83.1

ISOMORPHISM.

149

Cr2O), not only crystallize in the same form, but have a constitution perfectly analogous, and are therefore truly isomorphous. Mitscherlich, indeed, endeavoured to show that crystalline form is independent of the chemical nature of the atoms, and that it is determined only by their grouping and relative position; the same number of atoms combined in the same way, always producing the same crystalline form.

This statement is not strictly true: the elementary bodies have by no means all of them the same crystalline form, which may be due to their molecules possessing different atomic structures; and it is found that even when the chemical constitution is the same, though there may frequently be a close similarity in the form assumed, yet a careful measurement of the angles indicates differences in the length or inclination of the axes. For example -the carbonates of calcium, manganese, magnesium, iron, and zinc, all crystallize in rhombohedra; but the corresponding angles of these several crystals are all different, as the following table shows:

Calcic carbonate (calc spar)
Manganous carbonate (diallogite)
Ferrous carbonate (chalybite)
Magnesic carbonate (magnesite)
Zincic carbonate (calamine)

CaCO3 105° 5'

MnCO

106° 51'

FeCO3

107° 0'

MgCO3

107° 29′

ZnCog 107° 40'

These differences are in all probability partially due to differences in the crystalline arrangement of the elementary molecules of some of the components, and, as Kopp has shown, in the atomic volume or space occupied by these ultimate molecules. The crystals of metallic zinc and iron, for instance, belong to different systems, so that it is not surprising that some difference should be observed in the form of their corresponding compounds; and if Mitscherlich's law be confined to compound bodies, these very differences which have been supposed to militate against it, will prove to be remarkable corroborations of its truth, as they show that the number and collocation of the atoms may overcome the tendency of some of the atoms of the elementary components to assume different forms. It also shows, moreover, that it is unsafe to infer isomorphism in the elements simply from the occurrence of isomorphism in the compounds which they yield. It must, however, be borne in mind that bodies which are analogous in chemical composition and in properties, are not necessarily isomorphous for example, magnesic carbonate (MgCO3) crystallizes in

150

ISOMORPHISM.

[83.

rhombohedra, whilst strontic carbonate (SrCO) assumes the form of oblique rhombic prisms.

It not unfrequently happens that a compound group like ammonium (HN), if equivalent in function to a simple substance like potassium (K), will form compounds with the acid radicles, which are isomorphous with those of the simple substance with the same radicles; this is manifest in potassic chloride (KCI) and ammonic chloride (H,NCI), both of which crystallize in cubes. Potassic sulphate (K,SO,) is in like manner isomorphous with ammonic sulphate [(H,N),SO,], and so on through the greater number of the corresponding compounds of potassium and ammonium.

(84) Chemical Bearings of Isomorphism.-This discovery of the coincidence of similarity in crystalline form with similarity in chemical composition, is one of the most important generalizations yet arrived at in the science of crystallography. It has rendered great service to chemistry by facilitating the classification of compounds, and it has often called attention to analogies in composition which might otherwise have been overlooked. In determining the atomic weight of a substance it is also frequently of essential value; but its application to these purposes will be more advantageously examined at a future period.

Bodies which approach each other thus closely in crystalline form often occur mixed together in variable proportions in regularly crystallized minerals. Such isomorphous compounds cannot be separated by the method of crystallization. Indeed it is quite possible to obtain crystals consisting of alternate layers of different isomorphous salts, if they have nearly the same degree of solubility in water. An octohedral crystal of ordinary alum, for example, if transferred to a solution of chrome alum (a compound isomorphous with ordinary alum, and which differs from it in containing chromium in the place of aluminium), will continue to increase in size regularly, and a layer of the metallic salt will be deposited on the common alum. If the crystal be transferred again to the original solution of alum, a fresh layer of colourless alum will be formed upon the chromium salt, and so on in succession.

A large number of metals, when united with the same acid radicle, furnish salts which are isomorphous. For instance, the sulphates of magnesium, zinc, iron, nickel, cobalt, manganese, and cadmium, all crystallize in similar forms. The isomorphism of many acid radicles, when united with the same metal, such as potassium or sodium, is not less evident: sulphate, seleniate,

85.]

ISOMORPHOUS GROUPS.

151

chromate, and manganate of potassium, all have the same form; and the isomorphism of the corresponding phosphates and arseniates of sodium is equally striking.

(85) The following table exhibits some of the more important of the groups in which the existence of isomorphism has been distinctly ascertained :—

Salts of the following Acid Radicles when united with the same Metal M' representing any Monad or Monobasic Metal.

It appeared to be anomalous, upon the earlier supposition that the atomic weight of sulphur was 16, that 32 parts of sulphur should be isomorphous with 75 of arsenic, two atoms of sulphur apparently being isomorphous with one of arsenic; but if the atomic weight of sulphur is admitted to be 32, the anomaly disappears. A similar remark applies to the permanganates and perchlorates, if the atomic weight of manganese be taken as 27.5. The permanganates would

152

DIMORPHISM.

[85.

Salts of the following Metals when united with Equivalent Quantities of the same Halogen or Acid Radicle.

(86) Dimorphism.-Another very remarkable fact connected. with crystallization has been observed in a few bodies. Some substances, sulphur, for example, are capable of assuming two dissimilar forms, according to the temperature at which the crystals are produced. Sulphur, as it is found crystallized in nature, or as it is obtained by the spontaneous evaporation of its solution in carbonic disulphide or in chloride of sulphur, is deposited in the form of octohedra with a rhombic base, which is one of the forms of the 4th, or prismatic system. When obtained by the slow cooling of a mass of melted sulphur, beautiful amber-coloured prismatic crystals are obtained, belonging to the 5th, or oblique system. These oblique prisms, in the course of a few days, at the usual atmospheric temperature, become opaque, lose their cohesion, and are gradually converted into a congeries of octohedra. A similar change is produced in the octohedral crystals by exposing them for some time to a heat of about 110° C., but the opacity is in this case due to the formation of prismatic crystals. The crystalline axes of the two forms differ, and consequently the crystals belong to different systems. Bodies capable of thus assuming two forms geometrically incompatible are said to be dimorphous.

Many other instances might be mentioned. Carbon, in its pure state, as it occurs in the diamond, is crystallized in the 1st, or regular system, in octohedra, or in allied forms; but in graphite, as it separates from cast iron when fused, it assumes the shape of

then appear to contain two atoms of manganese, whilst the perchlorates contain only one of chlorine; but assuming, as we have done, on other grounds, that the atomic weight of manganese should be doubled, or should be 55, then it follows, as a matter of course, that the number of atoms of manganese and chlorine are alike in the two compounds.

86.]

DIMORPHISM.

153

Calcic

six-sided plates, which belong to the rhombohedral system. carbonate usually occurs in forms of the 3rd system, reducible by cleavage to rhombohedra, like those of Iceland spar, and it is thus formed by crystallization at low temperatures; but occasionally it occurs in the rectangular prisms of the 4th system, as in the mineral aragonite; and the microscopic crystals which are formed when calcic carbonate is deposited from its solution by carbonic acid in water, on the application of a heat of 100° C., have also this form (G. Rose). Another beautiful instance of dimorphism is afforded in mercuric iodide. When this body is heated, it fuses,

boils, and is converted into vapour, which condenses upon the side of the tube as a yellow crystalline crust, composed of minute rhombic plates. Slight friction, such as a mere scratch upon a single point, changes the form from the rhombic plate to that of an octohedron with square base, and the change is rendered visible to the eye by the accompanying substitution of a bright scarlet for the yellow colour. If the quantity of the iodide operated on be at all considerable, the temperature of the mass may be observed to rise as much as 3° C. during the conversion of the yellow into the red salt (Weber).*

In certain cases the forms of a crystal belonging to one system may approach very closely to those of crystals belonging to a totally different system: for instance, bismuth appears to crystallize in cubes, but in reality it assumes the form of a rhombohedron, the angles of which are 92° 20′, and 87° 40', or so close upon right angles, as to ordinary observation to be confounded with them the derivative forms, however, in such cases are always very different, and generally enable the observer to point out the true system to which the crystal belongs.

:

According to the observation of Pasteur, instances of dimorphism usually occur when one of the two forms is nearly upon the limit of the system to which it belongs (Ann. Chim. Phys. 1848 [3], xxiii. 271). For example, the angles of the yellow rhombic plates of mercuric iodide do not differ much from those of the octohedron of the prismatic system to which the red variety of this compound belongs, and a similar remark is applicable to the prisms and the octohedra of sulphur.

The following substances, according to Professor W. H. Miller, are also dimorphous :-Titanic anhydride, prismatic in brookite, pyramidal in rutile ; ferric disulphide, cubic in ordinary pyrites, prismatic in white pyrites (marcasite); potassic sulphate, usually prismatic, sometimes rhombohedral; nitre, usually prismatic, sometimes rhombohedral; diarsenide of nickel (NiAs), usually cubic, but prismatic in the white variety.