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9 - Chronology of Meteorite History
- Kunchithapadam Gopalan
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- Principles of Radiometric Dating
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Summary
The problem then is the identification, within that piece of matter, those observations which can establish the nature and chronology of events whose memory has persisted. Such an approach requires the use of concepts, observations and measurement techniques from rather diverse fields and together define a new field, that of cosmochemistry or cosmophysics
G J WasserburgINTRODUCTION
The last chapter contained a brief description of the processes leading up to the formation and subsequent changes of meteorites in the early Solar System. Figure 9.1 recapitulates the same, and, in addition, includes the later stages or events in the history of meteorites terminating with their capture by the earth.
A plausible list of distinguishable stages/events is:
1. Separation of a parcel of gas and dust from the interstellar medium, and its collapse into the proto-sun and proto-planetary nebular disc.
2. Formation from the cooling solar nebular disc of the precursor materials of chondrites, like CAIs, AOAs, low temperature compounds, and finally chondrules in a cool environment.
3. Accretion of mineral grains in various proportions, and chondrules into km-sized planetesimals (parent bodies of meteorites) including presolar grains directly from the interstellar medium
4. Metamorphism, fluid alteration, recrystallization on a local scale on the surface of, and even melting inside of parent bodies that escaped further growth in size into embryos and eventually planets.
5. Impact brecciation and shock reheating, presumably a few times.
6. Collisional ejection of metre-sized fragments (meteorites) from parent bodies, and their exposure to galactic cosmic rays in space.
7. Capture of meteorites by the earth, and their recovery later by chance (Finds).
8. Capture of meteorites by the earth and their prompt recovery (Falls).
This sequence of events is, of course, very general and meant as a useful framework for discussion. For example, not all stages may be recorded in a single meteorite. Some processes, like metamorphism, may be missing in primitive carbonaceous chondrites. Some events may have overlapped in time. The relative order of at least some of the events is obvious. For example, a carbonaceous chondrite is a nonequilibrium assemblage of refractory inclusions, metal, sulfide, and matrix, each of which formed independently. So, the chondrite should postdate these constituents. A long-range goal of meteorite research is to quantitatively date every stage precisely and accurately.
10 - Chemical Evolution of the Earth
- Kunchithapadam Gopalan
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- Principles of Radiometric Dating
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In astronomy we see things not as they are but as they were. In geology, we see things not as they were but as they are now.
Leon LongThe temporal sequence is converted into a simultaneous co-existence, the sideby- side existence of things into a state of mutual interpenetration … a living continuum in which time and space are integrated.
Tibetan monk, Lama Govinda's religious experience as cited by P DaviesCOMPOSITION OF TERRESTRIAL PLANETS AND CHONDRITIC METEORITES
The close similarity in the abundances of elements heavier than oxygen in chondritic meteorites and the solar atmosphere (Figure 1.5) suggests a chondritic composition as a reasonable assumption for the composition of the inner rocky planets—Mercury, Venus, Earth, and Mars. However, even simple considerations show that there may be important differences in chemical composition between meteorites and the inner planets. For example, Table 10.1 gives the densities of the four terrestrial planets and chondritic meteorites (Brown and Mussett, 1993). The table shows that the terrestrial planets have densities, which when corrected for their different internal pressure, vary significantly from that of chondritic meteorites. In fact, Mars with an uncompressed density of ∼ 3,700 kg m–3 is the only planet which lies in the chondritic range of 3,400–3,900 kg m–3. Earth, Venus, and Mercury are denser than chondrites, and the Earth's moon is less. The only sufficiently abundant element to influence such strong density difference is iron, because its atomic mass 56 is much higher than that of the next three most abundant elements, O(16), Mg(24), and Si(28).
More subtle is the evidence that volatile elements have been systematically depleted in terrestrial planets. Figure 10.1 shows a plot of the ratio of volatile elements, K and Rb to refractory (less volatile) elements U and Sr, respectively, in meteorites, inner planets, and the moon (Halliday and Porcelli, 2001). This shows the volatile depleted nature of the moon relative to the Earth, and the Earth and Mars relative to meteorites. The most depleted ratio in angrites is understandable as they are differentiated meteorites (Chapter 9).
The systematic decrease in iron metal/silicate ratios and systematic variations in ratios of volatile elements to refractory trace elements were probably caused by decreasing condensation pressures and temperatures, respectively, in the solar nebula away from the sun (Brown and Mussett, 1993).
Preface
- Kunchithapadam Gopalan
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- Principles of Radiometric Dating
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The time-dependent accumulation of helium and lead from the radioactive decay of uranium in minerals and rocks was suggested by Rutherford in 1905 as a means of determining their absolute ages. This seminal idea has been assiduously pursued in the last century by unorthodox physicists and chemists to detect and quantitatively measure numerous radioactive isotopes of widely varying lifetimes and abundances in natural systems. Absolute age determination based on these isotopes, called radiometric dating, now plays a central role in a broad range of Earth and planetary sciences: paleoseismology; paleomagnetism; paleooceanography; igneous, metamorphic and sedimentary petrology; geomorphology; geochemistry; tectonics; nucleosynthesis; cosmochemistry; planetary science; geobiology; paleoclimatology; paleoanthropology; and archeology. Assuming that the reader has only college level knowledge of physics, chemistry, and mathematics, this concise book (about 200 pages) focuses on the essential principles of radiometric dating in order to enable the students and teachers in various fi elds to quickly fi gure out the criteria to be met by parent-daughter systems and samples relevant to their specialization. This book draws heavily on three classic review articles which, in my view, capture the intellectual appeal and beauty of the subject for a very wide audience (Wetherill et al., 1981; Wasserburg, 1987; Allegre, 1987). I believe that this book will succeed in improving students’ understanding and appreciation of radiometric dating results generated and published by professionals. I hope it would also stimulate interest in students to take up isotope geology as a serious study and reach out for the excellent and comprehensive books on the subject.
The material presented in each of the 11 chapters is self-contained. However, the reader is urged to read all the chapters, as they are strung together into a concise, continuous, and easily comprehensible narrative to illuminate the subject as a whole. Vital points behind radiogenic isotope chronometry are stressed upon more than once. The reference list is mainly for students interested in further reading.
Chapter 1 covers the basic facts of nuclear and atomic physics, nuclear binding energy as a measure of nuclear stability, and the variety and relative abundance of different elements in the sun and the primitive meteorites. Chapter 2, then, moves on to the transformation of composition of nuclides, either spontaneously (radioactivity) or by external agents (induced nuclear reactions), and highlights the role of feeble natural radioactivity, both in driving and dating planetary processes.
7 - Error Analysis
- Kunchithapadam Gopalan
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- Principles of Radiometric Dating
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The uncertainty of a date is as important as the date itself.
K LudwigINTRODUCTION
The calculation of a radiometric age (strictly speaking, radioactive decay interval) of a natural object is ultimately based on the decrease in the concentration of a parent isotope in that object during the interval. The measurement of the initial and final concentrations (directly or otherwise) in terms of an internationally accepted unit (moles per unit weight of the sample) is always subject to analytical errors or uncertainties. These analytical errors will be reflected (propagated) in the final age result. In this chapter we will consider generally accepted methods of estimating analytical error in a measured quantity, and how it will affect the final result based on this measurement (Cunningham, 1981).
The absolute error in a measurement is the discrepancy between the measured value and its ‘true’ value. Except in the case of counting discrete objects, a measurement of a physical quantity in terms of an internationally-accepted unit will always be subject to an uncertainty. The true value that we are seeking is unknowable, unless it is already known in some other way. So, it is necessary to state from the results within what range of values the true value is likely to occur and the confidence that can be placed on the validity of this statement. The statement of a result without any indication, with a certain confidence, of the range of values bracketing the true value has virtually no significance to end users. The idea of errors is, therefore, not something of only secondary or peripheral interest in an experiment. On the contrary, it is related to the purpose of the experiment, the method of doing it and the relevance of the results to a significant scientific question. The quotation in the beginning of this chapter reflects the importance of error limits to an experimentally measured date or age.
SYSTEMATIC AND RANDOM ERRORS
Before proceeding further on error estimates, we must distinguish between two types of experimental errors—determinate or systematic, and indeterminate or random. Determinate errors generally shift the measured result in one direction with respect to the true value. They are often reproducible, and, in many cases, may be measured, and or corrected for by careful and meticulous experimentation.
Contents
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Principles of Radiometric Dating
- Kunchithapadam Gopalan
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The time-dependent decay of naturally occurring radioactive isotopes or in-growth of their radioactive or stable daughter products form the basis of radiometric dating of several natural processes. Developed in the beginning of the last century mainly to determine the absolute ages of rocks and minerals, radiometric chronology now plays a central role in a broad range of Earth and planetary sciences - from extra-solar-system processes to environmental geoscience. With the prerequisite of only college-level knowledge in physics, chemistry and mathematics, this concise book focuses on the essential principles of radiometric dating in order to enable students and teachers belonging to diverse fields of studies to select, understand and interpret radiometric dating results generated and published by professionals.
3 - Nucleosynthesis
- Kunchithapadam Gopalan
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I think there should be a law of Nature to prevent a star from behaving in this absurd way.
Arthur EddingtonINTRODUCTION
The variety and relative abundances of the 90 elements in the Solar System must have been produced somewhere else before its formation about 4.6 by ago. The earliest time some or all of them could have been produced somewhere is 13.7 billion of years ago when the universe is believed to have originated in a spectacular explosion—Big Bang—of what is known as a singularity in cosmological parlance. At least three sets of observations support the Big Bang theory.
1. Expanding universe Hubble discovered that galaxies are receding from each other at a speed proportional to the distance between them, based on red shifts of light coming from distant galaxies. This implies that at some time in the past all the matter in the universe must have been concentrated at one point.
2. Big Bang nucleosynthesis According to the Standard Cosmological model, the matter in the universe 30 minutes after the explosion must have consisted mostly of hydrogen (H) and helium (He) with only traces of deuterium (2H) and helium (3He), as confirmed by recent observations.
3. Cosmic microwave background Theory also predicts that the universe must now be filled with an isotropic background radiation in the microwave region of the electromagnetic spectrum as a relic of the initial radiation from the Big Bang. Penzias and Wilson (Penzias and Wilson, 1965) have indeed detected such a cosmic microwave background radiation corresponding to black body emission at 2.7 K.
The predicted sequence of events within the first 3 minutes of the Big Bang, according to the Standard Cosmological model, is given in Table 3.1.
STELLAR NUCLEOSYNTHESIS
For geologists used to events on a time scale of at least a few thousand years, incredibly short time intervals like 10–50, 10–43, and 10–35s make no sense. Even a comparatively much longer time interval like 10–10 s is so short that light with a velocity of as high as 3,00,000 kilometres per second will cover just about 3 centimetres in this interval. The important point for geologists to note is that Big Bang, or cosmological nucleosynthesis, was restricted to only H and He and to within the first 3 minutes.
1 - Basics
- Kunchithapadam Gopalan
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- Principles of Radiometric Dating
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11 - Chronology of Earth History
- Kunchithapadam Gopalan
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Geology is the study of complex natural experiments conducted on a large scale in both time and space. The experiments are neither reversible nor repeatable. They cannot be directly observed; but they must be reconstructed historically.
S A SchummWe view samples of the accessible universe as a library of experiments that have already been done (at different times and sites). Our art must be to select those materials which have a persistent memory and which together can bring testimony to the natural experiment of interest.
G J WasserburgINTRODUCTION
Simply stated, the present Earth is very different from the early Earth. The main objective of geology is to reconstruct the time sequence and nature of the key or major processes that shaped the Earth over 4.5 Gy. Schumm (1991) cautions that this task will be quite formidable by quoting a metaphorical statement of Pretorius in a different context, as follows:
It is the nature of the history of the earth that a geologist has available to him only partial information. Occasional lines from disconnected paragraphs in obscuranist chapters are what can be read. Violence in the handling of the book through time has caused many of these chapters to be ripped and reassembled out of context. That the gist of early chapters can be deciphered at all is a credit to the perseverance and imagination not always associated with other sciences. The geologist operates at all times in an environment characterized by a high degree of uncertainty and ornamented with end products which are the outcomes of the interactions of many complex variables. He sees only the end, and has to induce the processes and responses that filled the time since the beginning.
To extend this metaphor further, some of the missing pages of the book of genesis of the Earth may have to be found in the libraries of experiments carried out on other planets.
In this chapter we will consider how radiogenic isotope geochemistry has provided firm constraints on the timing of some major or large scale events in Earth's history.
Index
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8 - Meteorites: Link between Cosmo- and Geochemistry
- Kunchithapadam Gopalan
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It is as if Nature had taken a sample at each step of the planetary formation process, had kept it intact somewhere for 4.5 billion years, and had finally sent it to us from the sky so that we could study it in our laboratories
C J AllegreINTRODUCTION
From the point of view of a present-day observer in the Solar System, the time scale of the universe can be split into two major subdivisions—presolar and solar—as shown schematically in Figure 8.1. The presolar period begins with the big bang at time to (as measured from the present) and ends with the isolation from the Interstellar Medium (ISM) at time tt of a small portion of the dust and gas in the ISM to form the Solar System. The immediately following solar era begins at time ti with the formation of the solar nebula as a separate entity, and ends at the present time. Within these two broad time zones, one can distinguish discrete events and protracted processes even if some of the processes are yet unfamiliar. For example, the presolar era includes the cosmological or primordial synthesis of hydrogen (H) and helium (He) immediately after the Big Bang, formation of galaxies, synthesis of heavier elements from H and He in the interior of stars, and its termination in the material destined to form the Solar System. The solar era comprises the collapse of the isolated gas cloud into a central massive body (the potential sun) and a thin disc around the central object, condensation of the material in the disc into chemical compounds at tc, aggregation and accretion of the chemical species into the planets and other objects of the solar system at ta, and subsequent internal evolution of individual planets to the present time.
As geologists recognized the immensity of geologic and, hence, the solar time from observations of large scale geologic structures and processes, astronomers and astrophysicists relied on observations of large scale structures in the universe, like stars, star clusters, and galaxies to infer an even longer presolar time scale. The best known of such indirect dating methods is the mutual recession of galaxies, as evidenced by their spectral red shift. The most precise result, so far, for the Big Bang, as based on the rate of expansion of the universe, is 13.4 ±1.6 Ga (Lineweaver, 1999).
Frontmatter
- Kunchithapadam Gopalan
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Acknowledgments
- Kunchithapadam Gopalan
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2 - Nuclear Transformations
- Kunchithapadam Gopalan
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Summary
The discovery of radioactivity provided an additional (and continuous) heat source for earth's interior and revolutionized studies of earth history by permitting quantitative dating.
C H Langmuir and W Broecker (2012)INTRODUCTION
Certain nuclides with a specific combination of protons and neutrons may transform spontaneously or be transformed by external agents to another nuclide with a different combination of neutrons and protons. We will consider such transformations as relevant to radiometric dating in the present chapter.
SPONTANEOUS NUCLEAR TRANSFORMATIONS
Radioactivity
The spontaneous transformation or decay of a potentially unstable nuclide to a more stable nuclide is called radioactivity. The energy released by the decay is carried mainly by particles and radiation. The decaying nuclide and its product nuclide are customarily labelled parent (p) and daughter (d), respectively. If d is radioactive, it decays to another nuclide until a stable d is produced. The nuclear decay process obeys the following conservation laws of Physics: (1) Mass/energy, (2) Electric charge, (3) Linear momentum, (4) Angular momentum, and (5) Nucleon number (Kaplan, 1955; Beiser, 1973; Leighton, 1959).
It was noted in the first chapter that stable nuclides define a narrow band in a Z vs N plot (Figure 1.3) corresponding to the greatest stability of Z/N ratio as a function of N. Unstable nuclei that deviate from the path of stability eventually transform into stable nuclei by different decay modes and rates. A diagonal section across the path of the stability valley will contain isobaric nuclides with the most stable isobar in or close to the path. Neutron-rich isobars will fall below the path and proton-rich isobars above it. Unstable nuclides heavier than 209Bi along the path are also neutron-rich. Although nuclides decay in many modes, the modes most common and relevant to radiogenic isotope geochronometry are few (Dalrymple, 1991), and are shown in Figure 2.1.
Beta (β-) decay
Neutron-rich nuclei below the stability zone reach stability by converting one of their neutrons into a proton, an electron (β-), and an antineutrino (v), and then emitting the latter two. The electron created in the nucleus just before its emission is called a beta or b particle to distinguish it from an orbital or extra-nuclear electron.
5 - Radioactivity and Radiometric Dating
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References
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Dedication
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4 - Isotopics
- Kunchithapadam Gopalan
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The beginning of wisdom is to call things by their right names.
ConfuciusINTRODUCTION
The basic measurement in isotope geochemistry is the quantitative variation of the relative and absolute numbers of isotopes of an element caused by natural physical and chemical processes and created artificially in the laboratory. This chapter deals with various topics related to this end.
ISOTOPIC ABUNDANCE
The fundamental unit of chemistry is the atom or molecule. It is, therefore, necessary to be able to measure and express the number of atoms or molecules in a chemical system (natural or artificial). However, the numbers of atoms, or atomic groups (molecules), even in a very small chemical system are far too numerous to be counted. For example, just one microgram of sodium chloride (NaCl) will contain ∼1016 sodium chloride molecules, each with one sodium and one chlorine atom. Chemists have, thus, developed a practical method to count such enormous numbers of chemical units by simply weighing them. This is based on the fundamental atomic theory that equal numbers of any atom will be contained in one gram atomic weight (atomic weight expressed in grams) of its element. This ‘equal number’, measured experimentally, is 6.023 × 1023, and is called the Avogadro's number after its discoverer.
The fundamental unit of isotope chemistry is the isotope or isotopic molecule. Numbers of isotopes of an element will also be far too numerous to count, like atoms in a chemical system. So, like the gram atomic weight in chemistry, it is more convenient to use, in isotope chemistry, the unit ‘mole’ (gram molecular weight) defined as the amount of material which contains as many particles as there are carbon (C) atoms in exactly 12 gram of pure 12C. This number is the Avogadro's number, 6.023 × 1023. This definition emphasizes that the mole refers to a fixed number of any type of identical items (e.g. mole of electrons, mole of molecules, or even a mole of men). The product of mole and Avogadro's number gives the number of a given isotope in a chemical system, and the product of mole and atomic weight of the isotope gives the mass of that isotope in atomic mass units in the system. The definition of a mole permits the calculation of the value of the unified atomic mass unit, u.
6 - Mass Spectrometry and Isotope Geochemistry
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Much of the most promising modern Earth Science depends on the measurements and observations that can no longer be obtained with a hammer, Brunton compass, and hand lens alone. Although much that is important is still being done and will continue to be done in this way by first class minds, new expensive and frequently unavailable instrumentation is called for
Preston Cloud.INTRODUCTION
Basic analytical measurements in isotope geochemistry are absolute and relative abundances of isotopes of an element available in a solid, liquid, or gaseous form. X-ray Fluorescence (XRF) Spectrophotometer, Atomic Absorption Spectrophotometer (AAS), Inductively Coupled Plasma Atomic Emission Spectrophotometer (ICP-AES), and Electron Probe Micro Analyzer (EPMA) are commonly used for elemental analysis (Potts, 1987). These instruments rely on the excitation of orbital electrons and detection of the resulting emission of radiation, or absorption of external radiation, characteristic of each element. Isotopes of an element have the same electronic structure (Chapter 1), and, hence, are not distinguished by the above instruments. Mass sensitive instruments, called mass spectrometers, have become the preferred instruments for isotope geochemistry (De Laeter, 1998). Many types of mass spectrometers have been developed over the last century, but most of them consist of three main components:
1. An ion source for production, acceleration, and collimation of ions of different isotopes of an element(s);
2. A mass analyzer for separation of ions according to their mass/charge (m/e) ratio in space or time; and
3. A detector for the collection and measurement of mass-separated ions, sequentially or simultaneously.
PRINCIPLES OF MASS SPECTROMETRY
Figure 6.1 is the schematic of a very old design of a mass spectrometer (Dempster, 1918) showing all the three basic components. Consider a beam of two singly charged isotopic ions ‘a’ and ‘b’ of mass ma and mb (ma + δm), respectively, produced with negligible kinetic energy in front of a stack of metal plates with narrow rectangular slits, known as the ion source. The beam is accelerated by falling through a potential of V volts distributed between the plates of the ion source, and collimated to emerge as a narrow rectangular beam from the final slit of width, ws, called the Source Slit (SS).