Crystal

Crystal

Common classes of crystalline solids

Internal structures of metallic crystals

Common internal structures of crystals of ionic solids

Crystal structures of molecular compounds and network solids

Crystallinity in macromolecules

Crystal defects and growth of crystals

Gemstones

Resources

A crystal is a solid composed of atoms in a highly ordered, definite, geometric arrangement that is repeated in all directions within the crystal.

Crystals have always attracted the curiosity of humans. Archaeologists have unearthed shells, claws, teeth, and other crystalline solids dating to 25, 000 BC that have holes, as though worn as necklaces, and engraved with symbols of magic. The treasures of the ancient Egyptian king, Tutankhamen, abound with crystals in the forms of gems and jewels. These were not only intended for personal adornment, but were designed in symbolic fashion and believed to possess mystical and religious powers. Healers used crystals in their magical rites and cures.

In ancient Greece, Archimedes made a study of regular solids, and Plato and Aristotle speculated on the relationship between regular solids and the elements. In the sixteenth century, the German naturalist, Giorgius Agricola, classified solids by their external forms, and Johannes Kepler observed that snowflakes were always six-sided (circa 1611), commenting on geometrical shapes and arrangements that might produce this effect. In the seventeenth century, noted philosophers and mathematicians, including Rene´ Descartes, Robert Hooke, and Christiaan Huygens followed and expanded Kepler’s postulates.

In 1671, an English translation of a study by a Danish-born scientist, Nicolaus Steno, was published in London. It described his investigative work on crystals of quartz, which consists of silicon and oxygen. An Italian scientist, Domenico Guglielmini, developed a structural theory of crystals over the years 1688-1705. Later, measurements of crystals by the French scientist, Jean Baptiste Louis Rome´ Delisle, were published between 1772-1783. In 1809, the British scientist, William Hyde Wollaston, described an improved goniometer instrument for making accurate measurements on small crystals.

The study of crystals has led to major advances in our understanding of the chemistry of biological processes. In 1867, Louis Pasteur discovered two types of tartaric acid crystals that were related as the left hand is to the right; that is, one was the mirror image of the other. This led to the discovery that most biomolecules, molecules upon which living systems are based, exhibit this same type of handedness.

Detailed analyses of crystal structures are carried out by x-ray diffraction. In 1912, Max von Laue predicted that the spacing of crystal layers is small enough to cause diffraction (breaking of light, when it hits an opaque surface, into colored bands). William Henry Bragg and his son, William Lawrence Bragg, were awarded the Nobel Prize in chemistry (1915) for their development of crystal structure analysis using x-ray diffraction. In 1953, James Watson and Francis Crick deduced the double helix structure of DNA (deoxyribo-nucleic acid, one of the nucleic acids which controls heredity in living organisms) partly from the results of x-ray diffraction analysis of DNA. In recognition of this advancement in the study of the processes of life, they were awarded the Nobel Prize in 1962. Throughout the twentieth century the study of crystalline molecules has continued to expand our knowledge by providing detailed structures of vitamins, proteins (enzymes, myoglobin, bacterial membranes), liquid crystals, polymers, and organic and inorganic compounds.

Today, crystals are still worn for decorative purposes in the form of gems and jewels. There are still believers in the mystical powers of crystals, but there is no scientific basis for any of the many claims made regarding the powers of crystals. Crystals are used in modern technological applications, such as lasers.

Common classes of crystalline solids

The standard classes of crystalline solids are the metals, ionic compounds, molecular compounds, and network solids.

The metals are those elements occurring on the left side of the periodic table (a classification of elements based on the number of protons in their nuclei), up to the diagonal that connects boron and astatine. The nuclei of metal atoms take up highly ordered, crystalline arrangements; the atomic electrons are relatively free to move throughout the metal, making metals good conductors of electricity.

When a metallic element combines with a non-metal (an element which is on the right side of the boron-astatine diagonal) an ionic compound is obtained. Ionic compounds do not consist of molecules, but are made up of ordered arrays of ions. An ion is a charged atom or molecule; a positive ion (or cation) is produced when an atom gives up an electron, and a negative ion (or anion) is the result when an atom gains an electron. The attraction of opposite charges of cations and anions (electrostatic attraction) keeps them in close proximity to each other. In compounds, the ions assume the ordered arrangements characteristic of crystals. The strong electrostatic forces between oppositely charged ions make it very difficult to separate the ions and break down the crystal structure; thus, ionic compounds have very high

Table 1. Common Crystal Structures of Ionic Compounds . (Thomson Gale.)
Common crystal structures of ionic compounds
Compound	Structure Name	Radius ratio and C.N. of cation and anion	Packing and layering
halides of lithium, sodium, potassium, rubidium; ammonium halides; silver halides; oxides and sulfides of magnesium, clacium, strontium, and barium	soldium chloride	0.41 to 0.75 6:6	chloride ccp, sodium in every octahedral hole
zinc sulfide, copper(I) chloride, cadmium (II) sulfide, mercury (II) sulfide	sphalerite	0.23 to 0.41 4:4	sulfide ccp, zinc in half the tetrahedral holes
zinc sulfide, zinc oxide, beryllium oxide, manganese (II) sulfide, silver iodide, silicon carbide, ammonium fluoride	wurtzite	0.23 to 0.41 4:4	sulfide hcp, zinc in half the tetrahedral holes
calcium fluoride, barium chloride, mercury (II) fluoride, lead (IV) oxide, barium fluoride, strontium fluoride	fluorite	0.72 and up 8:4	calcium ccp, fluoride in all tetrahedral holes
cesium chloride, calcium sulfide, cesium cyanide	cesium chloride	0.72 and up 8:8	chloride in primitive cubes,cesium at the centers

melting points (generally higher than 1, 742°F [950°C]). Because the electrons in ionic compounds are not free to move throughout the crystal, these compounds do not conduct electricity unless the ions themselves are released by heating to high temperatures or by dissolving the compound.

When nonmetallic elements combine in reactions, the resulting compound is a molecular compound. Within such compounds the atoms are linked by shared electrons, so that ions are not present. However, partial charges arise in individual molecules because of uneven distribution of electrons within each molecule. Partial positive charges in one molecule can attract partial negative charges in another, resulting in ordered crystalline arrangements of the molecules. The forces of attraction between molecules in crystals of covalent compounds are relatively weak, so these compounds require much less energy to separate the molecules and break down the crystals; thus, the melting points of covalent compounds are usually less than 570°F (300°C). Because charged particles are not present, covalent compounds do not conduct electricity, even when the crystals are broken down by melting or by dissolving.

Network solids are substances in which atoms are bonded covalently to each other to form large networks of molecules of nondefinite size. Examples of network solids include diamond and graphite, which are two crystalline forms of carbon, and silicates, such as sand, rock, and minerals, which are made up of silicon and oxygen atoms. Because the atoms occupy specific bonding sites relative to each other, the resulting arrangement is highly ordered and, therefore, crystalline. Network solids have very high melting points because all the atoms are linked to their neighbors by strong covalent bonds. Thus, the melting point of diamond is 6, 332°F (3, 500°C). Such solids are insoluble because the energy required to separate the atoms is so high.

Internal structures of metallic crystals

A complete description of the structure of a crystal involves several levels of detail. Metallic crystals are discussed first for simplicity, because the atoms are all of the same type, and can be regarded as spherical in shape. However, the basic concepts are the same for all solids.

If the spheres are represented by points, then the pattern of repeating points at constant intervals in each direction in a crystal is called the lattice. Fourteen different lattices can be obtained geometrically (the Bravais lattices). If lines are drawn through analogous points within a lattice, a three-dimensional arrangement of structural units is obtained. The smallest possible repeating structural unit within a crystal is called the unit cell, much like a brick is the smallest repeating unit (the unit cell) of a brick wall.

The fourteen unit cell types are based on seven types of crystal systems. These are the cubic, triclinic, monoclinic, orthorhombic, trigonal, tetragonal, and hexagonal systems. The specific crystal system and type of unit cell observed for a given solid is dependent on several factors. If the particles that make up the solid are approximately spherical, then there is a tendency for them to pack together with maximum

Table 2. Gems. (Thomson Gale.)
Gems
Name	Composition	Impurity	Common color	Crystal system
Diamond	carbon		colorless and other	cubic
Ruby	aluminum oxide	chromium	red	hexagonal
Sapphire	aluminum oxide	titanium, iron	blue and other	hexagonal
Emerald	beryllium-aluminum silicate	chromium	green	hexagonal
Jade	calcium-magnesium-iron silicate	iron	green and other	monoclinic
Opal	silicon oxide hydrates	(scattered light)	various	various none
Topaz	aluminum fluoride-hydroxide-silicate	unknown	colorless and other	orthorhombic
Turquoise	copper-aluminum-hydroxide-phosphate	copper	blue and other	none
Zircon	zirconium silicate	iron	colorless and other	tetragonal

efficiency. Close-packed structures have the maximum packing efficiency, with 74% of the crystal volume being occupied by the particles. Close-packing occurs in two different ways: cubic close-packing (ccp), which gives rise to cubic unit cells (the face-centered cube), and hexagonal close-packing (hcp), which gives hexagonal unit cells.

The placement of atoms that produces each of these arrangements can be described in terms of their layering. Within each layer, the most efficient packing occurs when the particles are staggered with respect to one another, leaving small triangular spaces between the particles. The second layer is placed on top of the first, in the depressions between the particles of the first layer. Similarly, the third layer lies in the depressions of the second. Thus, if the particles of the third layer are also directly over depressions of the first layer, the layering pattern is ABCABC, in which the fourth layer is a repeat of the first. This is called cubic close-packing, and results in the face-centered cubic unit cell. Such close-packed structures are common in metals, including calcium, strontium, aluminum, rhodium, iridium, nickel, palladium, platinum, copper, silver, and gold. If the third layer particles are also directly over particles of the first, the repeating layer pattern is ABAB. This is called hexagonal close-packing, and produces the hexagonal unit cell. This packing arrangement also is observed for many metals, including beryllium, magnesium, scandium, yttrium, lanthanum, titanium, zirconium, hafnium, technetium, rhenium, rubidium, osmium, cobalt, zinc, and cadmium.

Other layering patterns in which the particles are not close-packed occur frequently. For example, particles within a layer might not be staggered with respect to one another. Instead, if they align themselves as in a square grid, the spaces between the particles also will be square. The second layer fits in the depressions of the first; the third layer lies in depressions of the second, and over particles of the first layer, giving the layering pattern (ABAB) with a space-filling efficiency of 68%. The resulting unit cell is a body-centered cube. Metals which have this arrangement of atoms include the alkali metals, barium, vanadium, niobium, tantalum, chromium, molybdenum, tungsten, manganese, and iron.

Common internal structures of crystals of ionic solids

Although ionic solids follow similar patterns as described above for metals, the detailed arrangements are more complicated, because the positioning of two different types of ions, cations and anions, must be considered. In general, it is the larger ion (usually, the anion) that determines the overall packing and layering, while the smaller ion fits in the holes (spaces) that occur throughout the layers.

Two types of holes occupied by cations exist (in close-packed ionic structures.). These are named tetrahedral and octahedral. An ion in a tetrahedral site would be in contact with four ions of opposite charge, which, if linked by imaginary lines, produces a tetrahedron. An ion in an octahedral site would be in contact with six ions of opposite charge, producing an octahedron. The number of oppositely charged ions in contact with a given ion is called its coordination number (CN). Therefore, an ion in a tetrahedral site has a coordination number of four; an ion in an octahedral site has a coordination number of six. The total number of octahedral holes is the same as the number of close-packed ions, whereas there are twice as many tetrahedral holes as close-packed atoms. Because tetrahedral holes are smaller, they are occupied only when the ratio of the smaller ion’s radius to the radius of the larger ion is very small. As the radiusratio of the smaller ion to the larger ion becomes greater, the smaller ion no longer fits into tetrahedral holes, but will fit into octahedral holes.

These principles can be illustrated by several examples. The repeating structural unit of crystalline sodium chloride (table salt) is the face-centered cubic unit cell. The larger chloride ions are cubic close-packed (ABCABC layering pattern). The radius ratio of sodium ion to chloride ion is about 0.6, so the smaller sodium ions occupy all the octahedral sites. Chloride and sodium ions both have coordination numbers of six. This structure occurs frequently among ionic compounds and is called the sodium chloride or rock salt structure (Table 1).

In the sphalerite (or zincblende) crystalline form of zinc sulfide, the larger sulfide ions are cubic close-packed (ABCABC layering), giving a face-centered cubic unit cell. The small zinc ions occupy tetrahedral sites. However, the number of tetrahedral holes is twice the number of sulfide ions, whereas the number of zinc ions is equal to the number of sulfide ions. Therefore, zinc ions occupy only half of the tetrahedral holes. In the wurtzite structure, another crystalline form of zinc sulfide, the sulfide ions are hexagonally close-packed, (ABAB layering), giving a hexagonal unit cell. Again, the zinc ions occupy half the tetrahedral sites.

Another common structure, the fluorite structure, is of ten observed for ionic compounds which have twice as many anions as cations, and in which the cations are larger than the anions. The structure is named after the compound, calcium fluoride, in which the calcium ions are cubic close-packed, with fluoride in all the tetrahedral sites.

As discussed for metals, many compounds have structures that do not involve close-packing. For example, in the cesium chloride structure, the larger chloride ions are arranged in primitive cubes, with cesium ions occupying positions at the cube centers.

Many other structures are observed for ionic compounds. These involve similar packing arrangements as described above, but vary in number and types of occupied holes, and the distribution of ions in compounds having more than two types of cation and/or anion.

Crystal structures of molecular compounds and network solids

The molecules that make up molecular compounds may not be approximately spherical in shape. Therefore, it is difficult to make detailed generalizations for molecular compounds. They exhibit many crystal structures that are dependent on the best packing possible for a specific molecular shape.

The most common network solids are diamond, graphite, and silicates. Diamond and graphite are two crystalline forms of carbon. In diamond, each carbon atom is covalently bonded to all four of its nearest neighbors in all directions throughout the network. The resulting arrangement of atoms gives a face-centered cubic unit cell. In graphite, some of the covalent bonds are double bonds, forcing the carbon atoms into a planar arrangement of fused six-membered rings, like a chicken-wire fence. Sheets of these fused rings of carbon lie stacked upon one another.

Silicates, present in sand, clays, minerals, rocks, and gems, are the most common solid inorganic materials. In the arrays, four oxygen atoms bond to one silicon atom to give repeating tetrahedral units. Silicate units can share oxygen atoms with adjacent units, giving chain silicates, sheet silicates, and framework silicates.

Crystallinity in macromolecules

Macromolecules are giant polymer molecules made up of long chains of repeating molecular units and bonded covalently to one another. Macromolecules occur widely in nature as carbohydrates, proteins, and nucleic acids. Polymers, plastics, and rubber also are macromolecules.

Macromolecules may be likened to a plate of spaghetti, in which the individual strands of the macromolecules are entangled. Notably, there is a lack of order in this system, and a lack of crystallinity. However, a marked degree of order does exist in certain regions of these entanglements where segments of neighboring chains may be aligned, or where chain folding may promote the alignment of a chain with itself. Regions of high order in macromolecules, called crystallites, are very important to the physical and chemical properties of macromolecules. The increased forces of attraction between chains in these regions give the polymer strength, impact resistance, and resistance to chemical attack. Polymers can be subjected to some form of heat treatment followed by controlled cooling and, sometimes, stretching, in order to promote greater alignment of chains, a higher degree of crystallinity, and a consequent improvement in properties.

Crystal defects and growth of crystals

The growth and size of a crystal depends on the conditions of its formation. Temperature, pressure, the presence of impurities, etc., will affect the size and perfection of a crystal. As a crystal grows, different imperfections may occur, which can be classified as either point defects, line defects (or dislocations), and plane defects.

Point defects occur: a) if a particle site is unoccupied (a Schottky defect); b) if a particle is not in its proper site (which is vacant) but is in a space or hole (a Frenkel defect); or c) if an extra particle exists in a space or hole, with no corresponding vacancy (an anti-Schottky defect). Line defects occur: a) if an incomplete layer of particles occurs between other, complete layers (an edge dislocation); or b) if a layer of particles is not planar, but is out of alignment with itself so that the crystal grows in a spiral manner (a screw dislocation). Plane defects occur; a) if two crystallites join to form a larger crystal in which the rows and planes of the two crystallites are mismatched (a grain boundary); or b) if a layer in an ABCABC pattern occurs out of sequence (a stacking fault).

Sometimes, imperfections are introduced to crystals intentionally. For example, the conductivity of silicon and germanium can be increased by the intentional addition of arsenic or antimony impurities. This procedure is called doping, and is used in materials, called semiconductors, that do not conduct as well as metals under normal conditions. The additional electrons provided by arsenic or antimony impurities (they have one more electrons in their outermost shells than do silicon or germanium) are the source of increased conductivity.

Experiments in decreased gravity conditions aboard the space shuttles and in Spacelab I demonstrated that proteins formed crystals rapidly, and with fewer imperfections, than is possible under regular gravitational conditions. This is important because macromolecules are difficult to crystallize, and usually will form only crystallites whose structures are difficult to analyze. Protein analysis is important because many diseases (including acquired immunity deficiency syndrome, AIDS) involve enzymes, which are the highly specialized protein catalysts of chemical reactions in living organisms. The analysis of other biomolecules may also benefit from these experiments. It is interesting that similar advantages in crystal growth and degree of perfection have also been noted with crystals grown under high gravity conditions.

Gemstones

Although the apparent perfection of gems is a major source of their attraction, the rich colors of many gemstones are due to tiny impurities of colored

KEY TERMS

Close-packing— The positioning of atoms, ions, or molecules in a crystal in such a way that the amount of vacant space is minimal.

Covalent bond—A chemical bond formed when two atoms share a pair of electrons with each other.

Diffraction— A wave-like property of light: when a ray of light passes through a tiny opening it spreads out in all directions, as though the opening is the light source.

Electrostatic attraction— The force of attraction between oppositely charged particles, as in ionic bonding.

Ionic compound— A compound consisting of positive ions (usually, metal ions) and negative ions (nonmetal ions) held together by electrostatic attraction.

Lattice— A pattern obtained by regular repetition of points in three dimensions. Liquid crystal—A compound consisting of particles which are highly ordered in some directions, but not in others.

Macromolecule— A giant molecule consisting of repeating units of small molecules linked by covalent bonds.

Periodic Table— A classification of the known elements, based upon their atomic numbers (the numbers of protons in the nuclei).

Unit cell— The simplest three-dimensional repeating structure in a crystal lattice.

metal ions within the crystal structure. Table 2 lists some common gemstones and their crystalline structures.

The value and desirable properties of crystals promote scientific attempts to synthesize them. Although methods of synthesizing larger diamonds are expensive, diamond films can be made cheaply by a method called chemical vapor deposition (CVD). The technique involves methane and hydrogen gases, a surface on which the film can deposit, and a microwave oven. Energy from microwaves breaks the bonds in the gases, and, after a series of reactions, carbon films in the form of diamond are produced. The method holds much promise for: a) the tool and cutting industry (because diamond is the hardest known substance); b) electronics applications (because diamond is a conductor of heat, but not electricity); and c) medical applications (because it is tissue-compatible and tough, making it suitable for joint replacements, heart valves, etc.).

See also Diffraction.

Resources

BOOKS

Rhodes, Gale. Crystallography Made Crystal Clear. 3rd ed. Burlington, MA: Academic Press, 2006.

Massimo D. Bezoari