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Chapter 1: Introduction
Chapter 1: Introduction
1.1 G EOCHEMISTRY
he term “geochemistry” was first used by the German-Swiss chemist Christian Friedrich Schönbein ‡^ in 1838. You might guess, merely from the etymology of the word, that the field of geochemistry is somehow a marriage of the fields of geo logy and chemistry. That would be a good guess. But just how are chemistry and geology combined within geochemistry; what is the rela- tionship between them? Perhaps the best explanation would be to state that in geochemistry, we use the tools of chemistry to solve geological problems; that is, we use chemistry to understand the Earth and how it works. The Earth is part of a closely related family of heavenly bodies, our Solar System, that formed simultaneously. Hence, the realm of geochemistry extends beyond the Earth to encompass the entire Solar System. The goals of geochemistry are thus no different from those of other fields of earth sci- ence; just the approach differs. On the other hand, while geochemists have much in common with other chemists, their goals differ in fundamental ways. For example, our goals do not include elu- cidating the nature of chemical bonding or synthesizing new compounds, although these may often be of interest and use in geochemistry. Though geochemistry is a subdiscipline of earth science, it is a very broad topic. So broad in fact that no one can really master it all; geochemists invariably specialize in one or a few aspects, such as geochemical thermodynamics, isotope geochemistry, marine chemistry, atmospheric chemistry, trace element geochemistry, soil chemistry, etc. Geochemistry has flourished in the quantitative approach that grew to dominate earth science in the second half of the twentieth century. This quantitative approach has produced greater advances in the understanding of our planet in the last 60 years than in all of prior human history. The contributions of geochemistry to this advance have been simply enormous. Much of what we know about how the Earth and the Solar System formed has come from research on the chemistry of meteorites. Through geochemistry, we can quantify the geologic time scale. Through geochemistry, we can determine the depths and temperatures of magma chambers. Through geochemistry, mantle plumes were recognized. Through geochemistry, we know that sediments can be subducted into the mantle. Through geochem- istry, we know the temperatures and pressures at which the various metamorphic rock types form and we can use this information, for example, to determine the throw on ancient faults. Through geochem- istry, we know how much and how fast mountain belts have risen. Through geochemistry, we are learning how fast they are eroding. Through geochemistry, we are learning how and when the Earth’s crust formed. Through geochemistry, we are learning when the Earth’s atmosphere formed and how it has evolved. Through geochemistry, we are learning how the mantle convects. Through geochemistry, we are learning how cold the ice ages were and what caused them. The evidence of the earliest life, at 3.8 gigayears (billion, or 10 9 years, which we will henceforth abbreviate as Ga), is not fossilized remains, but chemical traces of life. Not surprisingly, instruments for chemical analysis have been key part of probes sent to other heavenly bodies, including Venus, Mars, Jupiter, and Titan. Geochemistry lies at the heart of environmental science and environmental concerns. Problems such as acid rain, the ozone hole, the greenhouse effect and global warming, water and soil pollution are geochemical problems. Addressing these problems requires knowledge of geochemistry. Similarly, most of our non-renewable resources, such as metal ores and petroleum, form through geochemical processes. Locating new sources of these resources increasing requires geochemical approaches. In summary, every aspect of earth science has been advanced through geochemistry. Though we will rarely discuss it in this book, geochemistry, like much of science, is very much driven by technology. Technology has given modern geochemists tools that allow them to study the Earth in ways that pioneers of the field could not have dreamed possible. The electron microprobe al- lows us to analyze mineral grains on the scale of microns in minutes; the electron microscope allows us
‡ (^) Christian Friedrich Schönbein (1799 –1868) was born in Metzingen in Swabia, Germany and served as professor at
the University of Basel from 1835 until 1868. Among other things, he is credited with the discovery of ozone.
T
Chapter 1: Introduction
to view the same minerals on almost the atomic scale. Techniques such as X-ray diffraction, nuclear magnetic resonance, and Raman and infrared spectroscopy allow us to examine atomic ordering and bonding in natural materials. Mass spectrometers allow us to determine the age of rocks and the tem- perature of ancient seas. Ion probes allow us to do these things on micron scale samples. Analytical techniques such as X-ray fluorescence, inductively coupled plasma spectrometry, and laser ablation al- low us to perform in minutes analyses that would take days using “classical” techniques. All this is done with greater precision and accuracy than was possible just a few decades ago. Mega-computers with gigahertz of power and gigabytes of memory allow us to perform in seconds thermodynamic cal- culations that would have taken years or lifetimes half a century ago; the tera-computers now coming into use offer us even more power. New instruments and analytical techniques now being developed promise even greater sensitivity, speed, accuracy, and precision. Together, these advances will bring us ever closer to our goal understanding the Earth and its cosmic environment.
1.2 T HIS B OOK
The intent of this book is to introduce you to geochemistry and to further your understanding of the Earth through it. To do this, we must first acquire the tools of the trade. Every trade has a set of tools. Carpenters have their saws and T-squares; plumbers have their torches and wrenches. Psychologists have their blot tests, physicians their stethoscopes, accountants their balance sheets, geologists have their hammers, compasses, and maps. Geochemists too have a set of tools. These include not only a variety physical tools such as analytical instruments, but interpretative tools that allow them to make sense of the data these instruments produce. The first part of this book, entitled The Geochemical Tool- box , is intended to familiarize you with the tools of geochemistry. These include the tools of thermody- namics, kinetics, aquatic chemistry, trace element geochemistry, and isotope geochemistry. Once we have a firm grip on these tools, we can use them to dissect the Earth in the second part of the book, enti- tled Understanding the Earth and Cosmos. We begin at the beginning, with the formation of the Earth and the Solar System. We then work our way upward through the solid Earth, from core to mantle and crust and close by reviewing the intersection between geochemistry and life: organic geochemistry, the carbon cycle and climate. In filling our geochemical toolbox, we start with the tools of physical chemistry: thermodynamics and kinetics. Thermodynamics is perhaps the most fundamental tool of geochemistry; most other tools are built around this one. For this reason, Chapters 2, 3, and 4 are devoted to thermodynamics. Ther- modynamics allows us to predict the outcome of chemical reactions under a given set of conditions. In geochemistry we can, for example, predict the sequence of minerals that will crystallize from a magma under given conditions of temperature and pressure. The mineral assemblage of the resulting igneous rock, however, will not be stable at some other temperature and pressure. Thermodynamics allows us to predict the new suite of minerals that replace the original igneous ones. Thus thermodynamics pro- vides enormous predictive power for the petrologist. Since geologists and geochemists are more often concerned with understanding the past than with predicting the future, this might seem to be a point- less academic exercise. However, we can also use thermodynamics in the reverse sense: given a suite of minerals in a rock, we can use thermodynamics to determine the temperature and pressure conditions under which the rock formed. We can also use it to determine the composition of water or magma from which minerals crystallized. This sort of information has been invaluable in reaching our un- derstanding of how the Earth has come to its present condition. We can use this information to deter- mine the amount of uplift experienced by a mountain range, the temperature at which an ore deposit formed, or the composition of ancient seas. Thermodynamics has an important limitation: it is useful only in equilibrium situations. The rate at which chemical systems achieve equilibrium increases exponentially with temperature. Thermo- dynamics will be most useful at temperatures relevant to the interior of the Earth, say 500° C and above, because equilibrium will be more closely approached in those cases. At temperatures relevant to the surface of the Earth, many geochemical systems will not be in equilibrium and are governed by partly or largely by kinetics, the subject of Chapter 5. Kinetics deals with the rates and mechanisms of reactions. In this chapter, we will also touch upon such topics as diffusion and mineral surfaces. We will see that kinetics is intimately related to thermodynamics.
Chapter 1: Introduction
out its history. The last chapter is this history is currently being written as mankind short-circuits the carbon cycle through fossil fuel burning and deforestation, affecting climate in the process. Before we begin our study of geochemistry, we will devote the remainder of the chapter to review- ing some “fundamentals”. First, we briefly examine the philosophy and approach that is common to all science. Then we review the most fundamental aspects of chemistry: how matter is organized into at- oms of different elements, how the properties of the elements vary, and how these atoms interact to form compounds. Finally, we review a few fundamental aspects of the Earth.
1.3 T HE P HILOSOPHY OF S CIENCE
This book will concentrate on communicating to you the body of knowledge we call geochemistry. Geochemistry is just part of a much larger field of human endeavor known as science. Science is cer- tainly among humanity’s greatest successes; without it, our current civilization would not be possible. Among other things, it would simply not be possible to feed, cloth, and shelter the 7 billion people liv- ing today. This phenomenal success is due in large part to the philosophy of science. Science consists of two parts: the knowledge it encompasses and the approach or philosophy that achieves that knowledge. The goal of all science is to understand the world around us. The arts and humanities also seek understanding. Science differs from those fields as much by its approach and phi- losophy as by its body of knowledge. This approach and philosophy unite the great diversity of fields that we collectively call science. When one compares the methods and tools of a high energy physicist with those of a behavioral biolo- gist, for example, it might at first seem that they have little in common. Among other things, their vo- cabularies are sufficiently different that each would have difficulty communicating his or her research to the other. In spite of this, they share at least two things. The first is a criterion of “understanding”. Both the physicist and the behavioral biologist attempt to explain their observations by the application of a set of rules, which, by comparison to the range of phenomena considered, are both few and simple. Both would agree that a phenomenon is understood if and only if the outcome of an experiment related to that phenomenon can be predicted beforehand by applying those rules to measured variables*. The physicist and biologist also share a common method of seeking understanding, often called the “scien- tific method”.
1.3.1 Building Scientific Understanding
Science deals in only two quantities: observations and theories. The most basic of these is the ob- servation. Measurements, data, analyses, experiments, etc. are all observations in the present sense. An observation might be as simple a measurement of the dip and strike of a rock formation or as complex as the electromagnetic spectrum of a star. Of course, it is possible to measure both the dip of rock strata and a stellar spectrum incorrectly. Before an observation becomes part of the body of scientific knowl- edge, we would like some reassurance that it is right. How can we tell whether observations are right or not? The most important way to verify an observation is to replicate it independently. In the strictest sense, ‘independent’ means by a separate observer, team of observers, or laboratory, and preferably by a different technique or instrument. It is not practicable to replicate every observation in this manner, but critical observations, those which appear to be inconsistent with existing theories or which test the predictions of newly established ones should be, and generally are, replicated. But even replication does not guarantee that an observation is correct. Observations form the basis of theories. Theories are also called models, hypotheses, laws, etc. Scien- tific understanding is achieved by constructing and modifying theories to explain observations. Theories are merely the products of the imagination of scientists, so we also need a method of sorting out ‘correct’ theories from ‘incorrect’ ones. Good theories not only explain existing observations, but also make predictions about the outcome of still unperformed experiments or observations. Theories are tested by performance of these experiments and comparison of the results with the predictions of the theory. If the predic-
- (^) Both would admit that chance, or randomness, can affect the outcome of any experiment (though the effect might be slight). By definition, the effect of this randomness cannot be predicted. Where the effects of randomness are large, one performs a large collection, or ensemble, of experiments and then considers the average result.
Chapter 1: Introduction
tions are correct, the theory is accepted and the phenomenon considered to be understood, at least until a new and different test is performed. If the predictions are incorrect, the theory is discarded or modi- fied. When trying to explain a newly discovered phenomenon, scientists often reject many new theo- ries before finding a satisfactory one. But long-standing theories that successfully explain a range of phenomena can usually be modified without rejecting them entirely when they prove inconsistent with new observations. Occasionally, new observations are so inconsistent with a well-established theory that it must be dis- carded entirely and a new one developed to replace it. Scientific ‘revolutions’ occur when major theo- ries are discarded in this manner. Rapid progress in understanding generally accompanies these revo- lutions. Such was the case in physics in the early 20 th^ century when the quantum and relativity theories supplanted Newtonian theories. The development of plate tectonics in the 1960’s and 1970’s is an ex- cellent example of a scientific revolution in which old theories were replaced by a single new one. A range of observations including the direction of motion along transform faults, the magnetic anomaly pattern on the sea floor, and the distribution of earthquakes and volcanoes were either not predicted by, or were inconsistent with, classical theories of the Earth. Plate tectonics explained all these and made a number of predictions, such as the age of the seafloor, that could be tested. Thus scientific un- derstanding progresses through an endless cycle of observation, theory construction and modification, and prediction. In this cycle, theories can achieve “acceptance”, but can never be proven correct, be- cause we can never be sure that it will not fail some new, future test. Quite often, it is possible to explain observations in more than one way. That being the case, we need a rule that tells us which theory to accept. When this occurs, the principle is that the theory that explains the greatest range of phenomena in the simplest manner is always preferred. For example, the motion of the Sun across the sky is quite simple and may be explained equally well by imaging that the Sun orbits the Earth as visa versa. However, the motions of the planets in the sky are quite complex and require a very complex theory if we assume they orbit the Earth. If we theorize that the Earth and the other planets all orbit the Sun, the motions of the planets become simple elliptical orbits and can be explained by Newton’s three laws of motion. The geocentric theory was long ago replaced by the he- liocentric one for precisely this reason. This principle of simplicity, or elegance, also applies to mathe- matics. Computer programmers call it the KISS (Keep It Simple, Stupid!) Principle. In science, we call it parsimony , and can sum it up by saying: don’t make nature any more complex than it already is.
1.3.2 The Scientist as Skeptic
Though we often refer to “scientific facts”, there are no facts in science. A fact, by definition, cannot be wrong. Both observations and theories can be, and sometimes are, wrong. Of course, some obser- vations (e.g., the Sun rises each morning in the East) and theories (the Earth revolves around the Sun) are so oft repeated and so well established that they are not seriously questioned. But remember that the theory that the Sun revolves around the Earth was itself once so well established that it was not se- riously questioned. One of the ways science differs from other fields of endeavor is that in science nothing is sacred. It is best to bear in mind the possibility, however remote, that any observation or theory can be wrong. Conversely, we must also accept the possibility that even the wildest observations and theories might be correct: in quantum physics, for example, there is a great range of well-replicated observations that can only be labeled as bizarre (see, for example, Gribbin, 1984). ‘Intuition’ plays a greater role in sci- ence that most scientists might be willing to admit, even though scientific intuition is often very useful. Nevertheless, our intuition is based largely on our everyday experience, which is very limited com- pared to the range of phenomena that science attempts to understand. As a result, our intuition often deceives us. Sometimes we must put it aside entirely. That a clock will run slower if it moves faster, or that an electron can behave both as a wave and a particle, or that continents move great distances are all very counter-intuitive observations, but all are (apparently) correct. Thus skepticism is one of the keys to good science. In science, never totally believe anything, but never totally disbelieve anything either.
Chapter 1: Introduction
known elements, such as B, Sc, Ga, and Ge, but also their characteristics and probable mode of dis- covery. The periodic table led the way not only to the discovery of the remaining elements, but also to understanding the fundamental controls on chemical behavior. Figure 1.01 shows the periodic table as we know it today. Like most theories, Mendeleyev’s has gone through some revision since it was first proposed. Most importantly, we now organize the peri- odic table based on Atomic Number rather than atomic weight. The atomic number of an element is its most important property, and is determined by the number of protons in the nucleus (thus the terms atomic number and proton number are synonymous). The number of protons in turn determines both the number of electrons and how these electrons are organized. The mass of an atom is a function of both the proton number and the neutron number , i.e., the num- ber of neutrons in the nucleus*. Generally, several possible numbers of neutrons can combine with a given number of protons to form a stable nucleus (we will discuss nuclear stability in greater detail in Chapter 8). This gives rise to different isotopes of the same element, i.e., atoms that have the same atomic number but different masses. For example, helium has 2 stable isotopes: 3 He and 4 He. Both 3 He and 4 He †^ have 2 protons (and a matching number of electrons), but 4 He has 2 neutrons while 3 He has only 1. The atomic weight of an element depends on both the masses of its various isotopes and on the rel- ative abundances of these isotopes. This bedeviled nineteenth century chemists. William Prout (1785- 1850), an English chemist and physiologist, had noted in 1815 that the densities of a number of gases were integer multiples of the density of hydrogen (e.g., 14 for nitrogen, 16 for oxygen). This law ap- peared to extend to many elemental solids as well, and it seemed reasonable that this might be a uni- versal law. But there were puzzling exceptions. Cl, for example, has an atomic weight of 35.45 times that of hydrogen. The mystery wasn’t resolved until Thompson demonstrated the existence of 2 iso- topes of Ne in 1918. The explanation is that while elements such as H, N, O, C, and Si consist almost entirely of a single isotope, and thus have atomic weights very close to the mass number of that isotope, natural Cl consists of about 75% 35 Cl and 25% 37 Cl ‡^.
1.4.2 Electrons and Orbits
We stated above that the atomic number of an element is its most important property. This is true because the number of electrons is determined by atomic number, as it is the electronic structure of an atom that largely dictates it chemical properties. The organization of the elements in the periodic table reflects this electronic structure. The electronic structure of atoms, and indeed the entire organization of the periodic table, is de- termined by quantum mechanics and the quantization of energy, angular momentum, magnetic mo- ment, and spin of electrons. Four quantum numbers, called the principal, azimuthal, magnetic, and spin quantum numbers and conventionally labeled n , l , m , and m (^) s , control the properties of electrons associated with atoms. The first of these, n , which may take values 1, 2, 3, ..., determines most of the electron’s energy as well as mean distance from the nucleus. The second, l , which has values 0, 1, 2, ... n -1, determines the total angular momentum and the shape of the orbit. The third, m , which may have values -l , ...0... l , determines the z component of angular momentum and therefore the orientation of the orbit. The fourth, m (^) s , may have values of – 1 / 2 or + 1 / 2 and determines the electron’s spin. The first three quantum numbers result in the electrons surrounding the nucleus being organized into shell , subshells ,
- The neutron mass and proton mass are almost identical. † (^) By convention, the mass number, which is the sum of protons and neutrons in the nucleus, of an isotope is written as a preceding superscript. However, for historical reasons, it is often pronounced “helium–4”. Note also that the atomic number or proton number can be readily deduced from the chemical symbol (atomic number of He is 2). The neutron number can be found by subtracting the proton number from the mass number. Thus the symbol ‘^4 He’ gives a complete description of the nucleus of this atom. ‡ (^) The actual mass of an atom depends on the number of electrons and the nuclear binding energy as well as the number of protons and neutrons. However, the mass of the electron is over 1000 times less than the mass of the pro- ton and neutron, and the effect of nuclear binding energy on mass was too small for 19 th^ century chemists to detect.
Chapter 1: Introduction
and orbitals*. The Pauli Exclusion Principle requires that no two electrons in an atom may have identical values of all four quantum numbers. Because each orbital corresponds to a unique set of the first 3 quantum numbers and the spin quantum number has only 2 possible values, 2 electrons with opposite spins may occupy a given orbital. In Chapter 8 we will see that the properties of the nucleus are also dictated by quantum mechanics, and that the nucleus may also be thought of as having a shell struc- ture. Each shell corresponds to a different value of the principal quantum number. The periodic nature of chemical properties reflects the filling of successive shells as additional electrons (and protons) are added. Each shell corresponds to a ‘period’, or row, in the periodic table. The first shell (the K shell) has one subshell, the 1s , consisting of a single orbital (with quantum numbers n =1, l =0, m =0. The 1s or- bital accepts up to 2 electrons. Thus period 1 has 2 elements: H and He. If another proton and electron are added, the electron is added to the first orbital, 2s , of the next shell (the L shell). Such a configura- tion has the chemical properties of lithum, the first element of period 2. The second shell has 2 sub- shells, 2s (corresponding to l =0) and 2p (corresponding to l =1). The p subshell has 3 orbitals (which cor- respond to values for m of -1, +1, and 0), p (^) x , p (^) y , and p (^) z , so the L shell can accept up to 8 electrons. Thus period 2 has 8 elements. There are some complexities in the filling of orbitals beyond the L shell. In the M shell, which corre- sponds to period 3, there is the possibility of putting electrons in the d subshell ( l =2), but this is en- ergetically less favorable than electrons going in the subsequent shell. Thus the 3d subshell is vacant in period 3 element in their ground states, and in the first 2 elements of period 4. Only when the 4s orbital is filled do electrons begin to fill the 3d orbitals. The 5 3d orbitals are filled as one passes up the first transition series metals, Sc through Zn. This results in some interesting chemical properties, which we will consider in Chapter 7. Similarly, the second and third transition series metals correspond to filling of the 4d and 5d orbitals. The lan- thanide and actinide rare earth ele- ments correspond to the filling of the 4 f and 5 f shells are filled (again resulting in some interesting prop- erties, which we will consider subsequently). The predicted sequence in which orbitals are filled and their energy levels are shown in Figure 1.02. Figure 1. shows the electronic configuration of the elements.
1.4.3 Some Chemical Proper-
ties of the Elements
It is only the most loosely bound electrons, those in the out- ermost shells, which participate in chemical bonding, so elements sharing a similar outermost elec- tronic configuration tend to behave similarly. Elements within the same column, or group , share outer
- (^) It is often convenient to think of the electrons orbiting the nucleus much as the planets orbit the Sun. This analogy has its limitations. The electron’s position can not be precisely specified as can a planet’s. In quantum mechanics, the Schrödinger Wave function, ψ (or more precisely, ψ^2 ) determines the probability of the electron being located in a given region about the atom. As an example of failure of the classical physical description of the atom, consider an electron in the 1s orbital. Both quantum number specifying angular momentum, l and m , are equal to 0, and hence the electron has 0 angular momentum, and hence can not be in an orbit in the classical sense.
Figure 1.02. The predicted sequence of orbital energies for elec- trons in atoms. S levels can hold 2 electrons, p , d , and f can hold 6, 10, and 14 respectively.
Chapter 1: Introduction
2p orbital is filled and the 3s orbital effectively shielded, so there is no tendency to add a third electron. With the outer p (and s ) orbitals filled, a particularly stable configuration is reached. Thus Ne has little tendency to either add or give up an electron. The number of electrons that an element will either give up or accept is known as its valence. For ele- ments in the ‘wings’ of the periodic table (i.e., all except the transition metals), valence is easily de- termined simply by counting how far the element is horizontally displaced from Group 18 in the peri- odic table. For Group 18, this is 0, so these elements, the noble gases, have 0 valence. For group 1 it is 1, so these elements have valence of +1; for group 17 it is -1, so these elements have valence of -1, etc. Valence of the transition metals is not so simply determined, and these elements can have more than 1 valence state. Most, however, have valence of 2 or 3, though some, such as U, can have valences as high as 6. A final characteristic that is important in controlling chemical properties is ionic radius. This is de- duced from bond length when the atom is bonded to one or more other atoms. Positively charged at- oms, or cation , have smaller ionic radii than do negatively charged atoms, or anions. Also, ionic radius decreases as charge increases. This decrease is due both to loss of outer electrons and to shrinking of the orbits of the remaining electrons. The latter occurs because the charge of the nucleus is shared by fewer electrons and hence has a greater attractive force on each. In addition, ionic radius increases downward in each group in the periodic table, both because of addition of electrons to outer shells and because these outer electrons are increasingly shielded from the nuclear charge by the inner ones. Ionic radius is important in determining geochemical properties such substitution in solids, solubility, and diffusion rates. Large ions need to be surrounded, or coordinated , by a greater number of oppositely charged ions than do smaller ones. The ionic radii of the elements are illustrated in Figure 1.06. We can now summarize a few of the more important chemical properties of the various groups in the periodic table. Group 18, does not participate in chemical bonding in nature, hence the term ‘noble gases’. Group 1 elements, the alkalis, readily accept an electron (they are electropositive ) and hence are highly reactive. They tend to form ionic bonds rather than covalent ones and hence tend not to form
Figure 1.04. First ionization potential of the elements.
Chapter 1: Introduction
bonds that are as strong as other elements. They tend to be quite soluble in aqueous solutions. Because they have only a +1 charge, their ionic radii tend to be larger than those of other cations. Group 2 ele- ments, the alkaline earths , have these same characteristics, but somewhat moderated. Group 17 ele- ments, the halogens , are highly electronegative and readily accept an electron, are highly reactive, form ionic bonds, and are quite soluble. Their ionic radii tend to be larger than more highly charged anions. Elements of Groups 13-16 tend to form bonds that are predominantly covalent. As a result, they tend to be less reactive and less soluble (except where they form soluble radicals, such as SO 4 2 –^ ) than Group 1, 2, and 17 elements. Finally, the transition metals are a varied lot. Many form strong bonds (generally with O in nature) and can have quite variable solubility (which, as we shall see in Chapter 6, depends on their valence state). Some, the ‘noble metals’ (Ru, Rh, Pd, Os, Ir, Pt) in particular, tend to be very un- reactive and insoluble. The rare earths are of interest because all have 2 electrons in the 6s outer orbital, and vary only by the number of electrons in the 4 f shell. Because they almost always have the same va- lence (+3), bonding behavior is quite similar. They vary systematically in ionic radius, which results in a systematic variance in geochemical behavior, as we will see in Chapter 7.
1.4.4 Chemical Bonding
1.4.4.1 Covalent, Ionic, and Metal Bond
Except for the noble gases, atoms rarely exist independently: they are generally bound to other at- oms in molecules, crystals, or ionic radicals. Atoms bind to one another through transfer or sharing of electrons, or through electrostatic forces arising from uneven distribution of charge in atoms and mole- cules. A bond that results from the transfer of electrons from one atom to another is known as an ionic bond. A good example is the bond between Na and Cl in a halite crystal. In this case, the Na atom (the electropositive element) gives up an electron, becoming positively charged, to the Cl atom (the electro- negative element), which becomes negatively charged. Electrostatic forces between the Na +^ and the Cl - ions hold the ions in place in the crystal. When electrons are shared between atoms, such as in the H 2 O molecule or the SiO 4 4 –^ radical, the bond in known as covalent. In a covalent bond , the outer electrons of the atoms involved are in hybrid orbits that encompass both atoms.
Figure 1.05. Electronegativities of the elements.
Chapter 1: Introduction
Van der Waals interactions arise from asymmetric distribution of charge in molecules and crystals. There are three sources for van der Waals interactions: dipole-dipole attraction , induction, and London dis- persion forces. As we noted above, many molecules, including water, have permanent dipole moments. When two polar molecules encounter each other, they will behave much as two bar magnets: they will tend to orient themselves so that the positive part of one molecule is closest to the negative part of an- other (Figure 1.07a). This results in a net attractive force between the two molecules. When the dis- tance between molecules is large compared to the distance between charges within molecules, the en- ergy of attraction can be shown to be:
U D − D = −
μ^4
r^6
k T
where U (^) D-D is the interaction energy, μ is the dipole moment, T is temperature (absolute, or thermo- dynamic temperature, which we will introduce in the next chapter), k is a constant (Boltzmann’s con- stant, which we shall also meet in the next chapter), and r is distance. We don’t want to get lost in equations at this point; however, we can infer several important things about dipole-dipole interactions just from a quick glance at it. First, the interaction energy depends inversely on the sixth power of dis- tance. Many important forces, such as electromagnetic and gravitational forces, depend on the inverse square of distance. Thus we may infer that dipole-dipole forces become weaker with distance very rap- idly. Indeed, they are likely to be negligible unless the molecules are very close. Second, the interac- tion energy depends on the forth power of the dipole moment, so that small differences in dipole mo- ment will result in large differences in interaction energy. For example, the dipole moment of water (1.84 debyes) is less than twice that of HCl (1.03 debyes), yet the dipole interaction energy between two water molecules (716 J/mol) is nearly 10 times as great as that between two HCl molecules (72. J/mol) at the same temperature and distance (298 K and 50 pm). Finally, we see that dipole interaction energy will decrease with temperature. Dipole molecules may also polarize electrons in a neighboring molecule and distort their orbits in such a way that their interaction with the dipole of the first molecule is attractive. This is known as the induction effect (Figure 1.7b). The induction energy also depends on the inverse sixth power of inter- molecular distance, but only on the square of the dipole moment of the molecules involved. In addi- tion, another parameter, the polarizability of a molecule, is also needed to describe this effect. In gen- eral, the attraction arising from induction is less important than from dipole-dipole interaction. How- ever, because it depends only on the square of dipole moment, the induction attraction can be larger than the dipole-dipole attraction for some weakly dipolar molecules. Finally, van der Waals forces can also occur as a consequence of fluctuations of charge distribution on molecules that occur on time scales of 10 -16^ seconds. These are known as London dispersion forces. They arise when the instantaneous dipole of one molecule induces a dipole in a neighboring molecule. As was the case in induction, the molecules will orient themselves so that the net forces between them are attractive. The total energy of all three types of van der Waals interactions between water molecules is about 380 J/mol assuming an intermolecular distance of 5 pm and a tem- perature of 298 K (25° C). Though some in- teraction energies can be much stronger (e.g., CCl 4 , 2.8 kJ/mol) or weaker (1 J/mol for He), an energy of a few hundred Joules per mole is typical of many substances. By comparison, the hydrogen-oxygen bond
Figure 1.07. Van der Waals interactions arise because of the polar nature of some molecules. Illustrated here are (a) dipole-dipole interactions, which occur when two di- polar molecules orient themselves so oppositely charged sides are closest, and (b) the induction effect, which arise when the electron orbits of one molecule are perturbed by the electromagnetic field of another molecule.
Chapter 1: Introduction
energy for each H—O bond in the water molecule is 46.5 kJ/mol. Thus van der Waals interactions are quite weak com- pared with typical intramolecular bond energies. The Hydrogen Bond is similar to van der Waals interactions in that it arises from nonsymmetric distribution of charge in molecules. However, it differs from van der Waals interactions in a number of ways. First, it occurs exclu- sively between hydrogen and strongly electronegative atoms, namely oxygen, nitrogen and fluorine. Second, it can be several orders of magnitude stronger than van der Waals interactions, though still weak by comparison to covalent and ionic bonds. The exact nature of hydro- gen bonds is not completely understood. They arise principally from electrostatic interactions. In the water molecule, bind- ing between oxygen and hydrogen re- sults in hybridization of s and p orbitals to yield two bonding orbitals between the O and two H atoms and 2 non-binding sp 3 orbitals on the oxygen. The latter are prominent on the opposite side of the O from the hydrogens. The hydrogen in one water molecule, carrying a net positive charge, is attracted by the non-binding sp 3 electrons of the oxygen of another water molecule, forming a hydrogen bond with it (Figure 1.8). Hydrogen bonds typically have energies in the range of 20-40 kJ/mol. These are much higher than expected for electrostatic interactions alone and indeed approach values similar to intra-molecular bond energies. Thus there is the suspicion that the some degree of covalency is also involved in the hydrogen bond. That is to say that the non-binding electrons of oxygen are to some degree shared by with the hydrogen in another molecule. Hydrogen bonds are perhaps most important in water, where they account for some of the extremely usual properties of this compound, such as its high heat of va- porization, but they can also be important in organic molecules and are present in HF and ammonia as well.
1.5 A B RIEF L OOK AT THE E ARTH
1.5.1 Structure of the Earth
The Earth consists of 3 principal layers: the core, the mantle, and the crust (Figure 1.09). The core, roughly 3400 km thick and extending about half way to the surface, consists of Fe-Ni alloy and can be subdivided into an inner and outer core. The outer core is liquid while the inner core is solid. The man- tle is about 3000 km thick and accounts for about 2/3 the mass of the Earth; the core accounting for the other 1/3. The crust is quite thin by comparison, nowhere thicker than 100 km and usually much thin- ner. Its mass is only about 0.5% of the mass of the Earth. There are 2 fundamental kinds of crust: oce- anic and continental. Ocean crust is thin (about 6 km) and, with the exception of the eastern Mediter- ranean, is nowhere older than about 180 million years. The continental crust is thicker (about 35-40 km thick on average) and relatively permanent, with an average age of 2 billion years. Both the crust and the mantle consist principally of silicates. The mantle is comparatively rich in iron and magnesium, so ferromagnesian silicates, such as olivine and pyroxenes, dominate. Rocks hav- ing these compositional characteristics are sometimes called ultramafic. The continental crust is poor in iron and magnesium, and aluminosilicates such as feldspars dominate. Rocks of this composition are sometimes referred to as felsic. The oceanic crust is intermediate in composition between the mantle
Figure 1.08. Hydrogen bonding between water molecules. Hydogen positions shown as red; sp^3 hybrid orbitals in oxygen shown as dark gray. The δ+ and δ– indicate partial positive and negative charges respectively.
Chapter 1: Introduction
sufficient to continually reshape the surface of the Earth, creating the Atlantic Ocean, for example, in the last 200 million years. Rather than thinking of plate motion as being driven by mantle convection, it would be more correct to think of plate motion as part of mantle convection. Where plates move apart, mantle rises to fill the gap. As the mantle does so, it melts. The melt rises to the surface as magma and creates new oceanic crust at volcanos along mid-ocean ridges (Figure 1.10). Mid-ocean ridges, such as the East Pacific Rise and the Mid-Atlantic Ridge, thus mark divergent plate boundaries. As the oceanic crust moves away from the mid-ocean ridge it cools, along with the mantle immediately below it. This cooling produces a steadily thickening lithosphere. As this lithosphere cools, it contracts and its density increases. Because of this contraction, the depth of the ocean floor increases away from the mid-ocean ridge. When this lithosphere has cooled sufficiently, after 100 million years or so, it becomes denser than the underlying asthenosphere. The lithosphere may then sink back into the mantle in a process known as subduction. As the lithosphere sinks, it creates deep ocean trenches, such as the Peru-Chile Trench, or the Marianas Trench. Chains of volcanos, known as island arcs, invariably occur adjacent to these deep-sea trenches. The volcanism occurs as a result of dehydration of the subducting oceanic crust and lithosphere. Water released from the subducting oceanic crust rises into the overlying mantle, causing it to melt. The is- land arcs and deep sea trenches are collectively called subduction zones. Subduction zones thus mark convergent plate boundaries. It is primarily the sinking of old, cold lithosphere that drives the motion of plates. Thus the lithosphere does not merely ride upon convecting mantle, its motion is actually part of mantle convection. The density of the continental crust is always lower than that of the mantle, regardless of how cold the crust becomes. As a result, it cannot be subducted into the mantle. The Indian-Eurasian plate boundary is a good example of what happens when two continental plates converge. Neither plate readily subducts and the resulting compression has produced, and continues to uplift, the Himalayan Mountains and the Tibetan Plateau. This area of the continental crust is not only high it is also deep. The crust beneath this region extends to depths of as much as 100 km, nearly three times the average crustal thickness. Rocks within this thickened crust will experience increased temperatures and pres- sures, leading to metamorphism , a process in which new minerals form in place of the original ones. In the deepest part of the crust, melting may occur, giving rise to granitic magmas, which will then in- trude the upper crust. The topographically high Himalayas are subject to extremely high rates of erosion, and the rivers draining the area carry enormous quantities of sediment. These are deposited mainly in the northern Indian Ocean, building the Ganges and Indus Fans outward from the continental margin. As the mountains erode, the mass of crust bearing down on the underlying asthenosphere is reduced. As a re-
Figure 1.10. Cross section of the Earth illustrating relationships between lithosphere and astheno- sphere and plate tectonic processes. Oceanic crust and lithosphere are created as plates diverge at mid-ocean ridges and are eventually subducted back into the mantle. Continental lithosphere is thicker and lighter than oceanic lithosphere and not easily subducted.
Chapter 1: Introduction
sult of the decreased downward force, further uplift occurs. The third kind of plate boundary is known as a transform boundary and occurs where plates slide past one and other. A good example of this type of plate boundary is the San Andreas Fault system of California. Here the Pacific Plate is sliding northward past the North American Plate. The passage is not an easy one, however. The two plates occasionally stick together. When they do, stresses steadily build up. Eventually, the stress exceeds the frictional forces holding the plates together, and there is a sudden jump producing an earthquake. Earthquakes are also common in subduction zones and along mid-ocean ridges. They are much rarer in the interior of plates. Most volcanism and crustal deformation occur along plate boundaries. A small fraction of vol- canos, however, is located in plate interiors and appears to be entirely unrelated to plate tectonic proc- esses. Crustal uplift also occurs in association with these volcanos. Two good examples are Hawaii and Yellowstone. These phenomena are thought to be the result of mantle plumes. Mantle plumes are convective upwellings. In contrast to the convective upwelling occurring along mid-ocean ridges, which is typically sheet-like, mantle plumes appear to be narrow (~100 km diameter) and approximately cylindrical. Furthermore, it appears that mantle plumes rise from much deeper in the mantle, perhaps even the core-mantle boundary, than convection associated with plate motion.
1.5.3 Earth Materials
The most abundant elements in the Earth are O and Fe (both close to 32%), Mg (~15%), Si (~14%), Ni (~1.8%), Ca (1.7%), and Al (1.6%). The majority of the Earth’s Fe and Ni are in the core. The remaining rocky part of the Earth, the mantle and crust, consists of ~44% O, ~23% Mg, ~21% Si, ~8% Fe, ~2.5% Ca, and ~2.4% Al. As a consequence, the outer part of the Earth consists principally of compounds known as silicates. Silicates are compounds based on the silica tetrahedron, consisting of a silicon atom sur- rounded by four oxygens (Figure 11.13a). The bonds between the oxygens and silicon are about 50% covalent–50% ionic and are quite strong. The silicon atom shares an electron with each of the four oxy- gens. Since oxygen has two valence electrons, each oxygen can form an additional bond. There are two possibilities: the oxygen can form a second bond (which is usually more ionic) with another metal atom or it can form a bond with a second silicon. This latter possibility leads to linking of silica tetrahedra to form rings, chains, sheets, or frameworks. Oxygens bound to two silicons are called bridging oxygens. In orthosilicates, the silica tetrahedra are either completely independent or form dimers, that is, two linked tetrahedra. A good example of a mineral of this type is olivine, whose structure is illustrated in Figure 11.11b. The chemical formula for olivine is (Mg,Fe) 2 SiO 4. The notation (Mg,Fe) indicates that ei- ther magnesium or iron may be present. Olivine is an example of a solid solution between the Mg-end member, forsterite (Mg 2 SiO 4 ), and the Fe-end member, fayalite (Fe 2 SiO 4 ). Such solid solutions are quite common among silicates. As the formula indicates, there are two magnesium or iron atoms for each sil- ica tetrahedra. Since each Mg or Fe has a charge of +2, their charge balances the –4 charge oƒ each silica tetrahedra. Olivine constitutes roughly 50% of the Earth’s upper mantle, and is thus one of the most abundant minerals in the Earth. At great pressures, it disproportionates to a Fe-Mg oxide (mag- nesiowüstite) and (Mg,Fe)SiO 3 (Mg-perovskite). At the same time, silicon atoms become octahedrally coordinated (surrounded by 6 oxygens rather than 4 as in the silica tetrahedra). In chain silicates, the silica tetrahedra are linked together to form infinite chains (Figure 1.11c), with two bridging oxygen per tetrahedra. Minerals of this group are known as pyroxenes and have the gen- eral formula XSiO 3 where X is some metal, usually Ca, Mg, or Fe, which is located between the chains. Two pyroxenes, orthopyroxene ((Mg,Fe)SiO 3 ) and clinopyroxene (Ca(Mg,Fe)Si 2 O 6 are very abundant in the Earth’s upper mantle as well as mafic igneous rocks. The pyroxenes wollastonite (CaSiO 3 ) and jadite (NaAlSi 2 O 6 ) are found exclusively in metamorphic rocks. In double chain silicates, an additional one half bridging oxygen per tetrahedra joins two chains to- gether. Minerals of this group are known as amphiboles , which occur widely in both igneous and meta- morphic rocks. Among the important minerals in this group are hornblende (Ca 2 Na(Mg,Fe) (^4) Al 3 Si 8 O 22 (OH) 2 ), tremolite-actinolite (Ca 2 (Mg,Fe) 5 Si 8 O 22 (OH) 2 ), and glaucophane (Ca 2 (Mg,Fe) 3 Al 3 Si 8 O 22 (OH) 2 ). These minerals all contain OH as an essential component (Cl or F sometimes substitutes for OH). They are thus examples of hydrous silicates.
Chapter 1: Introduction
McSween, H. Y., Richardson, S. H. & Uhle, M. 2003. Geochemistry: Pathways and Processes, New York, Columbia Univeristy Press. Morris, R. 2003. The Last Sourcers: The Path from Alchemy to the Perioditic Table , Washington. DC, Joseph Henry Press. Strathern, P. 2000. Mendeleyev's Dream: The Quest for the Elements , London, Berkley. Walther, J. V. 2009. Essentials of Geochemistry , Sudbury, MA, Jones and Bartlett.
