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Abstract

The solid Earth consists for the most part of minerals and rocks, but fluids, glasses, melts and other non-crystalline substances are also found and they play an important role in a number of geochemical and geophysical processes. The mineral sciences and the field of geochemistry are greatly concerned with investigating the nature of all geomaterials. Indeed, one wants to describe and understand their fundamental chemical and physical properties and also their behaviour under different physical conditions. In many cases a level of scientific understanding of a material is best achieved when the atomistic-scale properties and interactions can be described or characterised. This is, for example, the case for investigating the adsorption behaviour of molecules or atoms on the surfaces of minerals or in studying the physical nature of viscosity of a silicate melt. Ultimately, it is the atomistic-scale properties that control the bulk macroscopic properties of a material and, thus, they have to be characterised and understood. One is interested in both the static and dynamic behaviour of atoms and molecules and their energetic properties and interactions with one another.

This is where spectroscopy1 enters the picture, because spectroscopic measurements can provide local or atomistic-level information on a variety of different materials, whether they are gas, liquid or solid phase.

Introduction

The solid Earth consists for the most part of minerals and rocks, but fluids, glasses, melts and other non-crystalline substances are also found and they play an important role in a number of geochemical and geophysical processes. The mineral sciences and the field of geochemistry are greatly concerned with investigating the nature of all geomaterials. Indeed, one wants to describe and understand their fundamental chemical and physical properties and also their behaviour under different physical conditions. In many cases a level of scientific understanding of a material is best achieved when the atomistic-scale properties and interactions can be described or characterised. This is, for example, the case for investigating the adsorption behaviour of molecules or atoms on the surfaces of minerals or in studying the physical nature of viscosity of a silicate melt. Ultimately, it is the atomistic-scale properties that control the bulk macroscopic properties of a material and, thus, they have to be characterised and understood. One is interested in both the static and dynamic behaviour of atoms and molecules and their energetic properties and interactions with one another.

This is where spectroscopy1 enters the picture, because spectroscopic measurements can provide local or atomistic-level information on a variety of different materials, whether they are gas, liquid or solid phase. This information can be compositional, structural and crystal chemical as well as dynamical. The traditionally trained mineralogist, petrologist or geochemist was instructed to use an optical microscope, a powder X-ray diffractometer and a couple of different devices for analytical chemistry determinations, such as the electron microprobe or an X-ray fluorescence unit, to characterise a rock or mineral, for example. Times have changed and this no longer suffices. Today, the research problems and directions in the Earth Sciences are often different from those of the past and new approaches and tools for study are required. Here, the development and application of various spectroscopic methods over the last approximately 30 years is most notable. The number of spectroscopic methods that are presently available to mineral scientists and geochemists is staggering. There has been both a birth of new spectroscopic techniques and rapid advances and refinements of the older more traditional methods (e.g. IR, Raman, XAS). Both developments are having a major influence on the type of investigations undertaken on a wide variety of geomaterials and, in addition, under different physical conditions.

1The word spectroscopy derives from the Latin spectrum meaning “a vision” or “an image” and the ancient Greek word σκoπειν (skopein) meaning “to see” or “to view”. A spectroscope provides for visual observation of a spectrum and a spectrometer provides for measurement of wavelength (energy, frequency, wavenumber).

The range of methodologies and the types of investigations are so great that it is sometimes difficult to decide on what kind of spectroscopic measurement should be made to address a scientific question. In general, many spectroscopic methods deliver chemical or structural information that is narrow or specific in scope in comparison to the important X-ray diffraction experiment used in structural investigations of crystalline materials, for example. However, the information that they can deliver can be very quantitative and unique. For example, 29Si MAS NMR spectroscopy can be used to determine quantitatively the short-range distribution of Si atoms in silicates or the type of SiO4 polymerisation in silicate melts and glasses. Such information cannot be easily obtained by nearly any other experimental method. On the other hand, NMR spectroscopy can only be applied to substances nearly free of paramagnetic ions and in the case of crystals one needs to know the crystal structure before a spectrum can be fully interpreted. A second example involves IR spectroscopy. If one wants to determine small concentrations of structural H2O or OH- in a nominally anhydrous mineral or in a silicate glass and also their energetic interactions with their environment, then IR spectroscopy is essentially unique in its ability to provide such information. Indeed, in the case of non-crystalline materials like gases or fluids or even nanoparticles, spectroscopy normally offers the best way to characterise their physical and chemical properties.

A difficulty for the beginner is to decide what method should be used or how one should start a spectroscopic investigation. Experience shows that, in general and in many cases, the different spectroscopic methods should be used in a complementary fashion (Calas & Hawthorne, 1988). These authors state “one can view the different spectroscopies […] as a series of tools that one uses to solve or examine a problem of interest; a single tool is generally not sufficient for one's needs – you cannot drive a nail and drill a hole with just a hammer”. It can be stated further that one cannot build a house with just a saw. Hence, if the goal is to understand the physical and chemical nature of some material or a system of phases (e.g. a rock or a mineral-fluid interface) in a complete sense, one must apply a number of different techniques. Ultimately, one wants to understand the properties of a material or a physicochemical system from the atomistic level through the nano- and microscopic scale up to the macroscopic state. In addition, the atomistic-level dynamic properties sometimes require a description over different time scales. Needless to say, there remains much work to be done in the Earth Sciences.

Observed in a historical context, the general scientific problem has not changed greatly with time. The ancient Greeks struggled to understand the nature of matter, as did Kepler almost 2000 years later (Schneer, 1995). Today, mineral scientists and geochemists are still struggling to understand why various geomaterials behave the way they do under certain geologic conditions or why they display the properties that characterise them. With this in mind, we begin with a short review of the history of spectroscopy and investigations on minerals and other geomaterials.

Brief history of spectroscopy with an emphasis on investigations of geomaterials

The field of mineralogy dates back hundreds of years and the discipline of geochemistry is closely linked to mineralogy2. Both disciplines underwent major changes in the 1900s following developments in chemistry and solid-state physics. Prior to this time, mineralogical and geochemical studies were largely observational and empirical in nature. They were mostly devoted to describing the distribution of minerals, rocks and ores in the Earth's crust and in determining their chemical compositions. Analytical wet-chemical measurements played a central role in systematising mineral and rock compositions and in providing a sense of order to the field. The nature of mineralogical investigations began to change with the establishment of atomic theory and then, later, with the development of quantum mechanics. Both theories revolutionised investigations on all materials. The discovery of X-ray diffraction by von Laue and co-workers in 1912 played a central role in the development of mineralogy, because the spatial arrangements of atoms in a crystal could be revealed for the first time. As a result, the internal crystal structures of all the rock-forming minerals, and hundreds of less common species as well, have been solved and refined a number of times. The static structural properties of the important silicates at ambient conditions, and often at high pressure and temperature as well, are known to great detail.

Newton first applied the term “spectra” in his study of light in 1672 and in 1800 Herschel studied the spectral distribution of heat from the sun. Fraunhofer built the first spectroscope in 1814 consisting of a telescope, a prism and a device for measuring the angle by which the various components of light from stars are refracted. Some of the first spectroscopic or spectrometric measurements were made prior to the birth of quantum theory by chemists like Bunsen and Kirchhoff around 1860 to detect different elements. The emission spectra of various materials in a flame, for example, had been investigated, and Balmer in 1885 fitted the emission lines observed in the spectrum of hydrogen with a mathematical formula.

Planck started the quantum mechanical revolution in 1900 with his proposal that energy emitted by a black box is quantised or that radiation is emitted in quanta. It followed that the energy of radiation, E, is proportional to its frequency, v, as shown by Einstein in his theoretical explanation of the photoelectron effect (i.e., E = hv, where h is Planck's constant – Table 1). Bohr proposed in 1913 his model for the hydrogen atom in which energy could only be emitted and absorbed between discrete levels and this explained the empirical formulations of Balmer, for example. The field of quantum mechanics developed extensively over the next couple of decades. Various experimental spectroscopic observations could now be interpreted using a quantitative theoretical background. The stage was set for the discovery and development of different spectroscopic techniques and for the interpretation of spectroscopic observations. Electromagnetic radiation was normally the energy source that was used to cause the different physical excitations.

2Taking the publication of De Re Metallica by Agricola in 1556 and later the work of Haüy in 1801 as the start of mineralogy as an exact science (Schneer, 1995).

Table 1.

Fundamental physical constants*.

cvelocity of light in vacuum2.997 924 58 · 108 m/s
hPlanck's constant6.626 069 · 10−34 J/s
ħ(= h/2π)1.054 571 · 10−34 J/s
eelectronic charge1.602 176 · 10−19 C
μeelectron magnetic moment−928.476 362 · 10−26 J/T
μBBohr magneton927.400 899 · 10−26 J/T
μNnuclear magneton5.050 783 17 · 10−27 J/T
meelectron mass9.109 381 88 · 10−31 kg
mPproton mass1.672 621 58 · 10−27 kg
mNneutron mass1.674 927 16 · 10−27 kg
kBBoltzmann's constant1.380 650 · 10−23 J/K
NAAvogadro's constant6.022 142 · 1023
Rmolar gas constantNA · kB = 8.314 472 J/mol·K
FFaraday constant96 485.3415 C/mol
geg electron factor−2.002 319
αfine structure constant (e2/4πε0ħc)7.297 352 533 · 10−3
cvelocity of light in vacuum2.997 924 58 · 108 m/s
hPlanck's constant6.626 069 · 10−34 J/s
ħ(= h/2π)1.054 571 · 10−34 J/s
eelectronic charge1.602 176 · 10−19 C
μeelectron magnetic moment−928.476 362 · 10−26 J/T
μBBohr magneton927.400 899 · 10−26 J/T
μNnuclear magneton5.050 783 17 · 10−27 J/T
meelectron mass9.109 381 88 · 10−31 kg
mPproton mass1.672 621 58 · 10−27 kg
mNneutron mass1.674 927 16 · 10−27 kg
kBBoltzmann's constant1.380 650 · 10−23 J/K
NAAvogadro's constant6.022 142 · 1023
Rmolar gas constantNA · kB = 8.314 472 J/mol·K
FFaraday constant96 485.3415 C/mol
geg electron factor−2.002 319
αfine structure constant (e2/4πε0ħc)7.297 352 533 · 10−3

Infrared absorption and emission investigations belong to the early stages of experimental spectroscopy and they can be traced back to the late 1800s. Some of the first simple measurements on minerals date from around the early 1900s and by 1906 systematic studies were published (e.g. Coblentz, 1906). Single-crystal IR investigations on the vibrational properties of the major silicate families, which used group theory and structural analysis, were published in the middle 1930s (e.g. Schaefer et al., 1934; Matossi & Krüger, 1936). After 1945 commercial IR spectrometers came onto the market and routine measurements began in full by mineralogists. In the 1970s it was shown that IR spectroscopy is a powerful tool for measuring and characterising small concentrations of H2O, OH- and other molecular species in minerals and glasses and today it is widely used in this regard. Farmer (1974) provides a good early treatment of the general subject of IR spectroscopy in mineralogy.

The inelastic scattering of light by matter and its physical explanation by Raman in 1928 led to the technique that bears his name – Raman spectroscopy3. The recording of the spectra of various minerals and their interpretation followed shortly thereafter (e.g. Nisi, 1932). Raman and Nedungadi investigated the αβ phase transition in quartz in 1940. The widespread and routine use of the technique in the 1960s depended upon technological advances including the development of intense monochromatic lasers and sensitive detectors that are necessary to measure more easily the weak inelastically scattered radiation. Griffith in Farmer (1974) undertook a number of early measurements on various rock-forming minerals. Today, Raman spectroscopy is widely used in many different mineralogical and geochemical research programs. Examples include polarised single-crystal measurements for lattice dynamic studies, investigations of mineral behaviour under high pressure and high temperature in a diamond anvil cell, and the characterisation of fluid inclusions.

3 However, it should be noted that Smekal predicted in 1923 the “Raman effect” and in the older literature one finds the term the Smekal-Raman effect.

Electronic absorption investigations of solid materials in the ultraviolet-visible (UV/VIS) region began in a serious way in the 1930s and 1940s by chemists and physicists following the formulation of crystal field theory by Bethe in 1929 that allowed for an interpretation of the spectra. Numerous mineralogical and geochemical investigations were made in the 1960s and are summarised in Burns' (1970) classic first edition of “Mineralogical Applications of Crystal Field Theory”. Optical absorption spectra are important for understanding the electronic properties of transition metals of the d- and f-series elements. Spectra are used to explain the origin of colour in minerals, and they can be used to explain the behaviour of transition metals in various geochemical and petrological processes. More recent developments and studies in optical absorption spectroscopy are discussed in Burns' second edition of his book in 1993.

The phenomenon of X-ray absorption was described quite early (Kossel, 1920) and led to the development of X-ray absorption spectroscopy (XAS). It is a fundamental and widely used spectroscopic method in nearly all areas of science, and mineralogy and geochemistry are no exception. However, extensive and quantitative XAS studies in the Earth Sciences largely began with the development and construction of synchrotron facilities that provide intense X-rays of various wavelengths. X-ray absorption studies are element specific and X-ray absorption near-edge structure (XANES) and extended X-ray absorption fine structure (EXAFS) measurements can be used to obtain local structural and crystal-chemical information on nearly any type of material either crystalline or non-crystalline. Dynamic properties of atoms can also be determined. Studies of surfaces involving, for example, the adsorption of molecules and atoms can be undertaken and this is currently an important field of investigation. Bassett (1988) and Brown et al. (1988) provide early compilations and reviews for various mineralogical and geochemical investigations.

Magnetic resonance measurements followed in time the vibrational and optical absorption spectroscopies. Electron spin resonance (ESR), or electron paramagnetic resonance (EPR) as it is sometimes called, was discovered by Zavoiski in 1946. Extensive investigations in materials or physics research did not begin, however, until around the end of the 1950s. ESR measurements are used in studies of radicals, paramagnetic ions (those ions with unfilled d and f shells) and electron-hole centres. The method has the advantage that paramagnetic ions can be measured at very low concentration levels. It appears, interestingly, that this spectroscopic method was more widely used in mineralogical and geochemical investigations in the former Soviet Union than in western countries, where relatively little ESR work has been done in these fields. Marfunin (1979) provides a good discussion of the method and his book gives a first summary of different mineralogical studies published up to that time. Calas (1988) also provides a review of the method.

Nuclear magnetic resonance (NMR) was discovered independently by Bloch and Purcell at nearly the same time as ESR in 1946. This technique has proved to be very important for a number of scientific disciplines. It is widely used in chemistry in the study of molecules and more recently in the field of medicine where it is used for imaging internal organs and processes in the human body, for example. Some of the first measurements on minerals were published in the middle 1950s. Quantitative mineralogical studies on crystals and glasses awaited technological developments such as Fourier-transform spectrometers and the technique of “magic angle spinning” (MAS), which acts to reduce line broadening and allows better spectral resolution. Lippmaa and co-workers (e.g. 1980) made some of the first high-resolution NMR studies of silicates using the isotopes 29Si and 27Al. Much of this work and other studies are summarised in the book “High-resolution solid-state NMR of silicates and zeolites” by Engelhardt & Michel (1987).

Mössbauer discovered the phenomenon of nuclear recoilless gamma-resonance absorption in 1958 and some of the first spectra on minerals, with an emphasis on 57Fe, began appearing in the middle and late 1960s. Thus, Mössbauer spectroscopy is one of the younger, more “standard” spectroscopic measurements that are widely used in the mineral sciences and geochemistry. It is used routinely for studying the crystal-chemical role of Fe in various substances. Other elements can also be studied such as 119Sn, 153Eu and 197Au, but they have received relatively little investigation. Bancroft (1973) provides an early summary of the method and discusses various geochemical and mineralogical studies, as does Hawthorne (1988).

Paralleling these years of discovery in which constant technological developments of spectrometers and the types of experimental measurements were also made, the theory of electronic structure was further developed. A determination of electronic structure and bonding properties plays a central role in many spectroscopic investigations, because in most materials it is the distribution of electrons that determines their chemical and physical properties. Many aspects of experimental spectroscopy and bonding theory developed “hand in hand”. Pauling wrote his first edition of “The Nature of the Chemical Bond” in 1939 and it had a major influence on many students in chemistry, and in other fields as well. Crystal field theory is the oldest model used to explain the bonding properties in crystals and it is still used today in mineralogy (Burns, 1970; 1993). It was followed by the more advanced molecular orbital and electron band theories. A recent book that discusses different bonding models and examples relating to solid materials, including minerals, is “Chemical Bonding in Solids” by Burdett (1995). Today, electronic structure calculations using ab initio methods are a standard part of research in chemistry, physics and materials science and now also in the mineral sciences and geochemistry (Gramaccioli, 2002).

What is the state of experimental spectroscopy in the mineral sciences and geochemistry today? The Mineralogical Society of America organised a short course entitled “Spectroscopic Methods in Mineralogy and Geology” (Hawthorne, 1988) and this marked, one could argue, a point where spectroscopic methods had come of age in the Earth Sciences. Since that time, there have been further increases in the number and scope of spectroscopic investigations. A large number of spectroscopic studies are being made today and it is not possible to pick up a mineralogical or geochemical journal without seeing results from many different types of measurements. The various methods and experimental set-ups are constantly undergoing new technological advancements and improvements. There has been and there is a trend towards making measurements over small spatial areas (e.g. micro-Raman, micro-IR, micro-Mössbauer, and other microanalytical measurements – see Potts et al., 1995) and on smaller amounts of material. Studies are also made at different pressure and temperature conditions or in different chemical environments. Raman measurements are being made on materials compressed with the diamond anvil cell to exceedingly high pressures in the megabar region to study the structural and physical properties of matter under extreme conditions. High-temperature in situ NMR measurements are made to investigate the structural properties of silicate melts. 57Fe Mössbauer measurements are being performed using synchrotron radiation to study the kinetics of electron transfer processes between aqueous and solid-phase materials. The list of examples is very long.

The different spectroscopic types, the various experimental set-ups and the sorts of measurements that can be performed are so great today that it is impossible to discuss them all in a single workshop or in a single book. What can be done? In a very general sense many spectroscopic investigations in mineralogy and geochemistry can be divided into two different categories – namely standard analytical versus fundamental – but the division is not strict. Analytical-type investigations typically employ standard spectroscopic measurements to characterise some chemical, structural or physical property of an Earth material. This information is then used to help interpret some geological process. For example, because the viscosity of a silicate melt is greatly affected by its volatile content, and thereby the eruption style of a volcano, IR, Raman and NMR spectroscopy can be used to determine the concentration and structural environment of molecular H2O, CO2 and various H-C-O species in melts and glasses. 57Fe Mössbauer spectroscopy can be used to measure the Fe3+/ΣFe ratio of some material in order that oxidation-reduction conditions in a geological environment can be described. Such applications of spectroscopy are, of course, extremely large in number and many examples will be discussed in the chapters of this book. On the other hand, more fundamental spectroscopic measurements can be undertaken in order to investigate basic physical and chemical properties. Here, the goal is not too different from many studies in solid-state physics or in inorganic, organic and physical chemistry. One wants to describe and understand the atomistic nature of the physical and chemical properties of some Earth material. If some physical level of understanding can be reached, then it is often possible to predict or estimate material behaviour at condition(s) outside of those where the measurements were made. Such investigations are necessary, because many geologic processes occur in regions of the Earth that are not accessible to direct observation. Thus, if one can understand the chemical and physical properties of some substance at ambient conditions, it may be possible to predict how they behave in the deep Earth, for example. As an example, IR and Raman measurements can be made at ambient conditions to study the lattice-dynamic behaviour of a mineral and this information can be used to determine macroscopic thermodynamic properties at different P–T conditions. At any rate, no matter what the approach, it is important to have some understanding of the physics behind the different spectroscopic methods.

Radiation

Spectroscopy involves the interaction of radiation with matter and different types of radiation can be used to investigate the chemical and physical properties of materials. They are (Calas & Hawthorne, 1988):

  1. electromagnetic radiation,

  2. elementary particles (e.g. electrons, neutrons and protons),

  3. atomic nuclei (e.g. α particles),

  4. ions and

  5. ultrasonic waves.

The first group contains a number of the most commonly used spectroscopies. They form, so to speak, the “bread and butter” methods and include, in decreasing order of the energy of the respective quantum transition (Fig. 1): Mössbauer spectroscopy, X-ray absorption spectroscopy, optical absorption spectroscopy, IR and Raman spectroscopy, electron spin resonance spectroscopy and nuclear magnetic resonance spectroscopy. Most of these methods and various mineralogical and geochemical applications are discussed in the different chapters of this book.

Fig. 1.

The electromagnetic spectrum showing the different regions (middle part of figure). The various quantum transitions associated with each region are shown along with the corresponding spectroscopic type (above). At the bottom the wavenumbers, wavelengths, frequencies and energies across the spectrum are given.

Fig. 1.

The electromagnetic spectrum showing the different regions (middle part of figure). The various quantum transitions associated with each region are shown along with the corresponding spectroscopic type (above). At the bottom the wavenumbers, wavelengths, frequencies and energies across the spectrum are given.

However, it should not be forgotten that other forms of radiation are used in a variety of spectroscopic studies. In terms of elementary particles, the neutron is used in several types of spectroscopic investigations (see Winkler, 1999, for mineralogical applications). Inelastic neutron scattering (INS) measurements on single crystals can be made to determine phonon energies and their dispersion relations within the Brillouin zone. The phonon density of states can also be determined from studies made on powders. Both kinds of measurements form the basis for the important field of lattice dynamics. This is a relatively new field of investigation in the mineral sciences, but experimental and computational lattice-dynamic studies are increasing in both number and scope (Gramaccioli, 2002). Quasielastic neutron scattering can be used to study the diffusive motions or dynamic behaviour of H2O in minerals at the picosecond to femtosecond time scale. In general, neutrons are very good for studying the H atom and here investigations of the nature of water-containing fluids or solutions or the behaviour of H2O in minerals come immediately to mind.

Electrons are also employed in a number of spectroscopies, for example, in electron microprobe measurements. Here, a finely focussed beam of accelerated electrons interacts with a substance, causing an emission of X-rays of different energies. These can be assigned to the different elements and the intensities of the X-rays are proportional to the concentration of the corresponding element. Electrons are also used in electron energy-loss spectroscopy (EELS) investigations. Such measurements yield absorption spectra that are comparable to those obtained from XAS. Energy-loss near-edge structure (ELNES) measurements made with a transmission electron microscope enable determinations of ferric-ferrous iron ratios (i.e., Fe3+/ΣFe) in minerals, for example, at a high spatial resolution of a few nm (e.g. van Aken et al., 1999).

Protons are used in proton-induced X-ray emission (PIXE) spectroscopy. This is a relatively new technique being used in the Earth Sciences. PIXE is an analytical chemical method and it has the advantage over conventional X-ray fluorescence measurements or the electron microprobe that low-Z elements can be measured at low concentration levels. Moreover, the proton beam can be focussed down to several μm in size, thus allowing for, once again, microanalytical measurements.

These and other particle techniques and those spectroscopies associated with categories (3), (4) and (5) are not considered in this book and they will not be discussed further. A number of the most common spectroscopic methods involving electromagnetic radiation are the focus herein and they will be reviewed very briefly in this chapter, but first a very short theoretical discussion of electromagnetic radiation and its interaction with matter will be given.

Electromagnetic radiation: Wave theory, particle-like behaviour, energy and interaction with matter

Electromagnetic radiation can be described in the classical physical description in terms of wave theory, and it includes what is commonly referred to as “light” as well as radiation at shorter and longer wavelengths. The entire wavelength range, which occurs over many orders of magnitude, builds the electromagnetic spectrum (Fig. 1). An electromagnetic wave consists of electric and magnetic components, which in the general case are unpolarised, but they can be made to be plane polarised as shown in Figure 2. Here, the radiation propagates along the Y axis and the electric component is polarised in the YZ plane, while the magnetic component is polarised in a perpendicular direction and resides in the XY plane. Magnetic excitations are not a subject of this book and thus the magnetic component will not be considered further. The distance between two successive points having the same phase within the wave defines the wavelength, λ, which can be given, for example, in units of Å (ångstrom), cm (centimetre), μm (micrometre) or nm (nanometre), where 1 Å = 10−8 cm = 10−10 m, 1 μm = 10−6 m, 1 nm = 10−9 m = 10 Å. The frequency, v (or ω = 2πv, where ω is termed the angular frequency), gives the number of wave oscillations per second. It is defined by  

formula
where c is the velocity of light (Table 1). Since λ has the dimension of length (e.g. centimetres), frequency has the dimension of 1/time (e.g. Eqn. 1: 1/s = [cm/s]/[cm]). This unit is called the “hertz” (Hz) and 1 kHz = 103 Hz, 1 MHz = 106 Hz and 1 GHz = 109 Hz (Table 2 gives a list of prefixes encountered in spectroscopic investigations). Another important unit that is often used in spectroscopy is the “wavenumber”, forumla and it is defined by  
formula

Table 2.

SI prefixes.

FactorPrefixSymbolFactorPrefixSymbol

1024yottaY10−1decid
1021zettaZ10−2centic
1018exaE10−3millim
1015petaP10−6microμ
1012teraT10−9nanon
109gigaG10−12picop
106megaM10−15femtof
103kilok10−18attoa
102hectoh10−21zeptoz
101dekada10−24yoctoy
FactorPrefixSymbolFactorPrefixSymbol

1024yottaY10−1decid
1021zettaZ10−2centic
1018exaE10−3millim
1015petaP10−6microμ
1012teraT10−9nanon
109gigaG10−12picop
106megaM10−15femtof
103kilok10−18attoa
102hectoh10−21zeptoz
101dekada10−24yoctoy
Fig. 2.

Wave representation of plane-polarised electromagnetic radiation. The electric and magnetic fields are at right angles to each other and propagate in the Y direction. The wavelength is given by λ. The amplitude is given at the wave maximum as shown by the thin lines with arrows.

Fig. 2.

Wave representation of plane-polarised electromagnetic radiation. The electric and magnetic fields are at right angles to each other and propagate in the Y direction. The wavelength is given by λ. The amplitude is given at the wave maximum as shown by the thin lines with arrows.

An electric wave propagates through time and space. It occurs in the form of an oscillating field (Fig. 2) whose strength, ε, in the YZ plane as a function of position and time is given by:  

formula
where ε0 is the amplitude, t the time, and ky the y component of the wavevector (k = 0, ky, 0). The modulus of k is k = 2π/λ. Because of quantum mechanical wave-particle duality, electromagnetic radiation has also particle-like characteristics and is termed a photon that has momentum. It can be shown that the momentum, p, is given by:  
formula
The energy of radiation is given by  
formula
One also has  
formula
If an electric field interacts with a substance, absorption of energy can only occur when “Bohr’s energy condition” is met. And this occurs between discrete levels according to quantum theory4: only when the energy of radiation corresponds to the difference between two energy levels, ΔE = E″ – E′ = hv, for some state of an atom, can absorption occur.

Table 3.

Energy units and conversion factors*.

UnitJm−1HzeV

1 J(1 J) = 1 J(1 J)/hc = 5.034 · 1024 m−1(1 J)/h = 1.509 · 1033 Hz(1 J) = 6.241 · 1018 eV
1 m−1(1 m−1)hc = 1.986 · 10−25 J(1 m−1) = 1 m−1(1 m−1)c = 299 792 Hz(1 m−1)hc = 1.240 · 10−6 eV
1 Hz(1 Hz)h = 6.626 · 10−34 J(1 Hz)/c = 3.335 · 10−9 m−1(1 Hz) = 1 Hz(1 Hz)h = 4.136 · 10−15 eV
1 eV(1 eV) = 1.602 · 10−19 J(1 eV)/hc = 8.065 · 105 m−1(1 eV)/h = 2.417 · 1014 Hz(1 eV) = 1 eV
UnitJm−1HzeV

1 J(1 J) = 1 J(1 J)/hc = 5.034 · 1024 m−1(1 J)/h = 1.509 · 1033 Hz(1 J) = 6.241 · 1018 eV
1 m−1(1 m−1)hc = 1.986 · 10−25 J(1 m−1) = 1 m−1(1 m−1)c = 299 792 Hz(1 m−1)hc = 1.240 · 10−6 eV
1 Hz(1 Hz)h = 6.626 · 10−34 J(1 Hz)/c = 3.335 · 10−9 m−1(1 Hz) = 1 Hz(1 Hz)h = 4.136 · 10−15 eV
1 eV(1 eV) = 1.602 · 10−19 J(1 eV)/hc = 8.065 · 105 m−1(1 eV)/h = 2.417 · 1014 Hz(1 eV) = 1 eV

Why is Equation 5a/b important? It is important because a determination of the magnitude of ΔE provides a measure or probe of the system under study and it can give chemical and/or structural information. Because h and c are known constants, all types of quantum transitions have well-defined energies. They can be expressed in various units. For example, if a system absorbs energy with a wavenumber of 1.0 cm−1, using Equation 5a one has5: 

formula
or in the case of molar quantities  
formula

Because of the tremendous range of radiation energies that are associated with the different spectroscopic methods and also because of historical developments and scientific tradition, different units are used to describe the various types of transitions that can occur. For Raman and IR spectroscopy the wavenumber, cm−1, is used to describe vibrational spectra, while in inelastic neutron scattering studies electron volts, eV or meV, are normally used. In both cases, the units of energy are straightforward to understand. In the case of Mössbauer and NMR spectroscopy the units of mm/s and ppm, respectively, are used to describe a given spectrum. This may seem unusual to many beginning students, but there are logical reasons for such choices. In Mössbauer spectroscopy the units of mm/s are used because of the physical construct of the measurement and the quantum transition involved. Here, the radiation source does not remain stationary as in nearly all other spectroscopic methods, but is moved relative to the sample. This allows, through the Doppler effect, the radiation energy to be very slightly modulated. For a 57Co source, with E = 14440 eV, moving at v = 1 mm/s, for example, one has an energy difference of:  

formula
This very small change in energy is generally sufficient to establish the absorption condition between the source and absorber in many substances. Thus, a Mössbauer spectrum is presented as the percentage of absorption or transmission of the γ radiation through the sample as a function of the velocity of the source in mm/s.

4 Classical mechanics fails catastrophically in this regard, as shown by Planck, because here energies and transitions can vary continuously.

5 Table 3 lists common different energy units and the conversion factors between them.

In NMR spectroscopy the resonant energies are reported relative to some well-known standard to facilitate comparisons between measurements made under different magnetic field strengths. 29Si NMR resonance lines are measured with regard to their chemical shift, δ, in parts per million (ppm) between that in the sample and that in a well-studied standard [i.e. typically tetramethyl silane, TMS: (CH3)4Si] and are defined as  

formula
An NMR spectrum, then, is presented as resonance intensity versus chemical shift.

Concluding, a proper understanding of spectroscopy can only be obtained with some knowledge of quantum mechanics and an understanding of various physical phenomena. A one-year university course in physics should be considered the minimum amount of study needed in order to begin laboratory spectroscopic work in the Earth Sciences. In addition, though not discussed here, symmetry plays an important role in interpreting some spectra and the nature of the so-called selection rules that give information on the types of transitions that can occur. An understanding of group theory is required to fully understand the Raman or IR spectrum of a crystal, for example. On the other hand, for some mineralogical and geochemical spectroscopic studies, the level of knowledge in both areas needs not be too great, but there is always the danger that without some understanding of the physics of the different processes various spectroscopic features can be misunderstood or misinterpreted.

Short description and review of some “standard” spectroscopies

Spectroscopic and transition types

The number of spectroscopic types being used today is quite large6. Further developments are constantly leading to new types of measurements and modifications of the older more established spectroscopic methods. It is useful to group the different methods based on their physical process. Figure 3 shows schematically various possible effects that can occur when a quantum of radiation or a photon interacts with an atom. One can define four types of interactions (modified from Janot & George, 1986):

(1) There is no interaction between the incident radiation and matter. The radiation is transmitted with no change in its properties [i.e., k (= 2π/λ) and ω (= 2πv)] as shown in Figure 3a.

(2) The interaction results only in a change in the wavevector, k, while the frequency of radiation remains the same. The incident radiation is scattered or diffracted elastically over a range of wavevectors. This is the situation for normal Bragg-type diffraction involving X-rays (Fig. 3b) and also with neutrons and electrons. This kind of study is used to characterise the static spatial properties of matter.

(3) The incident radiation causes some internal excitation or transition, which can be vibrational, electronic or nuclear. Two simple examples are IR and optical absorption spectroscopy (Fig. 3c), which involve vibrational and electronic excitations, respectively, from E′ to E″, where E″ > E′. Another process can occur that is termed “induced or stimulated” emission (Fig. 3d). Here a quantum of energy is required to “induce or stimulate” the transition and the emitted photon(s) has the same frequency, phase and direction as the incident photon. This effect is used in lasers (Light Amplification by Stimulated Emission of Radiation). A simpler related effect is that of spontaneous emission in which no incident electromagnetic radiation is involved (Fig. 3e). In this case, radiation is emitted spontaneously when an atom reverts to the ground state from some excited state. This is the process associated with classical flame emission spectroscopy. Resonance absorption occurs when an incident photon has the same energy as that associated with a transition from the ground state to the first excited state, and then in a short time a photon is emitted and the excited state returns to the ground state (Fig. 3f). The emitted radiation has the same frequency as the incident photon, but is different in phase. This process occurs in nuclear magnetic resonance and in electron spin resonance spectroscopy. A photon can also impact on an atom, be absorbed and cause the atom to be ionised (Fig. 3g). This occurs through the ejection of an electron. This is the process in XAS where a photoelectron is created when a core level electron is ejected by an X-ray photon.

(4) The incident radiation couples with an internal process, a transition occurs and radiation having a different frequency is emitted. When light is the incident radiation and it is scattered inelastically, the process is called Raman spectroscopy (Fig. 3h). It is also possible to cause a transition from the ground state to a higher excited level when the incident radiation has a certain frequency. Following this, energy is given off in a number of quantum transitions through spontaneous emission until the ground state is finally reached (Fig. 3i). An example is the absorption of ultraviolet light by valence electrons causing an excitation to some higher level, which is then followed by the stepwise emission of radiation in the visible light region to the ground state. This phenomenon is called photoluminescence. When the emission occurs faster than 10−8 seconds, it is called fluorescence, and when it is slower it is called phosphorescence. When high-energy electrons are used instead of a photon, one has the process of cathodoluminescence. This effect is sometimes seen when using the electron microprobe, for example.

6Calas & Hawthorne (1988) list more than 50 types and the number is even greater.

Fig. 3.

Schematic representations of various processes that can occur when radiation interacts with an atom. The incident photon is shown as a wave characterised by a given k and ω. The transmitted or scattered radiation can be in-phase or out-of-phase (k′) with the incident radiation and have the same or a different angular frequency (ω′). The spaced horizontal lines represent different energy levels of the atom and the lowest level represents the ground state. The various types of processes are: a) no interaction between radiation and matter, b) elastic scattering, c) absorption (no emitted photon), d) stimulated or induced emission, e) spontaneous emission (no incident photon as in flame emission spectroscopy), f) resonance absorption, g) absorption and photoelectron ejection, h) inelastic scattering, and i) photoluminescence.

Fig. 3.

Schematic representations of various processes that can occur when radiation interacts with an atom. The incident photon is shown as a wave characterised by a given k and ω. The transmitted or scattered radiation can be in-phase or out-of-phase (k′) with the incident radiation and have the same or a different angular frequency (ω′). The spaced horizontal lines represent different energy levels of the atom and the lowest level represents the ground state. The various types of processes are: a) no interaction between radiation and matter, b) elastic scattering, c) absorption (no emitted photon), d) stimulated or induced emission, e) spontaneous emission (no incident photon as in flame emission spectroscopy), f) resonance absorption, g) absorption and photoelectron ejection, h) inelastic scattering, and i) photoluminescence.

Categories (3) and (4) are considered to constitute different spectroscopic processes, and they give rise to the occurrence of absorption bands, emission lines, or resonance peaks etc. as observed in the various types of spectra. Each of these methods is explained very briefly below.

IR absorption spectroscopy

The set-up for a single-crystal IR absorption experiment7 is shown schematically in Figure 4. An IR radiation source, such as a “Globar” (i.e., SiC), generates radiation over a certain wavenumber range, for example, between 9,000 and 100 cm−1. The radiation, which can be polarised, impinges on a sample. A transition from one vibrational state to another can occur when the oscillating electric vector of the radiation interacts with an oscillating dipole (Fig. 5), μ, in a diatomic molecule, for example. For a polyatomic molecule one has  

formula
where μ0 is the equilibrium dipole moment and q is a normal coordinate describing a normal mode vibration. The coefficient (/dq) determines how the dipole moment changes during a vibration. If it is zero, the vibration is IR inactive and no absorption will occur. However, if any of the components x/dq, dμy/dq or z/dq along the coordinate axis is non-zero, the vibration is IR active.

Fig. 4.

Schematic experimental set-up of a polarised (polariser not explicitly shown) single-crystal IR absorption measurement. The direction and polarisation of the incident radiation are shown.

Fig. 4.

Schematic experimental set-up of a polarised (polariser not explicitly shown) single-crystal IR absorption measurement. The direction and polarisation of the incident radiation are shown.

The energy levels for a simple diatomic molecule are shown schematically in Figure 6. Transitions can take place between different vibrational levels and using a harmonic oscillator for a description of the fundamental normal mode vibrations only those transitions with Δυ = ±1 are allowed. The allowed energy levels for a harmonic oscillator are:  

formula
with n = 0, 1, 2, … . Of course, most real systems do not behave as perfect harmonic oscillators and transitions with Δυ = ±2, ±3, … can occur. These are the so-called overtone vibrations that are generally weak in intensity.

7 IR emission and reflection spectra can also be measured, but they are not covered here. Powder measurements can also be made and this is most often done.

Fig. 5.

Schematic representation of an electric monopole, a dipole and two types of a quadrupole.

Fig. 5.

Schematic representation of an electric monopole, a dipole and two types of a quadrupole.

For transitions of the type Δυ = ±1, the fundamental with υ = 0 ↔ 1 should be the strongest in vibrational (IR and Raman) spectra. This follows from the Maxwell-Boltzmann distribution law, which gives the population (P) ratio between different states. It is for the transition υ = 0 ↔ 1:  

formula
where ΔE is the energy difference between the two vibrational states, kB Boltzmann's constant, and T the temperature in kelvin. Following Equation 5a, the population ratio becomes smaller as  
formula
becomes larger. At 298 K one has: 
formula
Consider as an example the antisymmetric stretching vibration of the H2O molecule that has a wavenumber of forumla = 3756 cm−1 in the gas phase. One obtains:  
formula
Thus, most of the antisymmetric vibrations of the H2O molecules are in the ground state, i.e., υ = 0, at room temperature. At 1500 K, the ratio given by Equation 11 is 0.08 and about 8% of the vibrations are in the υ = 1 state and so on. In comparison, the bending mode of the H2O molecule at forumla = 1595 cm−1 gives forumla = 4.50 · 10−4 at 298 K. These results are important for understanding the lattice-dynamic (i.e., thermodynamic) behaviour of a system.

Fig. 6.

Schematic representation of various energy levels of a diatomic molecule. An absorption of a quantum of energy from the vibrational state υ = 0 to υ = 1 corresponding to an IR transition is shown (second arrow from the left). Vibrational energy levels associated with Raman scattering are also shown. The short dashed line represents a “virtual state” that has a lower energy than the first excited electronic state. S stands for a Stokes' transition and A for an anti-Stokes' transition. In addition to the pure vibrational transitions, one can also observe finely spaced rotational transitions. These only occur in the gas state in the far infrared or microwave region. An electronic transition is shown by the arrow at the far right of the figure. The energies between the various quantum levels are not to scale.

Fig. 6.

Schematic representation of various energy levels of a diatomic molecule. An absorption of a quantum of energy from the vibrational state υ = 0 to υ = 1 corresponding to an IR transition is shown (second arrow from the left). Vibrational energy levels associated with Raman scattering are also shown. The short dashed line represents a “virtual state” that has a lower energy than the first excited electronic state. S stands for a Stokes' transition and A for an anti-Stokes' transition. In addition to the pure vibrational transitions, one can also observe finely spaced rotational transitions. These only occur in the gas state in the far infrared or microwave region. An electronic transition is shown by the arrow at the far right of the figure. The energies between the various quantum levels are not to scale.

Optical absorption spectroscopy

The experimental set-up for optical absorption measurements is similar to that for IR absorption spectroscopy (Fig. 4). The difference is that electronic transitions are measured and they usually occur at higher energies than pure vibrational transitions. They occur in the NIR/VIS/UV regions. An atom consists of a nucleus surrounded by electrons occurring in different electron orbitals (Fig. 7) and various types of electronic transitions in the outer shells can occur when they are excited by radiation. In the case of crystals with transition metal cations having d electrons, for example, the absorption process can be described using crystal field theory (CFT). It can be explained briefly as follows: The energies of the five d orbitals are degenerate (i.e., energetically equal) when they are located in an environment that is perfectly spherical. However, when a transition metal cation is located, for example, in an octahedral field, i.e. surrounded by six identical ligands located at the corners of an octahedron, its d electrons are repelled by the negatively charged anions. The two eg (dz2 and dx2–y2) orbitals point towards the ligands and are repelled to a greater extent than those of the three t2g (dxz and dyz, dxy) orbitals (Fig. 7) that are directed between the ligands. Thus, the energy levels of the d orbitals are different and they split, whereby those of the eg orbitals lie at a higher relative energy level than those of the t2g orbitals (see Fig. 2 of Wildner et al., 2004, in this volume). This splitting can be described by CFT, which is based on a point-charge model, where it can be shown (e.g. Burns, 1993) that the electrostatic field produced by the six surrounding ligands interacting with a central cation is given by:  

formula
where (ZLe) is the charge on the ligands, R is the bond length, and x, y, z are Cartesian coordinates along with the radial distance r that describe the position of the electron with respect to an atom. The first term gives the spherical part of the ligand atoms potential, and it does not contribute to the splitting of the outermost 3d orbital energy levels and is not considered further. The second term in front of the round brackets, D, is equal to forumla It can be shown that the interaction of the ligand potential with the three t2g and two egd orbitals lead to the energies: 
formula
It can be shown further within the framework of CFT that:  
formula
where Q is the ligand charge and ‹r4› a term that is approximately the same for cations of the same valence in a transition series; one ultimately obtains 10DqR−5 in this formulation.

An orbital can contain up to two electrons. Each electron is characterised by a property that can loosely be described as spin (see below), which is described by its spin quantum number either ms = +1/2 or ms = –1/2. Without going into details, it can be shown that there are two possible configurations for electron spin and they are in opposite directions. These are referred to as the spin-up or spin-down configurations in orbital energy level diagrams and they are shown by the symbols ↑ (ms = +1/2) and ↓ (ms = –1/2), respectively.

Fig. 7.

Representation of the electron clouds for atomic s, p and d orbitals (from Fyfe, 1964).

Fig. 7.

Representation of the electron clouds for atomic s, p and d orbitals (from Fyfe, 1964).

X-ray absorption spectroscopy

X-ray absorption spectroscopy (XAS) is concerned with the absorption of X-rays by deep core electrons and their excitation to an empty bound or some continuum state, and the process normally involves the K, LI, LII, LIII or MI shells (Fig. 8). The schematic experimental set-up is shown in Figure 9. XAS is an element-specific spectroscopy in which many elements of the periodic chart can be studied. Measurements are typically made on powders and not single crystals. A synchrotron provides a source of continuous and intense X-rays over a range of energies. A spectrum, typically displayed as absorption as a function of X-ray energy, can be divided into three regions with increasing energy: (i) A pre-edge region occurring at lower energies than the absorption peak itself followed by the continuously rising absorption edge. Here, the incident X-ray energy is less than the binding energy, Eb, of an electron in an orbital, hv < Eb, and electronic transitions have low occurrence probabilities. The core-level electrons can be excited to some bound state. (ii) The absorption edge itself that is characterised by the condition hvEb. Here, there is a high probability of an electronic transition occurring. Absorption occurs over a relatively narrow range of incident X-ray energies and it produces photoelectrons normally in the energy range of a few eV. (iii) The fine-structure region behind the absorption edge that is characterised by the condition hv > Eb. Here, electronic transitions have a lower probability of occurring compared to those at the absorption edge. The first pre-edge region occurs about 2–10 eV below the absorption edge proper. The second region, beginning several eV above the pre-edge and extending about 50 eV above the edge, is called the “X-ray Absorption Near Edge Structure” or the XANES region. It is characterised by sharp absorption features arising from strong multiple scattering of photoelectrons by atoms around the absorber. The third region, extending from about 50 to 1000 eV above the edge, is termed the “Extended X-ray Absorption Fine Structure” or the EXAFS region. It is characterised by weak oscillations in the spectrum that arise from weak backscattering of photoelectrons in a single scattering process.

Fig. 8.

Schematic representation of the electron orbital levels and electronic state for Al: 1s22s22p63s23p1. The arrow shows the loss of a photoelectron from the 1 s level into the conduction band. This is the K-absorption shell (modified from Marfunin, 1979).

Fig. 8.

Schematic representation of the electron orbital levels and electronic state for Al: 1s22s22p63s23p1. The arrow shows the loss of a photoelectron from the 1 s level into the conduction band. This is the K-absorption shell (modified from Marfunin, 1979).

Fig. 9.

Schematic depiction of the experimental set-up of an X-ray absorption measurement (Brown et al., 1988). The various physical processes that can result from an X-ray photon interacting with matter are shown.

Fig. 9.

Schematic depiction of the experimental set-up of an X-ray absorption measurement (Brown et al., 1988). The various physical processes that can result from an X-ray photon interacting with matter are shown.

Mössbauer spectroscopy

Mössbauer spectroscopy also involves the absorption of radiation but here, unlike IR, optical or X-ray absorption spectroscopy, the γ radiation emitted from the source is monochromatic (i.e., it has a well-defined frequency or energy) and nuclear transitions are very involved. For 57Fe Mössbauer investigations, the γ radiation has an energy of 14.4 keV. The experimental set-up is shown in Figure 10. The absorption process can be described briefly as follows: The interaction between a positively charged nucleus and negative electrons can be described to first order by a Coulombic interaction (i.e., the monopole interaction – Fig. 5). Taking into account the finite size of the nucleus, one can consider the total energy of the system and the potential field generated by the nucleus. The potential outside a nucleus varies as a function of 1/r. Inside the nucleus the potential can be considered to be constant. The wave functions for the s electrons and p electrons (Fig. 7) have finite amplitudes at r = 0 and therefore they have a finite probability density at the nucleus. Thus, the potential of the system is slightly less than if the nucleus would be represented as a simple point charge. The interaction between electrons and the nucleus is lowered and the energy of each atomic state is increased by a slight amount compared to a state where no electrons would be present as in a bare nucleus. The magnitude of this interaction is a function of the effective radius of the nucleus and the probability density of the electrons at the nucleus. As a result, the energy levels of the nuclear states are changed by its volume variations. This effect cannot be measured absolutely, however, because there is no reference energy and because the change in energy is so small.

Fig. 10.

Schematic experimental set-up of a Mössbauer measurement. The source of the γ radiation is moved back and forth with a certain velocity relative to the stationary sample.

Fig. 10.

Schematic experimental set-up of a Mössbauer measurement. The source of the γ radiation is moved back and forth with a certain velocity relative to the stationary sample.

It is here that the Mössbauer effect enters the picture, because it is possible to measure the energy difference between two nuclei when, for example, the electron density at the nucleus in the source material is different from that in the absorber. Their Mössbauer transition energies will be slightly different and this is manifested by a shift of the absorption line in a Mössbauer spectrum. The Doppler effect, as already discussed above, brings about the absorption condition. This shift is known as the isomer shift, which is one of the Mössbauer hyperfine parameters, and it is a measure of the difference in electron contact densities between two nuclei in different materials (Fig. 11). It can be expressed as:  

formula

where ZN is the nuclear charge, e the electric charge, δR the difference between the average radii of the ground and excited nuclear states, R the mean radius of the ground and excited states, and |ψ(o)|2 the electron density at the nucleus (Abs is for absorber and S for source). It is typically measured in units of mm/s, which is the velocity at which the source is moved relative to the stationary absorber.

Fig. 11.

Schematic representation of the energy transitions that are associated with Mössbauer spectroscopy. The transition shown at the far left corresponds to the hypothetical case for a bare nucleus with no surrounding electrons. The transition shown in the middle corresponds to that associated with nuclei in two different electronic environments. Here, the nucleus has a slightly different size and energy state compared to the case of a bare nucleus resulting from the monopole interaction. The transitions on the right represent the splitting of the nuclear energy levels, mI, in the case where a nucleus occurs in an environment having a non-cubic electric field gradient (EFG). The displacements and energy transitions are not to scale.

Fig. 11.

Schematic representation of the energy transitions that are associated with Mössbauer spectroscopy. The transition shown at the far left corresponds to the hypothetical case for a bare nucleus with no surrounding electrons. The transition shown in the middle corresponds to that associated with nuclei in two different electronic environments. Here, the nucleus has a slightly different size and energy state compared to the case of a bare nucleus resulting from the monopole interaction. The transitions on the right represent the splitting of the nuclear energy levels, mI, in the case where a nucleus occurs in an environment having a non-cubic electric field gradient (EFG). The displacements and energy transitions are not to scale.

A second hyperfine interaction is the electric quadrupole interaction resulting from the interplay between the nuclear quadrupole moment and the surrounding electric field gradient of an atom. A nucleus has a quadrupole moment (Fig. 5) when I ≥ 1, where I denotes the nuclear spin (see below), and it may interact with any non-cubic component of a surrounding electric field producing a splitting of the states belonging to the same I. In the case of 57Fe, the degeneracy of the I = 3/2 excited state between mI = ±1/2 and mI = ±3/2 is lifted (Fig. 11). Thus, two transitions from the lower I = 1/2 ground state are possible and this often results in two absorption lines in a Mössbauer spectrum producing a so-called quadrupole doublet. The magnitude of the quadrupole splitting is a function of the electric field gradient (EFG). The electric field, E, at the nucleus is the negative gradient of the potential V, such that E = − ∇V, where ∇ is the grad operator. The electric field gradient is the gradient of E. One has:  

formula
and the EFG can be represented as a tensor of second rank:  
formula
The tensor can be diagonalised and it can be shown that the main axes of the EFG have the relationship:  
formula
where | Vzz| ≥ | Vyy| ≥ | Vxx|. The asymmetry parameter, η, is defined as  
formula
where 0 ≤ η ≤ 1.

Ultimately an expression for the quadrupole splitting, ΔEQ, is obtained:  

formula
where Q is the nuclear quadrupole moment of the first excited state of the nucleus.

In mineralogical studies of Fe-containing substances, it is these two hyperfine parameters (i.e., δ and ΔEQ) that are used for structural and crystal-chemical characterisation. The isomer shift gives information on the valence state of Fe, on the nature of Fe–O bonding and/or the polyhedral coordination around Fe. The value of the quadrupole splitting can also give information on the valence and spin state, but it is usually used to characterise Fe-site geometry and distortion.

Magnetic resonance spectroscopies

With regards to solid-state physics, electrons and certain atomic nuclei are characterised by their charge and a property known as spin. Spin is associated with an intrinsic angular momentum, where in a classical sense one can consider it originating from the particle spinning about its own axis. From quantum mechanics it follows that the magnitude of the spin angular momentum can only have certain discrete values. Each spin is associated with a magnetic moment, μmag, that is parallel to the spin for a positively charged particle and antiparallel for a negatively charged particle. The interaction energy between μmag and an external magnetic field, B, is given by:  

formula
The energy is at a minimum when the magnetic moment has the same direction as the magnetic field and at a maximum when they are in opposite directions. One can then consider the case of an electron or an atomic nucleus having a nuclear spin when they are subjected to an external magnetic field and their respective energy levels split. The magnitude of the splitting is measured by the frequency of the radiation that causes a transition from one state to another in electron spin resonance or in nuclear magnetic resonance. The difference in frequency of radiation used for the two methods (see Fig. 1) is a result of the difference in mass between a light electron and a heavier nucleus (Table 1). The general relationship that describes the resonance process in both spectroscopies is:  
formula
where γ is the gyromagnetic ratio, e the elementary charge and M the mass of the electron or nucleus.

Nuclear magnetic resonance

The NMR effect arises from the interaction between the magnetic moment of an atomic nucleus and an external magnetic field. The nuclear magnetic moment can only have certain discrete orientations with respect to the applied magnetic field, B. The corresponding energy values are given by  

formula
where mI is one of the possible values of the spin quantum number I, which can take values of I, I–1, I–2, … –I. Nuclides having an even mass number and even charge (e.g. 16O, 12C) have zero spin, I = 0, and will not produce a NMR signal. Nuclei with I ≠ 0 have a magnetic moment and in the absence of an external magnetic field the spin states are degenerate. When such a nucleus is placed in a strong magnetic field, however, the degenerate spin states split into 2I + 1 levels with different energies (corresponding to different orientations of the magnetic moment with respect to B). Not considering any additional hyperfine interactions as, for example, the quadrupole interaction, the energy difference between neighbouring levels is:  
formula
An example is 29Si with I = 1/2 and it is important in many solid-state studies (e.g. on silicates). Here, two nuclear energy levels arise with values of mI = –1/2 and mI = +1/2 (Fig. 12). If radiation with the resonance frequency (Eqn. 26) is applied, one has the NMR or “Larmor frequency” and a certain Maxwell-Boltzmann population distribution between the levels is attained and resonance occurs.

Fig. 12.

Schematic representation of the splitting of a degenerate nuclear spin energy level as the result of an applied magnetic field in the case where I = 1/2.

Fig. 12.

Schematic representation of the splitting of a degenerate nuclear spin energy level as the result of an applied magnetic field in the case where I = 1/2.

NMR spectroscopy is a very useful local probe of structure through a measure of the chemical shift. The chemical shift is sensitive to the electronic structure around a nucleus and is affected by local structural and chemical variations in a material. Variations in these properties cause small frequency shifts, vobs = v0 + Δv, away from the NMR frequency, v0, and thereby provide structural and chemical information. The schematic set-up for a NMR experiment is shown in Figure 13.

Electron spin resonance.

Electron spin resonance spectroscopy considers energy transitions between different electron spin states in the case of paramagnetic ions, for example, when they are placed in a magnetic field. Elements with unpaired electrons of the 3d, 4d, 5d, 4f and 5f groups come into play and they can produce an ESR signal. As already stated, an electron has spin and an associated magnetic moment. When placed in a magnetic field, the spin states can split into sublevels as defined by the magnetic spin quantum number, ms, which takes values of ±1/2 for the case S = 1/2, for example. The energy difference between the levels is given by:  

formula
where μB is the Bohr magneton, B the value of applied magnetic field and g the so-called g-factor. The experimental set-up is shown in Figure 14. Radiation in the microwave region causes the transition from a lower to an upper energy level and it is a function of the strength of the external magnetic field. In Figure 15 the case is shown where ms = ±1/2 and splitting into two levels occurs, where for a single electron the magnetic moment can align either parallel or antiparallel to the external field. Because of Maxwell-Boltzmann statistics, the lower energy state is more populated than the upper state and a net absorption of radiation can occur (i.e., there are more –1/2 → +1/2 than +1/2 → –1/2 transitions). In ESR spectroscopy the frequency of radiation is held constant and the magnetic field strength is cycled over the resonance energy. Thus, a spectrum is normally presented as absorption as a function of magnetic field strength. The absorption lines are not shown directly, however, but instead their first derivative versus the field strength is plotted (i.e., the point where the signal in the spectrum crosses the abscissa at a value of dχ″/dB = 0 corresponds to the resonance maximum). The value of the g-factor, given by hv and the experimentally determined magnetic resonance field (B), defines the transition, which, in turn, depends on the structural and chemical environment where the paramagnetic ion is located.

Fig. 13.

Schematic experimental set-up of a NMR measurement. RF stands for radio frequency.

Fig. 13.

Schematic experimental set-up of a NMR measurement. RF stands for radio frequency.

Fig. 14.

Schematic experimental set-up of an ESR measurement. The source of the microwave radiation is a device known as a klystron.

Fig. 14.

Schematic experimental set-up of an ESR measurement. The source of the microwave radiation is a device known as a klystron.

Fig. 15.

Schematic representation of the splitting of a degenerate electron spin energy level, S = 1/2, as the result of an applied magnetic field.

Fig. 15.

Schematic representation of the splitting of a degenerate electron spin energy level, S = 1/2, as the result of an applied magnetic field.

Raman spectroscopy

The Raman experiment involves yet another physical process. Here, the incident radiation, normally from an intense monochromatic laser, and its inelastic scattering produces the observed effect (Fig. 16). The energy of the incident light is chosen to be lower than the first excited electronic state of the system and this is shown in Figure 6, where the short dashed line defines a “virtual state” that is different from the true excited state. The frequency of the weak, inelastically scattered component can be shifted by a certain amount from the incident frequency (v0). Scattering can be of the anti-Stokes (v0 + vR) or Stokes (v0vR) type, where vR is the frequency of the molecular or lattice vibration, for example, and the value of the two frequency terms in parentheses define the so-called Raman shift. (The two cases are shown as A and S, respectively, in Fig. 6). The energy of the scattered radiation is thus given by  

formula
Following, once again, the Maxwell-Boltzmann distribution law (Eqn. 11), the population of the ground state at υ = 0 is much greater than at υ = 1 at room temperature. Therefore, the Stokes lines are more intense than the anti-Stokes lines.

Fig. 16.

Schematic experimental set-up of a polarised single-crystal Raman measurement in the 90° scattering geometry. The direction and polarisation of the incident and scattered radiation are shown. The Raman shift is given by (v0 ± vR) and can be of the anti-Stokes or Stokes type.

Fig. 16.

Schematic experimental set-up of a polarised single-crystal Raman measurement in the 90° scattering geometry. The direction and polarisation of the incident and scattered radiation are shown. The Raman shift is given by (v0 ± vR) and can be of the anti-Stokes or Stokes type.

In IR spectroscopy the dipole moment plays the important role in the interaction between radiation and atomic vibrations, while in Raman spectroscopy it is the polarisability or the induced dipoleμind. The governing equation using classical theory for light scattering is given by:  

formula
where α0 is the equilibrium polarisability, ε0 the equilibrium amplitude of the radiation, v0 the frequency of the incident light, t the time, Δq the change in a normal coordinate of a vibration and forumla the change in polarisability with respect to a change in a normal coordinate. The first term in Equation 29 describes the elastic Rayleigh scattering (Fig. 16) and the second and third terms in the curly brackets describe the anti-Stokes and Stokes scattering, respectively. Thus, for Raman scattering to occur one must have the condition:  
formula
That is, the polarisability must change during a normal vibration for the mode to be Raman active.

Consider the simple case for the vibrations of a free XY4 molecule of tetrahedral, Td, symmetry (see Fig. 2, Beran et al., 2004, in this volume). Such a molecule will have a total of 9 internal vibrations (i.e., 3N – 6, where N is the number of atoms), besides three external translations and three rotations. The 9 internal vibrations are obtained using group theory8:  

formula
The v4 (F2) and v3 (F2) modes are triply degenerate and the v2 (E) mode is doubly degenerate. The v4 and v3 vibrations are IR active because they involve a change in the dipole moment. They can be described as being antisymmetric in nature because they result in a shift in the centre of charge of the molecule upon vibration. In contrast, all the internal modes are Raman active, because all are associated with a change in the polarisability. Symmetric-type vibrations are intense in Raman spectroscopy because they are associated with a change in the polarisability of a molecule. Thus, IR and Raman spectroscopy deliver complementary information on the so-called optic phonons of a crystal. When one uses inelastic scattering of light to investigate the acoustic phonons of a substance, the effect is known as Brillouin scattering and the method Brillouin spectroscopy is used. This technique is mainly used in the Earth Sciences to determine the elastic constants of a material.

8 The uppercase letters denote the degeneracy, where three-fold degeneracy is given as F and two-fold as E.

Spectroscopic investigations in the mineral sciences and geochemistry

As discussed briefly above, the different spectroscopic methods involve various quantum transitions between different states. The states can be electronic, nuclear or vibrational. The question is: How does one obtain compositional, structural and crystal-chemical information from a spectrum? In addition, what can one determine about the dynamics of a material at an atomistic level?

Compositional information

Because every atomic element is characterised by its own unique energetic transitions, a determination of them can reveal what kind of atom is being probed in a sample. This forms the basis for the field of spectrochemical and/or spectrometric analysis, which employs a measurement of the wavelength and the intensity of spectral lines or bands to determine the presence of a given element and its concentration in a substance, respectively. This is the general principle behind atomic absorption spectroscopy (AAS) or inductively coupled plasma (ICP) spectroscopy, for example. X-ray fluorescence and electron microprobe analysis are also spectroscopic or spectrometric types of measurement (i.e., X-ray spectrometry). Many of these and other related methods find wide use in the fields of analytical chemistry and geochemistry. An excellent source describing X-ray spectrometric methods is Bertin (1975). Spectroscopic or spectrometric methods used for compositional studies are not the central theme of this book.

Structural and crystal-chemical information

In addition to compositional or analytical information, spectra can provide information on the atom(s) being probed and its environment. Thus, local structural and crystal-chemical properties can be determined, because the experimental length scales associated with the various spectroscopies are short (for this reason the structural properties of non-crystalline materials can also be investigated). Diffraction experiments, in contrast, give crystal structure properties of a material averaged over many hundreds to thousands of unit cells and they say little about the energetic states.

In Mössbauer spectroscopy the nuclear hyperfine parameters, δ and ΔEQ, reflect local interactions that are a function of the surrounding electric field. The isomer shift gives information on the electron density at the nucleus and this reflects the spin and valence states, bonding type and ligand coordination for the cation under study. Thus, 57Fe Mössbauer spectroscopy is routinely used to determine Fe3+/ΣFe ratios in a wide variety of substances. Such a determination is time consuming using wet chemical methods and problematic with the electron microprobe, but with Mössbauer spectroscopy the measurement is relatively simple. The magnitude of the quadrupole splitting gives information on the distortion of coordination polyhedra, for example, because it affects the nature of the electric field gradient acting on the quadrupole moment of the nucleus. Thus, Mössbauer spectroscopy is an excellent method to study the intracrystalline partitioning of Fe atoms over different crystallographic sites in minerals. Partitioning behaviour can be determined by measuring the relative areas of different quadrupole doublets that are proportional to the concentration of Fe cations on the different sites. Measurements can be made as a function of temperature and pressure and variations in the hyperfine parameters can be used to infer accompanying crystal-chemical modifications. Mössbauer spectroscopy can also be used to investigate electronic charge transfer processes and magnetic properties in materials.

Nuclear magnetic resonance spectroscopy is also an element-specific nuclear method and in Earth Science investigations Si, Al and H, for example, nuclei have received much attention. The introduction of magic angle spinning that eliminates line broadening in solid samples and the construction of Fourier-transform spectrometers resulted in a burst of studies on solid-state materials. NMR, like Mössbauer spectroscopy, offers a local probe of a substance. It can be used to study the structure of amorphous and poorly crystalline materials, the structural and dynamic properties of silicate melts, cation order/disorder (i.e., largely Al and Si) behaviour in silicates, reaction mechanisms and molecular-mineral interactions, for example. NMR 29Si spectra have been recorded on rock-forming silicates in order to investigate short-range cation order and on silicate glasses to study the nature of silicate polymerisation and melt structure.

Optical absorption spectroscopy is largely used to study solid and sometimes liquid phases containing first-row transition metals, although substances with f electrons can also be investigated. Spectra can give information on the type of atom that is present, its bonding properties and its valence state. Elemental concentrations can be determined using the Beer-Lambert law (see below). Thus, optical absorption spectra can be used to determine the crystallographic site locations of transition metal cations in crystals through a determination of the number and energies of the d-orbital bands. Spectra also yield information on crystal field stabilisation energies. This information is useful for understanding the intracrystalline and also the intercrystalline partitioning behaviour of an element between different phases. Optical absorption spectra provide information relating to the nature of colour in materials. The origin of colour in gemstones, for example, is of great importance and optical absorption spectroscopy is widely used to investigate this property. The nature of cation-ligand charge transfer and cation intervalence charge transfer processes can also be investigated as well as the magnetic properties of materials.

Electron spin resonance spectroscopy is used in studies of radicals, electron-hole centres, and in geochemical investigations for the characterisation of paramagnetic ions. In the latter type, ions with unpaired d and f orbitals come into play. The 3d elements Ti, V, Cr, Mn, Fe, Co, Ni and Cu along with some rare earth elements qualify. An experimental advantage of ESR is that it is a very sensitive method. Optimal concentrations of paramagnetic ions for study are normally between 0.0001 and 0.1 atomic percent. At concentration levels above 0.1–1.0% line broadening in the spectrum normally results, due to an exchange interaction between paramagnetic ions, and spectral interpretation becomes limited. The information that one can determine with ESR is increased if single-crystal measurements are undertaken, because the crystallographic site of the element under study can be determined.

IR and Raman spectroscopy, although they measure the vibrational states of a substance, can be used to obtain structural and chemical information. In fact, IR (powder) spectroscopy is routinely used in many fields for characterising different substances and extensive “libraries” of spectra exist for identification purposes. Raman spectroscopy can be used in a similar fashion. In terms of chemical information, the OH- radical, because it has a pronounced dipole moment, is strongly IR active and it typically absorbs energy between 3700 and 2500 cm−1 in many OH--bearing minerals. Very few other types of fundamental modes occur in this wavenumber region. IR spectroscopy is a powerful method for determining small concentrations of H2O and OH-, something that is difficult with most other analytical techniques. A disadvantage is that because the OH and H2O vibrations are so IR active, the study of H2O-containing solutions is often not possible. Here, Raman spectroscopy is more suitable. In the case of single-crystal IR transmission measurements (Fig. 4), the concentration of a chemical species can be determined by measuring the intensity of the related absorption band and application of the Beer-Lambert relationship: 

formula
where I0 and I are the intensity of the incident and transmitted radiation, respectively, ε the molar absorption coefficient, c the concentration of the species and d the sample thickness. The molar absorption coefficient is compositionally and structurally dependent and it must be determined independently. Both IR and Raman spectroscopy find application in a very wide range of structural studies. They have been used to investigate glass and melt structures. They are excellently suited to study the properties of molecules in solutions or in crystals and also their adsorption properties on surfaces. Order-disorder and solid-solution behaviour in minerals can be studied over different experimental length scales by measuring spectral variations (peak splitting, line widths and wavenumber changes) as a function of structural state and composition.

XAS has become a widely used method in various studies of structure and crystal chemistry and its importance in many fields is growing quickly. An advantage is that a large number of elements can be investigated, even some of those that cannot be studied by other spectroscopic methods (e.g. Ti4+). Moreover, measurements can be made on major, minor and even trace elements in some cases. Work on minor and trace elements has become possible because of the high photon brilliance that is now available at the younger generation synchrotron facilities. Interatomic distances and bond angles, coordination number, site distortion and atomic valence states are examples of properties that can be investigated. XAS can be used to determine short-range cation order in minerals and local structural environments in glasses. Indeed, it is widely used to characterise and investigate the properties of disordered materials such as glasses, melts, gels and solutions. Nucleation and crystallisation processes, as well as studies of mineral surfaces and interfaces, can also be investigated.

Dynamical information

Many mineralogical and crystallographic investigations are concerned with static structural properties of a material such as the crystallographic positions of atoms in a crystal and the associated bond lengths and angles etc. Many geochemical studies are analytical in nature. Atoms in a material are, of course, not static, but are characterised by very rapid vibrations in the picosecond to femtosecond timescale. They have frequencies between 1012 and 1014 Hz (Fig. 1). The nature of the vibrations determines the energetics of a system and influences bonding behaviour, for example. The atomistic-level dynamic properties of geomaterials have received relatively little attention in the past, but research in this direction is growing. It is necessary to obtain such information if a system is to be understood in its entirety and, here, several spectroscopies are well suited for dynamical investigations. Dynamic studies or investigations of the evolution of a system with time are determined by the time scale of the experimental measurement and by the characteristic time scale of the process or phenomenon being investigated. In many cases one wants to obtain an instantaneous description of a system and this can be done if the interaction time between the radiation and matter is short, whereas if the interaction is too long, one obtains a time-averaged description.

As already mentioned, IR and Raman spectroscopy are two methods that are widely used to study the vibrational states of matter. The frequency of atomic, molecular or lattice vibrations are directly measured by both spectroscopies and in the case of crystals the lattice dynamic properties can be determined (see Gramaccioli, 2002). XAS and Mössbauer spectroscopy can give information on the nature of the vibrations of an atom as revealed through a determination of their respective Debye-Waller factors (see Geiger, 2004, in this volume for examples). In the case of Mössbauer spectroscopy it is defined as:  

formula
where k is the magnitude of the wavevector and 〈x2〉 is the mean square vibrational amplitude of the atom or nucleus under study. NMR spectroscopy has been used to study diffusion processes and the dynamic evolution of a system with time (Stebbins, 1988). For example, the behaviour of weakly bound molecules and their interaction with minerals (e.g. H2O in zeolites) have been investigated. Optical absorption spectra can give information on dynamic electronic processes such as the time scale of charge transfer processes. Figure 17 shows the frequency (energy)-wavevector relationships for the different spectroscopies discussed herein. It is the accessible energies, the resolutions and the ranges of momentum transfer for the various spectroscopies that are of interest (Janot & George, 1986).

Diffusion and dynamical behaviour of atoms can be studied through measurements of spectral line widths, for example, especially as a function of temperature. Here, it is important to know the lifetime of the excited state and this is determined by the Heisenberg uncertainty principle that is normally given for a photon as: 

formula
where Δx gives the uncertainty in the position of the particle and Δp the uncertainty in its momentum. One also has the analogous relationship between time and energy:  
formula
For the decay of an excited or unstable transition, Δt is related to the average lifetime, τ, of the state and ΔE is the uncertainty associated with the emitted energy. One has:  
formula
Thus, in a qualitative sense, the interaction time depends on the line width (Eqn. 36) or on the energy of the radiation – τ ∼ ħ/E (Janot & George, 1986). Take as an example the case of 57Fe in Mössbauer spectroscopy. For a return from the upper I = 3/2 state to the I = 1/2 ground state, the excited state has a mean lifetime of τ = 1.4 · 10−7 s. This corresponds to a natural line half width of Γ ≈ 5 · 10−9 eV or 0.097 mm/s. For a Mössbauer measurement involving both a source and an absorber one has a minimum experimental half width of 0.194 mm/s for an absorption line. The relaxation times associated with NMR, ESR and Mössbauer spectroscopy are shown in Figure 17. One should not forget, however, that line broadening in spectroscopic investigations can result from a number of different and unrelated processes such as from local chemical and structural heterogeneities and fluctuations. The different effects must be eliminated or accounted for when one is interested in determining the line broadening related to dynamic processes.

Fig. 17.

The frequencies/energies and wavevector moduli for various regions of the electromagnetic spectrum. The thick line indicates the relationship between the radiation frequency/energy versus the modulus of the wavevector, k, for the case of photon absorption. The observation timescales for each of the different methods are qualitatively related to the inverse of the frequency/energy of radiation or to the relaxation time (TR) associated with a given transition. Taken and modified slightly from Janot & George (1986).

Fig. 17.

The frequencies/energies and wavevector moduli for various regions of the electromagnetic spectrum. The thick line indicates the relationship between the radiation frequency/energy versus the modulus of the wavevector, k, for the case of photon absorption. The observation timescales for each of the different methods are qualitatively related to the inverse of the frequency/energy of radiation or to the relaxation time (TR) associated with a given transition. Taken and modified slightly from Janot & George (1986).

Appendix I: Some books on general solid-state spectroscopy and those relevant for investigations in the mineral sciences and geochemistry and also on chemical bonding

Bancroft
,
G.M.
(
1973
):
Mössbauer spectroscopy. An introduction for inorganic chemists and geochemists
 .
New York (N.Y.)
:
McGraw-Hill
.
Bassett
,
W.A.
(
1988
):
Synchrotron radiation applications in mineralogy and petrology.
 
Athens
:
Theophrastus
.
Bertin
,
E.P.
(
1975
):
Principles and practice of X-ray spectrometric analysis.
  2nd ed.
New York (N.Y.)
:
Plenum Press
.
Berry
,
F.J.
Vaughan
,
D.J.
(
1985
):
Chemical bonding and spectroscopy in mineral chemistry.
 
London
:
Chapman & Hall
.
Burdett
,
J.K.
(
1995
):
Chemical bonding in solids.
 
New York (N.Y.)
:
Oxford Univ. Press
.
Burns
,
R.G.
(
1970
;
1993
):
Mineralogical applications of crystal field theory.
  1st and 2nd ed.
Cambridge
:
Cambridge Univ. Press
.
Engelhardt
,
G.
Michel
,
D.
(
1987
):
High-resolution solid-state NMR of silicates and zeolites.
 
New York (N.Y.)
:
Wiley
.
Farmer
,
V.C.
(ed.) (
1974
):
The infrared spectra of minerals /Mineral. Soc. Monogr.
 ,
4
/.
London
:
Mineral. Soc
.
Hawthorne
,
F.C.
(ed.) (
1988
):
Spectroscopic methods in mineralogy and geology /Rev. Mineral.
 ,
18
/.
Washington (D.C.)
:
Mineral. Soc. Am
.,
698
p.
Kieffer
,
S.W.
Navrotsky
,
A.
(ed.) (
1988
):
Microscopic to macroscopic – atomic environments to mineral thermodynamics /Rev. Mineral.
 ,
14
/.
Washington (D.C.)
:
Mineral. Soc. Am.
,
428
p.
Kittel
,
C.
(
1976
):
Introduction to solid state physics.
 
New York (N.Y.)
:
Wiley
.
Kuzmany
,
H.
(
1998
):
Solid-state spectroscopy.
 
New York (N.Y.)
:
Springer
.
Marfunin
,
A.S.
(
1979
):
Physics of minerals and inorganic materials.
 
New York (N.Y.)
:
Springer-Verlag
.
Marfunin
,
A.S.
(
1979
):
Spectroscopy, luminescence and radiation centers in minerals.
 
New York (N.Y.)
:
Springer-Verlag
.
Pauling
,
L.
(
1939
):
The nature of the chemical bond.
 
Ithaca (N.Y.)
:
Cornell Univ. Press
.
Potts
,
P.J.
Bowles
,
J.F.W.
Reed
,
S.J.B.
Cave
,
M.R.
(eds.) (
1995
):
Microprobe techniques in the earth sciences /Mineral. Soc. Monogr
 .,
4
/.
London
:
Mineral. Soc.
 ,
419
p.
Sherwood
,
P.M.A.
(
1972
):
Vibrational spectroscopy of solids.
 
Cambridge
:
Cambridge Univ. Press
.
Strens
,
R.J.G.
(
1976
):
The physics and chemistry of minerals and rocks.
 
New York (N.Y.)
:
Wiley
.
Teo
,
B.K.
Joy
,
D.C.
(
1981
):
EXAFS spectroscopy, techniques and applications.
 
New York (N.Y.)
:
Plenum Press
.

Appendix II: Two case spectroscopic studies

It is stated in the introduction of this article that the various spectroscopic methods should generally be used, if at all possible, in a complementary fashion. If this is done, the inherent power of each of the methods can be better exploited and uncertainties in the interpretation of experimental spectra minimised. Moreover, measurements should, in some cases, be done at different physical conditions (e.g.f(T)) so that a more complete description of the system under study is obtained. In order to demonstrate this approach, and also to show various types of experimental spectra, two case studies on the structurally similar silicates cordierite and beryl are briefly reviewed. The results on cordierite are taken from a multi-spectroscopic and diffraction study addressing the crystal-chemical role of Fe in natural crystals (see Geiger et al., 2000a; Geiger et al., 2000b). In the case of beryl vibrational spectroscopic results bearing on the orientation and vibrational states of the H2O molecule are presented (Kolesov & Geiger, 2000a).

1. Fe in natural cordierite

Cordierite has the ideal formula (Mg,Fe)2Al4Si5O18 · x(H2O,CO2) but the composition of natural crystals, nearly all of which are orthorhombic with space group Cccm, can be considerably more complicated. One of the complications concerns Fe2+. It is well known that most Fe2+ occupies the single octahedral M site (Fig. 18). However, various spectroscopic studies dating from the 1970s showed that small amounts of Fe2+ can also occupy an additional structural site. Some investigators argued that this non-octahedral Fe2+ is located in the centre of the six-membered rings of tetrahedra or in the channel cavities that run parallel to the c axis, while others proposed that it replaces Si4+ or Al3+in one of the various tetrahedral sites. The crystal-chemical role of Fe3+ was also unclear. Directionally dependent charge transfer between it and octahedral Fe2+ was thought to cause the notable blue colour and strong pleochroism that are characteristic of cordierite. However, the exact structural location of Fe3+ was uncertain, as was the amount that can be incorporated in the structure. Some early investigators argued that Fe3+, like the non-octahedral Fe2+, was located in channel cavities, while others proposed the M site. In addition, the amounts of Fe2O3 reported for natural cordierites, which had mostly been determined from older wet-chemical analyses, varied considerably from 0 to 3–4 wt%. The different issues were difficult to address because most of the earlier studies had been undertaken using just one or two spectroscopic methods and the data could be interpreted in different ways. Moreover, analytical electron microprobe study was also of little help in these questions, because cordierite can show considerable nonstoichiometry, and it can contain measurable quantities of light elements like Be and Li and the channels contain variable concentrations of H2O and CO2.

To address these various issues concerning Fe in cordierite, single-crystal X-ray diffraction structure refinements and 57Fe Mössbauer, single-crystal optical absorption, XAS, and single-crystal and powder ESR spectroscopic measurements were undertaken on selected samples (Geiger et al., 2000a; Geiger et al., 2000b). With regards to Fe2+, the Mössbauer and optical absorption measurements clearly show that it could, in some cordierites, occupy two distinct structural sites. The most intense Mössbauer doublet (with δ = 1.34 mm/s at 77 K – Fig. 19) and two optical absorption bands (at about 8200 and 10000 cm−1 with E//c – Fig. 20) could be assigned unequivocally to Fe2+ in octahedral coordination. A weaker Mössbauer doublet (with δ = 1.00 mm/s at 77 K) and one or two absorption bands in the NIR region with E//a and E//b of the optical spectra were more difficult to assign (Figs. 19 and 20). Here, the single-crystal X-ray measurements proved valuable. Careful structure refinement showed that there is slight “extra” electron density on the T11 site in those samples showing two Mössbauer doublets, above that which would be the case if this site would be occupied solely by Al atoms, which is the case for the ideal formula (no “extra” electron density was observed in those cordierites with just one Mössbauer doublet). However, the X-ray results alone cannot determine which element gives rise to the “excess” electron density. For the cordierites under study, the only element that comes under consideration is Fe (the presence of Be, Li and Mg would decrease the electron density). Thus, one can assign the weak Mössbauer doublet and the NIR bands in the E//a and E//b optical absorption spectra to Fe2+ on T11. The relative intensities of the two Mössbauer doublets give the intracrystalline partitioning of Fe2+between the M and T11 sites. It turns out that up to about 10 atomic % of the total Fe in cordierite can occupy the T11 site in some samples. The optical absorption measurements initially proved difficult to interpret, because Fe2+ in tetrahedral coordination should give rise to three separate bands and because the band around 10,500–10,000 cm−1 in the E//a and E//b spectra appears too intense for such small amounts for Fe2+. Both can be explained by having a large Fe2+ cation in a small and distorted tetrahedral site such as T11. The X-ray absorption spectra of cordierite measured at the Fe K edge are dominated in the XANES region by features similar to those of iron-containing olivine and are clearly related to the presence of major octahedral Fe2+ (Fig. 21). The pre-edge region is more interesting. It shows weak absorption features that can be fit by three separate Gaussians in all cordierites, and also in olivine, with all components having similar energies (Fig. 22). However, the relative intensities of the Gaussians are different between those cordierite samples containing tetrahedral Fe2+versus those that do not.

Fig. 18.

Polyhedral model of the cordierite structure, space group Cccm, projected onto (001). The blue octahedra are the M sites, the red tetrahedra contain Si and the light green tetrahedra edge-shared with the M site octahedra are the T11 tetrahedra. The yellow spheres represent alkali cations like Na or K.

Fig. 18.

Polyhedral model of the cordierite structure, space group Cccm, projected onto (001). The blue octahedra are the M sites, the red tetrahedra contain Si and the light green tetrahedra edge-shared with the M site octahedra are the T11 tetrahedra. The yellow spheres represent alkali cations like Na or K.

Fig. 19.

57Fe Mössbauer spectrum of four cordierites recorded at 77 K (modified from Geiger et al., 2000b). Note that two Mg-rich cordierites from Zimbabwe (DA-1) and Kiranur, India (42/IA) have two Fe2+ quadrupole split doublets, while the other two spectra (Sundsvall, Sweden, C005 and Dolni Bory, Czech Republic, TUB-1) only have one.

Fig. 19.

57Fe Mössbauer spectrum of four cordierites recorded at 77 K (modified from Geiger et al., 2000b). Note that two Mg-rich cordierites from Zimbabwe (DA-1) and Kiranur, India (42/IA) have two Fe2+ quadrupole split doublets, while the other two spectra (Sundsvall, Sweden, C005 and Dolni Bory, Czech Republic, TUB-1) only have one.

Fig. 20.

Polarised single-crystal optical absorption spectra of an iron-rich cordierite (Dolni Bory, TUB-1) and the Mg-rich crystal from Kiranur (42/IA) between 35,000 and 4,500 cm−1 recorded at room temperature. The polarisation directions of the radiation are shown. The two bands at about 10,000 and 8,000 cm−1 in the E//c spectrum (solid line) are related to Fe2+ in octahedral coordination. The band at about 10,500 cm−1 in the E//a (dashed line) and E//b (dotted line) spectra is thought to be due to Fe2+ located at T11, while the other two associated bands are much weaker and are located at lower energies. The weak, very broad band centred around 18,000 cm−1 is due to Fe2+–Fe3+ charge transfer. It is polarised and is most intense with E//b. The very sharp intense bands in the NIR are overtone and combination bands related to molecular H2O occurring in the channel cavities of cordierite (from Geiger et al., 2000b).

Fig. 20.

Polarised single-crystal optical absorption spectra of an iron-rich cordierite (Dolni Bory, TUB-1) and the Mg-rich crystal from Kiranur (42/IA) between 35,000 and 4,500 cm−1 recorded at room temperature. The polarisation directions of the radiation are shown. The two bands at about 10,000 and 8,000 cm−1 in the E//c spectrum (solid line) are related to Fe2+ in octahedral coordination. The band at about 10,500 cm−1 in the E//a (dashed line) and E//b (dotted line) spectra is thought to be due to Fe2+ located at T11, while the other two associated bands are much weaker and are located at lower energies. The weak, very broad band centred around 18,000 cm−1 is due to Fe2+–Fe3+ charge transfer. It is polarised and is most intense with E//b. The very sharp intense bands in the NIR are overtone and combination bands related to molecular H2O occurring in the channel cavities of cordierite (from Geiger et al., 2000b).

Fig. 21.

X-ray absorption spectrum at the Fe K edge for four natural cordierites and a natural Fe-Mg olivine recorded at room temperature (from Geiger et al., 2000b).

Fig. 21.

X-ray absorption spectrum at the Fe K edge for four natural cordierites and a natural Fe-Mg olivine recorded at room temperature (from Geiger et al., 2000b).

To address the issue of Fe3+ in cordierite, further spectroscopic measurements were made. Here, optical absorption spectroscopy is of little use, because there are no spin-allowed d-orbital transitions in the case of 3d5 cations. Mössbauer measurements can detect Fe3+ and be used to determine its site location, but the concentration of Fe3+ in cordierite is so low that Mössbauer spectroscopy lacks the necessary experimental sensitivity to make this determination. For the same reason, X-ray diffraction refinements are of no help. Fortunately, the ESR experiment is ideally suitable for this question, because Fe3+ has unpaired d electrons and is therefore ESR active and this spectroscopic method works excellently, moreover, at low concentration levels. In addition, single-crystal measurements can be used to determine the crystallographic site on which Fe3+ is located. Powder (Fig. 23) and single-crystal ESR measurements were undertaken on Mg-rich cordierites and they show that Fe3+, like the non-octahedral Fe2+, is located exclusively on the T11 site (Fig. 18). It is, therefore, intravalence electron charge transfer between octahedral Fe2+ and Fe3+ on T11 that causes the spectacular blue colour and pleochroism associated with cordierite. Indeed, a broad charge transfer band is located in the E//a and E//b optical spectra in the visible region around 17,500 cm−1 (Fig. 20). This band is polarised and, thus, “electron hopping” occurs in the a–b plane between edge-sharing octahedra and T11 tetrahedra. The intravalence charge transfer effect produces intense bands, although the concentration of neighbouring Fe2+–Fe3+ pairs is very low. The concentration of Fe3+ cannot be determined through ESR measurements because of a lack of suitable reference standards. Here, Mössbauer spectroscopy is of use, because it can set an upper limit on the amount of Fe3+. Its sensitivity is roughly 1 atomic % for Fe and, because most (if not all) cordierites show no clearly measurable Fe3+ doublet, one can infer that natural cordierite crystals must have less than 0.004 Fe3+ cations per formula unit.

Fig. 22.

Fe pre-K-edge XAS spectra for four natural cordierites (ad) and olivine (e) recorded at room temperature (from Geiger et al., 2000b). Note the difference in intensity of the band at about 7114.3 eV in the various samples (compare to Fig. 19).

Fig. 22.

Fe pre-K-edge XAS spectra for four natural cordierites (ad) and olivine (e) recorded at room temperature (from Geiger et al., 2000b). Note the difference in intensity of the band at about 7114.3 eV in the various samples (compare to Fig. 19).

As a result of these spectroscopic measurements and by using published analytical results on cordierite, many natural crystals can be described by the general formula Ch[Na, K]y(Mg, Fe2+, Mn2+, Li)2(Al, Be, Mg, Fe2+, Fe3+)4Si5O18 · xCh[H2O, CO2], where both y and x < 1.0. The distorted T11 site is clearly unusual crystal chemically because it can contain a variety of cations including Al, Be, Mg, along with Fe2+ and Fe3+.

Fig. 23.

Comparison of the experimental powder ESR spectrum of cordierite DA-1 and a calculated spectrum assuming that Fe3+ is located on the T11 site (from Geiger et al., 2000a). Trace amounts of Mn2+ are also present in the sample.

Fig. 23.

Comparison of the experimental powder ESR spectrum of cordierite DA-1 and a calculated spectrum assuming that Fe3+ is located on the T11 site (from Geiger et al., 2000a). Trace amounts of Mn2+ are also present in the sample.

2. H2O in synthetic alkali-free hydrous beryl

Beryl, space group P6/mcc, is isostructural with high cordierite that has a disordered distribution of Al and Si. Both of these ring silicates are interesting because they can incorporate very weakly bound molecules (e.g. H2O, CO2, N2 and possibly CH4) and neutral atoms (e.g. Ar) in their channel cavities (see Kolesov & Geiger, 2000a; Kolesov & Geiger, 2000b for a list of references). This situation allows one to study the dynamic and energetic states of the nearly “free” molecules over a range of temperature. Here, we are interested in the case of the H2O molecule, which is of central importance in many geochemical processes, in beryl. The room temperature polarised single-crystal IR spectrum of synthetic hydrous beryl, Al2Be3Si6O18 · x(H2O), is shown between 3400 cm−1 and 4000 cm−1 both parallel and perpendicular to the crystallographic c axis in Figure 24. Only a single band at 3700 cm−1 is present when the IR radiation is polarised parallel to the c axis and it corresponds to the antisymmetric stretching vibration, v3, of the H2O molecule. The high energy indicates that the molecule has little interaction with the beryl framework. The symmetric, v1, vibration is IR active, but it is too weak to be observed in any crystal orientation. Because v3 is most intense parallel to the c axis and absent perpendicular to it, demonstrates that the change in the dipole moment vector of the H2O molecule, and therefore the H–H vector, is parallel to this direction. In order to obtain more information on the H2O molecule it is necessary to consider beryl's Raman spectrum. Figure 25 shows a number of single-crystal Raman spectra in the wavenumber region of the internal H2O vibrations from 5 K to 300 K. The symmetric v1 vibration around 3600 cm−1 is present at all temperatures, while the v3 vibration at about 3700 cm−1 is only observable below about 260 K. The energy difference between 3 and 1 at 298 K is 93 cm−1 and is close to that for a “free” H2O molecule (i.e., 100 cm−1). In addition to the sharp bands related to internal H2O vibrations, broad bands are located at about 3686 and 3711 cm−1 at 5 K and they shift measurably with increasing temperature (see Fig. 25). They are combination modes of the sort (v3 ± nω) with ω ∼ 9 cm−1 and n = 1, 2, 3, 4…, where the ω bands are thought to represent low-energy external translations of the H2O molecule. The bands are broad because this is generally the case for combination modes and it reflects an anharmonic potential for the interaction. There are combination modes located on each side of v3, because both Stokes and anti-Stokes scattering occurs. The lower energy band increases slightly in its integrated intensity with increasing temperature, while the higher energy band decreases slightly. In addition, the lower energy combination band shifts to lower energies (∼3649 cm−1 at 295 K) and the higher energy band to higher energies with increasing temperature (3749 cm−1 at 295 K). This behaviour is in agreement with the Maxwell-Boltzmann relationship and the physical processes behind Stokes and anti-Stokes scattering. The nature of band broadening is related to the way the vibrational levels are populated as a function of temperature as shown schematically in Figure 26.

Fig. 24.

Polarised single-crystal IR spectrum of synthetic hydrous beryl at room temperature parallel (solid line) and perpendicular (dashed line) to the crystallographic c axis in the wavenumber range of the internal H2O stretching vibrations. The crystal platelet is 0.050 mm thick (from Kolesov & Geiger, 2000a).

Fig. 24.

Polarised single-crystal IR spectrum of synthetic hydrous beryl at room temperature parallel (solid line) and perpendicular (dashed line) to the crystallographic c axis in the wavenumber range of the internal H2O stretching vibrations. The crystal platelet is 0.050 mm thick (from Kolesov & Geiger, 2000a).

Fig. 25.

Single-crystal (XZ) Raman spectra of synthetic hydrous beryl between 5 and 300 K in the wavenumber region from 3550 to 3800 cm−1 showing the sharp v3 (3702 cm−1) and v1 (3600 cm−1) vibrations and combination modes of the type v3 ± nω, where v3 is the antisymmetric H2O stretching mode, ω a very low wavenumber Tz mode and n = 1, 2, 3… (from Kolesov & Geiger, 2000a). At 295 K the two combination modes are located at approximately 3649 cm−1 and 3749 cm−1, but note their wavenumber evolution with decreasing temperature.

Fig. 25.

Single-crystal (XZ) Raman spectra of synthetic hydrous beryl between 5 and 300 K in the wavenumber region from 3550 to 3800 cm−1 showing the sharp v3 (3702 cm−1) and v1 (3600 cm−1) vibrations and combination modes of the type v3 ± nω, where v3 is the antisymmetric H2O stretching mode, ω a very low wavenumber Tz mode and n = 1, 2, 3… (from Kolesov & Geiger, 2000a). At 295 K the two combination modes are located at approximately 3649 cm−1 and 3749 cm−1, but note their wavenumber evolution with decreasing temperature.

Fig. 26.

Schematic representation showing qualitatively the Stokes' and anti-Stokes' processes governing the scattering of the combination mode, v3 ± nω, as a function of temperature (from Kolesov & Geiger, 2000a).

Fig. 26.

Schematic representation showing qualitatively the Stokes' and anti-Stokes' processes governing the scattering of the combination mode, v3 ± nω, as a function of temperature (from Kolesov & Geiger, 2000a).

The ω modes have A1 symmetry, because from group theory one has: 

formula
Thus, they should represent external Tz translations of the H2O molecule that occur parallel to the C2 molecular axis. These translation modes are too low in energy to be measured by “standard” IR and Raman spectroscopy as they occur in the microwave part of the electromagnetic spectrum.

The intensity of the v1 stretching band as a function of the crystal orientation around the [0001] axis does not change at 298 K and this shows that the plane of the H2O molecule is disordered around the [0001] axis of the crystal. This is consistent with the C6 symmetry of the channel cavity in beryl. Thus, the H2O molecule is rotationally disordered having a rapid anisotropic motion. The v3 vibration becomes observable in the Raman spectra at low temperatures and this could possibly be related to the formation of very weak hydrogen bonds between the H2O molecule and the beryl framework at low temperatures, although this issue needs more work. These Raman scattering results are consistent with paraelectric resonance spectra9 and dielectric dispersion measurements by Rehm (1974) that show that the H2O molecule in beryl is rotationally disordered in the cavities down to 4.2 K. Proton NMR measurements suggest the same behaviour (Pare & Ducrois, 1996).

9 Here one is interested in the orientation polarisation of the H2O molecule and its associated dipole moment.

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Figures & Tables

Fig. 1.

The electromagnetic spectrum showing the different regions (middle part of figure). The various quantum transitions associated with each region are shown along with the corresponding spectroscopic type (above). At the bottom the wavenumbers, wavelengths, frequencies and energies across the spectrum are given.

Fig. 1.

The electromagnetic spectrum showing the different regions (middle part of figure). The various quantum transitions associated with each region are shown along with the corresponding spectroscopic type (above). At the bottom the wavenumbers, wavelengths, frequencies and energies across the spectrum are given.

Fig. 2.

Wave representation of plane-polarised electromagnetic radiation. The electric and magnetic fields are at right angles to each other and propagate in the Y direction. The wavelength is given by λ. The amplitude is given at the wave maximum as shown by the thin lines with arrows.

Fig. 2.

Wave representation of plane-polarised electromagnetic radiation. The electric and magnetic fields are at right angles to each other and propagate in the Y direction. The wavelength is given by λ. The amplitude is given at the wave maximum as shown by the thin lines with arrows.

Fig. 3.

Schematic representations of various processes that can occur when radiation interacts with an atom. The incident photon is shown as a wave characterised by a given k and ω. The transmitted or scattered radiation can be in-phase or out-of-phase (k′) with the incident radiation and have the same or a different angular frequency (ω′). The spaced horizontal lines represent different energy levels of the atom and the lowest level represents the ground state. The various types of processes are: a) no interaction between radiation and matter, b) elastic scattering, c) absorption (no emitted photon), d) stimulated or induced emission, e) spontaneous emission (no incident photon as in flame emission spectroscopy), f) resonance absorption, g) absorption and photoelectron ejection, h) inelastic scattering, and i) photoluminescence.

Fig. 3.

Schematic representations of various processes that can occur when radiation interacts with an atom. The incident photon is shown as a wave characterised by a given k and ω. The transmitted or scattered radiation can be in-phase or out-of-phase (k′) with the incident radiation and have the same or a different angular frequency (ω′). The spaced horizontal lines represent different energy levels of the atom and the lowest level represents the ground state. The various types of processes are: a) no interaction between radiation and matter, b) elastic scattering, c) absorption (no emitted photon), d) stimulated or induced emission, e) spontaneous emission (no incident photon as in flame emission spectroscopy), f) resonance absorption, g) absorption and photoelectron ejection, h) inelastic scattering, and i) photoluminescence.

Fig. 4.

Schematic experimental set-up of a polarised (polariser not explicitly shown) single-crystal IR absorption measurement. The direction and polarisation of the incident radiation are shown.

Fig. 4.

Schematic experimental set-up of a polarised (polariser not explicitly shown) single-crystal IR absorption measurement. The direction and polarisation of the incident radiation are shown.

Fig. 5.

Schematic representation of an electric monopole, a dipole and two types of a quadrupole.

Fig. 5.

Schematic representation of an electric monopole, a dipole and two types of a quadrupole.

Fig. 6.

Schematic representation of various energy levels of a diatomic molecule. An absorption of a quantum of energy from the vibrational state υ = 0 to υ = 1 corresponding to an IR transition is shown (second arrow from the left). Vibrational energy levels associated with Raman scattering are also shown. The short dashed line represents a “virtual state” that has a lower energy than the first excited electronic state. S stands for a Stokes' transition and A for an anti-Stokes' transition. In addition to the pure vibrational transitions, one can also observe finely spaced rotational transitions. These only occur in the gas state in the far infrared or microwave region. An electronic transition is shown by the arrow at the far right of the figure. The energies between the various quantum levels are not to scale.

Fig. 6.

Schematic representation of various energy levels of a diatomic molecule. An absorption of a quantum of energy from the vibrational state υ = 0 to υ = 1 corresponding to an IR transition is shown (second arrow from the left). Vibrational energy levels associated with Raman scattering are also shown. The short dashed line represents a “virtual state” that has a lower energy than the first excited electronic state. S stands for a Stokes' transition and A for an anti-Stokes' transition. In addition to the pure vibrational transitions, one can also observe finely spaced rotational transitions. These only occur in the gas state in the far infrared or microwave region. An electronic transition is shown by the arrow at the far right of the figure. The energies between the various quantum levels are not to scale.

Fig. 7.

Representation of the electron clouds for atomic s, p and d orbitals (from Fyfe, 1964).

Fig. 7.

Representation of the electron clouds for atomic s, p and d orbitals (from Fyfe, 1964).

Fig. 8.

Schematic representation of the electron orbital levels and electronic state for Al: 1s22s22p63s23p1. The arrow shows the loss of a photoelectron from the 1 s level into the conduction band. This is the K-absorption shell (modified from Marfunin, 1979).

Fig. 8.

Schematic representation of the electron orbital levels and electronic state for Al: 1s22s22p63s23p1. The arrow shows the loss of a photoelectron from the 1 s level into the conduction band. This is the K-absorption shell (modified from Marfunin, 1979).

Fig. 9.

Schematic depiction of the experimental set-up of an X-ray absorption measurement (Brown et al., 1988). The various physical processes that can result from an X-ray photon interacting with matter are shown.

Fig. 9.

Schematic depiction of the experimental set-up of an X-ray absorption measurement (Brown et al., 1988). The various physical processes that can result from an X-ray photon interacting with matter are shown.

Fig. 10.

Schematic experimental set-up of a Mössbauer measurement. The source of the γ radiation is moved back and forth with a certain velocity relative to the stationary sample.

Fig. 10.

Schematic experimental set-up of a Mössbauer measurement. The source of the γ radiation is moved back and forth with a certain velocity relative to the stationary sample.

Fig. 11.

Schematic representation of the energy transitions that are associated with Mössbauer spectroscopy. The transition shown at the far left corresponds to the hypothetical case for a bare nucleus with no surrounding electrons. The transition shown in the middle corresponds to that associated with nuclei in two different electronic environments. Here, the nucleus has a slightly different size and energy state compared to the case of a bare nucleus resulting from the monopole interaction. The transitions on the right represent the splitting of the nuclear energy levels, mI, in the case where a nucleus occurs in an environment having a non-cubic electric field gradient (EFG). The displacements and energy transitions are not to scale.

Fig. 11.

Schematic representation of the energy transitions that are associated with Mössbauer spectroscopy. The transition shown at the far left corresponds to the hypothetical case for a bare nucleus with no surrounding electrons. The transition shown in the middle corresponds to that associated with nuclei in two different electronic environments. Here, the nucleus has a slightly different size and energy state compared to the case of a bare nucleus resulting from the monopole interaction. The transitions on the right represent the splitting of the nuclear energy levels, mI, in the case where a nucleus occurs in an environment having a non-cubic electric field gradient (EFG). The displacements and energy transitions are not to scale.

Fig. 12.

Schematic representation of the splitting of a degenerate nuclear spin energy level as the result of an applied magnetic field in the case where I = 1/2.

Fig. 12.

Schematic representation of the splitting of a degenerate nuclear spin energy level as the result of an applied magnetic field in the case where I = 1/2.

Fig. 13.

Schematic experimental set-up of a NMR measurement. RF stands for radio frequency.

Fig. 13.

Schematic experimental set-up of a NMR measurement. RF stands for radio frequency.

Fig. 14.

Schematic experimental set-up of an ESR measurement. The source of the microwave radiation is a device known as a klystron.

Fig. 14.

Schematic experimental set-up of an ESR measurement. The source of the microwave radiation is a device known as a klystron.

Fig. 15.

Schematic representation of the splitting of a degenerate electron spin energy level, S = 1/2, as the result of an applied magnetic field.

Fig. 15.

Schematic representation of the splitting of a degenerate electron spin energy level, S = 1/2, as the result of an applied magnetic field.

Fig. 16.

Schematic experimental set-up of a polarised single-crystal Raman measurement in the 90° scattering geometry. The direction and polarisation of the incident and scattered radiation are shown. The Raman shift is given by (v0 ± vR) and can be of the anti-Stokes or Stokes type.

Fig. 16.

Schematic experimental set-up of a polarised single-crystal Raman measurement in the 90° scattering geometry. The direction and polarisation of the incident and scattered radiation are shown. The Raman shift is given by (v0 ± vR) and can be of the anti-Stokes or Stokes type.

Fig. 17.

The frequencies/energies and wavevector moduli for various regions of the electromagnetic spectrum. The thick line indicates the relationship between the radiation frequency/energy versus the modulus of the wavevector, k, for the case of photon absorption. The observation timescales for each of the different methods are qualitatively related to the inverse of the frequency/energy of radiation or to the relaxation time (TR) associated with a given transition. Taken and modified slightly from Janot & George (1986).

Fig. 17.

The frequencies/energies and wavevector moduli for various regions of the electromagnetic spectrum. The thick line indicates the relationship between the radiation frequency/energy versus the modulus of the wavevector, k, for the case of photon absorption. The observation timescales for each of the different methods are qualitatively related to the inverse of the frequency/energy of radiation or to the relaxation time (TR) associated with a given transition. Taken and modified slightly from Janot & George (1986).

Fig. 18.

Polyhedral model of the cordierite structure, space group Cccm, projected onto (001). The blue octahedra are the M sites, the red tetrahedra contain Si and the light green tetrahedra edge-shared with the M site octahedra are the T11 tetrahedra. The yellow spheres represent alkali cations like Na or K.

Fig. 18.

Polyhedral model of the cordierite structure, space group Cccm, projected onto (001). The blue octahedra are the M sites, the red tetrahedra contain Si and the light green tetrahedra edge-shared with the M site octahedra are the T11 tetrahedra. The yellow spheres represent alkali cations like Na or K.

Fig. 19.

57Fe Mössbauer spectrum of four cordierites recorded at 77 K (modified from Geiger et al., 2000b). Note that two Mg-rich cordierites from Zimbabwe (DA-1) and Kiranur, India (42/IA) have two Fe2+ quadrupole split doublets, while the other two spectra (Sundsvall, Sweden, C005 and Dolni Bory, Czech Republic, TUB-1) only have one.

Fig. 19.

57Fe Mössbauer spectrum of four cordierites recorded at 77 K (modified from Geiger et al., 2000b). Note that two Mg-rich cordierites from Zimbabwe (DA-1) and Kiranur, India (42/IA) have two Fe2+ quadrupole split doublets, while the other two spectra (Sundsvall, Sweden, C005 and Dolni Bory, Czech Republic, TUB-1) only have one.

Fig. 20.

Polarised single-crystal optical absorption spectra of an iron-rich cordierite (Dolni Bory, TUB-1) and the Mg-rich crystal from Kiranur (42/IA) between 35,000 and 4,500 cm−1 recorded at room temperature. The polarisation directions of the radiation are shown. The two bands at about 10,000 and 8,000 cm−1 in the E//c spectrum (solid line) are related to Fe2+ in octahedral coordination. The band at about 10,500 cm−1 in the E//a (dashed line) and E//b (dotted line) spectra is thought to be due to Fe2+ located at T11, while the other two associated bands are much weaker and are located at lower energies. The weak, very broad band centred around 18,000 cm−1 is due to Fe2+–Fe3+ charge transfer. It is polarised and is most intense with E//b. The very sharp intense bands in the NIR are overtone and combination bands related to molecular H2O occurring in the channel cavities of cordierite (from Geiger et al., 2000b).

Fig. 20.

Polarised single-crystal optical absorption spectra of an iron-rich cordierite (Dolni Bory, TUB-1) and the Mg-rich crystal from Kiranur (42/IA) between 35,000 and 4,500 cm−1 recorded at room temperature. The polarisation directions of the radiation are shown. The two bands at about 10,000 and 8,000 cm−1 in the E//c spectrum (solid line) are related to Fe2+ in octahedral coordination. The band at about 10,500 cm−1 in the E//a (dashed line) and E//b (dotted line) spectra is thought to be due to Fe2+ located at T11, while the other two associated bands are much weaker and are located at lower energies. The weak, very broad band centred around 18,000 cm−1 is due to Fe2+–Fe3+ charge transfer. It is polarised and is most intense with E//b. The very sharp intense bands in the NIR are overtone and combination bands related to molecular H2O occurring in the channel cavities of cordierite (from Geiger et al., 2000b).

Fig. 21.

X-ray absorption spectrum at the Fe K edge for four natural cordierites and a natural Fe-Mg olivine recorded at room temperature (from Geiger et al., 2000b).

Fig. 21.

X-ray absorption spectrum at the Fe K edge for four natural cordierites and a natural Fe-Mg olivine recorded at room temperature (from Geiger et al., 2000b).

Fig. 22.

Fe pre-K-edge XAS spectra for four natural cordierites (ad) and olivine (e) recorded at room temperature (from Geiger et al., 2000b). Note the difference in intensity of the band at about 7114.3 eV in the various samples (compare to Fig. 19).

Fig. 22.

Fe pre-K-edge XAS spectra for four natural cordierites (ad) and olivine (e) recorded at room temperature (from Geiger et al., 2000b). Note the difference in intensity of the band at about 7114.3 eV in the various samples (compare to Fig. 19).

Fig. 23.

Comparison of the experimental powder ESR spectrum of cordierite DA-1 and a calculated spectrum assuming that Fe3+ is located on the T11 site (from Geiger et al., 2000a). Trace amounts of Mn2+ are also present in the sample.

Fig. 23.

Comparison of the experimental powder ESR spectrum of cordierite DA-1 and a calculated spectrum assuming that Fe3+ is located on the T11 site (from Geiger et al., 2000a). Trace amounts of Mn2+ are also present in the sample.

Fig. 24.

Polarised single-crystal IR spectrum of synthetic hydrous beryl at room temperature parallel (solid line) and perpendicular (dashed line) to the crystallographic c axis in the wavenumber range of the internal H2O stretching vibrations. The crystal platelet is 0.050 mm thick (from Kolesov & Geiger, 2000a).

Fig. 24.

Polarised single-crystal IR spectrum of synthetic hydrous beryl at room temperature parallel (solid line) and perpendicular (dashed line) to the crystallographic c axis in the wavenumber range of the internal H2O stretching vibrations. The crystal platelet is 0.050 mm thick (from Kolesov & Geiger, 2000a).

Fig. 25.

Single-crystal (XZ) Raman spectra of synthetic hydrous beryl between 5 and 300 K in the wavenumber region from 3550 to 3800 cm−1 showing the sharp v3 (3702 cm−1) and v1 (3600 cm−1) vibrations and combination modes of the type v3 ± nω, where v3 is the antisymmetric H2O stretching mode, ω a very low wavenumber Tz mode and n = 1, 2, 3… (from Kolesov & Geiger, 2000a). At 295 K the two combination modes are located at approximately 3649 cm−1 and 3749 cm−1, but note their wavenumber evolution with decreasing temperature.

Fig. 25.

Single-crystal (XZ) Raman spectra of synthetic hydrous beryl between 5 and 300 K in the wavenumber region from 3550 to 3800 cm−1 showing the sharp v3 (3702 cm−1) and v1 (3600 cm−1) vibrations and combination modes of the type v3 ± nω, where v3 is the antisymmetric H2O stretching mode, ω a very low wavenumber Tz mode and n = 1, 2, 3… (from Kolesov & Geiger, 2000a). At 295 K the two combination modes are located at approximately 3649 cm−1 and 3749 cm−1, but note their wavenumber evolution with decreasing temperature.

Fig. 26.

Schematic representation showing qualitatively the Stokes' and anti-Stokes' processes governing the scattering of the combination mode, v3 ± nω, as a function of temperature (from Kolesov & Geiger, 2000a).

Fig. 26.

Schematic representation showing qualitatively the Stokes' and anti-Stokes' processes governing the scattering of the combination mode, v3 ± nω, as a function of temperature (from Kolesov & Geiger, 2000a).

Table 1.

Fundamental physical constants*.

cvelocity of light in vacuum2.997 924 58 · 108 m/s
hPlanck's constant6.626 069 · 10−34 J/s
ħ(= h/2π)1.054 571 · 10−34 J/s
eelectronic charge1.602 176 · 10−19 C
μeelectron magnetic moment−928.476 362 · 10−26 J/T
μBBohr magneton927.400 899 · 10−26 J/T
μNnuclear magneton5.050 783 17 · 10−27 J/T
meelectron mass9.109 381 88 · 10−31 kg
mPproton mass1.672 621 58 · 10−27 kg
mNneutron mass1.674 927 16 · 10−27 kg
kBBoltzmann's constant1.380 650 · 10−23 J/K
NAAvogadro's constant6.022 142 · 1023
Rmolar gas constantNA · kB = 8.314 472 J/mol·K
FFaraday constant96 485.3415 C/mol
geg electron factor−2.002 319
αfine structure constant (e2/4πε0ħc)7.297 352 533 · 10−3
cvelocity of light in vacuum2.997 924 58 · 108 m/s
hPlanck's constant6.626 069 · 10−34 J/s
ħ(= h/2π)1.054 571 · 10−34 J/s
eelectronic charge1.602 176 · 10−19 C
μeelectron magnetic moment−928.476 362 · 10−26 J/T
μBBohr magneton927.400 899 · 10−26 J/T
μNnuclear magneton5.050 783 17 · 10−27 J/T
meelectron mass9.109 381 88 · 10−31 kg
mPproton mass1.672 621 58 · 10−27 kg
mNneutron mass1.674 927 16 · 10−27 kg
kBBoltzmann's constant1.380 650 · 10−23 J/K
NAAvogadro's constant6.022 142 · 1023
Rmolar gas constantNA · kB = 8.314 472 J/mol·K
FFaraday constant96 485.3415 C/mol
geg electron factor−2.002 319
αfine structure constant (e2/4πε0ħc)7.297 352 533 · 10−3
Table 2.

SI prefixes.

FactorPrefixSymbolFactorPrefixSymbol

1024yottaY10−1decid
1021zettaZ10−2centic
1018exaE10−3millim
1015petaP10−6microμ
1012teraT10−9nanon
109gigaG10−12picop
106megaM10−15femtof
103kilok10−18attoa
102hectoh10−21zeptoz
101dekada10−24yoctoy
FactorPrefixSymbolFactorPrefixSymbol

1024yottaY10−1decid
1021zettaZ10−2centic
1018exaE10−3millim
1015petaP10−6microμ
1012teraT10−9nanon
109gigaG10−12picop
106megaM10−15femtof
103kilok10−18attoa
102hectoh10−21zeptoz
101dekada10−24yoctoy
Table 3.

Energy units and conversion factors*.

UnitJm−1HzeV

1 J(1 J) = 1 J(1 J)/hc = 5.034 · 1024 m−1(1 J)/h = 1.509 · 1033 Hz(1 J) = 6.241 · 1018 eV
1 m−1(1 m−1)hc = 1.986 · 10−25 J(1 m−1) = 1 m−1(1 m−1)c = 299 792 Hz(1 m−1)hc = 1.240 · 10−6 eV
1 Hz(1 Hz)h = 6.626 · 10−34 J(1 Hz)/c = 3.335 · 10−9 m−1(1 Hz) = 1 Hz(1 Hz)h = 4.136 · 10−15 eV
1 eV(1 eV) = 1.602 · 10−19 J(1 eV)/hc = 8.065 · 105 m−1(1 eV)/h = 2.417 · 1014 Hz(1 eV) = 1 eV
UnitJm−1HzeV

1 J(1 J) = 1 J(1 J)/hc = 5.034 · 1024 m−1(1 J)/h = 1.509 · 1033 Hz(1 J) = 6.241 · 1018 eV
1 m−1(1 m−1)hc = 1.986 · 10−25 J(1 m−1) = 1 m−1(1 m−1)c = 299 792 Hz(1 m−1)hc = 1.240 · 10−6 eV
1 Hz(1 Hz)h = 6.626 · 10−34 J(1 Hz)/c = 3.335 · 10−9 m−1(1 Hz) = 1 Hz(1 Hz)h = 4.136 · 10−15 eV
1 eV(1 eV) = 1.602 · 10−19 J(1 eV)/hc = 8.065 · 105 m−1(1 eV)/h = 2.417 · 1014 Hz(1 eV) = 1 eV

Contents

GeoRef

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