are included sulphur and ammonium nitrate; monotropy is exhibited by aragonite and calcite.
It is doubtful indeed whether any general conclusions can yet be drawn as to the relations between crystal structure and scalar properties and the relative stability of polymorphs. As a general rule the modification stable at higher temperatures possesses a lower density; but this is by no means always the case, since the converse is true for antimonious and arsenious oxides, silver iodide and some other substances. Attempts to connect a change of symmetry with stability show equally a lack of generality. It is remarkable that a great many polymorphous substances assume more symmetrical forms at higher temperatures, and a possible explanation of the increase in density of such compounds as silver iodide, &c., may be sought for in the theory that the formation of a more symmetrical configuration would involve a drawing together of the molecules, and consequently an increase in density. The insufficiency of this argument, however, is shown by the data for arsenious and antimonious oxides, and also for the polymorphs of calcium carbonate, the more symmetrical polymorphs having a lower density.
Morphotropy.—Many instances have been recorded where substitution has effected a deformation in one particular direction, the crystals of homologous compounds often exhibiting the same angles between faces situated in certain zones. The observations of Slavik (Zeit. f. Kryst., 1902, 36, p. 268) on ammonium and the quaternary ammonium iodides, of J. A. Le Bel and A. Ries (Zeit. f. Kryst., 1902, 1904, et seq.) on the substituted ammonium chlorplatinates, and of G. Mez (ibid., 1901, 35, p. 242) on substituted ureas, illustrate this point.
Ammonium iodide assumes cubic forms with perfect cubic cleavage; tetramethyl ammonium iodide is tetragonal with perfect cleavages parallel to {100} and {001}—a difference due to the lengthening of the a axes; tetraethyl ammonium iodide also assumes tetragonal forms, but does not exhibit the cleavage of the tetramethyl compound; while tetrapropyl ammonium iodide crystallizes in rhombic form. The equivalent volumes and topic parameters are tabulated:
| NH4I. | NMe4I. | NEt4I. | NPr4I. | |
| V | 57.51 | 108.70 | 162.91 | 235.95 |
| χ | 3.860 | 5.319 | 6.648 | 6.093 |
| ψ | 3.860 | 5.319 | 6.648 | 7.851 |
| ω | 3.860 | 3.842 | 3.686 | 4.933 |
From these figures it is obvious that the first three compounds form a morphotropic series; the equivalent volumes exhibit a regular progression; the values of χ and ψ, corresponding to the a axes, are regularly increased, while the value of ω, corresponding to the c axis, remains practically unchanged. This points to the conclusion that substitution has been effected in one of the cube faces. We may therefore regard the nitrogen atoms as occupying the centres of a cubic space lattice composed of iodine atoms, between which the hydrogen atoms are distributed on the tetrahedron face normals. Coplanar substitution in four hydrogen atoms would involve the pushing apart of the iodine atoms in four horizontal directions. The magnitude of this separation would obviously depend on the magnitude of the substituent group, which may be so large (in this case propyl is sufficient) as to cause unequal horizontal deformation and at the same time a change in the vertical direction.
The measure of the loss of symmetry associated with the introduction of alkyl groups depends upon the relative magnitudes of the substituent group and the rest of the molecule; and the larger the molecule, the less would be the morphotropic effect of any particular substituent. The mere retention of the same crystal form by homologous substances is not a sufficient reason for denying a morphotropic effect to the substituent group; for, in the case of certain substances crystallizing in the cubic system, although the crystal form remains unaltered, yet the structures vary. When both the crystal form and structure are retained, the substances are said to be isomorphous.
Other substituent groups exercise morphotropic effects similar to those exhibited by the alkyl radicles; investigations have been made on halogen-, hydroxy-, and nitro-derivatives of benzene and substituted benzenes. To Jaeger is due the determination of the topic parameters of certain haloid-derivatives, and, while showing that the morphotropic effects closely resemble those occasioned by methyl, he established the important fact that, in general, the crystal form depended upon the orientation of the substituents in the benzene complex.
Benzoic acid is pseudo-tetragonal, the principal axis being remarkably long; there is no cleavage at right angles to this axis. Direct nitration gives (principally) m-nitrobenzoic acid, also pseudo-tetragonal with a much shorter principal axis. From this two chlornitrobenzoic acids [COOH·NO2·Cl = 1.3.6 and 1.3.4] may be obtained. These are also pseudotetragonal; the (1.3.6) acid has nearly the same values of χ and ψ as benzoic acid, but ω is increased; compared with m-nitrobenzoic acid, χ and ψ have been diminished, whereas ω is much increased; the (1.3.4) acid is more closely related to m-nitrobenzoic acid, χ and ψ being increased, ω diminished. The results obtained for the (1.2) and (1.4) chlorbenzoic acids also illustrate the dependence of crystal form and structure on the orientation of the molecule.
The hydroxyl group also resembles the methyl group in its morphotropic effects, producing, in many cases, no change in symmetry but a dimensional increase in one direction. This holds for benzene and phenol, and is supported by the observations of Gossner on [1.3.5] trinitrobenzene and picric acid (1.3.5-trinitro, 2 oxybenzene); these last two substances assume rhombic forms, and picric acid differs from trinitrobenzene in having ω considerably greater, with χ and ψ slightly less. A similar change, in one direction only, characterizes benzoic acid and salicylic acid.
The nitro group behaves very similarly to the hydroxyl group. The effect of varying the position of the nitro group in the molecule is well marked, and conclusions may be drawn as to the orientation of the groups from a knowledge of the crystal form; a change in the symmetry of the chemical molecule being often attended by a loss in the symmetry of the crystal.
It may be generally concluded that the substitution of alkyl, nitro, hydroxyl, and haloid groups for hydrogen in a molecule occasions a deformation of crystal structure in one definite direction, hence permitting inferences as to the configuration of the atoms composing the crystal; while the nature and degree of the alteration depends (1) upon the crystal structure of the unsubstituted compound; (2) on the nature of the substituting radicle; (3) on the complexity of the substituted molecule; and (4) on the orientation of the substitution derivative.
Isomorphism.—It has been shown that certain elements and groups exercise morphotropic effects when substituted in a compound; it may happen that the effects due to two or more groups are nearly equivalent, and consequently the resulting crystal forms are nearly identical. This phenomenon was first noticed in 1822 by E. Mitscherlich, in the case of the acid phosphate and acid arsenate of potassium, KH2P(As)O4, who adopted the term isomorphism, and regarded phosphorus and arsenic as isomorphously related elements. Other isomorphously related elements and groups were soon perceived, and it has been shown that elements so related are also related chemically.
Tutton’s investigations of the morphotropic effects of the metals potassium, rubidium and caesium, in combination with the acid radicals of sulphuric and selenic acids, showed that the replacement of potassium by rubidium, and this metal in turn by caesium, was accompanied by progressive changes in both physical and crystallographical properties, such that the rubidium salt was always intermediate between the salts of potassium and caesium (see table; the space unit is taken as a pseudo-hexagonal prism). This fact finds a parallel in the atomic weights of these metals.
| V | χ | ψ | ω | |
| K2SO4 | 69.42 | 4.464 | 4.491 | 4.997 |
| Rb2SO4 | 73.36 | 4.634 | 4.664 | 5.237 |
| Cs2SO4 | 83.64 | 4.846 | 4.885 | 5.519 |
| K2SeO4 | 71.71 | 4.636 | 4.662 | 5.118 |
| Rb2SeO4 | 79.95 | 4.785 | 4.826 | 5.346 |
| Cs2SeO4 | 91.16 | 4.987 | 5.035 | 5.697 |
By taking appropriate differences the following facts will be observed: (1) the replacement of potassium by rubidium occasions an increase in the equivalent volumes by about eight units, and of rubidium by caesium by about eleven units; (2) replacement in the same order is attended by a general increase in the three topic parameters, a greater increase being met with in the replacement of rubidium by caesium; (3) the parameters χ and ψ are about equally increased, while the increase in ω is always the greatest. Now consider the effect of replacing sulphur by selenium. It will be seen that (1) the increase in equivalent volume is about 6.6; (2) all the topic parameters are increased; (3) the greatest increase is effected in the parameters χ and ψ, which are equally lengthened.
These observations admit of ready explanation in the following
