Substances which form very closely related crystals are said to be isomorphous, but it is not always very easy to decide when two substances are isomorphous. The term, moreover, is used somewhat loosely, for it originated from a consideration simply of the external form of crystals, and it was associated, by Mitscherlich’s law of isomorphism, with chemical composition.
It is now realized that the requirement for isomorphism is similarity of internal structure, and, on this basis, isomorphous substances are defined as substances forming crystals in which geometrically similar structural unit are arranged in similar ways.
Various criteria have been adopted to decide whether substances are isomorphous or exhibit isomorphism, as described below, but they must be used with some caution.
1. Similarity of External Crystalline Form
Different crystals may exhibit the same external symmetry and yet have different internal structures. If external symmetry be taken as the criteria, such crystals are isomophous, but they are not isomorphous so far as their internal structure is concerned.
The alums, for example, are often quoted as isomorphous substances. They have a general formula M SO4 M (SO4)3 24H2O or M+ M3+ (SO4)2 12H2O, where M+ stands for a number of monovalent cations such as Na+, K+, Rb+, Cs+ and (NH4)+, and M3+ stands for certain trivalent cations such as Al3+ Cr3+ and Fe3+.
The crystals of different alums are all very much alike, and exhibit the same external symmetry, but the interfacial angels do vary a little. This is because the ions in different alum crystals are of different sizes, and the slight distortion caused means that there are really three groups of alums, listed below, are, however, all in the same group, so that they are definitely isomorphous.
K2SO4.Al2 (SO4)3 .24H2O (potash alum) K2SO4.Cr2(SO4)3.24H2O(chrome alum)
(NH4)2SO4.Al2 (SO4)3 .24H2O(ammonium alum) (NH4)2SO4.Fe2(SO4)3.24H2O(iron alum)
Similarly, although the interfacial angles of calcium carbonate (calcite), iron(II) carbonate (chalybite) and manganese(II) carbonate (dialogite) very a little, the crystals have the same external symmetry, and the same internal arrangement, and are, therefore, isomorphous.
2. Similarity of Chemical Constitution
Mitcherlich’s law of isomorphism (1819) stated that substances which have similar chemical compositions are isomorphous.
This is true in such substances as the alums and the carbonate listed in a., and also in the two series of simple sulphates (VI):
K2SO4 RbSO4 Cs2SO4 (NH4)2SO4
ZnSO4 .7H2O MgSO4 .7H2O NiSO4.7H2O
But there is not necessarily any relation between chemical composition and isomorphism.
Very similar chemicals need not be isomorphous, e.g. caesium chloride and rudidium chloride; and compounds with no real chemical resemblances may be isomophous. Calcium carbonate and sodium nitrate(v), or barium sulphate(VI) and potassium manganate(VI) (permanganate), for example, are isomorphous because their crystals are made up of positive and negative ions of the same geometrical shape and comparable sizes. Similarly all substances with a sodium chloride crystal structure are isomorphous and these include such compounds as lead(II) sulphide, calcium oxide, calcium carbide, scandium nitride, and silver chloride as well as the halides of lithium, sodium, potassium, rubidium and caesium (excepting the chloride bromide and iodide of caesium).
Formation of Overgrowths
A crystal of potash alum can be overgrown on top of a crystal of chrome alum, and vice versa. Similarly, sodium nitrate (v) can be grown on top of a calcite (calcium carbonate) crystal.
It is, in fact, fairly common for isomorphous substances to give overgrowth, but the formation of such overgrowth will only occur within certain structural limits. Potassium sulphate and caesium sulphate, though isomorphous, will not form overgrowths because the Cs+ ion is so much bigger than the K+ ion. But rubidium and caesium sulphates, or rubidium and potassium sulphates, will form overgrowths.
Formation of Mixed Crystals or Solid Solutions
The crystals formed from a solution containing both potash and chrome alums will contain Cr3+ Al3+ and SO4 2- ions within a single crystal structure, the proportion of Cr3+ or Al3+ being variable over a very wide range depending on the composition of the original solution.
The crystals are known as mixed crystals, though that is something of a misnomer. There is only a single crystal containing a random arrangement of Cr3+ or Al3+ ions, and not a mixture of crystals of potash alum with crystals of chrome alum. The term solid solution is, therefore, a useful alternative.
In mixed crystals, Cr3+ and Al3+ ions are interchangeable. When two substances crystallize with identical space-lattices it is to be expected that points in the lattice might be occupied by alternative structural units from the two substances so long as the geometrical difference between the structural units is not too great. One unit can simply replace another similar one without affecting the crystal structure.
Thus, potassium chloride and potassium bromide form a continuous series of mixed crystals, i.e. they are miscible in all proportion, as the Cl– and Br– ions only differ in size by about 8 per cent. Potassium chloride and potassium iodide, however, have a difference in size between Cl– and I– ions of about 21 per cent, and only partial solid solutions occurs.
Isomorphous substances commonly form mixed crystals, but they do not necessarily do so. Potassium chloride, for instance, will not form mixed crystals, e.g. calcium fluoride and yttrium fluoride or silver bromide and silver iodide, are not necessarily isomorphous, or even chemically similar.