of SHRIMP development). SHRIMP enabled studies of within-grain age distribution, and was used for analyses that led to the discoveries of the world’s oldest zircon grains with ages up to 4.37 Ga in metasedimentary rocks from Archaean Yilgarn Craton, Western Australia (Compston & Pidgeon, 1986; Froude et al., 1983; Mojzsis, Harrison, & Pidgeon, 2001; Wilde, Valley, Peck, & Graham, 2001), and the oldest zircons in the Solar System with the age of 4563 ± 15 Ma in the Vaca Muerta mesosiderite (Ireland & Wlotzka, 1992). Isotopic analysis with even higher spatial resolution at the sub-micron level can be achieved with atom probe (Valley et al., 2014).

At present, chemical abrasion ID-TIMS and large ion mircoprobes are seen as equally important dating methods with complementary strengths and limitations. Both are mainstream methods in terrestrial geochronology, and find ever increasing use in chronological studies of lunar rocks and meteorites (including lunar and Martian ones). In some cases, both methods are applied to the same mineral populations to achieve the best combination of spatial resolution and age precision.

Studies in isotope chronology of meteorites and lunar rocks in the 1960s and early 1970s were based only on “extant radionuclide” chronometers based on decay of long-lived radionuclides such as 238U, 235U, 40K, and 87Rb with half-lives similar to the age of the Earth and the Solar System. It has been proposed that short-lived radionuclides also existed in the early Solar System and some of them, most likely 26Al, possibly played their role as a heat source for early planetary differentiation (Urey, 1955). However, there were no observations demonstrating their existence until Jeffery and Reynolds (1961) found correlated excesses of 128Xe produced by neutron irradiation of I, and 129Xe produced by decay of now extinct 129I with a half-life of 15.7 Ma, in the enstatite chondrite Abee. This correlation suggested that some radionuclides that decay too fast to be extant from their synthesis in stars existed in the early Solar System, were incorporated into meteorites, and decayed in situ. This discovery opened the field of extinct radionuclide chronometry that later became (together with U-Pb) the main tool for measuring the ages of the early Solar System materials. A major step that demonstrated the potential and value of extinct radionuclide age determination was the development of the 26Al-26Mg chronometer. Gray and Compston (1974) observed variations in 26Mg abundance in Allende CAIs and showed the existence of a mass independent component that was attributed to the decay of 26Al. Subsequent work by Lee, Papanastassiou, and Wasserburg (1976) demonstrated that 26Mg excesses in Allende CAIs are correlated with the Al/Mg ratio, providing evidence that 26Al was present in Allende CAIs at the time of their formation, and decayed in situ. The 26Al-26Mg chronometer eventually became the most widely used method for age determination of CAIs, chondrules, and some of the oldest achondrites (see review by McKeegan & Davis (2014)).

By the mid-1980s, convincing evidence for the existence of the short-lived radionuclides 26Al, 53Mn, 107Pd, 244Pu, and 146Sm was established (Podosek & Swindle, 1988). However, the studies of the decay products of these isotopes in meteorites were mainly concerned with stellar nucleosynthesis and the age of the elements. Meanwhile, dating of Solar System formation was based on the same long-lived radionuclide systems that were used in terrestrial geochronology (Tilton, 1988). Shortly thereafter, it was realized that the duration of Solar System formation from the first solids to planetary embryos was only of the order of 10 Ma. Only the short-lived (half-lives <20 Ma) chronometers and Pb-Pb can provide the required age resolution, and modern chronology of the earliest solids relies entirely on these chronometers. The longer-lived radionuclides are very important as terrestrial and planetary chronometers, and isotopic tracers for both terrestrial and extraterrestrial rocks, but their role in dating pre-planetary rocks is limited.

#### Mass Spectrometry Developments after 1980: Multicollector and Plasma Ionization

Early isotope ratio mass spectrometers, from Nier’s instruments of the 1930s to commercial instruments until the early 1980s, were equipped with one Faraday cup detector connected to an electrometer, and in some cases one electron multiplier for measuring very small ion beams. The isotopic ratios were measured by varying the magnetic field (or accelerating voltage) to sequentially steer the ion beams of various isotopes into the same detector. This arrangement has two limitations: first, any instability or drift of the ion beam propagates into the data and increases uncertainty, and second, each isotope is measured only a fraction of the time, and is wasted while other isotopes are measured. Both these limitations worsen as the number of isotopes that are being measured is increased. The best relative precision achievable with single collector beam acquisition is rarely better than 30–40 parts per million (ppm).

However, since magnetic sector mass analyzers produce spatially separated ion beams in the focal plane, it is possible to measure multiple beams at the same time using an array of Faraday cup collectors. The first commercial thermal ionization mass spectrometers equipped with arrays of five to seven Faraday cups were introduced by Finnigan MAT (MAT 261) and VG isotopes (VG 354) around 1982 (see Wieser & Schwieters (2005) for an overview of multiple collector mass spectrometers). These instruments, capable of three to four times more precise analyses and using small samples more efficiently, were crucial for the wide adoption of dating methods where radiogenic isotope variations are small, for example, 147Sm-143Nd, 176Lu-176Hf, and especially 146Sm-142Nd. Subsequent developments of better ion optics and electronics resulted in further increase of precision on modern multicollector TIMS instruments that currently can be as high as 2–3 ppm under carefully controlled measurement conditions.

An inherent limitation of thermal ionization is the low ionization efficiency of elements with high first ionization potential, as shown by the Saha–Langmuir equation that describes surface ionization (Dresser, 1968). This includes most parent and daughter elements used in geochronology. For some elements, such as Pb, the problem is circumvented by using emitters that can efficiently produce ions by other mechanisms, but for most elements, especially refractory ones (Lu, Hf, W), low efficiency of surface ionization poses severe restrictions for precision and sample size. In contrast to TIMS, an inductively coupled plasma source where ionization occurs in an extremely hot (>6000 °C) argon plasma is capable of nearly complete ionization of almost all elements (with the exception of those with an ionization potential higher than that of argon). The ion yield of the plasma source (number of ions registered divided by the number of atoms injected or loaded) depends on the efficiency of ion extraction.

The mass spectrometer with an inductively coupled plasma source was initially developed for single collector instruments in the 1980s, but these instruments had low precision because of ion beam instabilities inherent to the plasma source. This source was successfully matched to the magnetic sector analyzer and multicollector array in the Plasma 54, the first multicollector inductively coupled plasma mass spectrometer (MC-ICPMS) that was introduced in 1992 by VG Elemental (Walder & Freedman, 1992). Subsequent development significantly improved transmission (and hence sensitivity), precision, and reliability of MC-ICPMS, and converted it into the most versatile technique for precise isotope analysis (see Douthitt (2008) for an overview of MC-ICPMS). MC-ICPMS has a number of advantages compared with TIMS in addition to higher ionization efficiency, and in recent years surpassed the latter in popularity. Analyses by MC-ICPMS are generally faster, and can be more easily automated. Procedures require only a small adaptation when switching from one element to another, in contrast to TIMS where the methods of ionization are element-specific. Mass discrimination in the plasma source is stable as long as the conditions in the plasma and the source-analyzer interface are stable, which contrasts with TIMS where evaporation-induced isotopic fractionation drifts during the run. Stability of mass discrimination makes it possible to measure isotopic variations by sample-standard bracketing without using laborious and time-consuming isotope dilution with double spike. The latter feature made MC-ICPMS the method of choice for studies of stable isotope variations and inspired the development of an entirely new field of “non-traditional” stable isotope geochemistry that encompasses all elements in the periodic table that consist of two or more isotopes.

Parent and daughter elements of a few isotopic dating methods, both extinct (182Hf-182W, 26Al-26Mg) and extant (176Lu-176Hf), are refractory, and are hard to ionize in the thermal source. The initial developments of these methods were done using TIMS, but they remained exotic methods with limited application. Introduction of MC-ICPMS revolutionized these methods and moved them to the mainstream of geo- and cosmochronology.

It should be mentioned that for certain elements analyzed for isotopic dating, most notably Pb, and high-precision Nd isotope measurements for 146Sm-142Nd, TIMS still remains the method of choice due to its cleaner background, much higher transmission leading to higher total ion yield with certain ionization techniques (e.g., silica gel emitter for Pb, and NdO+), and more straightforward and better understood instrumental fractionation. Together, TIMS, MC-ICPMS, and SIMS form a triad of modern methods with complementary strengths for isotope analyses of solid and dissolved materials that forms the analytical foundation of today’s planetary chronology.

### Modern Isotope Chronology of Planetary Materials

#### Geochronology and Cosmochronology: Similarities and Differences

The dating of terrestrial and of extraterrestrial rocks share basic principles and many analytical techniques, and exchange of experience between the two research communities is mutually beneficial. For example, modern U-Pb zircon chronology was originally developed for geological applications, but found its way into the studies of lunar rocks and Martian meteorites that also contain zircon, baddeleyite, apatite, and other U-bearing minerals. This method significantly enhanced precision and reliability of the dates compared with the whole rock based approaches that are traditional for meteorite and planetary chronology. Likewise, extinct radionuclide dating methods based on the decay of 146Sm and 182W, initially intended for dating meteorites, became indispensable for determination of the timing of the magma ocean crystallization and core formation in planets including Earth. The methods of extant radionuclide chronology such as 40K-40Ar, 87Rb-87Sr, 147Sm-143Nd, and 176Lu-176Hf are equally applicable to dating of terrestrial and extraterrestrial rocks throughout the entire history of the Earth and the Solar System, and were developed by combined efforts of researchers with interests in geological and planetary processes.

The main difference between terrestrial and extraterrestrial chronology is in the way of using short-lived radionuclide systems to date with high temporal resolution the events in certain, particularly important, time intervals. In terrestrial chronology, the time of special significance is the Quaternary—the geological period from ca. 2.59 Ma to the present, the time since emergence of the genus Homo (humans), and in particular the Holocene—the last ~12,000 years (ka), the geological epoch when human civilization emerged and became a significant geological force. The temporal resolution of long-lived radionuclide chronometers is in most cases insufficient for constructing the detailed timescale of human evolution, so the methods based on the decay of cosmogenic short-lived radionuclides, most importantly 14C, are used instead, along with U-series disequilibrium and non-isotopic (e.g., luminescence-based) dating methods. These methods, although belonging to broadly defined planetary chronology, are specific to the recent Earth history and the human epoch, and are not further discussed here.

The special time interval in planetary studies is the period between formation of the Solar System’s first solids and the formation of planetary embryos or protoplanets—the rocky bodies between the sizes of the largest asteroids (~500–900 kilometers) and that of Mars. This period was extremely eventful and relatively short (up to 10–20 Ma), and some processes that occurred at that time, for example formation of CAIs and chondrules, only lasted for 1–2 million years or even less. Similarly to the studies of human evolution, the “conventional” extant radionuclide chronometers (except U-Pb) generally lack sufficient precision to resolve events in the Solar System’s earliest history. High-resolution chronometers based on decay of short-lived radionuclides (26Al, 53Mn, etc.) that were produced during, or immediately before, the onset of the collapse of the protosolar nebula and formation of the proto-Sun, are used instead. These chronometers are not directly applicable to the studies of planetary formation and evolution, because violent final stages of planet formation that involved high-energy collisions and planet-scale melting (formation of magma oceans) have reset these chronometer systems after complete decay of the parent nuclides and erased the preexisting chronological record.

#### Extant and Extinct Radionuclide Chronometers: Principles and Properties

Radionuclides that are commonly used for age determinations in Earth, planetary, and meteorite studies are listed in Table 1, ranked by the half-life values from the shortest to the longest. Some of the previously popular but now rarely used nuclides are also included. The properties of isotope chronometers that define their usage depend on the following features: half-life of the parent isotope, abundance of parent and daughter isotopes, extent and conditions of fractionation between parent and daughter elements, and the ability to measure concentrations and isotopic ratios of the parent and daughter elements with adequate precision and accuracy.

#### Table 1. Radionuclides Used in Geochronology and Cosmochronology

Parent isotope

Daughter isotope

Half-life (Ma)

Decay mode

Condensation T_parent (K)

Condensation T_daughter (K)

T_parent—T_daughter (K)

Abundance ratio

Abundance of reference nuclide (%)

Initial abundance

Bulk initial abundance

Lifespan, Ma to 10-7

Lifespan, Ma to 10-9

Applications

Ref.

41Ca

41K

0.0994

electron capture

1517

1006

511

41Ca/40Ca

96.92

4×10−9

3.88×10-9

0.2

Exotic cosmo

1

26Al

26Mg

0.705

β‎+ decay, electron capture

1653

1336

317

26Al/27Al

100

(5.23±0.13)×10-5

5.23×10-5

6.4

11.1

Mainstream cosmo

2

10Be

10B

1.387

β‎- decay

1452

908

544

10Be/9Be

100

(8.8±0.6)×10-4

8.8×10-4

18.2

27.4

Exotic cosmo

60Fe

60Ni

2.62

03B2‎- decay

1334

1353

-19

60Fe/56Fe

91.52

(7.1±2.3)×10-9

6.5×10-9

7.1

Exotic cosmo

53Mn

53Cr

3.7

electron capture

1158

1296

-138

53Mn/55Mn

100

(6.71±0.56)×10-6

6.71×10-6

22

47

Mainstream cosmo

107Pd

107Ag

6.5

β‎- decay

1324

996

328

107Pd/108Pd

51.35

(5.9±2.2)×10-5

3.03×10-5

54

97

Exotic cosmo

182Hf

182W

8.9

03B2‎- decay

1684

1789

-105

182Hf/180Hf

35.07

(9.81±0.41)×10-5

3.44×10-5

75

134

Mainstream cosmo

247Cm

235U

15.6

03B1‎ decay*)

unknown

1610

247Cm/235U

0.72

(1.1 ± 0.3) × 10−4

7.92×10-7

47

150

Exotic cosmo

3

129I

129Xe

15.7

03B2‎- decay

535

68

467

129I/127I

100

10-4

1×10-4

156

261

Exotic cosmo

92Nb

92Zr

34.7

electron capture

1559

1741

-182

92Nb/93Nb

100

(1.7±0.6)×10-5

1.7×10-5

257

488

Exotic cosmo

4

146Sm

142Nd

68

03B1‎ decay

1590

1602

-12

146Sm/144Sm

3.16

(8.28±0.44)×10-3

2.62×10-4

772

1,224

Early planetary differerentiation

5

235U

207Pb

704

03B1‎ decay*)

1610

727

883

0.72

0.242

Mainstream cosmo and terrestrial

40K

40Ca, 40Ar

1,249

03B2‎- decay (89%), electron capture (11%)

1006

1517 (Ca) 47 (Ar)

0.012

0.0015

Mainstream cosmo and terrestrial

238U

206Pb

4,468.3

α‎ decay*)

1610

727

883

99.3

0.758

Mainstream cosmo and terrestrial

232Th

208Pb

14,050

α‎ decay*)

1659

727

932

100

1.000

Exotic terrestrial and cosmo

176Lu

176Hf

37300

β‎- decay

1659

1684

-25

2.6

0.028

Mainstream terrestrial

6

187Re

187Os

41,500

β‎- decay

1821

1812

9

62.93

0.679

Mainstream terrestrial

87Rb

87Sr

49,610

β‎- decay

800

1464

-664

27.85

0.297

Mainstream cosmo and terrestrial

7

147Sm

143Nd

106,000

α‎ decay

1590

1602

-12

15.07

0.155

Mainstream terrestrial

Half-life and initial abundance values are as listed by Davis and McKeegan (2014) and Goderis et al. 2016, except where supeseded by more recent and more accurate determinations indicated in the reference columns.

Condensation temperatures—50% T_C from Table 8 in Lodders (2003).

Initial abundance is the number of atoms of the isotope in question divided by the number of atoms of the reference isotope (in denominator in the abundance ratio) at the time of Solar System formation. Abundance ratios and initial abundances are shown only for extinct radionuclides.

Bulk initial abundance is the number of atoms of the isotope in question divided by the total number of atoms of all isotopes at the time of Solar System formation.

“Lifespan to 10-7” and “lifespan to 10-9” is the time required for the bulk abundance of a short-lived radionuclide to go down from the initial Solar System value to 10-7 (an approximate usability range) or to 10-9 (the level that can be considered complete extinction), respectively. These values are shown only for extinct radionuclides.

* Decay chains of multiple α‎ and β‎ decay events.

1) Half-life from Jörg et al. (2012).

2) Half-life from Norris et al. (1983) and Nishiizumi (2014).

3) Initial abundance from Tissot et al. (2016).

4) Initial abundance from Iizuka et al. (2016).

5) Two proposed half-life values are 68 Ma (Kinoshita et al. 2012) and 103 Ma (Marks et al. 2014).

6) Half-life based on Scherer et al. (2001) and Söderlund et al. (2004).

7) Half-life from Villa et al. (2015).

Isotopes listed in lines 1–11 of Table 1 have essentially completely decayed (got extinct) since the formation of the Solar System. However, if the short-lived nuclide was present in the rock at the time of its formation and decayed in situ, its presence, and abundance, can be inferred from the co-variance between the abundance of the daughter nuclide (expressed as the ratio to a stable isotope of the same element, e.g., 26Mg/24Mg) and the abundance ratio of parent and daughter elements (expressed as the ratio of their stable isotopes, e.g., 27Al/24Mg). Using analyses of multiple mineral fractions (or grains, sputtering spots, etc. depending on the analytical technique) with variable parent–daughter elemental ratios, we can construct a linear array that is sometimes referred to as a fossil isochron, from the slope of which we can determine the relative abundance of the short-lived nuclide, for example, 26Al/27Al, at the time of the rock formation. From relative abundances of an extinct radionuclide with known half-life in two rocks we can calculate the time interval between their formation.

If the age of one of the rocks is known from an independent determination using an isotope chronometer based on the decay of long-lived (extant) nuclides (lines 12–19 in Table 1), for example U-Pb, then the age of the second rock can be calculated from the extinct chronometer time interval (Figure 4 in Amelin & Ireland, 2013). It is also possible to calibrate two (or more) extinct nuclide chronometers against each other if one of the samples can be dated with both systems. Accurate cross-calibration of extinct nuclide chronometers to either U-Pb or each other can be done if both chronometers were zeroed in the same, nearly instantaneous, event, and remained closed since then, and both systems show significant abundance variations of the daughter isotope that can be precisely and accurately measured. Once two or more chronometers are cross-calibrated, we can use them together for building the timescale.

The use of extinct nuclide chronometers is based on the assumption that the parent nuclide was uniformly distributed in the early Solar System, that is, that the abundance ratio of the parent nuclide to the reference stable isotope of the same element (26Al/27Al, 182Hf/180Hf, etc.) was the same throughout the solar protoplanetary disk at any moment of time, and changed only as a function of time. If these ratios were variable, the chronometers generally give inaccurate readings, although the method for age calculation in the case of heterogeneous distribution has been proposed (Gounelle & Russell, 2005). Homogeneous distribution is likely for the radionuclides that were inherited from the presolar molecular cloud. Heterogeneous distribution can be expected for the radionuclides that were synthesized shortly before formation of the proto-Sun and injected into the accreting disk, especially for those nuclides that were produced by more than one mechanism (e.g., stellar nucleosynthesis, and irradiation in interstellar medium or in the solar protoplanetary disk).

The dates and ages determined with extant nuclide chronometers are often called “absolute,” whereas the dates and ages determined with extinct nuclide systems are called “relative.” The term “absolute” does not imply perfection, or greater precision and accuracy. It simply means the time interval between the studied event and the present. In most cases, understanding early Solar System processes requires establishing sequence and duration of events, and this can be done equally well with both “absolute” and “relative” ages. However, if we want to use multiple isotopic systems to establish the timescale of the early Solar System, their cross-calibration is required. The U-Pb system, the most versatile and precise extant radionuclide chronometer used in early Solar System studies (e.g., Amelin, 2006), provides a convenient “common ground” for such cross-calibration, and also yields conversion of extinct nuclide dates to “absolute” ages as a by-product.

Extinct radionuclide chronometers have a limited usable time span, which can be defined as the period of time when the abundance of the parent nuclide is high enough to produce measurable radiogenic effects. The abundance of the nuclide at any given time depends on the half-life and the initial abundance at the time of the Solar System formation. In Table 1, the columns “lifespan to 10-7” and “lifespan to 10-9” show the time required for the bulk abundance of a short-lived radionuclide (the number of atoms of the isotope in question divided by the total number of atoms of all isotopes of the element) to go down from the initial Solar System value to 10-7 (an approximate usability range) or to 10-9 (the level that can be considered complete extinction).

The other factor that defines the usable time span, and precision of the dates, is the concentration of the parent and daughter elements in the studied material. The parent elements such as Ca, Al, Fe, and Mn that are major components in the rocks have an advantage due to larger numbers of radioactive atoms compared with the elements such as Be, Pd, Hf, I, and Sm that are present in minor or trace amounts. The initial abundance of the daughter element is equally important—the lower the better. High abundance of the daughter nuclide “dilutes” radiogenic excess and makes it harder to determine accurately. In many cases, a small sacrifice in the concentration of the parent element is less important than the low initial abundance of the daughter element. For example, Fe-Ni metal is the phase in meteorites that has a higher Fe content than any other mineral, but it also contains over 5% of Ni that has 26% 60Ni, the same isotope that is produced by the decay of radioactive 60Fe. High initial abundance of 60Ni makes it insensitive to the radiogenic addition. In contrast, ferromagnesian silicate minerals (e.g., olivine and pyroxene) have several times lower concentration of Fe than the metal, but their low initial Ni concentration makes radiogenic excess of 60Ni easily detectable.

High parent–daughter ratio is the defining quality of a geochronometer mineral for both extinct and extant nuclide chronometers. The best-known and mostly widely used geochronometer minerals are zircon, monazite, and baddeleyite for 235,258U-207,206Pb, micas and K-feldspar for 87Rb-87Sr and 40K-40Ar, apatite for 176Lu-176Hf, molybdenite for 187Re-187Os, Al-rich oxides (hibonite, corundum) for 26Al-26Mg, olivine for 53Mn-53Cr, and zircon for 182Hf-182W. For some isotopic systems, for example, 146,147Sm-142,143Nd and 92Nb-92Zr, minerals with very high parent–daughter fractionation are not known. In these cases we have to use the second-best option of analyzing sets of rocks or minerals with moderately high but variable parent to daughter ratios, and using them to construct isochrons, either live or fossil. The latter approach is applicable to any isotopic chronometers and expands the range of minerals that can be used for dating with U-Pb (apatite, garnet, pyroxene), 26Al-26Mg (anorthite, melilite, spinel, pyroxene), and 53Mn-53Cr and 182Hf-182W (various silicate and oxide rock-forming minerals).

The opposite of, and complementary to, geochronometer minerals are “time capsule” minerals that have a very low parent–daughter elemental ratio and preserve the initial isotopic composition of the daughter element without detectable radiogenic addition. Examples are zircon and baddeleyite for 176Lu-176Hf, apatite for 87Rb-87Sr, forsterite for 26Al-26Mg, and chromite for 53Mn-53Cr. Some minerals are geochronometers for one isotopic system, and a time capsule for another. From analysis of the time capsule minerals, we determine the time when their parent rock was separated from the reservoir in which the abundance of radiogenic isotope was growing fast enough to achieve adequate time resolution. The advantage of the time capsules is that they can survive secondary events that reset geochronometer minerals and allow us to “see through” metamorphism towards the protolith age. Their disadvantage is that the “time capsule” dating is intrinsically model dependent, and any mismatch between the model of the reservoir evolution and the real geochemical situation induces systematic uncertainties to the model ages.

#### The Processes Datable with Radionuclide Chronometers

In planetary environments, the processes that are datable with isotopic clocks (and related mechanisms of element fractionation) include the following: melt crystallization (crystal–melt partitioning), metamorphism (growth of minerals in the solid state), and metasomatism (solubility in fluids). Processes that were common in the early Solar System but are rare in the Earth and planetary environments are condensation and evaporation (volatility-induced fractionation), and metal–silicate separation (partitioning of certain elements between Fe–Ni and silicate melts and minerals).

#### Table 2. What Do We Date with the Isotopic Geo- and Cosmochronometers

Chronometer

Rock or component

Minerals

Event being dated

235, 238U-

207, 206Pb

Planetary igneous rocks

Zircon (various rocks), baddeleyite (mafic and alkaline rocks)

Melt crystallization

Planetary sedimentary rocks

Detrital zircon, monazite, and other minerals

Crystallization of source rocks

Igneous meteorites and components (CAIs, chondrules, achondrites)

CAIs: all minerals

Chondrules: Cpx and mesostasis

Achondrites: all minerals

Beginning of Pb retention upon cooling. If cooling is fast, approximates the time of melt crystallization. If cooling is slow, yields closure of Pb diffusion in silicate minerals (usually > 900 K)

Metamorphic minerals in planetary rocks and meteorites

Apatite, silicic apatite, merrillite, titanite, rutile, garnet

Closure of Pb diffusion (usually <900 K in phosphate minerals)

87Rb-87Sr

Planetary felsic (meta)-igneous rocks—whole rock dating

Bulk rocks

Igneous differentiation during protolith formation (imperfect chronometer, superseded by zircon U-Pb)

Planetary felsic igneous rocks—minerals

Mica (muscovite, biotite, phlogopite), K-feldspar

Closure to diffusion (approximates the time of igneous crystallization if cooling was fast)

Chondrules

Bulk chondrules

Primitive chondrites—chondrule formation (melting of nebular condensates); equilibrated (metamorphosed) chondrites—metamorphism

40K-40Ar

Planetary igneous rocks

Bulk rock and K-bearing minerals

Fast cooling—approximates crystallization; slow cooling—closure for Ar diffusion

Planetary metamorphic rocks

Bulk rock and K-bearing minerals

Closure for Ar diffusion after metamorphism

Meteorites

Bulk rock and K-bearing minerals

Closure for Ar diffusion, or impact

147Sm-143Nd

Planetary felsic (meta)-igneous rocks—whole rock dating

Bulk rocks

Igneous differentiation during protolith formation (imperfect chronometer, superseded by zircon U-Pb)

Planetary igneous rocks and meteorites—minerals

Olivine, pyroxenes, feldspar, phosphates

Igneous crystallization if cooling was fast, closure for diffusion if cooling was slow

Planetary metamorphic rocks

Garnet

Growth of garnet crystals or certain domains within crystals, or closure for diffusion

26Al-26Mg

Bulk CAIs, chondrules, and primitive (undifferentiated) achondrites

Bulk materials

Al/Mg fractionation in the solar nebula, or partial evaporation of Mg during reheating

Bulk differentiated igneous meteorites

Bulk rocks

Differentiation of the parent body (approximates the time of accretion), or crystal fractionation in the magma chamber (approximates the time of magmatism)

Minerals in CAIs, chondrules, and igneous meteorites

Hibonite, spinel, pyroxene, melilite, anorthite

Crystallization of the melt, or re-crystallization; may be reset by solid-state diffusion

53Mn-53Cr

Bulk chondrules and primitive (undifferentiated) achondrites

Bulk materials

Mn/Cr fractionation in the solar nebula

Bulk differentiated igneous meteorites

Bulk rocks

Differentiation of the parent body, or crystal fractionation in the magma chamber

Minerals in chondrules and igneous meteorites

Olivine, kirsteinite, pyroxene, chromite, spinel, ilmenite

Crystallization of the melt, or re-crystallization; may be reset by solid-state diffusion

Secondary minerals in carbonaceous chondrites

Fayalite, carbonates

Aqueous alteration in the parent body

182Hf-182W

CAIs

Bulk CAIs

Hf/W fractionation in the solar nebula

Chondrites and their fractions

Bulk chondrules or chondrule pools; silicate and metal fractions

Metal–silicate segregation, approximates accretion

Bulk differentiated igneous meteorites

Bulk rocks

Metal–silicate segregation in the parent body

Minerals in igneous meteorites

Pyroxene, olivine, bulk silicate fractions, metal

Crystallization of the melt, or metamorphism

Planetary rocks

Bulk rocks

Core formation, mantle differentiation (interpretation is model dependent)

146Sm-142Nd

Planetary felsic (meta)-igneous rocks

Bulk rocks

Mantle differentiation (interpretation is model dependent)

Meteorites and the earliest planetary rocks—minerals

Olivine, pyroxenes, feldspar, phosphates

Igneous crystallization if cooling was fast, closure for diffusion if cooling was slow

Initial 87Sr/86Sr

CAIs and achondrites

Bulk materials, plagioclase, phosphates

Separation of volatile-depleted solids from the nebula; approximates accretion, strongly model dependent

The processes that are dated with commonly used isotope chronometers are summarized in Table 2. Most parent–daughter pairs can be fractionated by several processes, depending on the mineral, rock, and geological/planetological setting. Let us consider U-Pb system as an example. In terrestrial environments, U and Pb are most efficiently fractionated during crystallization of minerals from a magma or a fluid. Some minerals (zircon, baddeleyite, opal) take up U and exclude Pb from the medium they grow, while the others (galena, K-feldspar) take up Pb and exclude U. The former serve as geochronometer minerals, the latter as time capsule minerals. There is also a significant difference in the condensation temperature, about 880 K (Table 1), between U (1610 K) and Pb (727 K). Evaporation of Pb during mineral formation is not very common in terrestrial environments, but it is an important fractionation mechanism when minerals and rocks are formed by condensation from the nebular gas, or by reheating of the nebular condensates. Chondrules and CAIs have lost Pb, presumably by evaporation, during their formation and, due to low initial Pb concentration, developed radiogenic Pb isotope composition that allows us to calculate their age from radiogenic 207Pb/206Pb ratios. Significant loss of Pb also occurred at larger (asteroidal and planetary) scales during accretion, resulting in much higher 238U/204Pb ratios in the Earth, Moon (e.g. Tera, Papanastassiou, & Wasserburg, 1974), and parent bodies of angrites (Amelin, 2008) compared with primitive chondrites and the solar photosphere (Palme, Lodders, & Jones, 2014). High 238U/204Pb ratios help in developing highly radiogenic Pb in lunar and asteroidal rocks and make it possible to construct precise 207Pb-206Pb isochrons with minerals such as pyroxene, but they can also cause complications if the early grown radiogenic Pb was redistributed and trapped in the rocks and minerals that crystallized later. Finally, U and Pb fractionate during metamorphic mineral growth. This allows for studying the cooling history of terrestrial metamorphic complexes by dating garnet with U-Pb (as well as 147Sm-143Nd and 176Lu-176Hf), and chondrite metamorphism by dating Ca phosphates apatite and merrillite (Göpel, Manhès, & Allègre, 1994).

Some isotopic systems are fractionated by certain mechanisms, and are insensitive to the others. The 60Fe–60Ni and 182Hf–182W isotopic systems are influenced by metal–silicate fractionation, such as during planetesimal core formation (Kleine & Rudge, 2011), but are insensitive to evaporation and condensation because the differences between condensation temperatures of the parent and daughter elements are small. In contrast, for 129I-129Xe and 40K-40Ar, the isotopic chronometer systems where daughter elements are noble gases with very low condensation temperatures, degassing is the main mechanism of resetting. This makes 40K-40Ar an excellent tool for dating metamorphic and impact events that have little or no effect on the chronometers where both parent and daughter elements are refractory and relatively immobile. In some cases, it is possible to date different processes with the same isotopic system using different scales of sampling, for example, whole rock versus mineral grains or microbeam analysis of minerals (Table 2).

Four isotopic systems are currently used most widely in the early Solar System chronology: 238,235U–206,207Pb, 26Al–26Mg, 53Mn–53Cr, and 182Hf–182W (Amelin & Ireland, 2013; Dauphas & Chaussidon, 2011: Kleine & Rudge, 2011; Nyquist, Kleine, Shih, & Reese, 2009). This combination of chronometers is very well suited for the studies of nebular and the earliest asteroidal and planetary evolution because of the high precision of ages that can be determined, the range of processes responsible for parent–daughter fractionation, and the applicability to a broad range of rocks and minerals. Precision of the dates achieved with all these systems is typically better than 0.5–1 Ma, and in favorable cases (significant parent–daughter fractionation, absence of disturbance, precise analyses) can be below 0.1 Ma. Accuracy of the dates is more difficult to evaluate, because it involves a number of additional sources of uncertainty. For example, propagation of uncertainties of the half-lives of 235U and 238U into the 207Pb/206Pb ages of the early Solar System materials adds an uncertainty of ± 9.2 Ma (Ludwig, 2000). However, the uncertainty of the intervals between two 207Pb*/206Pb* dates is much smaller: for example, the uncertainty in the 10 Ma interval between 4560–4550 Ma is only 0.02 Ma, and is smaller than the analytical uncertainty of the most precise 207Pb*/206Pb* dates. The accuracy of Pb-isotopic dates and the factors that influence it have been recently reviewed (Amelin et al., 2009; Condon, Schoene, McLean, Bowring, & Parrish, 2015; Tissot, Dauphas, & Grove, 2017), but similar evaluation for extinct radionuclide chronometers has yet to be done.

The 40K-40Ar is a very versatile system that is popular in the studies of both meteorites and planetary materials. In the old rocks with a complex history, this system yields the dates of the most recent events (such as metamorphism or impact) that caused loss of radiogenic Ar, and is an indispensable tool for studies of the impact history of planets and asteroids. In younger igneous rocks that remained closed to Ar loss, it yields the age of magmatism. Together with the U-Pb system in zircon, the K-Ar system (in the form of 40Ar/39Ar) in K-bearing minerals, micas, and sanidine, is the main chronometer for the calibration of the absolute geological timescale through precise age determination of minerals in felsic volcanic rocks that serve as time markers for sedimentary sequences and the fossils they contain.

The 147Sm–143Nd and 176Lu–176Hf isotope pairs were once popular chronometers for dating both planetary (terrestrial and lunar) rocks and meteorites, but they usually yield dates with uncertainties greater than ~10 Ma, and were largely (but not completely) superseded by modern high-precision U-Pb dating of accessory minerals. The Sm-Nd and Lu-Hf isotope systems are now more commonly used as isotopic tracers of the rock sources than as chronometers. One exception is dating metamorphic garnet, where using all three chronometers that have different closure temperatures for diffusion allows for reconstruction of the thermal history of metamorphism.

Two notable examples of the “time capsule” dating are determination of the time of crust-mantle differentiation events with 176Lu-176Hf system in zircon, and “initial Sr” dating of the time of accretion in the solar protoplanetary disk. Zircon contains about 1% Hf, and, despite relatively high Lu content of ca. 10–100 ppm, the 176Lu/177Hf ratio in zircon is sufficiently low to cause only a small increase in 176Hf/177Hf ratio due to radiogenic ingrowth, and initial 176Hf/177Hf at the time of crystallization can be reliably determined even for very old zircon (Patchett, Kouvo, Hedge, & Tatsumoto, 1981). The initial 176Hf/177Hf values can be used in two ways: to deduce mixing of mantle and crustal components in the source of a parental magma, or to estimate the time of separation of the magma from the mantle (Figure 4a). Development of laser ablation ICP-MS enabled rapid Lu-Hf measurements in hundreds of zircon grains (with the possibility of either sequential or simultaneous U-Pb dating), and turned the Lu-Hf method into the most popular radiogenic isotope system for the studies of terrestrial crust-mantle evolution (see compilations by Belousova et al. (2010) and Iizuka, Yamaguchi, Itano, Hibiya, and Suzuki (2017)). The method is equally useful for studies of crust-mantle systems in other planetary bodies (e.g. Taylor, McKeegan, & Harrison, 2009).

The initial 87Sr/86Sr chronometer is another method that uses the “time capsule” concept. This method, pioneered by Papanastassiou and Wasserburg (1969), uses initial 87Sr/86Sr isotopic ratio to estimate the timing of separation of the low-Rb/Sr achondrite precursor material from high-Rb-Sr solar nebula (Figure 4b). The method involves assumptions about the processes in which volatility-induced differentiation in the nebula took place (in the simplest case the nebula is assumed to have the Rb/Sr ratio of either solar photosphere or CI chondrites) (Halliday & Porcelli, 2001). With the best current methods of Sr isotope analyses by multicollector TIMS, the initial Sr chronometer can yield nebula separation ages with a precision of ca. 1 Ma or better (e.g. Hans, Kleine, & Bourdon, 2013).

Some important geological processes, as well as the processes in the protoplanetary disk, do not cause chemical fractionation of elements and therefore cannot be dated directly (Amelin & Ireland, 2013). These processes include erosion and sedimentation in the terrestrial environments, and accretion of solids into larger aggregates, planetesimal collisions, and planetary accretion in the disk. Their ages can be determined by bracketing or approximated using associated processes. For example, the age of sedimentation can be bracketed by dating underlying and overlying volcanic rocks that contain magmatic zircon and/or K-bearing minerals.

#### Applications

Stars and their planetary systems, including our Solar System, form by gravitational collapse of dense regions in interstellar molecular clouds (Krumholz, 2017; Stahler & Palla, 2004). The evolution of young stellar objects (YSO) is subdivided into four or five stages (classes 0, I, Flat (transitional between I and II), II, and III) on the basis of spectral energy distribution (Fiegelson & Montmerle, 1999; Williams & Cieza, 2011). It is thought (Kita et al., 2013) that CAIs, the first solids in the Solar System, formed during the first three stages of evolution (YSO classes 0, I, and/or transitional) with a total duration of 0.5–0.9 Ma (Evans et al., 2009), when the proto-Sun was actively growing by infall from the surrounding envelope of gas and dust, and a protoplanetary disk developed. A few hundred thousand years after gravitational collapse, the infall of material from the cloud core slowed down and ceased, leaving a T-Tauri pre-main-sequence star surrounded by the protoplanetary disk (YSO class II) that can last about 2–3 Ma. During this period, chondrules (solidified micron-to-millimeter droplets of mafic silicate melt) and larger 1–1000 km bodies (planetesimals) formed (Chambers, 2014). During the final stage of the disk evolution, collisions and growth of planetesimals led to formation of planetary embryos (Moon- to Mars-sized bodies) and terrestrial planets.

The current best estimate of the age of CAIs is 4567.30 ± 0.16 Ma, the weighted mean of overlapping Pb-Pb isochron dates of three CAIs from the CV chondrite Efremovka (Connelly et al., 2012) and one CAI from CV chondrite Allende (Amelin et al., 2010). Each of these dates is calculated using 238U/235U ratio measured in the same CAI. Earlier Pb-isotopic ages of CAIs that were published between 1976 and 2010 and were not supported by direct measurements of U isotopic composition cannot be considered reliable since the 238U/235U ratio in CAIs has been shown to be variable (Brennecka et al., 2010). One CAI (from CV chondrite Northwest Africa 6991) yielded a Pb-Pb isochron age with directly measured 238U/235U that is distinctly older at 4567.94 ± 0.31 Ma than the previous value (Bouvier, Brennecka, & Wadhwa, 2011). The cause of the discrepancy is currently unclear. CAIs from other classes of chondrites are too small to be individually dated with Pb-Pb, or to yield sufficiently precise 238U/235U ratios. Chronology of CAIs has been very extensively studied with the 26Al-26Mg method (see reviews by MacPherson, Davis, and Zinner (1995) and Davis and McKeegan (2014)). Most “bulk CAI” data indicate that Al-Mg formation of the precursors of CAIs by nebular condensation occurred over a short time interval of less than 20,000 years (Jacobsen et al., 2008). Internal 26Al-26Mg isochron dates show that many CAIs experienced remelting that occurred over the age span of ~0.7 Ma (MacPherson, Kita, Ushikubo, Bullock, & Davis, 2012). The age of CAIs is used as a reference point for the subsequent events, and is often colloquially referred to as the time of the Solar System formation.

Chondrules from various groups of carbonaceous and ordinary chondrites have been extensively dated with U-Pb, Al-Mg, and Mn-Cr methods. Internal 26Al-26Mg isochrons for chondrules from unequilibrated (petrologic types 3.00–3.15) L and LL ordinary chondrites indicate their formation between 1.8 and 3.0 Ma after CAIs (Pape, Mezger, Bouvier, & Baumgartner, 2019). Dating a set of chondrules from Allende with both “bulk” and internal isochron methods showed that their precursors condensed from the nebula by 1.5 Ma after CAI formation, and their melting continued for another 2 Ma (Luu, Young, Gounelle, & Chaussidon, 2015). Chondrules in CR chondrites have lower initial 26Al/27Al ratio than in CV and CO chondrites, consistent with their formation 3–4 Ma after CAI formation, or later (Schrader et al., 2017).

Recent Pb-isotopic studies of chondrule chronology by step leaching individual chondrules (Bollard et al., 2017; Connelly et al., 2012) suggest, however, that chondrule formation started simultaneously with CAI formation and continued for several Ma. There can be several causes of this disagreement: heterogeneous distribution of 26Al, dating different generations of chondrules, or unaccounted for sources of bias in either (or both) Pb-isotopic or Al-Mg dates. The cause can be identified if the same chondrules are dated with Pb-isotopic, and bulk and internal Al-Mg dating, but no such data have been published to date.

Accretion of the chondrite parent bodies cannot be dated directly, but can be bracketed between the age of the youngest chondrules (the older limit) and the age of the oldest metamorphic minerals (the younger limit). The metamorphic minerals can be dated with U-Pb (Ca-phosphates merrillite and apatite) (Göpel et al., 1994) and 53Mn-53Cr (carbonates and Fe-Ca silicates) (Fujiya, Sugiura, Hotta, Ichimura, & Sano, 2012; MacPherson, Nagashima, Krot, Doyle, & Ivanova, 2017). These dates show that the chondrite parent bodies of CV and CM chondrites accreted ~3.2–3.5 Ma after CAI formation, shortly after termination of chondrule formation.

Chronology of achondrites (igneous meteorites from asteroids that experienced melting and in many cases differentiation) addresses the timing of two events: formation of their parent asteroids, and igneous processes that formed the source rocks of meteorites. Accretion of these asteroids (and planets), like formation of the chondrite parent bodies, cannot be dated directly, but can be bracketed. The “older” limit is given by initial 87Sr/86Sr chronometry of volatile-depleted achondrites such as eucrites and angrites, which indicates their separation from the nebula within 1 Ma after CAI formation (Hans et al., 2013). The “younger” limit can be determined with 182W-182Hf systematics that yields the timing of core–mantle differentiation in the angrite parent asteroid within 2 Ma of CAI formation (Kleine, Hans, Irving, & Bourdon, 2012). Formation of the achondrite parent asteroids was thus simultaneous with the peak of chondrule formation.

The oldest recorded asteroidal magmatism, given by the U-corrected Pb-isotopic age of ungrouped eucrite-like achondrite Asuka 881394, occurred 2.4 ± 0.6 Ma after CAI formation (Wimpenny et al., 2019), shortly after accretion. Igneous processes that produced angrites, the exceptionally fresh achondrites that were dated with many isotopic systems (U-Pb, Al-Mg, Mn-Cr, Hf-W, initial Sr), took place over the period of 4 to 11 Ma after CAI formation. Ungrouped achondrites that are derived from diverse asteroids with various nucleosynthetic isotopic affinities, , formed between 4 and 6 Ma after CAI formation (Amelin et al., 2019). Dating eucrites and other HED meteorites, the largest groups of achondrites that are thought to be derived from the asteroid 4 Vesta (De Sanctis et al., 2012; McSween, Mittlefehldt, Beck, Mayne, & McCoy, 2011), has been more difficult because of more extensive secondary processing compared with angrites and many ungrouped achondrites.

Modern geochronological data suggest that formation of planetary embryos and gas giant planets also occurred very early, contemporaneously with chondrule formation and asteroidal accretion. Dauphas and Pourmand (2011) used the correlation between Th/Hf and 176Hf/177Hf ratios in Martian meteorites to constrain the Hf/W ratio of the Martian mantle, and estimate the time of the Mars accretion at 1.8+0.9/−1.0 Ma after Solar System formation. They suggested that Mars is a stranded planetary embryo. Kruijer, Burkhardt, Budde, and Kleine (2017) used 182W-182Hf chronology of iron meteorites with “carbonaceous” and “non-carbonaceous” affinity derived from Mo isotope systematics to estimate the time of formation of Jupiter’s core within 1 Ma after Solar System formation, and accretion of Jupiter to ~50 Earth masses >3–4 Ma after Solar System formation.

The age of the Earth and Moon is a more complex question. It is generally accepted that the Moon formed from material ejected in a giant collision between proto-Earth and a smaller planet or planetary embryo. Because of the complex history of differentiation of the proto-Earth and the impactor, the 182Hf-182W isotope data do not yield reliable constraints on the time of the impact (Fischer & Nimmo, 2018). A more reliable estimate of the minimum age of the Moon-forming collision has been derived from Lu-Hf systematics of well-preserved zircons with concordant U-Pb systems from lunar rocks (Barboni et al., 2017). These data indicate that differentiation of the lunar crust occurred before 4.51 Ga, or within 60 Ma after the Solar System formation.

Our ability to study the entire history of a planet depends on its accessibility for sampling. The most accessible (but by no means fully accessible) body is Earth—our home planet. The history of the Earth is too packed with action to describe it here in detail. The second-best sampled body is the Moon, represented by rocks delivered by Apollo and Luna missions and 349 lunar meteorites. Mars is represented by 215 Martian meteorites, Vesta—by 2067 HED meteorites (the numbers according to the Meteoritical Bulletin database as of October 27, 2018). Among these bodies, only Earth, and possibly Mars, appear to have significant recent endogenous activity. The recent changes in the other bodies are caused by collisions.

### Conclusion

Isotopic dating is a fundamental instrument for problem solving in earth and planetary sciences by resolving the temporal relationships of natural processes and events and establishing their causal relationships. The efficiency of isotopic dating as a problem solving tool depends on our ability to resolve events closely spaced in time. Increasing precision of dates in modern geochronology has brought about major advances in understanding the key problems regarding the timing and tempo of natural processes.

Since its start in the early 1900s, isotopic geochronology has come a long way. Modern U-Pb and 40Ar-39Ar dating have time resolution of ~1 million years over the entire lifespan of the Earth and the Solar System, and even better precision has been achieved with chronology using short-lived radionuclides for very old (first 10–20 million years after Solar System formation) and very young (last million years) events. The time markers can be attached to a great variety of processes including, but not limited to, condensation and evaporation, crystallization of melt, metal–silicate segregation, metamorphism, metasomatism, impacts, and biological evolution. Furthermore, fine structure of these events and processes can be resolved in many cases.

There are also a number of major problems in earth and planetary sciences that await more definitive solutions with geochronological methods. Was the onset of chondrule formation contemporaneous with formation of refractory inclusions, or was there a time gap? Were the chondrules building blocks or by-products of planetesimal evolution? How did the sizes of planets grow in time? When did the planetary cores form? When, and how, did magma oceans form? Did the Moon experience a terminal peak of bombardment? What were the nature, extent, and time of formation of the terrestrial and lunar early crusts? How did the volume and composition of the crusts of the Earth and other planets change in time? What is the relationship between geological evolution, changes in the biosphere, and the climate? Did volcanism or impact events trigger mass extinctions?

Future progress of geochronology is inseparable from analytical advances. Current techniques of isotope analyses are still far from the ultimate limits of precision and sensitivity imposed by the number of atoms of the parent and daughter elements. Half-lives and absolute isotopic compositions of many elements used in geochronology need to be verified. Fundamental parameters such as evaporation and condensation temperatures and the rates of diffusion require better experimental confirmation.

Is geochronology ready for anticipated sample delivery from other planets and asteroids? Mostly yes. Since the samples that will be delivered by the future robotic missions from distant bodies are likely to be small, the use of macroscopic, destructive methods of analysis (modern analogues of the methods that were used for analysis of Apollo rocks) will probably be limited, and microbeam methods will be required instead. Fortunately, recent developments of laser ablation ICPMS, ion microprobe, and atom probe techniques are making them more precise and sensitive than before, and the results of analyses of tiny samples from Genesis, Stardust, and Hayabusa missions prove their efficacy.

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