isomorphism

isomorphism (ī'səmôr`fĭzəm), 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. The substances sometimes crystallize together in a solid solution. Isomorphous substances usually have similar chemical formulas, and the polarizability and ratio of anion and cation radii are generally comparable (see ion). Isomorphism was discovered (c.1820) by Eilhard Mitscherlich, who stated the principle that isomorphous substances have similar chemical formulas; this principle was used by J. J. Berzelius in determining chemical formulas and combining weights. See polymorphism; mineral; crystal.

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isomorphism

1. Biology similarity of form, as in different generations of the same life cycle

2. Chem the existence of two or more substances of different composition in a similar crystalline form

3. Maths a one-to-one correspondence between the elements of two or more sets, such as those of Arabic and Roman numerals, and between the sums or products of the elements of one of these sets and those of the equivalent elements of the other set or sets

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isomorphism [¦ī·sə¦mȯr‚fiz·əm]

(mathematics)

A one to one function of an algebraic structure (for example, group, ring, module, vector space) onto another of the same type, preserving all algebraic relations; its inverse function behaves likewise.

(physical chemistry)

A condition present when an ion at high dilution is incorporated by mixed crystal formation into a precipitate, even though such formation would not be predicted on the basis of crystallographic and ionic radii; an example is coprecipitation of lead with potassium chloride.

(science and technology)

The quality or state of being identical or similar in form, shape, or structure, such as between organisms resulting from evolutionary convergence, or crystalline forms of similar composition.

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(mathematics)

isomorphism - A bijective map between two objects which preserves, in both directions, any structure under consideration. Thus a `group isomorphism' preserves group structure; an order isomorphism (between posets) preserves the order relation, and so on. Usually it is clear from context what sort of isomorphism is intended.