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In crystalline solids the atoms or molecules are stacked in a regular manner, forming a three-dimensional pattern which may be obtained by a three-dimensional repetition of a certain pattern unit called a unit cell. When the periodicity of the pattern extends throughout a certain piece of material, one speaks of a single crystal. A single crystal is formed by the growth of a crystal nucleus without secondary nucleation or impingement on other crystals. See Crystal structure, Crystal-
When grown from a melt, single crystals usually take the form of their container. Crystals grown from solution (gas, liquid, or solid) often have a well-defined form which reflects the symmetry of the unit cell. See Crystal growth
Ideally, single crystals are free from internal boundaries. They give rise to a characteristic x-ray diffraction pattern.
Many types of single crystal exhibit anisotropy, that is, a variation of some of their physical properties according to the direction along which they are measured. For example, the electrical resistivity of a randomly oriented aggregate of graphite crystallites is the same in all directions. This anisotropy exists both for structure-sensitive properties, which are strongly affected by crystal imperfections (such as cleavage and crystal growth rate), and for structure-insensitive properties, which are not affected by imperfections (such as elastic coefficients).
The structure-sensitive properties of crystals (for example, strength and diffusion coefficients) seem governed by internal defects, often on an atomic scale. See Crystal defects
an individual crystal that has a continuous crystal lattice and is characterized by anisotropy of its properties. The external shape of a single crystal is determined by its atomic-crystalline structure and the conditions of crystallization. A single crystal often acquires well-defined natural faceting; under nonequilibrium conditions of crystallization, the faceting is weakly manifested. Single crystals of quartz, salt, Iceland spar, diamond, and topaz are examples of faceted natural single crystals. Polycrystals and polycrystalline aggregates, which consist of a set of small single crystals of various orientation, are distinguished from single crystals.
Single crystals are valuable as materials that have special physical propertes. For example, diamond and borazon are extremely hard, fluorite is transparent to a broad range of wavelengths, and quartz is piezoelectric. Single crystals are capable of changing their properties under the influence of external factors (light, mechanical strains, electric and magnetic fields, radiation, temperature, or pressure); therefore, products and components made from them are used as various types of transformers in radio electronics, quantum electronics, acoustics, and computer technology. Originally, natural single crystals were used in engineering, but supplies are limited and the quality is not always sufficiently high. At the same time, many valuable properties have been found only in synthetic crystals. Therefore, the necessity of growing crystals artificially has arisen. The parent substance for growth of single crystals may be a solid (particularly a powder), a liquid (melt or solution), or a gas.
Methods of growing single crystals from a melt include the Stockbarger, Czochralski, and Verneuil methods and zone melting. In the Stockbarger method a crucible containing a melt is moved vertically through a furnace at a rate of 1–20 mm/hr (Figure 1). The temperature in the plane of the diaphragm is kept equal to the crystallization temperature of the substance. Since the crucible has a conical bottom, when it is slowly lowered the melt in the cone is at a temperature below the crystallization temperature, and very small crystals form. Because of geometric selection, only one crystal survives. The selection is related primarily to the anisotropy of the rates of growth of the single crystal’s facets. This method is used widely in the industrial production of large single crystals of fluorite, lithium fluoride, cadmium sulfide, and other chemicals.
In the Czochralski method the single crystal is slowly pulled from the melt (Figure 2) at a rate of 1–20 mm/hr. This method makes possible the production of single crystals of specific crystallographic orientation. The Czochralski method is used in growing single crystals of yttrium-aluminum garnet, lithium niobate, and semiconductors. Using this method, Stepanov devised another method of growing crystals with a cross section of prescribed form.
The Verneuil method uses no crucible. The substance, in the form of a powder (particle size, 2–100 microns [LI]), is fed from a bin (Figure 3) through an oxyhydrogen flame to the upper, molten face of a seed single crystal, which is slowly lowered by a mechanism. The Verneuil method is the principal industrial method of producing refractory single crystals, such as ruby, spinel, and rutile.
In the zone melting method, a melting zone of extremely limited width is created, and the single crystal is produced by sequential melting of an entire ingot. The zone melting method is widely used in the production of semiconductor single crystals (W. G. Pfann, 1927) and such refractory single crystals as molybdenum and tungsten.
There are three methods of growing crystals from solution: the low-temperature method (using water, alcohol, and acids as solvents), the high-temperature method (using molten salts), and the hydrothermal method. A low-temperature crystallizer is a vessel containing a solution in which supersaturation, which is necessary for growing crystals, is created by means of slow lowering of temperature or, less frequently, by evaporation of the
solvent (Figure 4). This method is used to produce large single crystals of Rochelle salt, potassium dihydrophosphate (KDP), naphthalene, and other chemicals.
A high-temperature crystallizer (Figure 5) has a crucible with a solvent and the compound to be crystallized. The crucible is placed in a furnace. The compound to be crystallized precipitates from the solvent as the temperature is slowly lowered (solution-melt crystallization). This method is used to produce single crystals of iron-yttrium garnet, mica, and various semiconductor films.
Hydrothermal synthesis of single crystals is based on the dependence of the solubility of the substance in aqueous solutions of acids and alkalies on pressure and temperature. The concentration of the substance in solution and the supersaturation required to produce single crystals are accomplished by means of high pressure (up to 300 meganewtons per sq m [MN/m2], or 3,000 kilograms-force per sq cm [kgf/cm2]) and a temperature difference between the upper part of the autoclave (T1∼ 250°C) and lower part (T2 ∼ 500°C) (Figure 6). The transfer of the substance is accomplished by convective mixing. Hydrothermal synthesis is the main process used to produce quartz single crystals.
The methods used to grow single crystals from a gaseous substance are evaporation of the parent substance in a vacuum, with subsequent precipitation of the vapor onto the crystal, in which case precipitation is sustained by a certain temperature difference T (Figure 7,a); vaporization in a gas (usually an inert gas), where transfer of the substance to be crystallized is accomplished by a directional gas flow (Figure 7,b); and precipitation of the chemical reaction products onto the surface of the seed single crystal (Figure 7,c). The gas-phase crystallization method is used extensively to produce single-crystal films and single crystals for integrated circuits and other purposes.
The selection of the method of growing single crystals is determined by the quality requirements (the number and nature of the defects in the single crystal). A distinction is made between macroscopic defects (extraneous inclusions, blocks, and strains) and microscopic defects (dislocations, impurities, or vacancies).
Special methods exist for reducing the number of defects in a single crystal (such as annealing or growing single crystals on defectless seeds).
Various methods of heating are used in growing single crystals; among them are resistance, high-frequency, gas-flame, and, less frequently, electron-beam, radiation (including laser), and electric-arc heating.
REFERENCESBuckley, H. Rost kristallov. Moscow, 1954. (Translated from English.)
Laudise, R. A., and R. L. Parker. Rost monokristallov. Moscow, 1973. (Translated from English.)
Mullin, J. Kristallizatsiia. Moscow, 1966. (Translated from English.)
Shubnikov, A. V. Obrazovanie kristallov. Moscow-Leningrad, 1947.
Shubnikov, A. V. Kak rastut kristally. Moscow-Leningrad, 1935.
Pfann [W. G.]. “Printsipy zonnoi plavki.” In Germanii: Sb. perevodov. Moscow, 1955. Page 92. (Redkie metally.)
KH. S. BAGDASAROV