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- Herausgeber: Wiley-VCH
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
This first book to discuss both separation chemistry and mass spectrometry for mineral and rock analysis compares the two frequently used techniques, analyzing both their scope and limitations by way of numerous practical examples.
The excellent and highly experienced author adopts a comprehensive and systematic approach, reviewing all the steps involved in an analytical workflow. In addition to thermal ionization mass spectrometry (TIMS), he also discusses applications of ICP-MS. Furthermore, alongside detailed protocols on sample preparation and mass spectrometric measurements, numerous practical hints are given.
A must-have handy guide for all isotope geochemists and anyone involved in isotope analysis.
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Seitenzahl: 694
Veröffentlichungsjahr: 2015
Ähnliche
Table of Contents
Related Titles
Title Page
Copyright
Dedication
Preface
Chapter 1: Analytical Geochemistry
1.1 Overview of Analytical Geochemistry
1.2 Element Synthesis in Stars
1.3 Errors
Chapter 2: Basics and Principles of Sample Digestion
2.1 Clean Technologies, Powdering, and Weighing of Sample Powder
2.2 Materials Used in Laboratory
2.3 Characterization of Elements
2.4 Sample Digestion Techniques
2.5 Fluoride Formation in Silicate Digestion and Coprecipitation Issues
Chapter 3: Basics and Principles of Chemical Separation
3.1 Ion Exchange Chromatography
Chapter 4: Mass Spectrometry
4.1 Introduction
4.2 Vacuum Techniques
4.3 Basics and Principles of an Ion Source
4.4 Basics and Principles of Mass Separators
4.5 Principles and Operation of Ion Detectors
4.6 Various Mass Spectrometers
Exercise
Chapter 5: Techniques in TIMS
5.1 Data Evaluation in TIMS
5.2 Data Acquisition and Calculation in TIMS
Chapter 6: Application of TIMS to Isotopic Ratio Analysis of Each Element
6.1 Precise Isotopic Measurement of Li
6.2 Precise Isotopic Measurement of B
6.3 Precise Isotopic Measurement of Mg
6.4 Precise Isotopic Measurement of S
6.5 Precise Isotopic Measurements of Cl and Br
6.6 Precise Isotopic Measurement of K
6.7 Precise Isotopic Measurement of Ca
6.8 Precise Isotopic Measurement of Ti
6.9 Precise Isotopic Measurement of V
6.10 Ultraprecise Isotopic Measurement of Cr
6.11 Precise Isotopic Measurement of Fe
6.12 Precise Isotopic Measurement of Ni
6.13 Precise Isotopic Measurement of Cu
6.14 Precise Isotopic Measurement of Zn
6.15 Purification Methods of Ga, In, and Tl
6.16 Precise Isotopic Measurement of Ge
6.17 Precise Isotopic Measurement of Se
6.18 Precise Isotopic Measurements for the
87
Rb–
87
Sr and
147
Sm–
143
Nd Isotope Systems
6.19 Precise Isotopic Measurements of Zr
6.20 Precise Isotopic Measurement of Mo
6.21 Precise Isotopic Measurement of Ru
6.22 Precise Isotopic Measurement for
107
Pd–
107
Ag Isotope System
6.23 Precise Isotopic Measurement of Cd
6.24 Precise Isotopic Measurement of Sn
6.25 Precise Isotopic Measurement of Sb
6.26 Precise Isotopic Measurement of Te
6.27 Precise Isotopic Measurement for
138
La–
138
Ba and
138
La–
138
Ce Isotope Systems
6.28 Ultra-Precise Isotopic Measurement for
146
Sm–
142
Nd Isotope System
6.29 Precise Isotopic Measurements of REEs by TIMS
6.30 Precise Isotopic Measurement for
176
Lu–
176
Hf Isotope System
6.31 Chemical Separation of Ta
6.32 Precise Isotopic Measurement for
182
Hf–
182
W Isotope System
6.33 Precise Isotopic Measurement for
187
Re–
187
Os and
190
Pt–
186
Os Isotope Systems
6.34 Precise Isotopic Measurement of Ir
6.35 Precise Isotopic Measurement of Pb
6.36
226
Ra Determination by Total Evaporation TIMS (TE-TIMS)
6.37 Precise Isotopic Measurement for
230
Th/
232
Th
6.38 Precise Isotopic Measurement for
235
U–
231
Pa Disequilibrium Studies
6.39 Precise Isotopic Measurement of U
Chapter 7: Conclusions
Appendix A: Bulk Analysis and Spot Analysis
Appendix B: Laser Ablation-Inductively Coupled Plasma Mass Spectrometry (LA-ICP-MS)
References
Index
End User License Agreement
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Guide
Table of Contents
Preface
Begin Reading
List of Illustrations
Chapter 1: Analytical Geochemistry
Figure 1.1 Classification of igneous rocks by SiO
2
and Na
2
O + K
2
O abundances. The classification is after Le Maitre [8]. The discrimination line between alkaline and subalkaline is after [9].
Figure 1.2 Schematic diagram of the scanning electron microscope (SEM). The electron beam is produced at the top of the column, and the shape of the electron beam is reformed using electron lenses and apertures. Finally, the beam is projected onto the sample. The electron beam is scanned over a small area, and the secondary electrons, scattered electrons, and the characteristic X-rays are detected by electron detectors and an X-ray detector, respectively. A semiconductor detector is used for X-ray detection. This configuration is called the energy dispersive spectrometry (EDS). The merits of SEM-EDS are (i) the spectra for all elements are recorded in one scan, so measurement time is very short; (ii) secondary and backscattering electron images are better than that of an electron probe micro analyzer (EPMA) (see Figure 1.3), because the detector positions are designed to collect these electrons; and (iii) the price of SEM-EDS is on-third to one-fourth of that of EPMA. In case that the electron beam does not cover the whole sample, an
x–y
stage is equipped to move the whole sample.
Figure 1.3 Schematic diagram of electron probe micro analyzer (EPMA). The electron gun, lenses, apertures are almost the same as those of SEM. The difference is in the collection and determination of characteristic X-rays. Characteristic X-rays emitted from the sample are diffracted by the crystals and collected by X-ray detectors. The position and material of the diffracting crystals are changed according to the wavelengths of characteristic X-rays of the target elements. This is called the wave length dispersive spectrometry (WDS). Five sets of diffracting crystals are maximally placed, and 10 elements can be determined in two scans. The merits of WDS are (i) the resolution of the characteristic X-ray is higher; therefore (ii) the background is lower; and (iii) X-ray diffraction is independent of the detector. Therefore, the diffracting crystal and the detector are chosen separately. Thus (iv) detection and diffraction correction are independent of the X-ray wavelength. Spot analysis of EPMA is simple. The polished and carbon-coated sample is set on the sample stage. The sample is bombarded by the electron beam, and the characteristic X-rays are measured. If more than five elements are to be measured, the diffraction crystals and their positions are changed, and the characteristic X-rays are measured again. The concentration is calculated by a so-called ZAF correction method using standard materials. Z, A, and F mean influences from the atomic number, X-ray absorption, and secondary fluorescence, respectively. The precision of elemental analysis is highly dependent on the standard materials. The stage is moved along the
x
and
y
directions on the
x–y
stage. The scanning (mapping) analysis is a feature of SEM-EDS and EPMA. The measurement time of each point is the X-ray integration time. Scanning measurement by WDS takes a very long time, and therefore only the spot analysis should be done by WDS. The size of the X-ray is 2.5 µm in diameter, and therefore a scanning stage of <2.5 µm is meaningless.
Figure 1.4 Schematic diagrams of (a) an X-ray fluorescence spectrometer and (b) a gas proportional counter. X-rays produced by the X-ray tube are made to fall on a sample bead. A Rh anode X-ray tube is often used. Secondary characteristic X-rays are emitted from the sample. X-rays are collimated onto the diffracting crystal by the primary collimator. From the entrance of the primary collimator to the detector, the chamber is kept in vacuum. Then the beams enter the diffracting crystal. There are various crystals suitable for the energy of X-rays, such as LiF, pentaerythritol crystal (PET), thallium acid phthalate crystal (TAP), and so on, and crystals can be exchanged easily without breaking the vacuum. The diffracted characteristic X-rays are measured by (b) a gas flow proportional counter, which counts the pulses. The counter is a metal box filled with a mixture of Ar and CH
4
. There are two windows made of PP (polypropylene) film for X-ray input and output. There is a wire in the center to which a high voltage is supplied and the preamplifier is connected. When X-rays fall on the counter, they ionize the gas and electrons are generated and amplified. Thus an electric pulse is counted. In a modern XRF spectrometer, wavelengths of characteristic X-rays of each element are automatically chosen, characteristics of the counter are automatically compensated, and deconvolution of peak overlaps is automatically performed.
Figure 1.5 Geochemical categorization of elements by Goldschmidt.
Figure 1.6 REE pattern of meteorites. Data are from Makishima and Masuda [12].Murchison, Granes, Holbrook, Barwise are CM2, L6, L6, and H5 chondrites, respectively. Camel Donga, Juvinas, and Millbillillie-1 are eucrites. The vertical axis shows the normalized value to CI chondrite [13]. All data were obtained by isotope dilution-thermal ionization mass spectrometry (ID-TIMS).
Figure 1.7 Definition of the 3
σ
detection limit.
Figure 1.9 Schematic diagram of inductively coupled plasma atomic emission spectrometer (ICP-AES). The temperature of the plasma is so high that most elements are atomized or ionized and emit various wavelengths of lights characteristic of the elements. The emitted light is collected, diffracted by a monochromator, and detected. The number of available elements in ICP-AES is much larger than in an atomic absorption spectrometer. Especially, geochemically important rare earth elements (REEs), such as La, Ce, …, Yb, and Lu) can be measured by ICP-AES. Thus ICP-AES is used widely.
Figure 1.10 3
σ
detection limits of ICP-AES for each element.
Figure 1.8 Inductively coupled plasma torch. Ar gas as a cooling gas, as an auxiliary gas, and as a sample gas is supplied to the plasma torch. The innermost sample gas carries an aerosol of a sample solution. The load coil, through which cooling water is circulated, surrounds the apex of the torch and supplies energy to the inductively coupled plasma. The inductively coupled plasma is Ar plasma at atmospheric pressure, and therefore handling is easy.
Figure 1.11 3
σ
detection limits of ICP-QMS for each element.
Figure 1.12 Example of the primitive mantle-normalized trace element patterns (PM-normalized trace element patterns) of the Horoman peridotite samples. Horoman is a peridotite massif located in the northern island, Hokkaido, Japan. The samples are plagioclase lherzolites and harzburgites. DMM means hypothetical Depleted MORB source Mantle.
Figure 1.13 Conceptual diagram of isotope dilution.
Figure 1.14 Error magnification. This function takes a minimum value of 1.25 at
R
= 8.32.
Figure 1.15 Biochemically important elements. “Essential” means essential elements to life. “Toxic” is toxic elements to life. “Useful (drugs, etc.)” indicates useful elements used in drugs, therapies, and so on. The data is mainly based on Crichton [26]. Lithium has psychopharmacological effects. Titanium is used for supporting fractured bones. Radioactive Ga isotope is used for tumor analysis of the whole human body. Zirconium, Pd, Ag, Pt, and Au are used in dental therapy. Barium and Gd are used for X-ray and magnetic resonance imagings (MRIs), respectively. Radium is contained in some hot springs.
Chapter 2: Basics and Principles of Sample Digestion
Figure 2.16 Schematic diagram of a separation method of fluorophile/oxophile elements.
Figure 2.17 Schematic diagram of preconcentration of Zr, Nb, Mo, Hf, Ta, and W by the Ti addition method.
Figure 2.18 Schematic diagram of analytical flows of elemental analysis – 1.
Figure 2.19 Schematic diagram of analytical flows of elemental analysis – 2.
Chapter 4: Mass Spectrometry
Figure 4.1 Schematic diagram of Pirani gauge.
Figure 4.2 Schematic diagram of a Penning gauge.
Figure 4.3 Schematic diagram of an ion gauge.
Figure 4.4 Cross section of a rotary pump.
Figure 4.5 Operation of the rotary pump. (a) Introduction of the gas has just started in the left side. Exhaust of the gas in the right side is almost finishing. (b) The gas goes into the left side, and the exhausting of the gas in the right side will start soon. (c) The maximum position for the gas introduction into the left side. The gas is exhausted on the right side. (d) The gas is introduced into the left side. The introduced gas will be exhausted soon on the right side.
Figure 4.6 Inside of an oil diffusion pump.
Figure 4.7 Cross-section of a turbo molecular pump.
Figure 4.8 Inside of an ion pump. (a) Ion pump. (b) Principle of operation.
Chapter 6: Application of TIMS to Isotopic Ratio Analysis of Each Element
Figure 6.20 Th amounts (ng) versus intermediate precision (2
σ
%), after Makishima
et al
. [334]. Solid squares, solid circles, and open squares represent the intermediate precision of Th with and without
229
Th acquisition and JB-2, respectively [334]. Each letter represents the intermediate precision of the previous studies. A [335], B [331], C [336], and D [337] were obtained by MC-ICP-MS, and E [332] was by TIMS.
List of Tables
Chapter 2: Basics and Principles of Sample Digestion
Table 2.5 Optional elemental addition techniques in the analyses of insoluble fluoride-forming elements and fluorophile elements
Chapter 4: Mass Spectrometry
Table 4.3 Vacuum pump suiTable for each range of pressure
Chapter 6: Application of TIMS to Isotopic Ratio Analysis of Each Element
Table 6.31 Sequential separation methods of Rb, Sr, Sm, and Nd [235]
Table 6.36 Three-stage column chemistry for separation of Zr by Münker
et al.
[240]
Table 6.61 Purification method of
233
Pa from
237
Np by Shen
et al.
[339]
Table 6.64 Cup configurations for U in MC-ICP-MS by Makishima
et al.
[334]
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Akio Makishima
Thermal Ionization Mass Spectrometry (TIMS)
Silicate Digestion, Separation, and Measurement
Author
Prof. Dr. Akio Makishima
Okayama University at Misasa
Institute for Study of the Earth's Interior
Yamada 827
682-0193 Misasa, Tottori
Japan
Image Credit
NASA/CXC/U.Texas
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Print ISBN: 978-3-527-34024-8
ePDF ISBN: 978-3-527-69642-0
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Mobi ISBN: 978-3-527-69643-7
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Cover Design Grafik-Design, Schulz
This book is dedicated in memory of the late Prof. Akimasa Masuda
Preface
To explain or understand all modern analytical techniques used in earth sciences is very difficult. A Handbook of Silicate Rock Analysis by P.J. Potts [1] is a milestone in this subject. Handbook of Ion Exchange Resins: Their Application to Inorganic Analytical Chemistry by Korkisch [2–6] is another landmark in analytical chemistry. Since then, few books have appeared that introduce modern silicate analytical techniques from sample digestion and elemental separation to the state-of-the-art thermal ionization mass spectrometry (TIMS).
The purpose of this book is to serve as a guide for silicate sample digestion, target element separation from the silicate sample, and precise elemental and isotopic measurements using TIMS. (If the ion source and mass spectrometry are presented as nonhyphenated as in “TIMS” and “SIMS,” “ICP-MS” should be presented as “ICPMS”; however, this book is not unified.)
For this purpose, the first half of this book (Chapters 1–5) presents overviews of sample digestion, chemical separation of the target element, and mass spectrometry. This book intentionally emphasizes TIMS because there have been few books treating TIMS techniques in a comprehensive manner.
TIMS can give accurate analytical data because (i) the variation of the energy of ions produced by thermal ionization is much smaller than that by ICP or sputtering, which are used in ICP-MS (inductively coupled plasma mass spectrometry) and SIMS (secondary ion mass spectrometry), respectively; (ii) the formation of molecular ions in TIMS is far less than in ICP-MS and SIMS, resulting in more accurate data; and (iii) element separation can be further performed on the filament by the difference in evaporation temperatures of the target and the interfering elements.
Although there are such merits in TIMS, two weak points also exist. One is that TIMS selects elements. There are several elements for which TIMS is not a good choice because the ionization efficiency of the target elements is too low. This basic problem has been significantly overcome by the development of negative-thermal ionization mass spectrometry (N-TIMS). The other weak point is that TIMS requires wet chemical separation, including column chemistry. However, this point is actually not true.
The second point is related to the question why ICP-MS is preferred to TIMS. It is erroneously believed that we should get relief from abhorrent wet chemistry. However, state-of-the-art chemical separation methods are available in the application of multicollector-inductively coupled plasma mass spectrometry (MC-ICP-MS). MC-ICP-MS requires similar or severer separation chemistry compared to TIMS because all elements in the plasma are ionized simultaneously, so the final sample needs to be as pure as possible.
Applications of TIMS are divided into three purposes. The first one is “elemental abundance determination” with the isotope dilution (ID) method. The second is “precise isotopic ratio analysis,” which is used for absolute atomic weight determination, radiogenic isotope ratio determination, and detection of isotopic anomalies. The third is “isotopic fractionation measurement” in inorganic elements with or without a double-spike technique. Both the first and second applications are required in age dating in earth sciences.
The first application has been replaced by Q-pole type inductively coupled plasma mass spectrometry (ICP-QMS), even though its precision is slightly lower than that of TIMS. For the third application, MC-ICP-MS is competing with TIMS, with an advantage that the isotopic fractionation of two-isotope elements, to which the double-spike method cannot be applied, can be determined by a standard sample bracketing (SSB) method.
Silicate sample digestion cannot avoid using hydrofluoric acid (HF), and HF makes insoluble fluorides. This book stresses the formation of fluorides and emphasizes their effects in elemental separation and trace element measurements.
The last half of this book (Chapter 6) gives chemical separation and TIMS measurement element by element. The author chose simple but robust chemistry for each element from many methods. The author takes pride in the choice because he himself has been developing separation methods of many elements over the past 30 years knowing both the merits and demerits of TIMS and ICP-MS. The author's comments and opinions occasionally appear as “the author's monology” or “AM” in this book. The author has included many ideas of analytical chemistry.
We cannot neglect the progress of ICP machines. The standing point of the author is not exclusion but co-prosperity with ICP-MS. Their analytical techniques as well as the performances are included in this book in a positive manner. Therefore, each section in Chapter 6 has a subsection on MC-ICP-MS.
The target of this book is silicate samples for earth sciences; however, if silicates can be analyzed, ceramics and environmental samples such as high-tech materials, sea and river water, soils, or biological samples such as bone, urine, or serum can also be analyzed by similar techniques.
Spot analytical techniques have improved, and their importance is growing day by day. Spot analyses are beyond the scope of this book, but are explained briefly in the Appendices. However, such analyses require standard materials, which need to be analyzed and certified by wet chemical techniques. Therefore, if you master or at least understand the wet chemical techniques using TIMS, you have a great advantage in your research, and even in your carrier.
The book is for graduate students, laboratory technicians, and professors in geology, geochemistry, environmental sciences, oceanology, or even biochemists, who want to know “What is TIMS?,” “What can TIMS be applied to?,” or “How to utilize TIMS?.”
The modern trend is to use green chemicals or chemistry. Unfortunately, many chemicals used in this book are nongreen. We cannot help avoid nongreen chemicals, but they could be banned or would require elaborate documentation under severer control in the near future. In this book, nongreen chemicals are highlighted because you should know them at the stage of research planning.
This book mainly cites research papers from 1995 to 2014 but skips many older references as common knowledge, because literature older than 1995 may be found in the masterpiece by Platzner [7].
Misasa
April 2015
Akio Makishima
Chapter 1Analytical Geochemistry
1.1 Overview of Analytical Geochemistry
In this chapter, we reconsider why we determine the concentration of elements or isotopic ratios in silicate materials. In this book, the application of analytical chemistry techniques to earth sciences is named as “analytical geochemistry.”
The purposes of the analytical geochemistry are to reveal the distribution of elements and to unravel origin and evolution of the solar system including the Earth, the Moon, other planets, asteroids, dwarf planets, and comets from atomic scale to solar system scale, namely, from nanometer to tetrameter scales (the SI prefixes are summarized in Table 1.1).
Table 1.1 SI prefixes
10
18
Exa
E
10
15
Peta
P
10
12
Tera
T
10
9
Giga
G
10
6
Mega
M
10
3
Kilo
k
10
−3
Milli
m
Empirical expression
10
−6
Micro
μ
µg g
−1
= ppm
10
−9
Nano
n
ng g
−1
= ppb
10
−12
Pico
p
pg g
−1
= ppt
10
−15
Femto
f
fg g
−1
=ppq
10
−18
Atto
a
Empirical expressions are sometimes used, but they are not recommended.
It is easy to say but difficult to accomplish. In order to reach the result, we need a strategy. It took more than a century to establish five strategies in analytical geochemistry. To execute these strategies, we had to wait for developments of analytical methods. In other words, the evolution of the analytical methods was directly related to the evolution in analytical geochemistry and earth sciences. The evolution includes the new strategies to determine as many elements as possible, to measure isotopic ratios as precisely as possible, and to analyze as small an amount of the samples as possible. For example, TIMS (thermal ionization mass spectrometry) is one of the analytical methods that seemed to satisfy the requirements of analytical geochemistry. In this chapter, the strategies in analytical geochemistry are briefly reviewed.
We have five strategies in analytical geochemistry: (i) major element geochemistry; (ii) trace element geochemistry; (iii) determination of mass fractionation; (iv) age dating; and (v) radiogenic isotopes for geochemical tracers.
1.1.1 Major Element Geochemistry
When geochemistry started, the strategy was only to determine the bulk major elements using classic wet chemistry. Then the classification of rocks was the first thing we would do. For the classification of igneous rocks, the use of a TAS (total alkali versus silica) diagram was one of the most common way (see Figure 1.1). This plots SiO2 versus Na2O + K2O abundances. Classifying the rocks is simple but important, but precise determination of the major elements is required.
Figure 1.1 Classification of igneous rocks by SiO2 and Na2O + K2O abundances. The classification is after Le Maitre [8]. The discrimination line between alkaline and subalkaline is after [9].
In order to replace the time-consuming and complex classic wet chemistry, X-ray fluorescence spectroscopy (XRF, see Section 1.1.1.1) was invented, which has been widely used since then. Furthermore, in order to observe and determine the major elements in spot areas, secondary electron microprobe with the energy dispersive spectrometry (SEM-EDS; see Figure 1.2) and electron probe micro analysis (EPMA; see Figure 1.3) were developed. The geochemists today first observe, describe, and analyze using these techniques to retrieve as much as possible the phase and information on the major elements from samples.
Figure 1.2 Schematic diagram of the scanning electron microscope (SEM). The electron beam is produced at the top of the column, and the shape of the electron beam is reformed using electron lenses and apertures. Finally, the beam is projected onto the sample. The electron beam is scanned over a small area, and the secondary electrons, scattered electrons, and the characteristic X-rays are detected by electron detectors and an X-ray detector, respectively. A semiconductor detector is used for X-ray detection. This configuration is called the energy dispersive spectrometry (EDS). The merits of SEM-EDS are (i) the spectra for all elements are recorded in one scan, so measurement time is very short; (ii) secondary and backscattering electron images are better than that of an electron probe micro analyzer (EPMA) (see Figure 1.3), because the detector positions are designed to collect these electrons; and (iii) the price of SEM-EDS is on-third to one-fourth of that of EPMA. In case that the electron beam does not cover the whole sample, an x–y stage is equipped to move the whole sample.
Figure 1.3 Schematic diagram of electron probe micro analyzer (EPMA). The electron gun, lenses, apertures are almost the same as those of SEM. The difference is in the collection and determination of characteristic X-rays. Characteristic X-rays emitted from the sample are diffracted by the crystals and collected by X-ray detectors. The position and material of the diffracting crystals are changed according to the wavelengths of characteristic X-rays of the target elements. This is called the wave length dispersive spectrometry (WDS). Five sets of diffracting crystals are maximally placed, and 10 elements can be determined in two scans. The merits of WDS are (i) the resolution of the characteristic X-ray is higher; therefore (ii) the background is lower; and (iii) X-ray diffraction is independent of the detector. Therefore, the diffracting crystal and the detector are chosen separately. Thus (iv) detection and diffraction correction are independent of the X-ray wavelength. Spot analysis of EPMA is simple. The polished and carbon-coated sample is set on the sample stage. The sample is bombarded by the electron beam, and the characteristic X-rays are measured. If more than five elements are to be measured, the diffraction crystals and their positions are changed, and the characteristic X-rays are measured again. The concentration is calculated by a so-called ZAF correction method using standard materials. Z, A, and F mean influences from the atomic number, X-ray absorption, and secondary fluorescence, respectively. The precision of elemental analysis is highly dependent on the standard materials. The stage is moved along the x and y directions on the x–y stage. The scanning (mapping) analysis is a feature of SEM-EDS and EPMA. The measurement time of each point is the X-ray integration time. Scanning measurement by WDS takes a very long time, and therefore only the spot analysis should be done by WDS. The size of the X-ray is 2.5 µm in diameter, and therefore a scanning stage of <2.5 µm is meaningless.
1.1.1.1 X-ray Fluorescence Spectrometer
Details of the XRF spectrometer are shown in Figure 1.4. XRF is mainly applied for the analysis of solid samples. Generally, about 100 mg sample is diluted with 10 times a flux, which is composed of a mixture of pure LiBO2 and Li2B4O7, and melted into a glass bead in a Pt crucible. As the mass number increases, the absorption of X-rays also increases, and therefore lithium borate is ideal material to make the glass bead for measurement of the emitted X-rays.
Figure 1.4 Schematic diagrams of (a) an X-ray fluorescence spectrometer and (b) a gas proportional counter. X-rays produced by the X-ray tube are made to fall on a sample bead. A Rh anode X-ray tube is often used. Secondary characteristic X-rays are emitted from the sample. X-rays are collimated onto the diffracting crystal by the primary collimator. From the entrance of the primary collimator to the detector, the chamber is kept in vacuum. Then the beams enter the diffracting crystal. There are various crystals suitable for the energy of X-rays, such as LiF, pentaerythritol crystal (PET), thallium acid phthalate crystal (TAP), and so on, and crystals can be exchanged easily without breaking the vacuum. The diffracted characteristic X-rays are measured by (b) a gas flow proportional counter, which counts the pulses. The counter is a metal box filled with a mixture of Ar and CH4. There are two windows made of PP (polypropylene) film for X-ray input and output. There is a wire in the center to which a high voltage is supplied and the preamplifier is connected. When X-rays fall on the counter, they ionize the gas and electrons are generated and amplified. Thus an electric pulse is counted. In a modern XRF spectrometer, wavelengths of characteristic X-rays of each element are automatically chosen, characteristics of the counter are automatically compensated, and deconvolution of peak overlaps is automatically performed.
To minimize loss of the secondary X-rays, the chamber is kept under vacuum. Air is made of N2 and O2, and their mass numbers are higher than those of Li or B. Therefore, X-rays are absorbed or scattered by these gases. Vacuum is also sought to prevent deliquescence of the diffracting crystals.
(The author's monology: Modern XRF is fully automatic and sophisticated, so we sometimes forget that the XRF machine is a spectrometer. It is suggested that you see a spectrum (energy or wavelength vs counts per second) of one element like phosphorus at least once when you use an XRF spectrometer.)
1.1.1.2 Loss on Ignition and Ferric/Ferrous Ratio of Iron
For the determination of the major elements precisely, determinations of H2O (−), H2O (+), LOI (loss on ignition), and the ferric/ferrous ratio (Fe(II)/Fe(III)) are required. H2O (−) is weight of absorbed water. This is measured by the difference between the weight of the sample at room temperature and that after heating it at 105 °C. For hard silicate rock, this is negligible, but this becomes important for fresh deep-sea sediments.
LOI is weight difference between the raw sample and that heated at 1000 °C in a porcelain crucible. This is easy to measure, so, in recent papers only LOIs are sometimes described. LOI is given by
where H2O (+) is the weight of water in structure. In XRF determination, the sample after the LOI measurement is used, and iron is calculated and obtained as Fe2O3, because all FeO is oxidized into Fe2O3 during making glass beads.
The amount of FeO or the ferric/ferrous ratio is obtained by a separate measurement of the sample [10] [11]. Briefly, the following reaction is used.
The excess V(V) is added and the sample is decomposed with HF + H2SO4. Then, the excess (unreacted) V(V) is back-titrated with Cr(VI). The method is robust, but uses non-green chemicals, which is a drawback of this method. Both V(V) and Cr(VI) are strongly toxic to the environment. The new method in which both V(V) and Cr(VI) are not used is required.
1.1.2 Trace Element Geochemistry
1.1.2.1 From REE Geochemistry to Trace Element Geochemistry
Modern geochemistry was started by Goldschmidt (1888–1947), who is called as Father of geochemistry. He categorized elements into lithophiles, chalcophiles, siderophiles, and atmophiles (see Figure 1.5). The lithophile elements reside in the silicate parts of earth such as the mantle and the continental crust. The chalcophile elements are preferentially combined with sulfur. The siderophile elements prefer metallic iron, and reside in the core. Although the boundary between siderophile and chalcophile is vague, this classification of elements is still used in modern analytical geochemistry.
Figure 1.5 Geochemical categorization of elements by Goldschmidt.
Goldschmidt advocated that the distribution of elements into minerals is controlled by the ionic radius and valence. This idea is still correct, and based on this rule, the rare earth element (REE) geochemistry started.
The REE pattern consists of a plot in which the REE is placed in the order of the atomic number in the horizontal axis and the logarithms of the REE concentration normalized to the chondritic value in the vertical axis (see Figure 1.6; it was also called as a Masuda–Coryell diagram). The REE pattern uses the smooth decrease of ionic radii of REE as the atomic number increases. As all data in Figure 1.6 were obtained by isotope dilution-thermal ionization mass spectrometry (ID-TIMS), the mono-isotopic elements such as Pr, Tb, Ho, and Tm could not be determined. Details of ID (isotope dilution) and TIMS will be explained in Sections 1.1.2.2 and 4.5.1, respectively.
Figure 1.6 REE pattern of meteorites. Data are from Makishima and Masuda [12].Murchison, Granes, Holbrook, Barwise are CM2, L6, L6, and H5 chondrites, respectively. Camel Donga, Juvinas, and Millbillillie-1 are eucrites. The vertical axis shows the normalized value to CI chondrite [13]. All data were obtained by isotope dilution-thermal ionization mass spectrometry (ID-TIMS).
Together with the REE pattern, the ideas of distribution coefficients and the partial melting were introduced into REE geochemistry. We assume that the total system is partially melted. The weights of the liquid, the solids, and the total are ML, MS, and M, respectively. Those of REEs, T, are distributed based on the distribution coefficient Kd. The Kd value is defined as
where CS and CL are concentrations of the element T in solid and liquid forms, respectively. When the melt fraction F is introduced
The weights of the element T in the liquid, solid, and total are mL, mS, and m, respectively. Then, Eqs. ((1.3))–((1.5)) become
or
This equation indicates that, if Kd is determined previously, and f is obtained from the sample, the fraction of partial melting, F, can be estimated.
As ID-TIMS was the only method to yield precise REE concentration data during 1960–1980s, and the REE pattern was the only sophisticated method to characterize the samples at that time, the cutting-edge studies in geochemistry were only for those who could analyze samples with ID-TIMS. However, REE measurement was not easy even for the bulk samples. Therefore, the REE geochemistry was used in or by a limited number of laboratories or scientists. Thus the REE geochemistry was in the golden era, and the famous books of Henderson [14] and Lipin and McKay [15] were published.
For the evaluation of the analytical methods, the detection limit is very important. The detection limit is generally defined as the 3σ detection limit. When the peak is larger than the 3σ of background, we judge the peak as significant (see Figure 1.7). The concentration that corresponds to the 3σ of background is defined as the “3σ detection limit” or simply the “detection limit” in this book.
Figure 1.7 Definition of the 3σ detection limit.
There already existed elemental analytical methods such as colorimetry and flame atomic absorption spectrometry (FAAS). However, with these methods, REEs could not be measured because of their poor detection limits. Fassel [16] invented the inductively coupled plasma atomic emission spectrometry (ICP-AES; Figures 1.8 and 1.9), which began to be used in geochemistry. The detection limits of many elements were in the nanograms per milliliter levels (see Figure 1.10) and measurements of geochemically important elements such as REE became available. In addition, multi-element measurements became possible. However, for the REE determination, there were severe overlaps of the photo-spectra between each REE, so that the accuracy was far lower than that of ID-TIMS by the overlap correction.
Figure 1.8 Inductively coupled plasma torch. Ar gas as a cooling gas, as an auxiliary gas, and as a sample gas is supplied to the plasma torch. The innermost sample gas carries an aerosol of a sample solution. The load coil, through which cooling water is circulated, surrounds the apex of the torch and supplies energy to the inductively coupled plasma. The inductively coupled plasma is Ar plasma at atmospheric pressure, and therefore handling is easy.
Figure 1.9 Schematic diagram of inductively coupled plasma atomic emission spectrometer (ICP-AES). The temperature of the plasma is so high that most elements are atomized or ionized and emit various wavelengths of lights characteristic of the elements. The emitted light is collected, diffracted by a monochromator, and detected. The number of available elements in ICP-AES is much larger than in an atomic absorption spectrometer. Especially, geochemically important rare earth elements (REEs), such as La, Ce, …, Yb, and Lu) can be measured by ICP-AES. Thus ICP-AES is used widely.
Figure 1.10 3σ detection limits of ICP-AES for each element.
The data are after Ref. [1].
In TIMS, the detection limit is not very significant. This is because, when TIMS is used, sufficient amounts of a sample are decomposed to prepare required amounts of the target element (∼10 ng). In addition, this amount is required for a signal of sufficient intensity to last for adequate data-acquisition time in order to obtain satisfactory precision.
At the beginning of 1980s, Houk et al. [17] and Date and Gray [18] invented the inductively coupled plasma Q-pole mass spectrometry (ICP-QMS; see Section 4.5.3 and Figure 4.29). The plasma in Figure 1.8 is 6000–10 000 K, and therefore it was a good source not only for the atomization but also for the ionization. Most elements including REEs are ionized to almost 100%. The detection limits of many elements became single-digit ppb levels (see Figure 1.11). When Figures 1.10 and 1.11 are compared, the detection limits seem to become worse in the case of ICP-QMS. However, mass spectrometry was simple and straightforward compared to photospectrometry like ICP-AES, and therefore the accuracy of measurement drastically increased. For example, when REEs are measured in ICP-AES, the major elements are needed to be removed. In addition, the separation of each REE is required. In contrast, REEs can be directly determined by just dilution of the sample solution in ICP-QMS.
Figure 1.11 3σ detection limits of ICP-QMS for each element.
The data are after Ref. [1].
The calibration curves that could not be used in TIMS can be employed in ICP-QMS. Thus ID was not required, and measurement of all REEs except Pm became possible. The advantage of mass spectrometry over photospectrometry such as ICP-AES is that the isotope ratios can be determined in the former. Therefore, ID can be applied in ICP-QMS when higher precision and accuracy in analytical results are required.
As the innovation in analytical methods occurred, lithophile element abundances in addition to those of the REEs became available. The REE pattern was expanded and evolved into the trace element pattern. Furthermore, the trace elements found their position one by one to make the normal mid-ocean ridge basalt pattern to be a smooth line. These orders of elements are determined partly empirically and partly by the Kd values in major rock-forming minerals.
This order was afterward named as incompatibility, and generally used for the horizontal order of the trace element pattern. The vertical axis is the trace element concentrations that are normalized by the primitive mantle values (PM-normalized trace element patterns; McDonough and Sun [13], see Figure 1.12). The smoothness of the trace element pattern comes from the smoothness of Kd (distribution coefficients) of the trace elements in the major rock-forming minerals.
Figure 1.12 Example of the primitive mantle-normalized trace element patterns (PM-normalized trace element patterns) of the Horoman peridotite samples. Horoman is a peridotite massif located in the northern island, Hokkaido, Japan. The samples are plagioclase lherzolites and harzburgites. DMM means hypothetical Depleted MORB source Mantle.
The plot is from Ref. [19] (Copyright Nature Publishing Group, authors permission from NPG, Ref. [19].)
The idea of the incompatibility, trace element patterns, and the distribution coefficients are used in modeling and simulation between melt-solid, magma-residue, iron melt-silicate melt, and so on. The trace element pattern has peculiar features. For example, if plagioclase was crystallized and lost from the magma, Sr and Eu negative anomalies will appear in the pattern of the melt (magma). Because Sr and Eu have valence +2, they have higher distribution coefficients in plagioclase. If zircon was crystallized, Zr and Hf would show negative anomalies in the pattern. The alkaline elements, B, Pb, Sr, and Li should show peculiar behaviors if fluids or metasomatism-related materials affected the magma source. Thus the bulk trace element pattern is becoming the basic database of the silicate samples. It is like basic datasets such as blood pressure, various values of blood, hepatic, and urine tests of a patient who goes to a hospital.
1.1.2.2 Isotope Dilution Method (ID)
The ID method has already appeared several times from the beginning of this book. ID is necessary for elemental determination by TIMS because the signal intensity in TIMS is not proportional to the sample amount put into the TIMS machine. TIMS can give the precise isotopic ratio but the signal intensity itself cannot be used for the quantification of the element. In contrast, in ICP-QMS the signal is proportional to the element concentration. Therefore, the ID method is a prerequisite for quantitative analysis using TIMS.
Here, ID is explained using Figure 1.13. ID cannot be applied to mono-isotopic elements, such as Na, P, Co, Au, and so on. A target element needs to have two or more isotopes (1 and 2 in Figure 1.13). We obtain a “spike,” which is artificially enriched in one isotope. Here, 2 is the enriched isotope in the spike. Usually, the spike is prepared to be a solution. p and P are the weights (g) of the target elements in the sample and spike; A, B, and R are the isotope 2/isotope 1 ratios of the sample, the spike, and the sample–spike mixture; Dsample and Dspike are the isotopic abundances of isotope 1 in the sample and spike; and Msample and Mspike are the atomic weights of the target element in the sample and spike, respectively.
Figure 1.13 Conceptual diagram of isotope dilution.
The mole number of the mixture for the isotope 1 is
The mole number of the mixture for the isotope 2 is:
Thus the isotopic ratio of the mixture, R, is as given in Eq. (1.8)/Eq. (1.7):
The amounts of the target element in the sample are calculated by the following equation by transforming Eq. (1.9) into Eq. (1.10).
Equation (1.10) can be rewritten as
where and Cspike are the concentrations of the target element in the sample and spike; msample and mspike are the sample and spike weights; p and P are the net sample and spike weights; and Q′ in Eq. (1.12) is the pseudo-concentration of the spike because it has the dimension of concentration. The pseudo-concentration of the spike solution is calibrated by measurements of several mixtures of the spike and the standard solutions using TIMS or ICP-QMS.
The merit of introducing Q′ is that there is no need to determine Dspike, which is the atomic abundance of the spike. For the atomic abundance calculation, all isotopes need to be measured. However, when a small interference exists on some isotopes of the target element, Dspike cannot be determined precisely. However, when Q′ is used, the ID equation (1.12) can be applied by only making mixtures of the spike and sample and measuring isotope ratio (isotope 2/isotope 1).
If A, B, and Q′ are determined previously, and msample and mspike are measured for each sample, the concentration of the target element is determined by only measuring R from Eq. (1.12). This equation stands as long as the isotope equilibrium for the target element is achieved. The largest merit of ID is that, once isotope equilibrium is achieved, losses of the target element by the ion exchange column chemistry or solvent extraction, or by poor handling, do not affect the determination of the result.
The precision of the spike concentration affects directly the precision of the measurement. In addition, isotope ratios of natural and spike abundance also affects the accuracy of the measurement. Therefore, the most accurate analytical method such as TIMS is recommended for the calibration of these basic parameters even when ICP-QMS is used for ID. The isotopic abundances of the spike are provided in the analytical sheet issued by the company, but it is only for reference and the isotope ratios must be determined by yourself.
1.1.2.3 Error Magnification
Here we investigate how the error in the determination of R is propagated to the concentration result (the error magnification or error propagation) in ID. To make the equation simpler, Q″ = Q′ × msample/mspike is applied, and derivative of Eq. (1.12) for R becomes
From Eq. (1.12)
where
F(R) is a function that indicates that the deviation of R (dR/R) is magnified to the deviation of the concentration .
If we take the derivative of F(R), we get
This function becomes a minimum when dF(R)/dR = 0 at R = (A·B)0.5.
For example, if we plot F(R) against R when A = 0.9142, B = 74.75 (a case of Sm; 149Sm/147Sm), the result is as shown in Figure 1.14. According to the figure, the function F(R) takes a minimum value of 1.25 at R = 8.32. F(R) means, for example, when the measurement error is 0.1%, the minimum error using ID is 0.125% (1.25 × 0.1%). If R is smaller or larger than 8.32, the error in ID is magnified by F(R). When you want 0.2% error after ID, R should be between ∼2 and ∼40. If R is outside this range (underspiked or overspiked), the error in ID is >0.2%, and therefore the data should be discarded.
Figure 1.14 Error magnification. This function takes a minimum value of 1.25 at R = 8.32.
1.1.2.4 Isotope Dilution with Internal Standardization Method (ID-IS)
If the intensity ratios for element J over the isotope 1 of the target element T is proportional to the concentration of element J, in other words, isotope 1 can be used as the internal standard, an isotope dilution with internal standardization method (ID-IS) can be applied [20–23].
We prepare a multielement standard solution, which contains the target element J. The target element can be plural. We also prepare the sample solution that is already spiked for the element T. Intensity ratios for each isotope of the element J over the isotope 1 of the target element of the sample and the standard solution are defined as
and
where I is the intensity. Note that no spike is added in the standard solution.
The author suggests the use of the GSJ (Geological Survey of Japan) standard material, JB-3, as the internal standard material, because it is still available (in 2014). The elemental or isotopic ratios of JB-3 sometimes appear through this book. The recommended concentrations of the elements by the author are summarized in Table 1.2.
Table 1.2 Recommended elemental concentrations in JB-3 for the ID-IS method
Makishima and Nakamura [20]
Lu
et al
. [23]
(µg g
−1
)
(µg g
−1
)
(µg g
−1
)
Li
7.28
Sc
34.2
B
20.7
Be
0.628
V
384
Zr
86.2
Rb
14.0
Co
35.1
Nb
1.87
Sr
414
Ni
37.0
Mo
1.12
Y
23.1
Cu
179
Sn
1.04
Cs
0.928
Zn
114
Sb
0.104
Ba
239
Ga
20.7
Hf
2.65
La
8.12
Ta
0.114
Ce
20.9
(%)
(%)
Pr
3.14
Al
2
O
3
17.5
TiO
2
1.37
Nd
15.9
Fe
2
O
3
T
12.0
Sm
4.17
MnO
0.184
Eu
1.31
MgO
5.19
Gd
4.77
CaO
9.7
Wang
et al
. [24]
Tb
0.741
Na
2
O
2.74
(µg g
−1
)
Dy
4.66
K
2
O
0.790
F
261
Ho
0.949
P
2
O
5
0.294
Cl
292
Er
2.69
Tm
0.380
Makishima
et al
. [22]
Yb
2.50
(µg g
−1
)
Lu
0.377
Cd
0.111
Pb
4.85
In
0.069
Th
1.30
Tl
0.047
U
0.480
Bi
0.031
Makishima and Nakamura [25]
(µg g
−1
)
S
5.64
Makishima and Nakamura [21]
(µg g
−1
)
Ge
1.23
As
1.43
Se
0.057
Te
0.0010
The relative concentration factor () for the element J against isotope-1 of the element T, which is the ratio of the concentration in the solution per the signal intensity of the measured isotope, is defined as
where and are the concentrations of the element J and T in the standard solution. The concentration of the element J in the sample () is obtained from measurement of the sample solution as
where is the intensity of the element J in the sample solution and is the net intensity of isotope 1 from the sample without a spike contribution. In ID, is obtained as
From Eqs. (1.20) to (1.22), we obtain
To apply the ID-IS method, the relative concentration factor (fJ) needs to be constant. This can be achieved by ICP-QMS, because in this method the ionization efficiencies of all elements are ∼100%. However, in TIMS, a single element is loaded on the filament, and therefore it cannot be applied in most cases.
1.1.3 Determination of Mass Fractionation
We have other strong weapons in analytical geochemistry: stable isotopes. As soon as isotopes were discovered, isotopic fractions were observed in H, O, C, N, S, and so on. For this purpose, the stable isotope mass spectrometer or the isotope ratio mass spectrometer (IRMS) has been developed. Such mass spectrometry is beyond the scope of this book. Briefly, the target element is separated using gas lines and ionized by electron bombardment. The target element ions are separated by a sector magnet and detected in similar way as in TIMS.
The determination of isotopic fractionation of metallic elements such as Li, Mg, Ca, Fe, and so on, was sometimes tried by TIMS, but only a small number of elements were successful, because thermal ionization occurs only in a limited number of elements and the condition of loaded samples on the filaments was reproducible.
There are similar terms, “mass fractionation” and “mass discrimination.” In this book, the mass fractionation indicates “mass-dependent mass fractionation that occurs in nature,” and mass discrimination is “mass-dependent phenomena that occur in the mass spectrometer or under artificial conditions such as evaporation or ion exchange column chemistry in sample preparation.”
Here, mass fractionation is explained in more detail. When there are two isotopes of the target element T, and the isotope ratio is R, the mass fractionation is usually expressed as
where Rsample and Rstandard indicate the isotope ratios of the sample and standard, respectively. Generally, when the isotope ratio R is defined, the heavier and the lighter isotope become the numerator and denominator, respectively.
If there are more than three isotopes in one element, the mass fractionation occurs following mass fractionation laws. We choose two of the three isotopes for the reference isotope ratio. Then, the mass fractionation of the third isotope, which is not used in the reference isotope, could follow the mass fractionation law as described below.
Here we assume that u, v, and r are the denominator, target, and reference isotopes; Rm is the observed target isotope ratio v/u; Rc is a constant ratio without the mass fractionation ratio v/u; Rr is a constant reference isotope ratio r/u; Rrm is the observed reference isotope ratio (r/u); and α is a mass fractionation factor per mass. Then, the isotope ratios follow the mass fractionation law (the linear law), which is written as
The Rayleigh fractionation is as follows:
Similar equations appear in the mass discrimination correction (Section 5.2.2).
After the invention of multicollector-inductively coupled plasma-mass spectrometry (MC-ICP-MS, which is always compared with TIMS), natural isotopic fractionation of metallic elements such as Fe, Cu, Zn, Mo, Cd, Tl, and so on, has been extensively studied by large number of researchers, because these elements are expected to be biologically important and detectable fractionation is expected to occur. Furthermore, the standard-sample-bracketing (SSB) method or a simultaneous mass discrimination correction by other elements added to the target element in MC-ICP-MS increased the precision of the isotopic measurement and the number of available elements. These techniques expanded analytical geochemistry into bio-geochemistry. Biochemically important elements are shown in Figure 1.15, and many of them show mass fractionation.
Figure 1.15 Biochemically important elements. “Essential” means essential elements to life. “Toxic” is toxic elements to life. “Useful (drugs, etc.)” indicates useful elements used in drugs, therapies, and so on. The data is mainly based on Crichton [26]. Lithium has psychopharmacological effects. Titanium is used for supporting fractured bones. Radioactive Ga isotope is used for tumor analysis of the whole human body. Zirconium, Pd, Ag, Pt, and Au are used in dental therapy. Barium and Gd are used for X-ray and magnetic resonance imagings (MRIs), respectively. Radium is contained in some hot springs.
1.1.4 Age Dating
The fourth strategy of analytical geochemistry is age dating. The naturally existing radioactive isotopes are shown in Table 1.3. The change of isotopic ratios by the radioactive decay can be used for age dating. In order to detect such isotopic ratio change of the daughter isotope or the radiogenic isotope, a mass spectrometer with higher precision is preferred. Magnetic-sector type mass spectrometers have the advantage over Q-pole type mass spectrometers because the precision of the former is far better. For example, 0.01% can be achieved by a magnetic-sector type mass spectrometer like TIMS, while 0.3% is the best precision by ICP-QMS. The higher precision in mass spectrometry can enable the detection of smaller radiogenic variation of isotopic ratios by the radioactive decay, resulting in higher resolution for age dating of geological events.
Table 1.3 Radioactive isotopes and decay constants
Radioactive isotope
Decay scheme
Daughter isotope
Decay constant (yr
−1
)
40
K
EC
40
Ar
5.81 × 10
−11
β
−
40
Ca
4.962 × 10
−10
87
Rb
β
−
87
Sr
1.42 × 10
−11
138
La
EC
138
Ba
4.44 × 10
−12
β
−
138
Ce
2.29 × 10
−12
147
Sm
α
143
Nd
6.54 × 10
−12
176
Lu
β
−
176
Hf
1.867 × 10
−11
187
Re
β
−
187
Os
1.666 × 10
−11
190
Pt
β
−
190
Os
1.477 × 10
−12
228
Ra
Decay chain
0.12
232
Th
Decay chain
228
Ra
4.9475 × 10
−11
231
Pa
Decay chain
2.116 × 10
−5
235
U
Decay chain
231
Pa
9.8485 × 10
−10
226
Ra
Decay chain
4.28 × 10
−4
230
Th
Decay chain
226
Ra
9.1577 × 10
−6
234
U
Decay chain
230
Th
2.826 × 10
−6
238
U
Decay chain
234
U
1.55125 × 10
−10
Decay constants are from Dickin [27].
1.1.4.1 Types of Radioactive Decay
There are six main radioactive decay types of radioactive isotopes: α-decay, β−-decay, double β−-decay, β+-decay, electron capture (EC), and spontaneous fission (SF). α-Decay is where an α-particle is emitted. There is a decrease of two protons and two neutrons, and the mass number decreases by four. β−-Decay corresponds to electron emission. Therefore, the proton number increases by one with the same mass number. A double β−-decay occurs when a single β−-decay nucleus has higher energy or is forbidden. The β+-decay is a positron emission. Therefore, the proton number decreases by one with a constant mass number. EC occurs when an electron is absorbed in the nucleus. Therefore, the proton number decreases by one with a constant mass number. SF occurs when the nucleus decays into two nuclei. This occurs only in heavy nuclei such as 235U, 238U, and 240Pu.
The change in the N (neutron number) versus Z (proton number) plot is summarized in Figure 1.16a, and the fission yield of 235U is shown in Figure 1.16b. The curve shows the two maxima of the fission yield ∼85–105 (Sr, Y, Zr, Nb, Mo, Tc, and Ru) and ∼135–155 (Xe, Cs, Ba, La, Ce, Pr, Nd, Pm, Sm, Eu, and Gd).
Figure 1.16 Radioactive decays. (a) The changes of N (neutron number) and Z (proton number) by the radioactive decays. (b) Possibility of spontaneous fission yield of 235U. Note that the vertical axis is logarithmic.
1.1.4.2 Age Dating by Radioactive Isotopes
Radioactive decay is expressed by the following equation, when N is the number of radioactive isotopes:
λ is called as the decay constant. The half-life, T1/2, is related to λ as
When Eq. (1.29) is integrated, we get
N0 is the initial number of the radioactive isotope and t is the elapsed time from the start. The number of the daughter isotope is
However, in geochemistry, T = 0 and T is the age of the sample. In this case, N0 = NPeλT from Eq. (1.32), and Dt = DP, where the suffix “P” indicates “present.” Thus Eq. (1.32) changes to
For example, we consider the decay of 87Rb to 87Sr. From Eq. (1.32), we obtain the following equation where 87RbP is the “present” amount of Rb and T is the age of this isotopic system:
Strontium has a stable isotope, 86
