Minerals such as zircon are routinely used by geochronologists to confidently provide the U-Pb and Pb-Pb ages which underpin the conventional multi-millions-of-years’ timescale. These dating methods and the underlying assumptions are reviewed. The recognition of Pb loss from minerals after they form to explain discordant dates has resulted in the demonstration that both U and Pb mobility can occur in them. But how much U and Pb have been mobilized and how far they have migrated cannot be known with certainty. The radiation released by U decay damages crystal lattices and volume expansion generates micro-fractures, providing preferential pathways for U and Pb migration. Heat aids U and Pb mobility, but also causes recrystallization and defect recovery, locking migrated U and Pb atoms into their new locations. The current locations of U and Pb atoms within minerals can be studied at the atomic level. But there can be no certainty as to whether those atoms have always been in those locations, or whether they have migrated there. Also, there is no way of knowing what and how much migration happened in the past. Thus, even if the outer portions of crystals are removed before isotopic analysis and the U-Pb ages obtained for the cores of crystals are concordant, there can be no certainty that they represent the dates when the crystals formed. These uncertainties are compounded by the underlying unprovable assumptions on which the radioisotope dating methods are based, especially the assumption of time-invariant decay rates, built on the foundation of an assumed deep time history. The resultant U-Pb and Pb-Pb ages obtained are thus subjective, even though geochronologists take numerous precautions to make the U-Pb and Pb-Pb methods still have a strong semblance of validity. Nevertheless, since the amount of U and Pb mobility in most cases has been small, then the determinations can be used to provide useful relative ages. Thus, those absolute ages cannot be used to dismiss the history of the earth and its chronology provided in God’s infallible Word.

Keywords: radioisotope dating, 238U, 235U, 206Pb, 207Pb, U-Pb dating, Pb-Pb dating, concordia, discordia, Pb-Pb isochrons, Pb loss, zircons, inheritance, radiation damage, metamictization, dislocations, diffusion, recrystallization, U and Pb mobility, differential mass diffusion, uncertainties, sample pre-treatments

Introduction

Radioisotope dating of minerals, rocks, and meteorites is perhaps the most potent claimed proof for the supposed old age of the earth and the solar system. The absolute ages provided by the radioisotope dating methods provide an apparent aura of certainty to the claimed millions and billions of years for formation of the earth’s rocks. Many in both the scientific community and the general public around the world thus remain convinced of the earth’s claimed great antiquity.

The decay of 238U and 235U to 206Pb and 207Pb, respectively, forms the basis for one of the oldest methods of geochronology (Dickin 2005, Faure and Mensing 2005, Reiners et al. 2018, 171). While the earliest studies focused on uraninite (an uncommon mineral in igneous rocks), there has been intensive and continuous effort over the past five decades in U-Pb dating of more-commonly occurring trace minerals. Zircon (ZrSiO 4 ) in particular has been the focus of thousands of geochronological studies, because of its ubiquity in felsic igneous rocks and its claimed extreme resistance to isotopic resetting (Begemann et al. 2001).

However, accurate radioisotopic age determinations require that the decay constants or half-lives of the respective parent radionuclides be accurately known and constant in time. Ideally, the uncertainty of the decay constants should be negligible compared to, or at least be commensurate with, the analytical uncertainties of the mass spectrometer measurements entering the radioisotope age calculations (Begemann et al. 2001). Clearly, based on the ongoing discussion in the conventional literature this is still not the case at present. The stunning improvements in the performance of mass spectrometers during the past four or so decades, starting with the landmark paper by Wasserburg et al. (1969), have not been accompanied by any comparable improvement in the accuracy of the decay constants (Begemann et al. 2001; Steiger and Jäger 1977), in spite of ongoing attempts (Miller 2012). The uncertainties associated with direct half-life determinations are, in most cases, still at the 1% level, which is still significantly better than any radioisotope method for determining the ages of rock formations. However, even uncertainties of only 1% in the half-lives lead to significant discrepancies in the derived radioisotope ages due to how the half-life uncertainties are dealt with in the procedures for propagation of errors (Mattinson 2010; Schoene et al. 2006). The recognition of an urgent need to improve the situation is not new (for example, Min et al. 2000; Renne, Kamer, and Ludwig 1998). It continues to be mentioned, at one time or another, by every group active in geo- or cosmochronology (Boehnke and Harrison 2014; Schmitz 2012).

From a creationist perspective, the 1997–2005 RATE ( R adioisotopes and the A ge of T he E arth) project successfully made progress in documenting some of the pitfalls in the radioisotope dating methods, and especially in demonstrating that radioisotope decay rates have not always been constant at today’s measured rates (Vardiman, Snelling, and Chaffin 2000, 2005). Ongoing research continues to make further inroads into not only uncovering the flaws intrinsic to these long-age dating methods, but towards a thorough understanding of radioisotopes and their decay during the earth’s history within a biblical creationist framework.

One area the RATE project did not get to investigate was the issue of how reliable are the determinations of the radioisotope decay rates, which are so crucial for calibrating these dating “clocks.” Thus, as follow-on to the RATE effort, in a recent series of papers Snelling (2014a, 2014b, 2015a, 2015b, 2016, 2017a) reviewed how the half-lives of the parent radioisotopes used in long-age geological dating have been determined and collated all the determinations of them reported in the literature to discuss the accuracy of their currently accepted values. He documented the methodology behind and history of determining the decay constants and half-lives of the parent radioisotopes 87Rb, 176Lu, 187Re, 147Sm, 40K, 238U, and 235U which are used as the basis for the Rb-Sr, Lu-Hf, Re-Os, Sm-Nd, K-Ar, Ar-Ar, U-Pb, and Pb-Pb long-age dating methods respectively. He showed that there is still some uncertainty in what the values for these measures of the 87Rb, 176Lu, 40K, and 235U decay rates should be, in contrast to the apparent agreement on the 187Re, 147Sm, and 238U decay rates. This uncertainty is especially prominent in determinations of the176Lu decay rate by physical direct counting experiments. Furthermore, the determined values of the 87Rb decay rate differ when Rb-Sr ages are calibrated against the U-Pb ages of either the same terrestrial minerals and rocks or the same meteorites and lunar rocks. Ironically it is the slow decay rates of isotopes such as 87Rb, 176Lu, 187Re, and 147Sm used for deep time dating that makes precise measurements of their decay rates so difficult. Thus, it could be argued that direct measurements of their decay rates should be the only acceptable experimental evidence, especially because measurements which are calibrated against other radioisotope systems are already biased by the currently accepted methodology employed by the secular community in their rock dating methods.

Ultimately, the 87Rb, 176Lu, 187Re, 147Sm, and 40K decay half-lives have all been calibrated against the U-Pb radioisotope systems. This is the case even for the 147Sm decay half-life whose accepted value has not changed since it was calibrated against the U-Pb dating of two meteorites in the 1970s, in spite of the fact that more recent thorough physical direct counting experiments suggest a higher value. However, confidence in U-Pb radioisotope dating as the “gold standard” is very questionable, as there are now known measured variations in the 238U/235U ratio that is critical to that method (Brennecka and Wadhwa 2012; Goldmann et al. 2015; Hiess et al. 2012; Tissot and Dauphas 2015), as well as uncertainties as to the 238U and 235U decay rate values (Boehnke and Harrison 2014; Mattinson 2010; Schoene et al. 2006; Schön, Winkler and Kutschera 2004; Snelling 2017a; Villa et al. 2016). It is to be expected that every long-lived radioactive isotope is likely to show similar variation and uncertainty in half-life measurements because these are difficult measurements to make. However, even small variations and uncertainties in the half-life values result in large variations and uncertainties in the calculated ages for rocks and minerals due to how the half-life uncertainties are dealt with in the procedures for propagation of errors (Mattinson 2010; Schoene et al. 2006). This, of course, in no way diminishes or casts uncertainties on the conclusions of the RATE project that radioisotope decay rates have not always been constant at today’s measured rates, and that as a result radioisotope ages can still be used as relative ages (Vardiman, Snelling, and Chaffin 2000, 2005). Yet the question still remains as to whether the half-life values for each long-lived parent radioisotope are independently determined.

Nevertheless, accurate radioisotope age determinations not only depend on accurate determinations of the decay constants or half-lives of the respective parent radioisotopes, but on the reliability of the three assumptions these supposed absolute dating methods rely on. Those are the starting conditions, no contamination of closed systems, and time-invariant decay rates. All of these assumptions are unprovable. Yet they can supposedly be circumvented somewhat via the isochron technique, because it is claimed to be independent of the starting conditions and sensitive to revealing any contamination, which is still significantly better than any of the model radioisotope age methods for determining the ages of rock formations. Data points that do not fit on the isochron are simply ignored because their values are regarded as due to contamination. Often (if not usually for many investigators) discordant points are interpreted that the sample itself is thus problematic and should not be used for dating. That this is common practice is illustrated with numerous examples cited from the literature by Faure and Mensing (2005) and Dickin (2005). Nevertheless, the discarding discordant points by practitioners would appear to be justifiable in many cases. On the other hand, some may argue that this discarding of data points which do not fit the isochron is arbitrary and therefore is not good science, because it is merely assumed the “aberrant” values are due to contamination rather than that being proven to be so. Indeed, in order to discard such outliers in any data set, one must establish a reason for discarding those data points which cannot be reasonably questioned.

Undoubtedly the U-Pb and Pb-Pb radioisotope dating methods are now the cornerstone in current geochronology studies. Thus it is imperative every aspect of the methodology used in these methods be carefully examined to investigate whether the age results obtained by them are really as accurate and absolute as portrayed in the geological literature. Therefore, it is highly significant that Amelin et al. (2009) listed the potential problems which cause possible inaccuracies in obtaining reliable U-Pb and Pb-Pb ages. These are:

Presence of non-radiogenic Pb of unknown isotopic composition; Deviations from closed system evolution (gain or loss of U, loss of intermediate daughters such as the inert gas Rn, and loss of Pb); Misidentification of the processes that start or reset the isotopic clocks; Analytical problems (fractionation, instrument specific, etc.) and blank subtraction; Fractionation of radiogenic Pb isotopes induced by leaching of alpha recoil tracks; Variations in the 238U/235U ratio; Uncertainties in the half lives of 238U and 235U; and Deviations of the 234U/238U ratio from secular equilibrium.

It should be noted that Amelin et al. (2009) totally ignored the “elephant-in-the-room” issue of the time-invariance of the decay rates, because as uniformitarians they regard decay rates as constant at today’s measured rates. Yet, of these eight potential problems, Amelin et al. (2009) admitted that the first five are important and common, whereas the last three they considered insignificant or unlikely. But recent research has even found that these last three problems are more critical than they estimated, not least the variations in the 238U/235U ratio (Goldmann et al. 2015; Tissot and Dauphas 2015), and the uncertainties in the half lives of 238U and 235U (Boehnke and Harrison 2014; Snelling 2017a). Goldmann et al (2015) stated that “the investigated meteorites show U isotope variation between 137.71 and 137.89 (1.3%).” And Tissot and Dauphas (2015) reported:

Using the mass fractions and isotopic compositions of various rock types in Earth’s crust, we further calculate an average δ238U isotopic composition for the continental crust of –0.29 ± 0.03‰ corresponding to a 238U/235U isotopic ratio of 137.797 ± 0.005. We discuss the implications of the variability of the 238U/235U ratio on Pb-Pb and U-Pb ages and provide analytical formulas to calculate age corrections as a function of the age and isotopic composition of the sample.

Thus, each of these potential problems needs to be investigated closely.

Snelling (2017b) has already closely examined the first of them, the problem of the presence of non-radiogenic Pb of unknown isotopic composition, that is, common, initial, or primordial Pb. So now we will turn to the second and third of these problems. The second problem listed was the deviations from closed system behaviour evident from loss of Pb, or gain or loss of U, which requires monitoring U-Pb discordance and studying distribution of U and radiogenic Pb. The third problem Amelin et al. (2009) listed was the misidentification of the processes that start or reset the isotopic clocks. That requires studying the distribution of U and radiogenic Pb to look for element migration caused by diffusion and alteration. But before that, there is a need to go over some important background informational issues germane to the subsequent focus on the issues of the distribution of U and radiogenic Pb that is indicative of Pb loss or U loss or gain, and on the effects of diffusion and/or alteration.

Uranium and Lead Geochemistry

Uranium is element 92 (Z= 92) and a member of the actinide series in which the 5f orbitals are progressively filled with electrons. It occurs naturally in the tetravalent oxidation state U4+ with an ionic radius of 1.05 Å. But under oxidizing conditions it forms the uranyl ion (UO 2 2+) in which U has a valence of 6+. The uranyl ion forms compounds that are soluble in water, so U is a mobile element under oxidizing conditions. In contrast to U, Pb (Z= 82) is in period 6 and is a group 14 post-transitional metal. It is insoluble in water, but is a chalcophile element because it reacts with sulfur. It forms Pb2+ and Pb4+ ions with ionic radii of 1.32 Å and 0.91 Å respectively, so Pb ions cannot substitute for U ions in minerals.

In the course of the earth’s history, during partial melting of the rocks in the earth’s mantle U was concentrated in the liquid (melt) phase and thus became incorporated into the more silica-rich products. Therefore, the progressive geochemical differentiation of the earth’s upper mantle has enriched the rocks of the earth’s continental crust in U compared to those of the upper mantle. At an average of 1.3 ppm U is the 51st most abundant element in the earth’s crust, whereas Pb is regarded as quite a common element in the earth’s crust with an average of 11 ppm (Rudnick and Gao 2003). The concentrations of U and Pb increase from basaltic rocks (0.43 ppm U and 3.7 ppm Pb) to granites (4.8 ppm U and 23.0 ppm Pb) (Faure and Mensing 2005, 215). The concentrations of U in the common rock-forming silicate minerals are uniformly low, on the order of a few ppm or less. Instead, U occurs primarily in certain accessory minerals in which it is either a major constituent or replaces other elements. These minerals include uraninite, zircon, baddeleyite, monazite, apatite, and sphene (titanite).

All six naturally-occurring U isotopes are unstable and decay. Of these, 238U is the dominantly abundant isotope in natural U. It and 235U, the next most abundant isotope, are the starting radioisotopes in two decay chains or series (figs. 1 and 2), with 234U one of the early steps in the 238U decay chain. There are also several other trace U isotopes. 239U is formed when 238U undergoes spontaneous fission, releasing neutrons that are captured by other 238U atoms. 237U is formed when 238U captures a neutron but emits two more, which then decays to 237Np (neptunium). And then 233U is formed in the decay chain of that 237Np. 233U is also made from 232Th by neutron bombardment, usually in a nuclear reactor.

On the other hand, Pb has four stable isotopes, three of which (206Pb, 207Pb, and 208Pb) are the end members of decay chains (238U, 235U, and 232Th respectively). Only stable 204Pb has no radioactive precursor from which it is derived, and thus it is often called common Pb. Thus, the isotopic concentration of Pb in a natural rock sample depends on how much U and Th are also present. For example, the relative amount of 208Pb can range from 52.4% in normal samples to 90% in thorium ores. Similarly, the ratios of 206Pb and 207Pb to 204Pb increase in different samples, since the former two are supplemented by radioactive decay of U and the latter is not. For this reason, the atomic weight of lead is given to only one decimal place. Both 214Pb and 210Pb are short-lived intermediates in the 238U decay chain (fig. 1), while 211Pb and 212Pb are short-lived intermediates in the 235U and 232Th decay chains respectively (fig. 2). Lastly, very minute traces of 209Pb are also present from the cluster decay of 223Ra, one of the daughter products of natural 235U (fig. 2). Hence, natural Pb consists of not only the four stable isotopes, but also minute traces of another five short-lived radioisotopes.

Primordial Pb, which comprises the amounts of the isotopes 204Pb, 206Pb, 207Pb, and 208Pb at the time the earth formed, has been defined as the Pb isotopic composition of troilite (FeS) in the Canyon Diablo iron meteorite (Chen and Wasserburg 1983; Tatsumoto, Knight, and Allègre 1973). It is postulated to have been mostly “created” as a result of repetitive rapid and slow neutron capture processes occurring in stars. Yet there are serious questions about the so-called r-process in supernova which is postulated to generate all the elements heavier than Fe (Thielemann et al. 2011). Indeed, the supernova origin of heavy elements via the r-process has very recently fallen out of favor. Instead, the detection of merging neutron stars via gravitational waves and, concurrently, via electromagnetic radiation has resulted in the new view that merging neutron stars are the primary r-process site. Whether this is borne out in quantitative terms remains to be seen. Thus, it should be noted that this is not an absolute value, but merely an artifact of the reigning popular model for the naturalistic formation of the universe and its component stars and planetary systems.

238U and 235U Decay

The decay of the uranium isotopes 238U and 235U to the stable lead isotopes 206Pb and 207Pb respectively is the basis for the several most important methods of radioisotope dating. These not only derive from the transformation of 238U and 235U to 206Pb and 207Pb respectively, but also derive from the time-dependent “evolution” of common lead 204Pb from the decay of the intermediate daughters of 238U and 235U, and from the resulting isotopic composition of the accumulating daughter He (helium). Of course, 204Pb is not produced from 238U or 235U decay. However, 204Pb is assumed to be primordial and thus is hypothetically used as an indicator of the 206Pb, 207Pb, and 208Pb present due to radioactive decay. Age determinations of rocks based on the decay of U and the resulting accumulation of Pb and He were first attempted in the early years of the 20th century by Rutherford (1906) and Boltwood (1907). Subsequently, Holmes (1913) used chemical U-Pb and U-He dates to propose the first geological timescale based on radioisotope dating in his book on the age of the earth.

The invention of the first mass spectrometer by Thomson (1911) was followed by the work of Dempster (1918) and Ashton (1919), who designed the mass spectrographs which they used in subsequent years to discover the naturally-occurring isotopes of most of the elements in the periodic table and to measure their masses and abundances. The design of mass spectrographs was further improved in the 1930s, but it was the mass spectrometers based on a design by Nier (1940) that made possible the measurement and interpretation of variations in the isotopic composition of certain elements in natural materials such as minerals and rocks. Modern mass spectrometers follow his design and achieve a high level of accuracy and reliability of operation which enable isotope ratios to be measured for radioisotope dating, such as that based on the isotopic composition of Pb due to the decay of U to Pb, but also on the isotope ratios of common Pb. As a result of continuing refinement of the analytical procedures and of the sophistication of the instrumentation, the U-Pb and Pb-Pb methods of radioisotope dating are now regarded as the most precise and accurate geochronometers for determining the ages of terrestrial and extra-terrestrial minerals and rocks.

As already indicated, U has three naturally occurring isotopes, 238U, 235U, and 234U, all of which are radioactive. The decay of 238U gives rise to what is called the uranium series, which includes 234U as one of the intermediate daughters and ends in stable 206Pb (fig. 1). The decay of 238U to 206Pb can be summarized by the equation

where Q = 47.4 MeV per atom or 0.71 calories per gram per year (Wetherill 1966). Each atom of 238U that decays produces one atom of 206Pb by emission of eight α-particles and six β-particles. The parameter Q represents the sum of the decay energies of the entire series in units of millions of electron volts and calories of heat produced per gram per year. Several intermediate daughters in this series (fig. 1) undergo branched decay involving the emission of either an α-particle or a β-particle. The chain therefore splits into separate branches but 206Pb is the stable end product of all possible decay paths.

The decay of 235U gives rise to what is called the actinium series (fig. 2), which ends with stable 207Pb after emission of seven α-particles and four β-particles, as summarized by the equation

where Q = 45.2 MeV per atom or 4.3 calories per gram per year (Wetherill 1966). This series also branches as shown in Fig. 2.

In spite of there being 33 isotopes of 12 elements formed as intermediate daughters in these two decay series (not counting 4He), none is a member of more than one series. In other words, each decay chain always leads through its unique set of intermediate isotopes to the formation of a specific stable Pb isotope. The decay of 238U always produces 206Pb, and 235U always produces 207Pb.

The half-lives of 238U and 235U are very much longer than those of their respective intermediate daughter isotopes. Therefore, these decay series satisfy the prerequisite condition for the establishment of secular equilibrium, provided none of the intermediate daughters escaped from the U-bearing mineral or were added from external sources (Faure and Mensing 2005, 218). When secular equilibrium exists in a U-bearing mineral because it is a closed system, the decay rates of the intermediate daughters are equal to those of their respective parents, and thus the production rate of the stable daughter at the end of the decay chain is equal to the decay rate of its parent at the head of that chain. Therefore, the decay of 238U and 235U in minerals in which secular equilibrium has established itself can be treated as though it occurred directly to the respective 206Pb and 207Pb isotopes. As a result, the growth of these radiogenic Pb isotopes can be described by means of equations (1) and (2), which are similar to the equations used to represent the decay of 87Rb to 87Sr and 147Sm to 143Nd.

The U-Pb Dating Method

The accumulation of stable daughter atoms from the decay of parent atoms over time is expressed by the equation known as the law of radioactivity, namely

where D* is the number of measured stable radiogenic daughter atoms, N is the number of measured parent atoms remaining, λ is the decay constant (decay rate), and t is the time since decay of the parent atoms began (Faure and Mensing 2005). Since D* and N can be measured in a mineral, then if λ is known the equation can be solved for t, which is thus declared to be the age of the mineral. Thus the accumulation of stable radiogenic 206Pb and 207Pb by decay of their respective parents 238U and 235U in a mineral is governed by equations derivable from equation (3) as follows

where λ 1 and λ 2 are the decay constants of 238U and 235U respectively; 238U/204Pb and 235U/204Pb are ratios of these isotopes calculated from the measured concentrations of U and Pb in the mineral; and the subscript i refers to the initial values of the 206Pb/204Pb and 207Pb/204Pb ratios.

To date U-bearing minerals by the U-Pb methods, the concentrations of U and Pb are measured by an appropriate analytical technique (usually isotope dilution), and the isotopic composition of Pb is determined by using a solid-source mass spectrometer, an ion-probe mass spectrometer, or an ICP mass spectrometer. The U-Pb dates are calculated by means of equations (4) and (5) being solved for t using assumed values of the initial isotope ratios of Pb (for example, Ludwig 1993) as follows

These are known as 206Pb and 207Pb model ages respectively. They are independent of each other, but will be concordant (that is, agree with each other) if the mineral samples satisfy the conditions for dating (Faure and Mensing 2005, 218–219):

The mineral has remained closed to U and Pb, and all the intermediate daughters throughout its history; Correct values are used for the initial Pb isotope ratios; The decay constants of 238U and 235U are known accurately; The isotopic composition of U is normal and has not been modified by isotope fractionation or by occurrence of a natural chain reaction based on induced fission of 235U; and All analytical results are accurate and free of systematic errors.

The assumption that the samples being dated remained closed to U, Pb, and all intermediate daughters throughout their history “is satisfied only in rare cases because U is a mobile element in oxidizing environments and therefore tends to be lost during chemical weathering” (Faure and Mensing 2005, 219, emphasis in the original). In addition, the emission of α-particles causes radiation damage to the crystal structures of the U-hosting minerals, which facilitates the loss of Pb and the other intermediate daughters in both decay chains. Consequently, U-Pb dates for rocks and minerals are rarely concordant, so procedures have been devised to overcome that problem.

The choice of the initial Pb isotope ratios would seem to only be a problem for dating rocks and minerals that have low U/Pb ratios and additionally are young. It is claimed that the numerical values of the initial Pb isotope ratios do not appear to significantly affect the calculated U-Pb ages of Precambrian rocks and minerals having high U/Pb ratios because their present Pb isotope ratios in most cases reach large values.

The decay constants and half-lives of 238U and 235U were fixed by the International Union of Geological Sciences (IUGS) Subcommission of Geochronology in 1975 (Steiger and Jäger 1977). At the same time a value of 137.88 was adopted for the 238U/235U ratio. Since then these values have been used in almost all U-Pb age calculations so as to avoid any potential confusion by the use of different values. It has been continually claimed that the numerical values of the 238U and 235U decay constants and half-lives are probably more accurately known than those of other long-lived radionuclides because of their importance in the nuclear industry. Therefore, refractory U-bearing minerals such as zircon (ZrSiO 4 ) that often yield concordant U-Pb ages have been used to refine (that is, adjust) the decay constants of other radionuclides used in geochronology (Begemann et al. 2001; Snelling 2014a, 2014b, 2015a, 2015b, 2016).

It should be mentioned here that decay rates are not just measured and expressed by the parameter known as the decay constant (λ), but also by the parameter called the half-life (t ½ ). The decay constant can be defined as the probability per unit time of a particular nucleus decaying, whereas the half-life is the time it takes for half of a given number of the parent radionuclide atoms to decay. The two quantities can be almost used interchangeably, because they are related by the equation:

The issue of the abundances of the U isotopes and thus the adopted value of the 238U/235U ratio has already been discussed in detail by Snelling (2017a), so further comment is not warranted here. Suffice it to say, real differences in the isotopic composition of terrestrial and extra-terrestrial U have been reported in the past decade. So until very recently there has been no compelling evidence not to base age determinations of terrestrial and lunar rocks and minerals, and of meteorites and their minerals, by the U-Pb method on a value of 137.88 for the present-day 238U/235U ratio.

It is claimed that the effect of Pb loss on U-Pb dates can be minimized by calculating a date based on the 207Pb/206Pb ratio which is supposed to be insensitive to recent Pb loss provided that the Pb which was lost from the mineral had the same isotopic composition as the Pb which remained, that is, there has been no isotopic fractionation. The relationship between the 207Pb/206Pb ratio and time results from the difference in the half-lives of 238U and 235U. The desired equation is obtained by combining equations (4) and (5) above:

This equation has several interesting properties (Faure and Mensing 2005, 219–220):

It involves the 235U/238U ratio which at 1/137.88 is regarded as a constant for all U of normal isotopic composition on and in the earth, the moon, Mars, and meteorites at the present time. The equation does not require knowledge of the concentrations of U and Pb and involves only isotope ratios of Pb. The left hand side of equation (9) is equal to the 207Pb/206Pb ratio of radiogenic Pb: where the asterisk * identifies the radiogenic Pb isotopes produced since the “clock” was reset by a metamorphic or complete melting/recrystallization event. Equation (9) cannot be solved for t by algebraic means because it is transcendental, but it can be solved by iteration and by interpretation in a table.

A difficulty arises in the solution of equation (9) when t = 0, because it yields the indeterminate result 0/0 (Faure and Mensing 2005, 220). It is claimed thus that this difficulty is overcome by means of l’Hôpital’s rule, which requires that the differentiated functions in the ratio are differentiable over the entire open interval in question, that is, over millions to billions of years (Faure and Mensing 2005, 220). However, it appears questionable whether this is a proper application of l’Hôpital’s rule. This is because the decay rates of 235U and 238U are not equal, and therefore the quantities of 235U and 238U are functions of time and thus the 235U/238U ratio must be a function of time. Hence the right side of equation (9) is not in a form amenable to l’Hôpital’s rule, that is, there are four functions of time involved in the open interval 0 < t < t a , where t = the elapsed time since the “clock” was reset. However, only applying this rule to the value of (207Pb/206Pb)* at time t = 0 (the instant of clock reset) yields

Equation (11) indicates that the (207Pb/206Pb)* which forms by the decay of 238U and 235U over the time interval equalling the age of the mineral is equal to the rates of decay of these two U isotopes at the present time. Substituting into equation (11) the relevant values for the 235U/238U ratio, and the decay constants λ 1 and λ 2 , yields a value at time (t = 0) for (207Pb/206Pb)* of 0.04604 (see Table 1).

Table 1. Numerical values of eλ 1 t–1 and eλ 2 t–1 and of the radiogenic ( 207Pb/206Pb)* ratio as a function of age t (after Faure and Mensing 2005; Wetherill 1956, 1963). The expressions listed at the head of each column of the table occur in equations (9) and (10) in the text. t, × 109 y eλ 1 t–1 eλ 2 t–1 207Pb*/206Pb 0 .0 0.0000 0.0000 0.04604 0.2 0.0315 0.2177 0.05012 0.4 0.0640 0.4828 0.05471 0.6 0.0975 0.8056 0.05992 0.8 0.1321 1.1987 0.06581 1.0 0.1678 1.6774 0.07250 1.2 0.2046 2.2603 0.08012 1.4 0.2426 2.9701 0.08879 1.6 0.2817 3.8344 0.09872 1.8 0.3221 4.8869 0.11004 2.0 0.3638 6.1685 0.12298 2.2 0.4067 7.7292 0.13783 2.4 0.4511 9.6296 0.15482 2.6 0.4968 11.9427 0.17436 2.8 0.5440 14.7617 0.19680 3.0 0.5926 18.1931 0.22266 3.2 0.6428 22.3716 0.25241 3.4 0.6946 27.4597 0.28672 3.6 0.7480 33.6556 0.32634 3.8 0.8030 41.2004 0.37212 4.0 0.8599 50.3878 0.42498 4.2 0.9185 61.5752 0.48532 4.4 0.9789 75.1984 0.55714 4.6 1.0413 91.7873 0.63930

The numerical values of (eλ 1 t–1) and (eλ 2 t–1) are listed in Table 1 and yield the (207Pb/206Pb)* ratios for increasing values of t ranging from t = 0 to t = 4.6 Byr. This table can be used to solve equation (9) for t by linear interpolation based on the (207Pb/206Pb)* ratio calculated from equation (10). Conversely, by determining the (207Pb/206Pb)* ratio in a mineral from measurements of its Pb isotope ratios, the age (t) of the mineral can be calculated by linear interpolation between the (207Pb/206Pb)* ratio values in Table 1. This is known as the 207Pb-206Pb model age.

Although U occurs in a large number of minerals, only a few are suitable for dating by the U-Pb methods. To be useful for dating, a mineral must be retentive with respect to U, Pb, and the intermediate daughters, and it should be widely distributed in a variety of rocks. The minerals that satisfy these conditions include zircon, baddeleyite, monazite, apatite, and sphene (titanite). All of these minerals contain trace amounts of U but low concentrations of Pb, giving them high U/Pb ratios favourable for dating. For example, concentrations of U in zircons range from a few hundred to a few thousand parts per million and average 1350 ppm (Faure and Mensing 2005, 221). The presence of U in zircon is due to the isomorphous substitution within the zircon crystal lattice of U4+ (ionic radius 1.05 Å) for Zr4+ (0.87 Å), although this substitution is limited by the differences in their ionic radii and may well be an exothermic reaction due to the substitution sites having to expand by 20%. However, whereas U4+is admitted into zircon crystals, Pb2+ is regarded as being excluded because of its large ionic radius (1.32 Å) and its low charge (2+). Therefore, zircons are supposed to contain very little initial Pb at their time of formation and have high U/Pb ratios. This appears to enhance their sensitivity as a geochronometer, so zircons have for several decades become increasingly used for dating via the U-Pb methods.

The Wetherill Concordia and Pb-Loss Discordia

The effect of the loss of Pb or U and the gain of U on U-Pb dates of minerals can be compensated by a graphical procedure developed by Ahrens (1955) and Wetherill (1956, 1963). Equations (4) and (5), which govern the time-dependent increase of the 206Pb/204Pb and 207Pb/204Pb ratios of U-bearing minerals or rocks, can be rearranged to yield ratios of radiogenic 206Pb to 238U and of radiogenic 207Pb to 235U:

where the asterisk * is used to identify the radiogenic origin of the Pb isotopes. These equations assume that there is no 206Pb or 207Pb present when t = 0. Yet this begs the question as to whether t = 0 at the formation of the earth and solar system, or when the mineral forms and remains a closed system.

The values of eλ 1 t–1 and eλ 2 t–1 for different values of t are listed in Table 1 and were used to plot the curve in Fig. 3. The coordinates of all points on this curve are the 206Pb*/238U and 207Pb*/235U ratios that yield concordant U-Pb dates. Therefore, the curve in Fig. 3 is known as the concordia and is associated with its inventor (Wetherill 1956, 1963) in order to distinguish it from a different concordia diagram developed later by others. U-bearing minerals that contain no radiogenic 206Pb* and 207Pb* yield t = 0, while those containing radiogenic 206Pb* and 207Pb* will yield U-Pb ages of 1.0 Byr, 1.5 Byr, and so on, located sequentially along the concordia curve.

Fig. 3 shows a hypothetical history of zircon grains that originally crystallized from a magma. At the time of crystallization, the zircons contained no radiogenic Pb and so plotted at the origin of the concordia diagram. During the subsequent 2.5 Byr the 206Pb*/238U and 207Pb*/235U ratios of the zircons increased by decay of 238U and 235U causing them to move upwards along the concordia. After 2.5 Byr there was an episode of thermal metamorphism during which some of the zircon grains lost all the radiogenic Pb they had accumulated and they therefore now plot back at the origin (t = 0). Yet it could be equally argued that these zircon grains may have lost more U than radiogenic Pb because U is more mobile. Furthermore, this happening introduces a discontinuity in the equations describing the process and hence could invalidate the application of l’Hôpital’s rule to the original equation. Meanwhile, the other grains lost varying amounts of radiogenic Pb, so they plot on a straight line chord, labelled as discordia A on Fig. 3 because all the zircon grains on this chord would yield discordant U-Pb dates. At the end of this short episode of thermal metamorphism the U in all the zircon grains continued decaying and so the grains resumed accumulating radiogenic Pb. At the present time 1 Byr after the episode of thermal metamorphism, the zircon grains that had previously lost all their radiogenic Pb have moved 1 Byr up along the concordia, while the other grains that had previously lost varying amounts of radiogenic Pb have maintained their linear relationship to one another. The net result is that the zircon grains now plot along discordia B in Fig. 3, extending from 1 Byr (the time elapsed since the thermal metamorphism) to 3.5 Byr (2.5 Byr + 1 Byr). Thus at 1 Byr after the episode of thermal metamorphism (which occurred at 2.5 Byr after the crystals formed) the zircon grains that previously defined discordia A now form discordia B, which intersects the concordia at two points, labelled P and Q in Fig. 3. The coordinates of point Q represent concordant U-Pb dates of 3.5 Byr which represents the time elapsed since the original crystallization of the zircon grains that now define discordia B.

Furthermore, the coordinates of point P yield concordant U-Pb dates of 1 Byr, but the interpretation of that date depends on the circumstances. If the loss of radiogenic Pb did occur during the short episode of thermal metamorphism, then the date of 1 Byr at point P is the time elapsed since that episode. This is called episodic loss of radiogenic Pb from the zircon grains. At the same time the thermal metamorphism should have caused loss of radiogenic 40Ar from other minerals in the same rock, which should thus yield a K-Ar date also of 1 Byr. Alternatively, radiogenic Pb loss may have occurred by continuous diffusion at elevated temperature. In that case, the trajectory of the U-Pb system in the zircons would follow a straight line that became non-linear near the origin (t= 0). As a result, linear extrapolation of discordias would yield a lower intercept with concordia that corresponds to a fictitious date. Therefore, the date calculated for the lower intercept point P of discordia B in Fig. 3 must be confirmed by a K-Ar date for another mineral in the same rock before it can be interpreted as the age of an episode of thermal metamorphism.

Thus the concordia diagram can indicate the U-bearing minerals that plot on a discordia line were altered. As well as loss of radiogenic Pb from a mineral, a discordia may represent a gain or loss of parent U. However, on this concordia diagram the gain of Pb by the mineral is not predictable unless the isotopic composition of the new Pb can be specified. The concordia model also includes a further constraint that the Pb loss must occur without discrimination between the Pb isotopes on the basis of their masses (that is, fractionation). Thus it has been shown by Faure and Mensing (2005) how both Pb loss and U gain will cause a mineral’s grains to plot along a discordia below the date of their original formation and yield younger discordant U-Pb dates. On the other hand, a loss of U from the mineral will cause its grains to plot along that same discordia above the date of their original formation and yield older discordant U-Pb dates.

The Tera-Wasserburg Concordia

The U-Pb dates of some lunar rocks were found to be significantly older than the Rb-Sr and K-Ar dates yielded by the same rocks (Tatsumoto and Rosholt 1970, compared with Tera and Wasserburg 1972, 1973). For example, a lunar basalt yielded 238U-206Pb and 235U-207Pb model ages of 4.24 Byr and 4.27 Byr respectively compared to Rb-Sr and K-Ar dates of only 3.88 Byr (Tera and Wasserburg 1972). The postulated reason for this discrepancy is that these lunar rocks contain excess radiogenic 206Pb and 207Pb that was incorporated into these lunar basalts at the time of crystallization, but no explanation is given as to where this excess radiogenic Pb came from. Tera and Wasserburg (1972) therefore devised a new concordia that does not require prior knowledge of the initial 206Pb/204Pb and 207Pb/204Pb ratios.

The number of 206Pb and 207Pb atoms in a unit weight of U-bearing rocks or minerals can be expressed by the equations:

where 206Pb i and 207Pb i are the initial 206Pb and 207Pb respectively. Tera and Wasserburg (1972) used these equations to define a concordia in parametric form where the x-coordinate is derived from equation (14) as follows:

and the y-coordinate is obtained by combining equations (14) and (15) as follows:

The concordia is constructed by solving equation (16) (x-coordinate) and equation (17) (y-coordinate) for selected values of t. However, in order to plot two such parameters against each other, a postulated relation must exist between them. Thus, it could be questioned as to whether these two parameters are actually in a linear relationship to begin with. Nevertheless, the results are listed in Table 2. The resulting graph in Fig. 4 is the locus of all points representing U-Pb systems that yield concordant dates.

Table 2. Coordinates of points that define the Tera-Wasserburg concordia, where the x-coordinate is 1/(eλ 1 t–1) in equation (16) and the y-coordinate is 1/137.88 [(eλ 2 t–1)/(eλ 1 t–1)] in equation (17) (after Faure and Mensing 2005). Note that the x- and y-values were calculated from data in Table 1. t, Ga x y 0.2 31.746 0 0.05012 0.4 15.625 0 0.05575 0.6 10.256 0 0.05992 0.8 7.570 0 0.06581 1.0 5.959 0 0.0725 0 1.2 4.887 0 0.0801 0 1.4 4.122 0 0.0887 0 1.6 3.549 0 0.0987 0 1.8 3.104 0 0.1100 0 2.0 2.748 0 0.1229 0 2.2 2.458 0 0.1378 0 2.4 2.216 0 0.1548 0 2.6 2.012 0 0.1743 0 2.8 1.838 0 0.1968 0 3.0 1.687 0 0.2226 0 3.2 1.555 0 0.2524 0 3.4 1.439 0 0.2867 0 3.6 1.336 0 0.3263 0 3.8 1.245 0 0.3721 0 4.0 1.162 0 0.4249 0 4.2 1.088 0 0.4862 0 4.4 1.021 0 0.5571 0 4.6 0.9603 0.6393 0

The discordia line in Fig. 4 intersects the Tera-Wasserburg concordia at two points corresponding to dates t 1 (3.2 Byr) and t 2 (0.2 Byr). Extrapolation of this discordia line beyond t 1 yields an intersection point I 0 on the y-axis where 238U/206Pb* = 0. Obviously, this means that the 206Pb* concentration must be non-zero when there is no 238U, and calculating the relevant values infers that the 206Pb* is approximately four times larger than the 207Pb* concentration. In any case, the numerical value of I 0 is the radiogenic 207Pb/206Pb ratio that formed in the interval of time between t 1 and t 2 (Tera and Wasserburg 1974) as follows:

where λ 1 and λ 2 are the decay constants of 238U and 235U respectively, and t 1 and t 2 are the upper and lower intersections with the discordia as depicted in Fig. 4.

The U-Pb system whose postulated geological history is depicted in Fig. 4 originally contained no radiogenic Pb, that is, 238U/206Pb* = ∞ when it formed at t 1 = 3.2 Byr. Subsequently, radiogenic 207Pb and 206Pb accumulated by decay of 235U and 238U respectively until the system apparently recrystallized or differentiated at t 2 = 0.2 Byr. The radiogenic 207Pb/206Pb ratio of the Pb that had accumulated from t 1 = 3.2 Byr to t 2 = 0.2 Byr is equal to I 0 in Fig. 4 and is expressed by equation (18). If the U-free mineral (for example, plagioclase) formed during the recrystallization event at t 2 , it would contain Pb whose radiogenic 207Pb/206Pb ratio is equal to I 0 .

The postulated U-bearing system represented by t 2 on the Tera-Wasserburg concordia in Fig. 4 was apparently Pb-free at the end of the metamorphic event (that is, 238U/206Pb* = ∞). All the Pb it contains at the present time apparently formed by decay of the U isotopes after the end of the recrystallization event at t 2 = 0.2 Byr. This interpretation implies that both t 1 and t 2 are valid dates in the geological history of a volume of U-bearing rocks. Keep in mind that t 1 and t 2 are obtained as result of where the discordia plotted on the Tera-Wasserburg diagram from the U and Pb isotope analyses of the rock unit being investigated intersects the Tera-Wasserburg concordia, as depicted in Fig. 4.

Alternately, the radiogenic 207Pb/206Pb ratio represented by I 0 may be the result of a complex process unrelated to the U-Pb system that recrystallized at t 2 . In that case, the discordia is the locus of U-Pb systems that formed by mixing of two components. One of the components is I 0 and the other component is the U-Pb system represented by the point of intersection at t 2 in Fig. 4. In that case, the date derived from the coordinates of point t 1 has no geological significance (Tera and Wasserburg 1974).

A follow-on example illustrates how the Tera-Wasserburg concordia diagram has been utilized to obtain a corrected age for a rock with discordant U-Pb model ages. One of the rock samples obtained by the Apollo 14 mission from the Fra Mauro region of the moon was lunar basalt 14053. This sample yielded highly discordant and improbable whole-rock U-Pb model ages of 5.60 Byr (238U-206Pb), 5.18 Byr (235U-207Pb), and 5.01 Byr (207Pb/206Pb), corrected for the postulated presence of primeval Pb which the moon supposedly inherited from the solar nebula (Tera and Wasserburg 1972). The same sample had yielded an internal (mineral and whole-rock) Rb-Sr isochron date of 3.88 ± 0.04 Byr (Papanastassiou and Wasserburg 1971). Furthermore, the same sample had been dated by Turner et al. (1971) by the 40Ar*/39Ar method applied to both the whole-rock and plagioclase. The partial-release spectra indicated well-defined plateau dates of 3.95 Byr (whole rock) and 3.93 Byr (plagioclase), using then current recommended decay constants.

The U-Pb data reported by Tera and Wasserburg (1972) for lunar basalt 14053 define a discordia line that intersects the y-axis (238U/206Pb* = 0) at (207Pb/206Pb)* = 1.46, as depicted in Fig. 5. The slope of the discordia line is –0.88366 based on an unweighted linear regression of three data points representing two whole-rock and one magnetite (the magnetic fraction) analyses. The slope m of the discordia is related to the initial (207Pb/206Pb)* ratio and to the age of the U-Pb system by the equation:

This equation was solved graphically by Tera and Wasserburg (1972) for (207Pb/206Pb) i = 1.46 for values of t between 3.87 and 4.00 Byr. Their graph indicates that a slope of –0.88366 corresponds to a date of 3.91 Byr, which represents the intersection point of the discordia with the Tera-Wasserburg concordia in Fig. 5. A more accurate date could be obtained by interpolating in a table values of the slope for selected values of t or by numerical iteration.

This interpretation of the U-Pb data for lunar basalt 14053 by means of the Tera-Wasserburg concordia yielded a date that is in good agreement with the Rb-Sr and 40Ar*/39Ar dates for this same rock. The essential feature of this concordia is that it permits an explicit determination of the radiogenic 207Pb/206Pb ratio at 238U/206Pb* = 0 without requiring an estimate of the initial isotope ratios of Pb at the time of crystallization of the basalt.

Pb-Pb Isochron Dating

Equations (4) and (5) above describe the accumulation of the radiogenic 206Pb and 207Pb from 238U and 235U respectively. The same equations can be used with multiple samples to plot independent isochrons. The slopes of the 238U-206Pb and 235U-207Pb isochrons yield dates that are concordant only when the samples remained closed to Pb diffusion and had identical initial Pb isotopic ratios. However, in most cases, U-Pb isochrons based on whole-rock samples have not been successful, primarily because rocks which are exposed to chemical weathering lose a significant fraction of U. Thus the U-Pb isochron method of dating igneous and metamorphic rocks composed of silicate minerals does not work in most cases because of the variable losses of U by chemical weathering, which occurs not only at the earth’s surface, but also in the subsurface where rocks are in contact with oxygenated groundwater.

On the other hand, igneous and metamorphic rocks that have lost U by recent chemical weathering may also have lost Pb. However, the isotopic ratios of the remaining Pb may not have changed if the isotopes of Pb were not fractionated. In other words, the isotope ratios of Pb in the weathered rocks are not changed if the Pb that was lost had the same isotope composition as the Pb that was present before the loss occurred. If chemical behavior is the only consideration, then perhaps this assumption could be justified; however, there are other factors such as any movement of the various Pb isotopes within the material matrix containing the Pb isotopes. Nevertheless, it is maintained that a date can be calculated based on the slope of the Pb-Pb isochron obtained from samples of even weathered rocks.

The equation for Pb-Pb isochrons is derived from combining equations (4) and (5) above to yield equation (10) above, which expresses the ratio of radiogenic 207Pb to 206Pb and then yields equation (9) above:

This is the equation for a straight line in coordinates of 206Pb/204Pb (x) and 207Pb/204Pb (y) whose slope m is

Age determinations by this Pb-Pb isochron method depend on the assumptions that all the samples that define the isochron (Faure and Mensing 2005, 241):

Had the same initial Pb isotope ratios; Formed at the same time; and Remained closed to U and Pb until the recent past, when they were exposed to chemical weathering.

In addition, the 238U/204Pb and 235U/204Pb ratios of the samples must have sufficient variation to allow Pb having different isotope ratios to form within them. The slope of Pb-Pb isochrons can be used for dating by solving equation (21) for t by interpolating within Table 1. Alternately, equation (21) can be solved by iteration on a computer to any desired level of precision.

The Pb-Pb isochron method has been used very widely for dating igneous and metamorphic rocks, especially those of Precambrian age, as well as meteorites. The method is claimed to yield the time elapsed since the isotopic homogenization of Pb and subsequent closure of rocks to U and its intermediate daughters. However, this ignores the known measurable leakage of the intermediate daughter Rn gas, which thus reduces the amount of in situ final 206Pb and 207Pb. Furthermore, this Pb-Pb isochron method also ignores the demonstrable fact that what are interpreted as isochron lines may instead be mixing lines between two end-member Pb isotope compositions, and there is no known way to definitively tell the difference between an isochron and a mixing line.

The several assumptions involved in the various U-Pb and Pb-Pb model and isochron dating methods have a somewhat tenuous validity, because they are based on an unknown and unconfirmed uniformitarian evolutionary past history. Yet in spite of that, all these methods depend on the U-Pb system within the minerals and rocks being dated being closed to loss from within and to contamination from without. That condition might seem to be easily resolved if the multiple ages derived by these methods all agree (are concordant), but even then there is no guarantee loss and/or contamination has not occurred. So we need to look more closely at these issues.

Recognition of the Problem of Pb Loss

As noted earlier, two potential problems which cause possible inaccuracies in obtaining reliable U-Pb and Pb-Pb ages were listed by Amelin et al. (2009). They are “deviations from closed system evolution (gain or loss of U, loss of intermediate daughters such as the inert gas Rn, and loss of Pb),” and “misidentification of the processes that start and reset isotopic clocks.” Amelin et al. (2009) assessed these two problems as being “important and common.” Of the closed system problem, they commented that it “requires monitoring of U-Pb concordance and studying distribution of U and radiogenic Pb.” Similarly, they commented regarding the processes which start and reset isotopic clocks that it “requires studying distribution of U and radiogenic Pb” and “for element migration caused by diffusion, alteration and shock.” Furthermore, they admitted that the “significance of some potential problems cannot be estimated at the present level of knowledge,” and thus they require “detailed and theoretical studies.”

An additional problem related to “deviations from closed system evolution” that Amelin et al. (2009) assessed as “insignificant” is “deviations from the 234U/238U ratio from secular equilibrium.” To be fair, Amelin et al. (2009) made that assessment in the context of the radioisotope dating of meteorites and their components. And yet, Amelin and Zaitsev (2002) in their radioisotope dating study of minerals from phoscorites and carbonatites from the Kola Peninsula of Russia had warned of the “geochronological pitfalls of initial radioactive disequilibrium” and “differential migration of isotopes.”

The concordia diagram developed by Wetherill (1956) has been widely used by geochronologists to interpret discordant U-Pb ages where Pb appears to have been lost. However, Tilton (1960) offered an alternative explanation for the loss of radiogenic Pb based on continuous diffusion of Pb from crystals at a rate governed by the mineral’s diffusion coefficient, the effective radius of diffusion of the crystals, and the concentration gradient of Pb in them. He assumed that U is uniformly distributed throughout the crystals, that diffusion of U and its intermediate daughters is negligible compared to that of Pb, that the diffusion coefficient is constant independent of time, and that diffusion is governed by Fick’s law. The solutions of Tilton’s diffusion equation generate curves on the concordia diagram which are the loci of points that represent U-Pb systems of specific ages that have suffered continuous Pb loss by diffusion.

Thus Tilton (1960) demonstrated that a linear array of data points representing discordant U-Pb systems on a concordia diagram can be interpreted in two fundamentally different ways. If Pb loss was due to an episode of metamorphism, then the U-Pb date calculated from the lower intercept point on the concordia apparently indicates the time of closure after the Pb loss. On the other hand, if the Pb was lost continuously by diffusion, then the U-Pb date calculated from the lower intercept point would be fictitious. The problem is that both episodic and continuous Pb loss results in daughter-parent ratios that appear to fit a straight-line discordia. This is why the U-Pb date derived from the lower intercept of the discordia with concordia must be confirmed by K-Ar or Rb-Sr dates of other minerals in the same rock before it can be accepted as the time elapsed since cooling after an episode of metamorphism. This Pb loss by continuous diffusion model implicitly assumes the temperature has remained constant throughout the history of the mineral grains (for example, zircon) and thus the diffusion coefficient and the effective radius are invariant with time. The general case in which the diffusion coefficient is a function of time and both Pb and U diffused was subsequently considered by Wasserburg (1963) and Wetherill (1963).

Yet another alternative interpretation of the discordance of U-Pb dates for U-bearing minerals was proposed by Goldich and Mudrey (1972). Minerals such as zircon suffer radiation damage as a result of the kinetic energy of the α-particles ejected by α-decay of U, Th, and daughter atoms. The extent of that radiation damage increases with age and with the U and Th concentrations in the minerals. The apparent relationship between the radioactivity of zircons and the discordance of their U-Pb dates was first demonstrated by Silver and Deutsch (1963), and was used by Wasserburg (1963), who related the diffusion parameter D/a2 to the radiation damage of zircon crystals. Goldich and Mudrey (1972) thus postulated that radiation damage causes the formation of microcapillary channels which permit water to enter the crystals. They argued that this water is tightly held until uplift and erosion cause the pressure on the minerals to be released. The resulting dilatance of the zircons allows the water to escape together with dissolved radiogenic Pb. Consequently, the loss of radiogenic Pb from zircon crystals in the crystalline basement complexes of Precambrian shields may be related to the uplift and erosion of those complexes. Such relatively recent Pb loss is consistent with the observation that the 207Pb-206Pb dates commonly approach the conventional true age of the U-bearing minerals (Faure and Mensing 2005).

This dilatancy model therefore appeared to provide a rational explanation for the observation emphasized by Tilton (1960) that U-bearing minerals, particularly zircons, from different continents all seem to have lost radiogenic Pb supposedly 500–600 million years ago, even though no worldwide metamorphic event is recognized by secularists in that period of their version of the earth’s history. Yet according the dilatancy model, the 500–600 million-year date corresponding to the lower intercept of the discordia based on apparent cogenetic suites of U-bearing minerals from a particular region on Tilton’s (1960) concordia plot indicates the time of uplift and erosion of that region.

The rocks and minerals used for U-Pb dating are usually collected from surface outcrops where they have been exposed to chemical weathering. Therefore, the discordance of model U-Pb ages may also be due to disturbances of the daughter-to-parent ratios caused by chemical weathering. This was confirmed as a problem by Stern, Goldich, and Newell (1966) who U-Pb dated zircons removed from residual clay formed by weathering of the Morton Gneiss in Minnesota. Model U-Pb dates of three weathered zircon crystals were found to be grossly discordant, whereas the 207Pb-206Pb dates were the oldest dates in all cases and approached the conventional known original age of these zircons. The weathered zircons plotted on a straight-line that started from a discordia and projected to the origin. Thus the displacement of those weathered zircons from their original position on the discordia indicated that they had lost up to 85% of their radiogenic Pb as a result of the ongoing chemical weathering.

The Problem of Inherited and Discordant Age Zircons

Another significant problem for zircon U-Pb dating is that zircon crystals in some metamorphic and granitic rocks yield much older ages than the accepted ages of the rocks. During episodes of crustal anatexis, radiogenic isotopes and other trace elements contained within the mineral phases comprising the source rock are redistributed. Dependent upon the extent of melting and homogenization, the geochronologic (radiogenic daughter isotopes 206Pb, 207Pb, 208Pb, 143Nd, 147Hf) and geochemical (for example, REEs) information contained within these mineral phases may be perturbed, or in the extreme be completely lost. With specific reference to accessory minerals, this information is lost if the mineral is completely consumed during partial melting, or if diffusion of the element within the restitic fraction of the mineral of interest is sufficiently rapid to allow equilibration on the time scale of the partial melting event. Alternatively, restitic minerals may be transported from the source region by the departing melt fraction, and under some circumstances carry not only information characteristic of the source region, but also information characteristic of the time-temperature history of crustal melting and transport. In metamorphic rocks this has been interpreted as inheritance of those zircon grains from the original sediment sources, the zircons somehow surviving metamorphism without resetting of the U-Pb isotopic system (Froude et al. 1983; Kröner, Jaeckel, and Williams 1994). The older zircons in granitic rocks are likewise interpreted as being inherited from the source rocks that melted to produce the magmas (Chen and Williams 1990; Williams, Compston, and Chappell 1983).

Evidence of inherited U-Pb ages in zircon from Phanerozoic granites is common (Harrison et al. 1987; Muir et al. 1996; Parrish and Tirrul 1989; Pasteels 1970; Pidgeon and Aftalion 1978; Pidgeon and Johnson 1974; Williams 1992), indicating that zircon may not be totally soluble during the formation of some granitic magmas. Experimental measurements of zircon solubility under crustal conditions have confirmed this conclusion (Watson and Harrison 1983). In some published studies the inherited zircons are 5–10 times older than those matching the accepted ages of the granites—for example, up to 1753 Ma in a 21 Ma Himalayan granite (Parrish and Tirrul 1989), up to 3500 Ma in a 426 Ma southeast Australian granodiorite (Williams 1992), and up to 1638 Ma in a 370 Ma New Zealand granite (Muir et al. 1996). Significantly, monazite grains can also yield negative ages, such as –97 Ma in a 20 Ma Himalayan granite that also contains zircons yielding ages up to 1483 Ma (Parrish 1990), a discordancy of almost 7500%.

The literature abounds with evidence for extremely strong retentivity of radiogenic Pb in zircons at high grade temperatures and in melts (for example, Dunn et al. 2005; Pidgeon and Nemchin 2006; Pidgeon et al. 2007). In apparent contradiction to this, examples of severe discordance reflecting more than 50% loss of radiogenic Pb, are also very common. Discordia lower intercepts, in many cases ill-defined, range from zero age to ca. 800 Ma (for example, Dunn et al. 2005; Kröner et al. 1999; Pidgeon and Nemchin 2006). It is noteworthy that in Precambrian zircons from the Canadian Shield, such discordance can mostly be avoided by abrading zircon grains before analysis. Also, secondary ion mass spectrometry (SIMS) data on Canadian Shield or West Greenland Archaean zircons also show little discordance (for example, Bowring and Williams 1999; Nutman et al. 2004). [In the SIMS technique a beam of energetic primary O- ions is focused on the sample surface, where their impact breaks chemical bonds and liberates a mixture of molecules and different (secondary) ions, which are extracted by an electric field and thus introduced to the mass spectrometer for analysis (Reiners et al. 2018, 48–49).] Lunar zircons, even those with high U-contents, do not show discordance beyond the analytical uncertainty limits (Nemchin et al. 2006; Pidgeon et al. 2007). It has thus been suggested that this type of discordance may be caused by groundwater acting on a metamict structure (Black 1987; Mezger and Krogstad 1997; Stern, Goldich and Newell 1966).

Furthermore, if Pb is lost from some mineral grains, then it could be inherited by other crystals in the host rocks subsequent to the formation of those rocks. Thus Ludwig and Silver (1977) found that many K-feldspars in Precambrian rocks contained unsupported or excess radiogenic Pb (that is, no parent isotopes in the mineral), though the composition of the unsupported Pb was compatible with the supposed ages of the host rocks. On the other hand, Williams et al. (1984) found unsupported (excess) radiogenic Pb in a zircon crystal in an Antarctic gneiss, which thus produced anomalously high ages. Similar situations also result in ages hundreds of millions of years more than expected and are interpreted as due to excess radiogenic Pb, the origin of which is either explained as mixing from older source materials which melted to form the magmas, and/or due to subsequent migration as a result of fluids, temperature and pressure (Copeland, Parrish, and Harrison 1988; Zhang and Schärer 1996). This all begs the question—should “anomalously old” zircons be interpreted as inheritance of the zircon crystals, or as due to “excess” radiogenic Pb in the crystals?

Zircon is now the most widely-used mineral in U-Pb geochronology, due to a combination of favorable properties, including high U content (typically hundreds of ppm), assumed lack of initial (or common) Pb, apparent good retention of radiogenic Pb (up to 900°C), and a diversity of geological occurrences (Cherniak and Watson 2000; Corfu 2013; Davis, Williams, and Krogh 2003; Harley, Kelly, and Möller 2007). However, the Achilles’ heel of zircon is the accumulation of radiation damage over time, critically affecting its properties (Ewing et al., 2003). Self-irradiation enhances diffusion, facilitates mineral–fluid interaction, leads to possible reduction of Pb4+ to Pb2+, and more generally results in open system behavior at low temperatures (< 200°C) and discordance between the two decay chains of U, namely, 238U-206Pb and 235U-207Pb (Geisler, Schaltegger, and Tomaschek 2007; Nasdala et al. 2010; Xu et al. 2012). Of course, one way to avoid these problems is simply not to use heavily radiation damaged or metamict zircons for geochronological purposes, but there are many situations where that is not feasible.

Pioneering publications (for example, Silver and Deutsch 1963) established a correlation between U concentration and discordance in zircon. They inferred that episodic Pb loss, rather than U gain, is the most probable cause for discordance and it was promoted by structural radiation damage. Since then, three main reasons for discordance of analyses are commonly cited: loss or redistribution of radiogenic Pb, introduction of common Pb, and mixed sampling of more than one generation of zircon (Corfu 2013). In the literature, papers invoking U-gain to explain discordance are rare. Yet analyzing detrital zircon grains from a quartzite inclusion in pegmatite, Grauert, Seitz, and Soptrajanova (1974) proposed that U penetrated along tiny cracks, during metamorphism without new zircon growth.

Utilizing the SHRIMP (ion microprobe) in situ analytical technique, radiogenic Pb was found by Compston (1997) to vary within most tested zircon grains on a 20 µm spatial scale. Some spots were characterized by huge excess radiogenic Pb, up to 30 times the “expected” values. However, zircon is not the only U-bearing mineral suitable for U-Pb dating using the SHRIMP. Monazite, sphene (titanate), rutile, perovskite, and uraninite are all potential candidates. Baddeleyite was the first mineral to be U-Pb dated using an ion microprobe, but Wingate and Compston (2000) found a flaw—the measured 206Pb/238U values and thus the U-Pb dates varied by up to ± 10% depending on the orientation of the crystals relative to the ion beam. They also tested monazite and zircon, but found no indication that the orientation of those crystals affected the results. Yet the flaw using baddeleyite has not been explained.

Indeed, Wingate and Compston (2000) demonstrated that there were pronounced reproducible differences in radiogenic 206Pb/238U and thus apparent U-Pb ages between four differently oriented faces of a large baddeleyite crystal (fig. 6a), as well as correlated variation in radiogenic 208Pb/206Pb with 232Th/238U for the same four differently oriented faces (fig. 6b). They concluded that the latter effect could be a primary crystal growth feature. In a second experiment, Wingate and Compston (2000) measured the isotopic ratios on the same crystal faces of 47 baddeleyite crystals but at different orientations with respect to the SHRIMP’s beam over a 180° range, the results revealing a striking, approximately sinusoidal, variation in 206Pb/238U apparent ages with orientation (fig. 6c). However, similar significant differences in radiogenic 206Pb/238U or radiogenic 207Pb/206Pb related to orientation were not detected in zircon or monazite crystals (within the analytical statistics), although radiogenic 208Pb/206Pb and 232Th/238U both vary with orientation. These differences in radiogenic 208Pb/206Pb again correlated precisely with those in 232Th/238U, which could be a real compositional variation reflecting zones of anisotropic primary crystal growth.





Furthermore, the problem of identifying in an igneous rock to be U-Pb dated which zircons were inherited by the magma and which crystallized from the magma is still fraught with difficulties due to the subjectivity of the criteria used. Siégel et al. (2018) have reviewed the techniques available to discriminate zircons crystallized from the magma from inherited zircons and proposed a new methodology to assist in the identification of the zircons crystallized from the magma for emplacement age determinations and a separate evaluation of inherited zircon components. Their approach used two strands of data:

Zircon data such as zircon morphologies, textures, compositions, and U-Pb ages; and Whole-rock data, in particular SiO 2 and coupled geothermometry (T Zircsat and T Magma ) to estimate whether the magma was zircon-saturated or undersaturated.

They tested this protocol using several Phanerozoic granitic rocks where contextual information was limited, and showed how zircons which didn’t crystallize from the granitic magmas could be distinguished. They also realized that where zircons are metamict (for example, high U and Th-rich zircons), much of the ability to discriminate between them is impacted because such zircons have suffered Pb loss and have modified compositions (for example, higher T ZircTi ). Thus, they recommended an integrated approach incorporating whole-rock chemistry, independent geothermometric constraints, zircon composition, textures, and U-Pb ages obtained by routine cathodoluminescence and LA-ICP-MS or ion microprobe analyses to provide increased confidence for the discrimination of inherited zircons from those zircons which crystallized from the magmas.

The Extent and Cause of Pb Mobility

Davis and Krogh (2000) undertook U and Pb isotopic analyses of HF-washed Archean zircon grains from a trondhjemite (dated at 2732 ± 2 Ma) and a dacite (dated at 2728 ± 1 Ma) and demonstrated that altered domains can be selectively removed by treatment with HF at moderate temperatures. The threshold value of radiation damage for solubility under these conditions is probably slightly in excess of 1.5 × 1015 α-decay events per mg. Residues appeared to contain no alteration but showed evidence of preferential leaching of radiogenic Pb isotopes and 234U from damaged crystal lattice sites.

Davis and Krogh (2000) found that the age of the HF-leached Pb, as calculated from its isotopic composition, was younger than the apparent crystallization age of the sample, resulting in anomalously old Pb in the residue fractions. They argued that this was likely to be due to the annealing of early radiation damage in the zircons. Their most plausible explanation for this was early burial and residence at temperatures above the long-term annealing point, followed by differential uplift and cooling. The supposed times when radiation damage began to accumulate were calculated at 2500 ± 20 Ma for the trondhjemite and 2295 ± 35 Ma for the dacite. Comparisons with temperatures of regional metamorphism and similar Ar-Ar uplift ages on biotite from nearby terrains suggested that the temperature for annealing of α-recoil damage is about 250–300°C.

Davis and Krogh (2000) also found that the two rock samples showed different relative proportions of leachability for accessible radiogenic Pb and 234U, but the average of the two was close to 1. This supported their suggestion that the leachability of different radiogenic isotopes from zircon is not significantly affected by the number of α-recoil events in the preceding decay chain.

The results of these experiments indicated to Davis and Krogh (2000) that leaching of radiogenic atoms from α-recoil-damaged sites in otherwise non-metamict and insoluble crystal domains is an important process during HF washing of Archean zircon grains as a pre-treatment to U-Pb analyses. There was also a suggestion that nitric acid leaches radiogenic atoms to a much lesser degree. These data combined with previous results of theirs using brines implied to Davis and Krogh (2000) that ancient geological leaching may be an important cause of discordance. They concluded that the typical Archean zircon grain population probably contains altered, leachable, and non-leachable domains, which must be considered in trying to interpret natural discordance due to low temperature processes, as well as in laboratory leaching experiments.

Furthermore, Davis and Krogh (2000) concluded that 234U and radiogenic Pb in damaged lattice sites are leachable to roughly the same extent. This conclusion, combined with the observation of significant 234U anomalies in groundwater and the oceans, seemed to imply that preferential leaching of radiogenic Pb must occur from zircon and other minerals in the natural environment. This in turn suggested that dissolved Pb in near-surface environments is biased toward 206Pb enrichment, especially in relatively recently metamorphosed or uplifted terrains. Such an enrichment mechanism may thus have implications for the interpretation of high 206Pb/204Pb lead in groundwater-precipitated ore deposits and perhaps for other aspects of the Pb cycle. Finally, Davis and Krogh (2000) maintained that their experiments, as well as those conducted by many others, demonstrated that leachability is a function of radiation dose level.

Geisler et al. (2002) reported the results of an investigation of the stability of partially metamict zircon in leaching experiments at 175°C with 2 M AlCl 3 and 1 M HCl–CaCl 2 solutions as hydrothermal fluids for 1340 hours (almost 56 days). Cathodoluminescence (CL) and backscattered electron (BSE) images showed that the zircon grains had developed either a reaction rim several micrometers thick, or deeply penetrating reticulated alteration zones with sharp boundaries to unaltered metamict zircon. Those zones had experienced severe loss of Si, U, Th, and Pb, and gain of Al or Ca, and a water species as revealed by electron microprobe, sensitive high-resolution ion microprobe (SHRIMP) analyses, and infrared spectroscopy. Micro-Raman and infrared measurements on the altered areas showed that disordered crystalline remnants of the partially metamict zircon structure were partially recovered, whereas recrystallization of the embedding amorphous phase was not observed. No detectable structural or chemical changes were found inside the unaltered areas. Intensive fracturing, which was most intense in the HCl–CaCl 2 experiment, occurred inside the altered areas due to the volume reduction associated with the recovery of the disordered crystalline material, and probably with the leaching reactions.

Geisler et al. (2002) explained the formation of the deep penetrating alteration zones by a percolation-type diffusion model. That model assumes the existence of percolating interfaces or areas of low atomic density between crystalline and amorphous regions, as well as between amorphous domains, along which fast chemical transport is possible. The idea of the existence of these fast diffusion interfaces is supported by the sharp chemical gradients at the margins to unreacted zircon. This model was used to estimate for the first-time coefficients for U, Th, and Pb diffusion in amorphous zircon at 175°C by assuming that volume diffusion inside the amorphous domains is the loss-rate-limiting process. Their estimates showed that volume diffusion in metamict zircon can cause significant loss of U and Th, and especially loss of radiogenic Pb over presumed geological time scales, even at temperatures as low as 175°C. Their results showed that recent Pb loss discordias can be generated:

By predominate Pb loss from metamict zircon through volume diffusion at low temperatures where thermal healing of the structure is insignificant; and By leaching of Pb (and U and Th) from metamict zircon by an external fluid.

Thus, it has been shown that the fast transport of chemical species from and into the metamict network can be well explained by the microstructure of a partially metamict zircon, that is, by the existence of percolating domain boundaries or areas of low atomic density, which act as fast diffusion pathways. According to the percolation-type model for diffusion proposed by Geisler et al. (2002), the effective diffusion of any species within the zircon lattice should vary with the α-decay dose, that is, the degree of metamictization. This model provided for the first time a physical explanation for the relationship between the degree of metamictization and age discordance as observed by SHRIMP and Micro-Raman measurements (Nasdala et al. 1998), and more generally for the correlation between the U content and age discordance in zircon often reported in U-Pb zircon studies (for example, Silver and Deutsch 1963). In addition, the stability of U and the higher degree of structural recovery observed in hydrothermal experiments, which were performed at higher temperatures (Geisler et al. 2001b), indicated that the dynamics of structural rearrangements of metamict zircon during fluid-zircon interaction play an important role in controlling the leaching process, and especially the loss of U and Th. The difference of the kinetics of rim formation in both experiments is evidence that the leaching kinetics (that is, rim formation) is not only controlled by structural properties, but also by the composition and the pH of the solution. All this only emphasizes the need to avoid metamict zircons for radioisotope dating of rocks if at all possible.

Although both solutions have no direct natural analogs and thus the experimental results of Geisler et al. (2002) cannot be directly transferred to natural conditions, they suggested that within presumed geological timescales, leaching of metamict zircon through natural waters can be significant even at temperatures below 200°C, as indicated by studies on natural zircons (for example, Högdahl, Gromet, and Broman 2001; Lumpkin 2001). This is further supported by reports of natural Ca- and Al-rich metamict zircons (for example, Geisler and Schleicher 2000; Speer 1980), some of which unambiguously have not suffered any high temperature metamorphic imprint (Geisler and Schleicher 2000). The results of Geisler et al. (2002) also suggested that volume diffusion of Pb in metamict zircon must be taken into account seriously as a possibility when interpreting recent Pb loss discordias, although a fluid is much more effective in resetting or disturbing the isotopic system of a metamict zircon.

Bowring and Schmitz (2003) reported that zircon analyses which are apparently too young and/or exhibit discordance attributable to Pb loss are also common in the study of volcanic ash beds. Such Pb loss had been inferred from large data sets obtained by both conventional and ion-microprobe analyses (for example, Compston 2000a, b), indicating the various spatial scales of the phenomenon. Experimental measurements of Pb diffusivity in zircon also indicate that Pb loss is not likely dominated by volume diffusion through crystalline zircon (Cherniak and Watson 2000; Lee, Williams, and Ellis 1997), but rather is related to loss from radiation-damaged domains through crystal defects and fractures. While the selection of the best quality, diamagnetic zircons for analyses and the aggressive abrasion of their outer portions would seem to minimize the effects of Pb loss, it is still a problem that can be difficult to recognize without a large number of analyses. Discordance of analyses is obviously the best indicator of Pb loss, but unfortunately, for Late Paleozoic and younger zircons the limited curvature of concordia combined with the imprecision in the measured 207Pb-235U dates can limit the discernment of discordance as an obvious signal of Pb loss.

Another problem is the apparently systematic analytical bias encountered in the application of laser ablation inductively-coupled-plasma mass spectrometry (LA-ICP-MS) to young (<100 Ma) zircons. Sliwinski et al. (2017) noted that where the majority of studied units are young, the LA-ICP-MS zircon U-Pb dates are often discordant with established 40Ar-39Ar eruption ages or high-precision ID-TIMS U-Pb crystallization ages. They argued that the zircon lattice properties, particularly the degree of lattice damage caused by the radioactive decay of U and Th, impart analytical bias by causing differential ablation rates and therefore differential fractionation of U and Pb throughout each analysis. They suggested that although it is possible to normalize the zircon lattice strengths to calibration reference zircons by thermal annealing to some extent, this may not entirely alleviate the problem. Therefore, Sliwinski et al. (2017) examined the effects of α-decay dose (that is, the degree of radiation damage) on analytical biases in age determination by analyzing a number of zircon reference materials under well-constrained analytical parameters. They demonstrated that a regression based, multi-standard correction method improved the accuracy of age data, particularly in young (Cenozoic) zircons. They also introduced a novel data reduction scheme which runs in conjunction with a widely-used platform and performs a correction for α-dose and Th disequilibrium. They found that their scheme improved the accuracy of presumed age data for unannealed zircons, and demonstrated its utility by applying it to zircons from several well-studied units.

Yet another problem is reversed discordance, that is, Pb is gained rather than lost, or U-Pb ages are greater than 207Pb-206Pb ages. (This is further discussed below in the section “Atomic Scale Studies of Diffusion of Pb and U.”) Kusiak et al. (2013) reported that in some well-documented cases (for example, Williams et al. 1984), zircon data are reversely discordant, with U-Pb ages older than 207Pb-206Pb ages. They interpreted this as corresponding to apparent “Pb gain” because strongly lattice-bound U is unlikely to be mobilized. A sub-class of reverse discordance in SIMS analyses, in which Pb/U ratios increase at constant 207Pb/206Pb ratio, is readily detected by horizontal arrays on the inverse (Tera-Wasserburg) concordia diagram (fig. 4) and is attributed to matrix-related ion yield effects in high-U and/ or metamict zircon (for example, White and Ireland 2012; Williams and Hergt 2000). More difficult to explain are cases of reverse discordance in which data points extend along a discordia line with correlated Pb/U and 207Pb/206Pb ratios opposite to the common Pb-loss discordia, as noted for example in SIMS studies of early Archean zircon from Mount Sones in Antarctica (Black, Williams, and Compston 1986; Williams et al. 1984). Such arrays define apparent “Pb gain,” which, in principle, can be explained by ancient redistribution of radiogenic Pb that locally “locks in” higher 207Pb/206Pb and Pb/U ratios than would be expected from the true age and U content (Hinton and Long 1979). Typically, analyses on these arrays are characterized by within-run fluctuations in the secondary Pb ion signal that are independent of the U and Th ion signals (for example, Kelly, Clarke, and Fanning 2004; Williams et al. 1984), indicating Pb heterogeneity on a scale much smaller than a typical SIMS analytical volume.

A number of mechanisms have been proposed to account for this behavior, including localized intra-grain accumulations of radiogenic Pb (Carson et al. 2002), radon migration through radiation damage (Suzuki 1987), U loss (the corollary of Pb gain) via 234U ejection from porous zircon (Romer 2003), or a sputtering effect due to Pb concentration in a silica glass phase in annealed zircon grains (McLaren, FitzGerald, and Williams 1994). Regardless of the precise mechanism, the documentation of reverse discordance and apparent Pb gain, primarily from high-spatial resolution studies, provides a clue to the scale of the process, as it must be small enough to escape detection in relatively high-sample-volume conventional methods of analysis but sufficiently large that heterogeneities will be manifest at the ~15–25 μm scale of a typical SIMS analysis.

Finally, zircon crystals in high-grade metamorphic rocks and igneous rocks of granitic composition, in some cases, contain cores (that are conventionally interpreted as xenocrystic) surrounded by zones of overgrowths which formed later during regional metamorphism or during crystallization of the magmas (Bickford et al. 1981; Silver and Deutsch 1963). Nasdala et al. (1999) reported that overgrowths of zircons in monzonites yielded concordant U-Pb dates which agreed with 40Ar-39Ar dates of amphiboles in the metamorphic rocks hosting those intrusions, whereas the U-Pb dates of the cores ranged from slightly discordant (low U and Th) to highly discordant (high U and Th) and indicated a Proterozoic age. It was concluded that the relationship between the discordance of the U-Pb isotope systematics of the cores and their U and Th concentrations was caused by radiation damage of the crystal lattices, which increases the diffusion rate of radiogenic Pb in zircon. Cherniak and Watson (2000) confirmed that the diffusion coefficient of Pb in zircon is very small, but increases with increasing radiation damage. Therefore, the U-Pb chronometers deviate from concordia depending on the extent of radiation damage. The low diffusion rate of Pb in undamaged zircon overgrowths evidently causes their U-Pb dates to be concordant and gives such zircons a closure temperature in excess of 900°C.

The Impact of Radiation Damage

Even though zircon has proved to be by far the most useful mineral for U-Pb geochronology because it is mechanically and chemically inert, and has one of the highest known blocking temperatures, significant Pb loss from it is common in low temperature environments. The blocking temperature is defined as the temperature at which the loss of Pb by diffusion out of the zircon becomes negligible compared to its rate of accumulation (Faure and Mensing 2005, 82). For zircon it is >1000°C (Flowers et al. 2005). This Pb loss is often correlated with accumulated radiation damage, which of course is related to U concentration. Physical property changes in damaged zircon were well documented by Holland and Gottfried (1955) and expanded on by Murakami et al. (1991).

Holland and Gottfried (1955) and Murakami et al. (1991) distinguished three stages of damage accumulation in zircon:

A pre-metamict Stage I (<3 × 1015 α-decay events per mg); Stage II (3–8 × 1015 α-decay events per mg) during which crystal structure gradually becomes aperiodic and significant physical changes occur, such as reduction in density and refractive index; and Stage III (>8 × 1015 α-decay events per mg) in which the structure becomes entirely aperiodic.

Metamict zircons exhibit a 17% volume expansion, a decrease in refractive index and luster, a darkening of color, and an increasing susceptibility to chemical alteration and dissolution. Where zircons are highly zoned in U, volume changes produce cracks in adjacent less-damaged zones that are perpendicular to growth surfaces (Chakoumakos et al. 1987). Metamict zircon is susceptible to chemical alteration by fluids that can penetrate into the crystal along such fractures and preferentially remove radiogenic Pb (Krogh and Davis 1974, 1975).

Early work by Silver and Deutsch (1963) demonstrated that zircons with the lowest paramagnetic susceptibility (and U level) are the least discordant. Coupled substitution by REEs can potentially explain the correlation between U level and paramagnetism. Krogh (1982a) showed that altered domains tend to be higher in U and more paramagnetic, resulting in a correlation between Pb loss and magnetic susceptibility. Analyses of variably magnetic zircon grains commonly produce linear to quasi-linear arrays of discordant data. Upper concordia intercepts are usually close to the presumed ages of crystallization defined by concordant data from high quality zircons. On the other hand, lower concordia intercepts can be variable in rocks from the same area and usually correspond to no known geologic event (for example, Davis et al. 1985). They probably represent an average age for multiple Pb loss events and may depend on local factors such as the concentration and distribution of U in the crystals, as well as the nature of the host rock in providing access to fluids.

Another possible mechanism for Pb loss, in addition to chemical alteration, is preferential leaching of radiogenic atoms from damaged crystal lattice sites. Radiation damage is largely caused by recoil of nuclei during α-particle emission (Murakami et al.1991). This disrupts crystal bonds in the vicinity of a radiogenic atom, making Pb potentially more leachable than U, which is in undamaged sites. Pidgeon, O’Neil, and Silver (1966, 1973) demonstrated that up to 60% of the radiogenic Pb could be leached from zircon by 2 M NaCl at hydrothermal conditions in the laboratory with minor loss of U. In other studies, significant amounts of radiogenic Pb and U were leached from relatively low U zircon using NaCl and weak nitric acid solutions (Sinha, Wayne, and Hewitt 1992), and even spring water (Hansen and Friderichsen 1989). In some cases, residues moved up the Pb loss line, suggesting dissolution and removal of discordant, previously leached or altered domains. Ewing et al. (2003) helpfully reviewed the status of investigations of the radiation damage in zircons and the mechanisms involved. They reported that although the concentrations of U and Th are generally low in natural zircons (typically <5000 ppm), some zircon crystals are supposedly of great age (the claimed oldest zircon grains being >4 Ga), and thus have calculated doses of >1016 α-decay events per mg, well beyond the dose required for the radiation-induced transformation to the aperiodic, metamict state. In an α-decay event, the α-particle dissipates most of its energy (4–6 MeV for actinides) by ionization processes over the range of 10 to 20 µm, but undergoes enough elastic collisions along its path to produce approximately 100 isolated atomic displacements.

The largest number of atomic displacements occurs near the end of the α-particle trajectory. The more massive, but lower energy, α-recoil (70 keV 234Th from decay of 238U) dissipates nearly all its energy in elastic collisions over only 30–40 nm, transferring enough kinetic energy to cause ~1000 atomic displacements, as calculated by Weber (1993). This creates a “cascade” of atomic displacements in which the total energy can be as much as 1 eV per atom, and whose structure and evolution can only be modelled by computer simulations. The cascade duration is extremely short (<10-12 sec), after which displacements by elastic interactions cease and the cascade gradually loses energy as it cools to ambient temperature, typically “quenching” in nanoseconds. During this cooling phase, relaxation and diffusion reduce the number of displaced atoms in the cascade, and the final damage state consists of a small low-density core surrounded by a halo of interstitials (Brinkman 1954; Slater 1951; Trachenko, Dove, and Salje 2002, 2003).

A single α-decay event generates approximately 700–1200 “permanently” displaced atoms, significantly more than the 0.1 displacements generated per β-decay event (Weber 1993; Weber et al. 1998a). In the decay chain of 238U, there are eight α-decay events; 232Th has six. Because of the large number of atomic displacements during an α-decay event, the accumulation and overlap of individual cascades, as well as the presence of still crystalline but highly-strained domains, there is a dramatic decrease in density (17%), a decrease in birefringence until isotropic, a decrease in elastic moduli (69%), a decrease in hardness (40%), an increase in fracture toughness (Chakoumakos et al. 1987, 1991), and an increase in dissolution rate of one to two orders of magnitude (Ewing, Haaker, and Lutze 1982). Over extended time, the final damage microstructure is both time and temperature dependent because of annealing and recrystallization of damaged and strained domains (Weber, Ewing, and Meldrum 1997). Again, all this only emphasizes the need to avoid metamict zircons for radioisotope dating of rocks if at all possible.

Zircon figured prominently in the earliest studies of the metamict state and radiation damage (Ewing 1994). Von Stackelberg and Rottenbach (1940a, 1940b) had noted changes in density, refractive indices and birefringence with increasing α-decay dose, and even tried to test this hypothesis by irradiating a thin slab of zircon with α-particles. Metamict minerals though remained a mineralogical oddity for over a decade until the systematic review of radiation-induced property changes by Pabst (1952). Hurley and Fairbairn (1953) completed the first systematic study of a suite of increasingly damaged zircon crystals and quantified the amount of damage based on x-ray diffraction data. Although their interpretation was limited by a lack of experimental data (for example, they estimated that 5000 atoms were permanently displaced by each α-decay event), their approach was sound and laid the foundations of later work.

Holland and Gottfried (1955) completed a classic study of the effects of α-decay events on density, optical properties, and unit cell parameters as determined by x-ray diffraction. But further advances in knowledge had to await the development of more controlled irradiation experiments. Accelerated damage techniques, including doping with extremely short-lived actinides that transmuted by α-decay, such as 238Pu with a half-life of 87.7 years (Burakov et al. 2002; Exarhos 1984; Weber 1991; Weber, Ewing, and Wang 1994), neutron irradiation (Crawford and Wittels 1956; Hayashi et al. 1990), and ion beam irradiation (Cartz and Fournelle 1979; Ewing et al. 2000; Wang and Ewing 1992a, 1992b) have been used to great advantage in simulating the α-decay event damage in natural zircon. Ewing et al. (2003) concluded that we now have experimental data from irradiation experiments with dose rates that vary by more than 15 orders of magnitude (displaced atoms per sec) over a range of temperature from –260 to 800°C (Meldrum et al. 1999). Therefore, one can now safely state that there is no other mineral for which there is so much information on the process and effects of radiation damage.

During the1990s there was a small “explosion” of work on radiation damage effects in zircon specifically (Ewing et al. 2000). The experimental work was of three types:

Natural zircon crystals—In these studies, there was generally no lack of material and a wide variety of analytical techniques used. However, the conclusions from them were always limited by a lack of knowledge of the thermal history of the zircon crystals. 238Pu-doped synthetic zircon crystals—These studies were generally conducted under ambient conditions, followed by thermal annealing studies. These were long-term studies lasting several decades. Because of restrictions handling Pu-bearing samples, analytical studies have been limited to simple density determinations, structural analysis using x-ray diffraction, electron microprobe analysis, and some spectroscopic studies. Ion-beam irradiated zircon crystals—In these studies, both heavy- and light-ion irradiations have been completed at precisely controlled temperatures. Although the physics of the damage process allows one to correlate the results to α-decay damage, the experimental configuration had limitations.

In situ irradiations combined with high resolution electron microscopy allowed changes in the atomic-scale structure to be observed in real time, and the dose to be determined at which the material became amorphous as a function of temperature. However, the high surface area to volume ratio of the thin wedge of the electron transparent region may have affected the damage accumulation process as defects migrated to the surface. More recent bulk irradiations, followed by examination of samples cut perpendicular to the surface (parallel to the trajectory of the ion), have allowed damage effects to be followed because the amount of damage varies along the trajectory of the implanted ion. These samples were generally examined by high-resolution transmission electron microscopy (HRTEM) (Lian et al. 2001, 2003) or utilized surface techniques such as x-ray photoelectron spectroscopy (XPS) (Chen et al. 2002). Such studies have provided critical information on oxidation states, defect deformation, and migration mechanisms.

Ewing et al. (2003) maintained that several observations can be drawn from TEM studies which support and clarify the x-ray diffraction results. First, the amorphization process is clearly heterogeneous. Even at low doses there are isolated regions that appear to be amorphous in high-resolution images. The rotated crystalline islands observed by TEM in highly damaged zircon also suggests the presence of considerable strain or shearing due to volume expansion of the amorphous material. Diffuse x-ray scattering also suggests the presence of shear waves in the crystalline lattice (Ríos and Salje 1999).

Furthermore, extended x-ray absorption fine structure (EXAFS) spectroscopy is a sensitive probe of the local coordination and bonding geometry at the nearest neighbor level. Thus, it has been very useful for characterizing the fully-damaged state of zircon. Farges and Calas (1991) and Farges (1994) completed the first detailed EXAFS study of 