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polymorphism,of minerals, property of crystallizing in two or more distinct forms. Calcium carbonate is dimorphous (two forms), crystallizing as calcite or aragonite. Titanium dioxide is trimorphous; its three forms are brookite, anatase (or octahedrite), and rutile. Polymorphism of an element is called allotropyallotropy
[Gr.,=other form]. A chemical element is said to exhibit allotropy when it occurs in two or more forms in the same physical state; the forms are called allotropes.
..... Click the link for more information. . The process was discovered (1821) by Eilhard Mitscherlich. See isomorphismisomorphism
, of minerals, similarity of crystal structure between two or more distinct substances. Sodium nitrate and calcium sulfate are isomorphous, as are the sulfates of barium, strontium, and lead. Crystals of isomorphous substances are almost identical.
..... Click the link for more information. ; mineralmineral,
inorganic substance occurring in nature, having a characteristic and homogeneous chemical composition, definite physical properties, and, usually, a definite crystalline form. A few of the minerals (e.g.
..... Click the link for more information. ; crystalcrystal,
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
..... Click the link for more information. .
A form of genetic variation, specifically a discontinuous variation, occurring within plant and animal species in which distinct forms exist together in the same population, even the rarest of them being too common to be maintained solely by mutation. Thus the human blood groups are examples of polymorphism, while geographical races are not; nor is the diversity of height among humans, because height is “continuous” and does not fall into distinct tall, medium, and short types. See Mutation
Distinct forms must be controlled by some switch which can produce one form or the other without intermediates such as those arising from environmental differences. This clear-cut control is provided by the recombination of the genes. Each gene may have numerous effects and, in consequence, all genes are nearly always of importance to the organism by possessing an overall advantage or disadvantage. They are very seldom of neutral survival value, as minor individual variations in appearance often are. Thus a minute extra spot on the hindwings of a tiger moth is in itself unlikely to be of importance to the survival of the insect, but the gene controlling this spot is far from negligible since it also affects fertility. See Recombination (genetics)
Genes having considerable and discontinuous effects tend to be eliminated if harmful, and each gene of this kind is therefore rare. On the other hand, those that are advantageous and retain their advantage spread through the population so that the population becomes uniform with respect to these genes. Evidently, neither of these types of genes can provide the switch mechanism necessary to maintain a polymorphism. That can be achieved only by a gene which has an advantage when rare, yet loses that advantage as it becomes commoner.
Occasionally there is an environmental need for diversity within a species, as in butterfly mimicry. Mimicry is the resemblance of different species to one another for protective purposes, chiefly to avoid predation by birds. Sexual dimorphism falls within the definition of genetic polymorphism. In any species, males and females are balanced at optimum proportions which are generally near equality. Any tendency for one sex to increase relative to the other would be opposed by selection.
In general, a gene having both advantageous and disadvantageous effects may gain some overall advantage and begin to spread because one of the features it controls becomes useful in a new environment. A balance is then struck between the advantages and disadvantages of such a gene, ensuring that a proportion of the species carry it, thus giving rise to permanent discontinuous variation, that is, to polymorphism. See Protective coloration
Polymorphism is increasingly known to be a very common situation. Its existence is apparent whenever a single gene having a distinct recognizable effect occurs in a population too frequently to be due merely to mutation. Even if recognized by some trivial effect on the phenotype, it must in addition have important other effects. About 30% of the people in western Europe cannot taste as bitter the substance phenylthiourea. This is truly an insignificant matter; indeed, no one even had the opportunity of tasting it until the twentieth century. Yet this variation is important since it is already known that it can affect disease of the thyroid gland. See Genetics, Population genetics
The existence of different crystal structures with the same chemical composition. If only one chemical element is present, the forms are called allotropes. Graphite and diamond are allotropes of carbon, whereas quartz and cristobalite are polymorphs of silica (silicon dioxide, SiO2). Although properties are different in these forms, reversible transformations, which involve small shifts in atom positions and no bulk transport of material, are common. The quartz transformation at 1063°F (573°C) is a reversible, atom-displacement transformation.
In metals and ceramics, similar transformations are called martensitic. Advantage is taken of the localized nature of reversible transformation in steel by controlling the melting atmosphere, temperature, composition, mechanical working (alloying), and tempering and quenching operations.
Control over transformations to achieve desirable properties as either devices or structural materials in extreme environments is a frequent objective. In the case of tin, reversibility on the atomic scale can have devastating consequences for bulk properties. Similar transformations may be beneficial in the right place and in the desired degree. Such transformation is attempted with metals and ceramics. See Crystal structure
in biology, the presence within a single species of individuals differing distinctly in appearance and having no transitional forms. If there are two such forms, the phenomenon is called dimorphism; a frequently enountered example is sexual dimorphism.
Polymorphism includes diversity of external appearance in individuals of the same or different populations. Polymorphism within a genetically homogeneous population is known in colonies of many Hydroida, among which hydranths of varying structure may develop on one stolon, for example, trophozooids, dactylozooids, and acanthozooids in the polyps Podocoryne. Polyps and medusae belonging to a single species and differing completely in appearance are examples of polymorphism related to the alternation of generations. Of the same type is the polymorphism of rust fungi, among which the fruit bodies and spores, developing on different hosts, differ distinctly in appearance and in physiological characteristics. Such polymorphism, as well as the type with a diversity of larval forms in the same species, for example, trematodes, is called pleomorphism.
When there is polymorphism among sexually distinct animals, individuals within one sex differ in appearance: for example, female aphids and the males of some coccids are winged or wingless. Typical of social insects is polymorphism related to a division of the functions of various individuals in a family or colony—the queen and workers among common honeybees, and the queens and various types of workers and soldiers among ants and termites. To the same type of polymorphism may be ascribed seasonal polymorphism, as well as characteristics related to population density, among them differences in coloration, body proportions, and behavior in Acridoidea (phase variation) and in the caterpillars of some butterflies and moths.
REFERENCESMayr, E. Zoologicheskii vid i evoliutsiia. Moscow, 1968. (Translated from English.)
Sheppard, P. M. Estestvennyi otbor i nasledstvennost’. Moscow, 1970. (Translated from English.)
M. S. GILIAROV
(in physics, mineralogy, and chemistry), the ability of some substances to exist in states with differing atomic crystal structures. Each such state, or thermodynamic phase, is called a polymorphic modification and is stable under certain external conditions (temperature and pressure). The modifications are usually indicated by the Greek letters α, β, γ, and so on. The difference in structure results in a difference in the properties of the polymorphic modifications of a given substance. Polymorphism was discovered in 1798 when it was found that CaCO3 may exist as two minerals, calcite and arago-nite. Polymorphism is a property both of free elements (allo-tropy) and of inorganic and organic compounds. Thus, carbon has two modifications, the cubic (diamond) and hexagonal (graphite) forms, which differ sharply in their physical properties. White tin, which has a tetragonal body centered lattice, is a ductile metal, whereas gray tin, a low-temperature modification with a diamond like tetragonal lattice, is a brittle semiconductor. Some compounds, such as SiO2, have more than two polymorphic modifications. The rearrangement of the crystal lattice during a polymorphic transition reduces to shifting of atoms, a change in the type of packing, and rotation of certain structural groups (for example, NH4 and NO3 in the various modifications of ammonium nitrate). Polymorphism is also observed in liquid crystals.
Polymorphism results from the ability of the same atoms and molecules to form any of several stable lattices in a space. Since any small distortion of a stable lattice is related to an increase in lattice energy, the existing structural states correspond to energy minimums of various depths (see Figure 1). At 0”K, the most probable form is the α-modification, which corresponds to
a deep minimum. At temperatures above 0°K, the thermodynamic state of the lattice is determined by its free energy U = &— TS. The free energy includes not only the energy S but also the entropy term TS (S is entropy), which is associated with the thermal vibrations of the crystal lattice. The more stable a-lattice, which has a lower energy, is less susceptible to vibrational excitation and is characterized by a less steep U(T) curve. The U α (T) and U β(T) curves intersect at a certain temperature T0. The α-phase is more stable below T0, and the β-phase is more stable above T0; T0 is the equilibrium temperature of the α- and β-phases. Heating the α-modification above T0 leads to its conversion to the β-modification. Upon a further increase in temperature, the -modification may become less stable than the α-modification, which, in turn, may then convert to the δ-modification, and so on until the melting point of the crystal is reached.
Each modification is stable in a certain region of temperature, pressure, and other external conditions. Phase structural diagrams determine the regions of stability of the polymorphic modifications. The theoretical calculations of structural diagrams is based on a calculation of the thermodynamic characteristics, energy, and vibrational spectrum of the crystal lattice for the various polymorphic modifications. For example, the calculation of the structural diagram for carbon indicates that the onset of the region of the diamond structure is at pressures of about 50 kilobars; this facilitated work toward the synthesis of diamonds.
The transition of a less stable modification to a more stable modification is related to overcoming an energy barrier, which is significantly lower when the transition occurs continuously by nucleation and subsequent growth of regions of the new phase. The barrier is overcome through thermal fluctuations. Therefore if the fluctuation probability is low, the less stable phase may exist in a metastable state for a long period. For example, diamond, which is metastable at atmospheric pressure and room temperature, may exist for an unlimited period without converting to graphite, which is stable under these conditions. In other substances, however, the various modifications interconvert easily with changes in temperature or other conditions. As the transition passes through a stage of coexisting original and newly forming phases, an elastic interaction arises between the phases that affects the progress of the transition. These interactions are particularly pronounced in martensite transformations.
A special case of polymorphism is polytypism, which is observed in several crystals with laminar structure. Polytypic modifications are constructed of identical layers or laminar “packets” of atoms that differ in the type and periodicity of the overlap of the packets. Polytypic modifications are observed in clay minerals and silicon carbide.
REFERENCESVerma, A. R. and P. Krishna. Polimorfizm i politipizm v kristallakh, Moscow, 1969. (Translated from English.)
Bokii, G.B. Kristallokhimiia. 3rd ed. Moscow, 1971.
A. L. ROITHURD
length :: [a] -> Int
is a function which operates on a list of objects of any type, a (a is a type variable). This is known as parametric polymorphism. Polymorphic typing allows strong type checking as well as generic functions. ML in 1976 was the first language with polymorphic typing.
Ad-hoc polymorphism (better described as overloading) is the ability to use the same syntax for objects of different types, e.g. "+" for addition of reals and integers or "-" for unary negation or diadic subtraction. Parametric polymorphism allows the same object code for a function to handle arguments of many types but overloading only reuses syntax and requires different code to handle different types.
See also generic type variable.
In object-oriented programming, the term is used to describe a variable that may refer to objects whose class is not known at compile time and which respond at run time according to the actual class of the object to which they refer.