Structure of minerals

The discovery of the internal structures of minerals by the use of X-ray diffraction was pivotal in the history of mineralogy and crystallography. X-ray analysis revealed that the physical properties and chemical behavior of minerals are directly related to the highly organized arrangements of their atoms, and this knowledge has had important scientific and industrial applications.

The Father of Crystallography

During the seventeenth and eighteenth centuries, natural philosophers used two basic ideas to explain the external structures of minerals: particles, in the form of spheres, ellipsoids, or various polyhedra; and an innate attractive force, the emanating “glue” needed to hold particles together. These attempts to rationalize mineral structures still left a basic problem unanswered. Namely, how does one explain the heterogeneous physical and chemical properties of minerals with homogeneous particles? This problem was not answered satisfactorily until the twentieth century, but the modern understanding grew out of the work of scientists in the eighteenth and nineteenth centuries. The most important of these scientists was René-Just Haüy, often called the “father of crystallography.”

Haüy, a priest who worked at the Museum of Natural History in Paris, helped to make crystallography a science. Before Haüy, the study of crystals had been a part of biology, geology, or chemistry; after Haüy, the science of crystals was an independent discipline. His speculations on the nature of the crystalline state began when he accidentally dropped a calcite specimen, which shattered into fragments. He noticed that the fragments split along straight planes that met at constant angles. No matter what the shape of the original piece of calcite, he found that broken fragments were rhombohedra (slanted cubes). He reasoned that a rhombohedron, similar to the ones he obtained by cleaving the crystal, must be in the fundamental shape of the crystal. For Haüy, then, the cleavage planes existed in the crystal like the mortarjoints in a brick wall. When he discovered similar types of cleavage in a variety of substances, he proposed that all crystal forms could be constructed from submicroscopic building blocks. He showed that there were several basic building blocks, which he called primitive forms or “integral molecules,” and that they represented the last term in the mechanical division of a crystal. With these uniform polyhedra, he could rationalize the many mineral forms observed in nature. Haüy’s building block was not, however, the same as what later crystallographers came to call the unit cell, the smallest group of atoms in a mineral that can be repeated in three directions to form a crystal. The unit cell is not a physically separable entity, such as a molecule; it simply describes the repeat pattern of the structure. In contrast, for Haüy, the crystal was a periodic arrangement of equal molecular polyhedra, each of which might have an independent existence.

Geometrical and Symmetrical Analyses

In the nineteenth century, Haüy’s ideas had many perceptive critics. For example, Eilhardt Mitscherlich, a German chemist, discovered in 1819 that different mineral substances could have the same crystal form, whereas Haüy insisted that each substance had a specific crystal structure. Some crystallographers shunned the concrete study of crystals (leaving it to mineralogists), and they defined their science as the study of ordered space. This mathematical analysis bore fruit, for crystallographers were able to show that, despite the great variety of possible mineral structures, all forms could be classified into six crystal systems on the basis of certain geometrical features, usually axes. The cube is the basis of one of these systems, the isometric, in which three identical axes intersect at right angles. Symmetry was another factor in describing these crystal systems. For example, a cube has fourfold symmetry around an axis passing at right angles through the center of any of its faces. As some crystallographers were establishing the symmetry relationships in crystal systems, others were working on a way to describe the position of crystal faces. In 1839, William H. Miller, a professor of mineralogy at the University of Cambridge, found a way of describing how faces were oriented about a crystal, similar to the way a navigator uses latitude and longitude to tell where his ship is on the earth. Using numbers derived from axial proportions, Miller was able to characterize the position of any crystal face.

Friedrich Mohs, a German mineralogist best remembered for his scale of the hardness of minerals, was famous in his lifetime for his system of mineral classification, in which he divided minerals into genera and species, similar to the way biologists organized living things. His system was based on geometrical relationships that he derived from natural mineral forms. He wanted to transform crystallography into a purely geometrical science, and he showed that crystal analysis involved establishing certain symmetrical groups of points by the rotation of axes. When these point groups were enclosed by plane surfaces, crystal forms were generated. The crystallographer’s task, then, was to analyze the symmetry operations characterizing the various classes of a crystal system.

Bravais Lattices

Beginning in 1848, Auguste Bravais, a French physicist, took the same sort of mathematical approach in a series of papers dealing with the kinds of geometric figures formed by the regular grouping of points in space, called lattices. Bravais applied the results of his geometric analysis to crystals, with the points interpreted either as the centers of gravity of the chemical molecules or as the poles of interatomic electrical forces. With this approach, he demonstrated that there is a maximum of fourteen kinds of lattices, which differ in symmetry and geometry, such that the environment around any one point is the same as that around every other point. These fourteen Bravais lattices are distributed among the six crystal systems. For example, the three isometric Bravais lattices are the simple (with points at the vertices of a cube), body-centered (with points at the corners, along with a point at the center of a cube), and face-centered (with corner points and points at the centers of the faces of the cube). With the work of Bravais, the external symmetry of a mineral became firmly grounded on the idea of the space lattice, but just how actual atoms or molecules were arranged within unit cells remained a matter of speculation.

In the latter part of the nineteenth century, various European scientists independently advanced crystallography beyond point groups and Bravais lattices by recognizing additional forms of symmetry. In the late 1880’s, the Russian mineralogist Evgraf Fedorov introduced the glide plane, in which a reflection in a mirror plane is combined with a translation without rotation along an axis. Bricks in a wall are a familiar example (although they have additional symmetry as well).Using various symmetry elements, Fedorov derived the 230 space groups, which represent all possible distributions that atoms can assume in minerals.

Pauling’s Rules

Shortly after the work of Fedorov, William Barlow, an English chemist, began to consider the problem of crystal symmetry from a more concrete point of view. He visualized crystals not in terms of points but in terms of closely packed spherical atoms with characteristic diameters. In considering atoms to be specifically sized spheres, he found that there are certain geometric arrangements for packing them efficiently. One can appreciate his insight by thinking about arranging coins in two dimensions. For example, six quarters will fit around a central quarter, but only five quarters will fit around a dime. Barlow showed that similar constraints hold for the three-dimensional packing of spherical atoms of different diameters.

As scientists determined more and more mineral structures, they became convinced that minerals are basically composed of spherical atoms or ions, each of characteristic size, packed closely together. Silicate minerals were of central concern to William Lawrence Bragg in England and Linus Pauling in the United States. The basic unit in these minerals is the tetrahedral arrangement of four oxygen atoms around a central silicon atom. Each tetrahedral unit has four negative charges, so one would expect that electric repulsion would force these tetrahedral building blocks to fly apart. In actual silicate minerals, however, these units are linked in chains, rings, or sheets and in ways that bring about charge neutralization and stability. These tetrahedra may also be held together by such positively charged metal ions as aluminum, magnesium, and iron. These constraints lead to a fascinating series of structures. Pauling devised an enlightening and useful way of thinking both about these silicate structures and about complex inorganic substances in general. In the late 1920’s, he proposed a set of principles (now known as Pauling’s Rules) that govern the structures of ionic crystals—that is, crystals in which ionic bonding predominates. The silicate minerals provide striking examples of his principles. One of his rules deals with how a positive ion’s electrical influence is spread among neighboring negative ions; another rule states that highly charged positive ions tend to be as far apart as possible in a structure. Pauling’s Rules allowed him to explain why certain silicate minerals exist in nature and why others do not.

Temperature and Pressure Studies

In the 1960’s the structure determination of minerals became an important activity in some large geology departments. By this time, through computerized X-ray crystallography, it was possible to determine, quickly and elegantly, the exact atomic positions of highly complex minerals. In the 1970’s and 1980’s, scientific interest shifted to the study of minerals at elevated temperatures and pressures. These studies often showed that temperature and pressure changes cause complex internal structural modifications in the mineral, including shifts in distances between certain ions and their orientation to others. New minerals continue to be discovered and their structures determined. Structural chemistry has played an important role in deepening understanding both of these new minerals and of old minerals under stressful conditions. This knowledge of mineral structure has benefited not only mineralogists, crystallographers, and structural chemists but also inorganic chemists, solid-state physicists, and many Earth scientists.

Study of External Structure

The first methods for examining the external structure of minerals were quite primitive. In the seventeenth century, Nicolaus Steno cut sections from crystals and traced their outlines on paper. A century later, Arnould Carangeot invented the contact goniometer. This device, which enabled crystallographers to make systematic measurements of interfacial crystal angles, was basically a flat, pivoted metal arm with a pointer that could move over a semicircular protractor. William Hyde Wollaston invented a more precise instrument, the reflecting goniometer, in 1809. This device used a narrow beam of light reflected from a mirror and directed against a crystal to make very accurate measurements of the angles between crystal faces. The reflecting goniometer ushered in a period of quantitative mineralogy that led to the multiplication of vast amounts of information about the external structure of minerals.

The discovery of the polarization of light in the nineteenth century led to another method of mineral investigation. Ordinary light consists of electromagnetic waves oscillating in all directions at right angles to the direction of travel, but a suitable material can split such light into two rays, each vibrating in a single direction (this light is then said to be plane polarized). Various inventors perfected the polarizing microscope, a versatile instrument using plane-polarized light to identify minerals and to study their fine structure. Even the darkest minerals could be made transparent if sliced thinly enough. These transparent slices produced complex but characteristic colors because of absorption and interference when polarized light passed through them.

Study of Internal Structureint

In the twentieth century, X-ray diffraction provided scientists with a tool vastly more powerful than anything previously available for the investigation of internal mineral structures. Before the development of X-ray methods in 1912, the internal structure of a mineral could be deduced only by reasoning from its physical and chemical properties. After X-ray analysis, the determination of the detailed internal structures of minerals moved from speculation to precise measurement. The phenomenon of diffraction had been known since the seventeenth century. It can be readily observed when a distant street light is viewed through the regularly spaced threads of a nylon umbrella, causing colored fringes around the light source to be seen. In a similar way, Max von Laue reasoned that the closely spaced sheets of atoms in a crystal should diffract X rays, with closely spaced sheets diffracting X rays at larger angles than more widely spaced ones. William Lawrence Bragg then showed how this technique could be used to provide detailed information about the atomic structure of minerals. The play of colors on a compact disk is a familiar example of the diffraction of visible light. If a laser pointer is aimed at the disk, multiple spots will appear on nearby surfaces because the regular spacing of tiny pits on the disk causes diffracted light to be reinforced in certain directions. X-ray diffraction is exactly the same phenomena applied to the arrays of atoms in a crystal.

The powder method of X-ray diffraction consists of grinding a mineral specimen into a powder that is then formed into a rod by gluing it to a thin glass fiber. As X rays impinge on it, this rod is rotated in the center of a cylindrical photographic film. The diffraction pattern on the film can then be interpreted in terms of the arrangement of atoms in the mineral’s unit cell.

Although X rays have been the most important type of radiation used in determining mineral structures, other types of radiation—in particular infrared (with wavelengths greater than those of visible light)—have also been effective. Infrared radiation causes vibrational changes in the ions or molecules of a particular mineral structure, which permits scientists to map its very detailed atomic arrangement. The technique of neutron diffraction makes use of relatively slow neutrons from reactors to determine the locations of the light elements in mineral structures (the efficiency of light elements in scattering neutrons is generally quite high).

In recent decades, scientists have continued to develop sophisticated techniques for exploring the structure of minerals. Each of these methods has its strengths and limitations. For example, the electron microprobe employs a high-energy beam of electrons to study the microstructure of minerals. This technique can be used to study very small amounts of minerals as well as minerals in situ, but the strong interaction between the electron beam and the crystalline material produces anomalous intensities, and thus electron-microprobe studies are seldom used for a complete structure determination. Many new techniques have helped scientists to perform structural studies of minerals in special states—for example, at high pressures or temperatures near the melting point—but the most substantial advancements in determining mineral structures continue to involve X-ray analysis.

Scientific and Economic Applications

A central theme of modern mineralogy has been the dependence of a mineral’s external form and basic properties on its internal structure. Because the arrangement of atoms in a mineral provides a deeper understanding of its mechanical, thermal, optical, electrical, and chemical properties, scientists have determined the atomic arrangements of many hundreds of minerals by using the X-ray diffraction technique. This great amount of structural information has proved to be extremely valuable to mineralogists, geologists, physicists, and chemists. Through this information, mineralogists have gained an understanding of the forces that hold minerals together, and have even used crystal-structure data to verify and correct the formulas of some minerals. Geologists have been able to use the knowledge of mineral structures at high temperatures and pressures to gain a better understanding of the eruption of volcanoes and other geologic processes. Physicists have used this structural information to deepen their knowledge of the solid state. Through crystal-structure data, chemists have been able to expand their understanding of the chemical bond, the structures of molecules, and the chemical behavior of a variety of substances.

Because minerals often have economic importance, many people besides scientists have been interested in their structures. Rocks, bricks, concrete, plaster, ceramics, and many other materials contain minerals. In fact, almost all solids except glass and organic materials are crystalline. That is why knowledge of the structure and behavior of crystals is important in nearly all industrial, technical, and scientific enterprises. This knowledge has, in turn, enabled scientists to synthesize crystalline compounds to fill special needs, such as high-temperature ceramics, electrical insulators, semiconductors, and many other materials.

Principal Terms

cleavage: the capacity of crystals to split readily in certain directions

crystal: externally, a solid material of regular form bounded by flat surfaces called faces; internally, a substance whose orderly structure results from a periodic three-dimensional arrangement of atoms

ion: an electrically charged atom or group of atoms

ionic bond: the strong electrical forces holding together positively and negatively charged atoms

mineral: a naturally formed inorganic substance with characteristic physical properties, a definite chemical composition, and, in most cases, a regular crystal structure

X ray: radiation that can be interpreted in terms of either very short electromagnetic waves or highly energetic photons (light particles)

Bibliography

Blake, Alexander, J., and Jacqueline M. Cole. Crystal Structure Analysis: Principles and Practices. 2d ed. New York: Oxford University Press, 2009. Written for advanced undergraduate and graduate students. Covers diffraction, crystal structures, data collection, and crystal-structure determination and analysis.

Bragg, William Lawrence. Atomic Structure of Minerals. Ithaca, N.Y.: Cornell University Press, 1937. Primarily a discussion of mineralogy based on the vast amount of new data generated by the successful application of X-ray diffraction analysis to crystalline minerals. Text is highly readable, but the reader’s knowledge of elementary physics and chemistry is assumed. Useful to mineralogists, physicists, chemists, and any scientists interested in the physical and chemical properties of minerals.

Bragg, William Lawrence, G. F. Claringbull, and W. H. Taylor. The Crystalline State. The Crystal Structures of Minerals 4. Ithaca, N.Y.: Cornell University Press, 1965. A comprehensive compilation of crystal-structure information on minerals. Analyses of structures are authoritative. Accessible to anyone with a basic knowledge of minerals, as crystallographic notation is kept to a minimum and the actual structures take center stage.

Cepeda, Joseph C. Introduction to Minerals and Rocks. New York: Macmillan, 1994. Provides a good introduction to the structure of minerals for students just beginning their studies in Earth science. Includes illustrations and maps.

Deer, William A., R. A. Howie, and J. Zussman. An Introduction to Rock-Forming Minerals. 2d ed. London: Pearson Education Limited, 1992. Standard references on mineralogy for advanced college students and above. Each chapter contains detailed descriptions of chemistry and crystal structure, usually with chemical analyses. Discussions of chemical variations in minerals are extensive.

Evans, Robert Crispin. An Introduction to Crystal Chemistry. 2d ed. New York: Cambridge University Press, 1964. Analyzes crystal structures in terms of their correlation with physical and chemical properties. Discusses only those structures that are capable of illustrating basic principles that govern the behavior of these crystals. Assumes some knowledge of elementary chemistry and physics on the part of the reader.

Ferraris, Giovanni, Emil Makovicky, and Stefano Merlino. Crystallography of Modular Materials. New York: Oxford University Press, 2004. Contains advanced discussions of crystal structure. Includes discussion of OD structures, polytypes, and modularity. Contains a long list of references.

Hammond, Christopher. The Basics of Crystallography and Diffraction. 2d ed. New York: Oxford University Press, 2001. Covers crystal form, atomic structure, physical properties of minerals, and X-ray methods. Illustrations help clarify some of the more mathematically complex concepts. Includes bibliography and index.

Haussühl, Siegfried. Physical Properties of Crystals: An Introduction. Weinheim: Wiley-VCH, 2007. Begins with foundational information and discusses tensors. Text contains some mathematical equations and is best suited for advanced students, professionals, and academics.

Lima-de-Faria, José. Structural Mineralogy: An Introduction. Dordrecht: Kluwer, 1994. Provides a good college-level introduction to the basic concepts of crystal structure and the classification of minerals. Illustrations, extensive bibliography, index, and a table of minerals on a folded leaf.

Lipson, Henry S. Crystals and X-Rays. New York: Springer-Verlag, 1970. Written for high school students and college undergraduates. Stresses the observational and experimental by showing, for example, how the X-ray diffraction technique was used to determine the structures of some simple minerals.

Pauling, Linus. The Nature of the Chemical Bond and the Structure of Molecules and Crystals: An Introduction to Modern Structural Chemistry. 3d ed. Ithaca, N.Y.: Cornell University Press, 1960. The beginner will encounter difficulties, but readers with a good knowledge of chemistry will find this book informative and inspiring.

Sinkankas, John. Mineralogy for Amateurs. New York: Van Nostrand Reinhold, 1966. Intended primarily for the amateur mineralogist. Has become popular with nonprofessionals and includes a good chapter on the geometry of crystals, in which the basic ideas of mineral structure are cogently explained. Well illustrated with photographs and drawings.

Smith, David G., ed. The Cambridge Encyclopedia of Earth Sciences. New York: Crown, 1981. Written by authorities from England and the United States. Primarily a reference work, the text is both readable and informative. Some knowledge of elementary physics and chemistry is needed for a full understanding of most sections. Profusely illustrated with helpful diagrams and photographs.

Tilley, Richard J. D. Crystals and Crystal Structures. Hoboken, N.J.: John Wiley & Sons, 2006. Discusses the characteristics, structure, and chemical dynamics of crystals. Provides information on specific crystals and specific structure types. Includes appendices, practice problems and exercises, bibliographies, and indexes.