For the generalisation to apply absolutely it is essential that the interchangeable elements shall belong strictly to the same family group of the periodic classification of Mendeleéff. Potassium, rubidium, and cæsium fulfil this condition absolutely, and so the law of progression of the crystal properties with the atomic weight of the interchangeable elements applies rigidly to their salts. Now there are two bases, the metal thallium and the complex radicle group ammonium NH4, which are not thus related to the group of three alkali metals just mentioned, but which are yet capable of replacing those metals isomorphously in their crystals without more change of angle or of structural constants than is provoked by the replacement of potassium by cæsium; and often indeed the amount of change has been singularly like the lesser amount observed when rubidium has been interchanged for potassium. But although this is so, the directions of the changes are irregular, being sometimes the same as when rubidium or cæsium is introduced, and sometimes contrariwise, and in the case of thallium there are also striking optical differences, the thallium salts being exceptionally highly refractive. Still, morphologically the ammonium and thallium salts may legitimately be included in the same isomorphous series with the salts of potassium, rubidium, and cæsium, and a somewhat wider interpretation has to be given to the term “isomorphism” in order to admit these cases. To distinguish the inner group formed by family analogues, that is, the more exclusive group obeying the law of progression according to the atomic weight, the term “eutropic” is employed.
Thus the “isomorphous series” of rhombic sulphates, selenates, permanganates, and perchlorates, and the monoclinic series of double sulphates and double selenates, comprise the potassium, rubidium, cæsium, thallium and ammonium salts and double salts of sulphuric, selenic, permanganic, and perchloric acids, while the inner more exclusive “eutropic series,” following the law absolutely, comprises in each case only the salts containing the family analogues, potassium, rubidium, and cæsium.
In this beautiful manner has the controversy between the schools of Haüy and Mitscherlich now been settled, the interesting law described in this chapter having definitely laid down the true nature and limitations of isomorphism, while at the same time absolutely proving as a law of nature the constancy and specific character of the crystal angles of every definitely chemically constituted substance.
CHAPTER XI
THE EXPLANATION OF POLYMORPHISM, AND THE RELATION BETWEEN ENANTIOMORPHISM AND OPTICAL ACTIVITY.
Polymorphism. It has been shown in Chapter VII. that Mitscherlich had in several instances proved the possibility of the occurrence of the same substance in two different forms, notably sodium dihydrogen phosphate NaH2PO4.H2O, calcium carbonate CaCO3 (as calcite and aragonite), the metallic sulphates known as vitriols, and the chemical element sulphur, and that he gave to the phenomenon the name “dimorphism.” Since that time large numbers of dimorphous substances have been discovered, and several which occur in three forms and even a few in no less than four totally distinct forms. Until the establishment of the geometrical theory of crystal structure, as expounded in Chapter IX., this phenomenon of polymorphism gave rise to endless fruitless discussion. It was most generally attributed to the different nature of the so-called “physical molecule,” which was supposed to be an aggregate of chemical molecules and the unit of the space-lattice determining the crystal system; the different polymorphous varieties were supposed to be built up of structural units or physical molecules consisting of an aggregation of a different number of chemical molecules. Several attempts were made by various investigators, notably by Muthmann and by Fock, to determine the number of chemical molecules constituting the physical molecule.
All these efforts, however, ended unsatisfactorily, and in the year 1896 the author showed, in a memoir[[11]] on “The Nature of the Structural Unit,” that in general the physical molecule is a myth, and that the chemical molecule is the only structural unit possessing the full chemical composition of the substance in question; and that its centre of gravity, or better, any representative point within it, such as a particular atom, is the unit point of the Bravais space-lattice of the crystal structure, while the atoms of which the chemical molecule are composed, arranged stereometrically identically similarly in all the molecules, are the points of the individual point-systems which make up the combined point-system. This does not imply a necessarily parallel and identically orientated arrangement of all the molecules, as at first postulated by Sohncke and which is a fact for his sixty-five point-systems; for in accordance with the conclusions of Schönflies, von Fedorow, and Barlow discussed in Chapter IX., cases are possible in which alternate molecules may be arranged as each other’s mirror images. Such are the cases of external molecular compensation or molecular combination, two oppositely enantiomorphous sets of molecules balancing each other within the structure, but by exterior compensation as regards the molecule itself. Moreover, the principle of mirror-image symmetry enters, as stated in Chapter IX, altogether into the constitution of no less than 165 of the 230 types of homogeneous structure possible to crystals.
Hence the conception of a physical molecule is totally unnecessary and, moreover, erroneous. The alkali sulphates and selenates exhibit dimorphism, one member of the series, ammonium selenate, having only hitherto been observed in the pure state in the second, monoclinic, form, and never in the ordinary rhombic form; and the author has conclusively proved for these salts, and also for the double salts which they form with the sulphates and selenates of magnesium, zinc, iron, nickel, cobalt, manganese, copper, and cadmium, that the chemical molecule is the only kind of molecule present, and that its representative points are, as just stated, the nodes of the Bravais space-lattice of the crystal structure, determining both the system of the crystal and its obedience to the law of rational indices.
The explanation of polymorphism thus proves, in the light of the results which have now been laid before the reader, to be a remarkably simple one. Special pains were taken in explaining those results to show that the temperature had a great deal to do with the conditions of equilibrium of the crystal structure, for it determines the intermolecular distances, that is, the amount of separation of the molecules, and thus controls their possibility of movement with respect to one another. Now the behaviour of the chemical molecules on the advent of crystallisation is undoubtedly largely influenced by the stereometric arrangement of the atoms composing them, and it is possible for the latter to be such that the molecules may take up several different parallel or enantiomorphously related positions; or as we have just seen, a regular alternation within the crystal structure of such mirror-image positions may be taken up. These different arrangements, whether parallel or enantiomorphously opposite, may be, and probably will be, of different degrees of stability, each of these different forms finding its maximum stability of equilibrium at some particular temperature, which is different for the different varieties. Hence, at a series of ascending or descending temperatures, assuming the pressure to remain the ordinary atmospheric, these different types of homogeneous crystal structures will be most liable to be produced, each at its own particular temperature, for which stable equilibrium of that crystal structure occurs.
These different assemblages are as a rule quite dissimilar, certainly in the crystal elements, often in class and not infrequently in system. Generally two such different crystalline forms are all that are possible within the life-range of temperature of the substance. But occasionally three or even as many as four such different forms are found to be capable of existence within the temperature life-limits of the substance.
Polymorphism is thus completely and simply explained as a direct result of the establishment of the geometrical theory of crystal structure as laid down in Chapter IX. The equilibrium of the homogeneous structure is a function of the temperature, and the stereometric arrangement of the atoms in the chemical molecule of a substance may be such as permits of two or more homogeneous arrangements of the molecules in assemblages of varying degrees of stability, but each of which has a maximum stability at a particular temperature. Hence, within any given range of temperature such a substance will assume that type of homogeneous arrangement of its molecules in a crystal which corresponds to the stablest equilibrium within these temperature limits, assuming the pressure constant within the bounds of the usual atmospheric variations. Employing the language of physical chemistry, such a substance will thus present two or more different solid “phases,” each characterised by its specific crystalline form, the elementary parallelepipedon of which is quite a distinct one. Each phase possesses also its own specific optical and other physical properties, such as melting point, solubility, thermal expansion, and elasticity.