Crystal
From Encyclopædia
A crystal is a solid body composed of a chemical element or compound and bounded by plane surfaces that intersect each other at particular angles. All matter is composed of
atoms and
molecules. Solid materials behave in certain ways, depending on the type and internal arrangement of their
atoms or
molecules. Matter in which the spatial arrangement of
atoms or
molecules is regularly repeated is said to be crystalline. Matter in which the positions of
atoms or
molecules bear no orderly, patterned relationship is said to be noncrystalline, or amorphous. The
science of crystallography, then, is the study of the external form of crystalline matter and its relation to the chemistry and the spatial arrangement of
atoms and
molecules. The study of the crystalline state contributes to fields as diverse as biochemistry,
materials engineering, ceramics, and synthetic gem production.DEVELOPMENT OF THE SCIENCECrystallography as a
science came into being with the work of Nicolaus STENO. A physician by
education, Steno had a side
interest in geology, which led him to publish a study of the process of crystal
growth, The Podromus of Nicolaus Steno's Dissertation Concerning a Solid Body Enclosed by Process of Nature Within a Solid (1669; Eng. trans., 1916). Steno stated that the angles between crystal faces on all samples of a single substance are the same, an observation that has become known as Steno's law or the "law of constancy of interfacial angles." Steno also concluded that crystals grow by the addition of particles to existing external faces of a seed crystal from solution. Steno's work was continued and expanded on by noted scientists such as Robert BOYLE,
Pierre GASSENDI and Sir
Isaac NEWTON.Not until the work of Rene-Just HAUY in the late 18th and early 19th centuries, however, did crystallography become a mathematically exact
science. "Hauy's Law" or the "law of rational indices" states that when the shape of a crystal is referred to three intersecting axes, all faces of the crystal can be described by numerical indices related to the intercepts of the faces on these axes. Hauy's work was based on his observations of
cleavage phenomena in the mineral calcite. Some years later, Christian Westfeld (1746-1823) expressed the belief, after studying the same phenomena, that "all crystals of spar (calcite) are constituted of rhombohedral pieces." From this linking of some fundamental internal unit to the resulting external form of a crystal grew the concept of the unit
cell, a basic tenet and integral part of modern crystallography.THE UNIT CELLThe search for the shape of the unit
cell, or "integrant
molecule" of Hauy, was vigorously pursued by 19th-century crystallographers who, rather than attempting to infer the arrangement of
atoms within this "integrant
molecule," sought only to determine its shape. The scientists of the time believed that a single shape would explain all forms of all types of crystals. Hauy, correctly recognizing that this was impossible, held that there were three "integrant
molecules": the tetrahedron, the triangular
prism, and the parallelepipedon.Hauy's postulations on the internal packing of the three
molecules enabled him to predict the interfacial angles of several minerals (see MINERAL), but careful measurements by
William Wollaston (1766-1828) revealed discrepancies between Hauy's predicted angles and the measured angles of calcite. As measurements of interfacial angles became more refined, it was clear that the concept of these three "integrant
molecules" forming the basis for all crystal shapes was untenable. Although this aspect of Hauy's work was disproved, his approach and methodology in the study of crystals profoundly influenced the
science as a whole. What had previously been at best a conjectural pastime had been transformed into a theoretical
science with a mathematical basis.Hauy's work had formed a basis from which later scientists were able to begin constructing a geometrically exact discipline. Shortly after Hauy, Christian Weiss (1780-1856) was able to recognize the importance of the law of rational indices, and he set about classifying crystals on the basis of the axes of reference that he defined, as well as on symmetry elements inferred from them. Symmetry elements recognized by Weiss included symmetry planes (planes in a crystal about which a crystal appears to be reflected), rotation axes (axes through a crystal around which a face can be repeated two, three, four, and six times), centers of inversion (points through which half the crystal seems to be inverted and projected), and axes of roto-inversion (a combination of the rotation and inversion process.)Dividing crystals into systems on the basis of their axes and symmetry elements, Weiss was able to distinguish the hexagonal, orthorhombic, tetragonal, and ISOMETRIC SYSTEMS (without naming them as such). He also systematically named crystal faces according to the numerical values of their intercepts on the three axes he defined. Weiss's facial indices are still used in calculating the indices by which crystal faces and planes are named today.THE CRYSTAL SYSTEMSInvestigations of the geometrical theory of crystals continued throughout the latter half of the 19th century, eventually producing all seven crystal systems, classified on the basis of the three axes first delineated by Hauy and on the apparent symmetry of the forms derived therefrom. A complete delineation of the 32 crystal classes, or "point groups," was published (1848) by Auguste Bravais (1811-63). Bravais investigated the types of geometric figures formed by points distributed regularly in space, demonstrating that points with varying symmetry and geometry could only be grouped in 14 ways and yet allow continuous repetition in space. These 14 "lattices" could be grouped by symmetry so that 7 different lattice symmetries corresponding to the 7 crystal systems could be recognized. By combining the 14 lattices with symmetry operations, exactly 32 symmetry groupings resulted.Leonard Sohncke (1842-97) recognized two additional symmetry elements, but it was not until the late 1880s that
Russia's Evgraf Stepanovich Federov (1853-1919) outlined the 230 space groups that were thought to represent all possible combinations of lattice-type and symmetry operations. This classification scheme did not need amending until 1982, when a new type of fivefo?d symmetry was discovered in an alloy of aluminum and
manganese. The alloy contained 20-sided, or icosahedral, structures that showed long-range positional order but repeated in an apparently random, or "quasiperiodic," manner that did not allow for rotational symmetry. Several such solids, now called quasicrystals, have since been found and the fact that they exhibit fivefold symmetry has been verified. The manner in which they form remains a subject of debate, however, since they require at least two different types of unit
cell to achieve long-range order.X-RAY DIFFRACTIONMax Theodor von LAUE, a German physicist, was the first to think of bombarding a crystal with
X rays, then newly discovered, in order to disclose the arrangement of
atoms within. He reasoned that crystals should diffract
X rays in much the same way that a closely ruled grating diffracts
light. This prediction was borne out when two graduate students in
physics at the
university of
Munich, experimenting on a
Copper sulfate crystal, produced (1912) the first tangible
evidence of the internal order of crystalline matter. Thereafter,
X-ray diffraction methods developed rapidly, and their use on powdered materials is now a standard identification technique in every materials laboratory.
X-ray diffraction of single crystals has led to the determination of such complex structures as hemoglobin and DNA, thereby revolutionizing biochemistry and
medicine.MODERN CRYSTALLOGRAPHYThe frontiers of crystallography lie in applying transmission
electron microscopy (see
electron MICROSCOPE) and field ion emission imaging and diffraction to the study of crystals. Today, features as small as 1.4
angstroms can be imaged and photographed, and pictures of actual atomic crystal arrangement appear routinely in the crystallographic
literature. The knowledge obtained has applications in almost every field of
science and
technology. Advances in the understanding of crystal structure are also important for the production of pure or specifically designed crystals, for example, essential for
semiconductor technology, INTEGRATED CIRCUITS, and systems employing PIEZOELECTRICITY. Methods for producing such crystals now include advanced techniques such as molecular-beam EPITAXY and, potentially, the use of the gravity-free environment of outer space.Joan FitzpatrickGlaser, A. M., The Structure of Crystals (1987); Holden, Alan, and Morrison, P. S., Crystals and Crystal Growing (1982); Horgan, John, "Quasicrystals: Rules of the Game,"
science, Mar. 2, 1990, Laudise, R. A., "Hydrothermal Synthesis of Crystals," Chemical and Engineering News, Sept. 28, 1987; Steinhardt, P. J., "Icosahedral Solids: A New Phase of Matter?"
science, Nov. 27, 1987; Van der Eerden, J.P., Fundamentals of Crystal
growth (1988); Whittaker, E. J., Crystallography (1981).
