the transfer of impurities (trace constituents) to a precipitate concurrently with the deposition of some primary substances (macroscopic constituent) from a solution, melt, or vapor containing several substances. Coprecipitation occurs when a solution (vapor) is supersaturated with the substance forming the precipitate or when a melt is supercooled. Coprecipitation begins only at the conclusion of a latent period. The length of this period can be prolonged from microseconds to tens of hours by altering the degree of supersaturation (supercooling), the degree of mixing, and the purity and temperature of the medium from which the precipitate separates.

Coprecipitation proceeds in two stages. It begins with the entrapment of impurities during the growth of precipitate particles upon separation and concludes with the redistribution of the impurity between precipitate and medium. In the first stage, the impurity is trapped either on the surface (surface coprecipitation) or inside (volume coprecipitation) the growing particles. If the growing particles have a crystal structure, then in the case of volume coprecipitation the impurity will become localized either at regions of the solid phase with a perfect structure (isomorphous mixed crystal formation) or in the vicinity of structural defects (occlusion, interstitial trapping, dislocation trapping). Data describing the first stage of coprecipitation have been generalized as Hahn’s rule.

An important quantitative indicator for the first stage of coprecipitation is the effective distribution coefficient K of the impurity between the precipitate and medium. It is defined as the ratio of the average concentration of the impurity in the precipitate to the impurity’s average concentration in the medium. Isomorphous mixed crystal formation is described by the effective coefficient of isomorphous mixed crystal formation, defined as the product of K and the average concentration of the substance being crystallized in the medium divided by the density of the solid phase. If the medium is only slightly supersaturated and the precipitation proceeds very slowly, the effective coefficient of distribution (isomorphous mixed crystal formation) will not change during coprecipitation and will remain equal to the coefficient of the equilibrium distribution K_eq. During rapid precipitation, the growing particles will trap nonequilibrium amounts of impurities, which are usually inhomogeneously distributed throughout the volume of the solid phase. Here, the value of K, as a rule, increases mon-otonically with the rate of precipitation when K_eq < 1 and decreases when K_eq > 1, approaching unity when the precipitation is exceptionally rapid.

In the second stage of coprecipitation, the concentration of defects within the precipitate decreases, and the particles flocculate. Impurities trapped during the first stage return either partially or completely to the medium. The concentration of impurities in various regions of the solid phase becomes equalized, and as a consequence the crystals acquire an equilibrium composition that depends only on the composition and temperature of the medium. The value of the coefficient K approaches that of K_eq. Experimental data on equilibrium isomorphous mixed crystal formation have been generalized as Khlopin’s law.

The laws governing coprecipitation form the basis of hydro-metallurgy and of methods involving isomorphous mixed crystal formation and sublimation, for example, fractional crystallization and zone melting, for separating and purifying substances. The principles of coprecipitation also figure in methods for obtaining solids with a specified concentration of activator that are used in, among other fields, radio electronics and optics. In analytical chemistry and radiochemistry, coprecipitation is used as a technique for concentrating substances. It is also used to detect and separate trace constituents present at concentrations of 10^–10–10^–12 gram-ion/liter.