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crystal, a solid body bounded by natural plane faces that are the external expression of a regular internal arrangement of constituent atoms, molecules, or ions. The formation of a crystal by a substance passing from a gas or liquid to a solid state, or going out of solution (by precipitation or evaporation), is called crystallization.
Classification of Crystals
The particles in a crystal occupy positions with definite geometrical relationships to each other. The positions form a kind of scaffolding, called a crystalline lattice; the atomic occupancies of lattice positions are determined by the chemical composition of the substance. A crystalline substance is uniquely defined by the combination of its chemistry and the structural arrangement of its atoms. In all crystals of any specific substance the angles between corresponding faces are constant (Steno's Law, or the First Law of Crystallography, published by the Danish geologist Nicolaus Steno in 1669). Crystalline substances are grouped, according to the type of symmetry they display, into 32 classes. These in turn are grouped into seven systems on the basis of the relationships of their axes, i.e., imaginary straight lines passing through the ideal centers of the crystals.
Crystals may be symmetrical with relation to planes, axes, and centers of symmetry. Planes of symmetry divide crystals into equal parts (mirror images) that correspond point for point, angle for angle, and face for face. Axes of symmetry are imaginary lines about which the crystal may be considered to rotate, assuming, after passing through a rotation of 60°, 90°, 120°, or 180°, the identical position in space that it originally had. Centers of symmetry are points from which imaginary straight lines may be drawn to intersect identical points equidistant from the center on opposite sides.
The crystalline systems are cubic, or isometric (three equal axes, intersecting at right angles); hexagonal (three equal axes, intersecting at 60° angles in a horizontal plane, and a fourth, longer or shorter, axis, perpendicular to the plane of the other three); tetragonal (two equal, horizontal axes at right angles and one axis longer or shorter than the other two and perpendicular to their plane); orthorhombic (three unequal axes intersecting at right angles); monoclinic (three unequal axes, two intersecting at right angles and the third at an oblique angle to the plane of the other two); trigonal, or rhombohedral (three equal axes intersecting at oblique angles); and triclinic (three unequal axes intersecting at oblique angles). In all systems in which the axes are unequal there is a definite axial ratio for each crystal substance.
Physical Properties of Crystals
Crystals differ in physical properties, i.e., in hardness, cleavage, optical properties, heat conductivity, and electrical conductivity. These properties are important since they sometimes determine the use to which the crystals are put in industry. For example, crystalline substances that have special electrical properties are much used in communications equipment. These include quartz and Rochelle salt, which supply voltage on the application of mechanical force (see piezoelectric effect), and germanium, silicon, galena, and silicon carbide, which carry current unequally in different crystallographic directions, as semiconductor rectifiers.
See solid-state physics.
See F. C. Phillips, An Introduction to Crystallography (1970); J. D. Dana, Manual of Mineralogy (18th ed., rev. by C. S. Hurlbut, Jr., 1971); B. K. Vainshtein, Modern Crystallography (2 vol., 1981–82).
A solid in which the atoms or molecules are arranged periodically. Within a crystal, many identical parallelepiped unit cells, each containing a group of atoms, are packed together to fill all space (see illustration). In scientific nomenclature, the term crystal is usually short for single crystal, a single periodic arrangement of atoms. Most gems are single crystals. However, many materials are polycrystalline, consisting of many small grains, each of which is a single crystal. For example, most metals are polycrystalline. See Single crystal
In electronics, the term crystal is restricted to mean piezoelectric crystal. Piezoelectric crystals contract or expand under application of electric voltages, and conversely they generate voltages when compressed. They are used for oscillators, pressure sensors, and position actuators. See Piezoelectricity
The anisotropic microscopic structure of a crystal is often reflected in its external form, consisting of flat faces and sharp edges. Crystal structure is generally determined via diffraction of x-rays, neutrons, or electrons. Unlike disordered materials such as glasses or liquids, the diffraction pattern of a periodic array of atoms consists of individual sharp spots. The symmetry and structure of the crystal can be inferred from the symmetry of the diffraction pattern and the intensities of the diffracted beams. See Electron diffraction, Neutron diffraction, X-ray diffraction
A crystal can be characterized by the symmetry operations that leave its structure invariant. These can include rotation about an axis through a specific angle, reflection through a plane, inversion through a point, translations by a unit cell dimension, and combinations of these. For a periodic structure, the only allowable rotational symmetries are 2-fold, 3-fold, 4-fold, and 6-fold. A quasicrystal is a solid which yields a sharp diffraction pattern but has rotational symmetries (such as 5-fold or 10-fold) which are inconsistent with a periodic arrangement of atoms. See Quasicrystal
A plastic crystal is generally composed of organic molecules which are rotationally disordered. The centers of the molecules lie at well-defined, periodically spaced positions, but the orientations of the molecules are random. Plastic crystals are often very soft and may flow under their own weight.
A liquid crystal is a material which is intermediate in structure between a liquid and a solid. Liquid crystals usually flow like liquids but have some degree of internal order. They are generally composed of rodlike organic molecules, although in some cases they are composed of disklike molecules. In a nematic liquid crystal, the rods all have the same general orientation, but the positions of the rods are disordered. In a smectic liquid crystal, rodlike molecules are ordered into sheets, within which there is only liquidlike order. A smectic can thus be thought of as being crystalline in one dimension and liquid in the other two. In a discotic liquid crystal, disklike molecules are ordered into columnar arrays; there is short-range liquidlike order within the columns, but the columns form a two-dimensional crystal. See Crystal defects, Crystal growth, Crystal structure, Crystallography
a special type of glass containing large quantities of lead oxide or barium oxide. The name “crystal” was given by analogy with rock crystal. Crystal may be decorated by etching, faceting, cutting, and polishing. Because of the lead content and the specific arrangement of angles formed by the facets, objects made from crystal disperse a play of unusually bright, multicolored light.
What does it mean when you dream about a crystal?
A crystal can represent something beautiful or even spiritual. Alternatively, it can mean something that has “crystallized,” either in the sense of manifesting or in the sense of becoming rigid. We are also familiar with “crystal” balls that are used to divine the future.
A recursion equation parallel language.
["A Parallel Language and its Compilation to Multiprocessor Machines or VLSI", M.C. Chen, 13th POPL, ACM 1986 pp.131-139].