Crystallography is the study of materials in which the atoms stack in a three-dimensionally ordered geometric arrangement. In a single crystal a single pattern extends throughout the entire material. Polycrystalline materials have discontinuities in the periodicity of the material. In amorphous materials, there is still less periodicity within the material; the amount of non-ordered atoms in amorphous materials is at least comparable with that exhibiting periodicity.
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 diffract light of the appropriate wavelength. 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. The Braggs' found that when x-ray radiation was scattered by a crystalline material both constructive and destructive interference occurred; this interference occurs because the wavelength of the x rays is of similar magnitude to the spaces between the atoms of the crystal. Analysis of the resulting diffraction pattern, the position of the lines of the scattered radiation along with their relative intensities, is the basis of the x-ray diffraction technique; this analysis allows the determination of the precise location of the atoms in the crystal.
The x-ray diffraction technique has been one of the most important structural methods throughout the twentieth century. It has expanded our knowledge by providing detailed structures of vitamins, proteins (enzymes, bacterial membranes, liquid crystals, polymers, organic compounds and inorganic compounds.
The idea that a crystal is composed of identical structural subunits was first proposed in 1784 based on observations of the cleavage of calcite. Subsequent investigations have shown that the structures of these subunits can be inferred from a crystal's symmetry. Even casual observation suggests that the symmetry of a crystal as a whole is related to some smaller subunit within it. The subunit is called a unit cell and it contains all of the essential information, such as the symmetry and elemental composition, of the crystal. Repeated translation along the edges of the unit cell can be used to derive the entire crystal lattice; in other words, the crystal lattice is the unit cell repeated many times in a periodic fashion.
The unit cells are often categorized in terms of space lattices called Bravais lattices; in such lattices, imaginary points called lattice points replace all of the atoms of the crystals. There are only fourteen distinct types of Bravais lattices, and these are associated with seven crystal systems. The crystal systems are all parallelepipeds whose shapes are completely defined by the lengths of the three sides and by the three angles characterizing the parallelepiped.
The most important symmetry elements in the consideration of crystal structures are axes of rotation and mirror planes. An n-fold rotation axis brings the crystal into self-coincidence after rotation by 360° a mirror plane occurs when the crystal can be bisected in such a way that one half is the reflection of the other. The seven crystal systems, distinguished by their axes of symmetry are as follows (see Figure 1 for examples): 1) triclinic no symmetry elements; all unit cell lengths different, no 90° unit cell angles. 2) monoclinic one 2-fold axis or one plane; all unit cell lengths different, two 900 unit cell angles and one non-900 unit cell angle. 3) orthorhombic three mutually perpendicular axes, or two planes intersecting in a 2-fold axis; all unit cell lengths different, all unit cell angles = 900. 4) tetragonal one 4-fold axis or a 4-fold inversion axis; two unit cell lengths are identical and one is different, all unit cell angles = 900. 5) trigonal one 3-fold axis; all unit cell lengths are identical, all unit cell angles are identical but are not = 900. 6) hexagonal one 6-fold axis; two unit cell lengths identical and one different, two unit cell angles = 900 and the third = 1200. 7) cubic four 3-fold axes; all bond lengths identical, all bond angles = 900. The cubic form is the most symmetric, and the triclinic form the least. Generally speaking, crystals of lower symmetry are more common in nature than those of higher symmetry.
Another issue in crystallography is the physical basis for the crystal packing. How and why do crystals form? In what patterns do different types of materials crystallize? Crystals form since the ordered states of most solids are energetically more favorable (lower in energy) than disordered or irregularly packed ones. Hardness is one indication of the packing efficiency of atoms in a material. Materials with small atoms, packed closely together with strong covalent bonds throughout tend to be the hardest materials. The softest materials may contain metallic bonds or weaker van der Waals interactions.
The placement of atoms in a crystal 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. In one packing arrangement, the third layer lies in the depressions of the second and directly over depressions of the first layer. These so-called face-centered cubic close-packed structures are common in metals such as aluminum, rhodium, iridium, copper, silver, and gold. If the third layer particles are directly over atoms of the first, one has hexagonal close packing. This packing arrangement also is observed for many metals, including rubidium, osmium, cobalt, zinc, and cadmium.
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.
The energy associated with crystal formation, the lattice energy, can be calculated by consideration of the different types of bonds within the solid: van der Waals bonds, ionic bonds, hydrogen bonds, covalent bonds, and/or metallic bonds. In the case of van der Waals solids (e.g., Ne, CO2), the lattice energy can be calculated by summing up the pair potentials of interacting atoms using a secondary bond potential for atomic interactions. For ionic solids (e.g., NaCl, ZnS), the Coulomb interaction, supplemented with a strongly repulsive force, is used in place of the secondary bond potential. In covalent (e.g., diamond, graphite) and hydrogen-bonded (e.g., H2O) materials, the calculation of the lattice energy is much more complicated, and the lattice energy cannot simply be calculated as a sum over pair potentials acting between atoms.
The growth and size of any crystal depends on the conditions of its formation.Temperature, pressure, the presence of impurities, etc., will affect the size and perfection of the crystal. As a crystal grows, different imperfections may occur which can be classified as either point defects, line defects (or dislocations), or plane defects. Point defects include missing atoms or substituted atoms; line defects are defects that extend along straight or curved lines in a crystal; plane defects extend along true planes or curved surfaces within crystals.
Sometimes, imperfections are introduced to crystals intentionally. For example, the conductivity of semiconductors such as silicon and germanium can be modulated by the intentional addition of arsenic or antimony impurities. This procedure is called "doping." In this case, the additional electrons provided by arsenic or antimony impurities result in increased conductivity of the semiconductors.
Experiments in decreased gravity conditions aboard the space shuttles and in SpacelabI demonstrated that proteins formed crystals rapidly, and with fewer imperfections, than is possible under normal 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 Immune Deficiency Syndrome, AIDS) involve enzymes, which are the highly specialized protein catalysts of chemical reactions in living organism. 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.
There is continued scientific interest in learning new ways to grow crystals due to the promise of new or improved crystalline materials with valuable properties. Although methods of synthesizing larger diamonds are expensive, polycrystalline 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 since diamond is the hardest known substance; b) electronics applications since diamond is a conductor of heat, but not electricity; and c) medical applications since it is tissue- compatible and tough. Thus it is suitable for use in items such as joint replacements and heart valves.
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