DEFORMATION OF ELECTRON SHELLS AND ITS EFFECT ON THE PROPERTIES OF SALT-FORMING COMPOUNDS1

K. Fajans.

1. Introduction. 2. Ideal ionic bond: a. Effect of the charge and size of ions. b. Effect of the structure of the outer electron shell. 3. Deformation of ions: a. One-sided polarization of ions in a homogeneous and inhomogeneous field. b. Deformation of electron orbits in the lattice. 4. Molar refraction and deformation. 5. Deformation by hydrogen nuclei. 6. Deformation by other ions. 7. Volatility of the halide salts of alkali metals from the standpoint of the concept of deformation. 8. Absorption of light and deformation of electron orbits. 9. Distances between ions and lattice energy. 10. Photoelectric conductivity of salts. 11. Solubility of salts. 12. “Loosening” of the crystal lattice. 13. Structure of the electron shell and deformation. 14. Continuous and discontinuous deformation.

1. Introduction.

Thanks to the remarkable successes of Bohr’s theory [1], we can form a definite conception of the distribution and motion of electrons within the atoms of various elements and, on this basis, explain not only the spectral properties of atoms but also, in general outline, their behavior in chemical processes. This, however, does not directly touch upon the problem of the properties of chemical compounds. That could be said only if, in the molecules of compounds, the atoms of the elements remained completely, or in essential features, unchanged. And indeed, such a conception, in hidden form, underlay earlier attempts to calculate the properties of organic substances (for example, refraction or magnetic susceptibility) by the rule of additivity from definite values assigned to atoms. Even at the present time there are adherents of the view that the so-called atomic refractions, calculated from the molecular refraction of organic compounds, actually represent the refractions of free atoms. Such a view, however, is undoubtedly incorrect: however far we still are at present from a complete explanation of the process of formation

molecules from atoms; however, there is no doubt that in all cases where neutral atoms are bound by strong affinities, the electronic systems of these atoms, and at the same time the greater part of their properties, undergo profound changes. Therefore it is impossible to derive the properties of compounds additively from the properties of free atoms. In order to explain the properties of compounds we must set ourselves the aim of reducing the structure of molecules not only to atoms, but to individual electrons. This may at first seem a hopeless undertaking, since as yet a complete quantitative analysis of the motions of electrons has not been achieved even in the simplest neutral molecule, H$_2$. However, the problem of the properties of chemical compounds can be illuminated from the point of view of the structure of the atom, without delving too deeply into the still obscure domain of electronic motions. Conversely, a careful study of the connection between the various properties of substances may give us some indications of the fate of electrons even in more complex compounds.

2. Ideal ionic bond.

In order to explain the varied behavior of chemical compounds, it was necessary first of all to classify them. As is well known, the old electrical theory of chemical forces of Berzelius (1819) collapsed because the rapidly developing field of carbon compounds in the middle of the last century did not obey the principle of polarity, which Berzelius applied to all chemistry. However, after the ionic theory of Arrhenius (1887) proved the real existence of electrical charges in many atoms, and the principle of polarity was definitively established with respect to salt-like compounds, the old dispute was resolved by drawing a boundary between two different modes of formation of the chemical bond. At present, substances of dualistic (W. Nernst), heteropolar (R. Abegg), or simply polar structure are contrasted with those constructed in the so-called unitary, homeopolar, or nonpolar manner. Although there can be no doubt that the acceptance of these two types of bond is quite insufficient for understanding the entire diversity in the behavior of substances, nevertheless the formation of these two extreme idealized schemes is extremely useful for initial orientation. We imagine a molecule or crystal of extremely polar structure as consisting of oppositely charged ions closed in upon themselves. According to the idea first expressed by J. J. Thomson1 (1904) [2]

and in the theory, broad in conception, laid down by W. Kossel (1916) [³], the formation of a polar molecule in binary compounds proceeds in such a way that one or several electrons leave one of the combining atoms, forming positive ions, and are captured by other atoms, which thereby become negative ions. In this case an electrostatic attraction acts between the oppositely charged ions, providing the bond between the parts of the molecule or crystal.

It may be regarded as proven, at least in its essential features and for several cases, that in crystals of salt-like compounds the atoms or groups of atoms exist in the form of ions supplied with excess charges. This at once explains to us one essential feature in the structure of crystals of this kind: the electrostatic field of an ion acts in all directions of space; therefore the Na ion in the crystal lattice of common salt groups around itself several (the six nearest) negative Cl ions and conversely—the negative ion groups around itself six positive ones.

This action, directed in all directions and almost uniform, of the forces issuing from an ion was regarded as a refutation of the conception, accepted in chemistry, of directed valences and, in particular, of the existence in the atom of a definite number of positions possessing special properties and determining its behavior in chemical reactions. It should be remembered, however, that in discussing questions of chemical valence and chemical forces we are concerned not so much with the behavior of ions as with the behavior of neutral atoms. At the present time it is known that the monovalence of sodium is connected with the easy detachment of one definite electron from the neutral sodium atom, while the monovalence of chlorine is connected with the tendency of the neutral chlorine atom to fill with an electron one definite vacant place in its outer electron shell. Thus the valence of an atom is conditioned by quite definite positions in the atom. The electrostatic attraction, directed in all directions, of ready-made ions is the last act of the process of combination of neutral atoms that interests chemists, whereas the no less important process of electron transfer has an entirely different mechanism.

We shall not here examine more closely the nature of chemical forces. Accepting the existence not only in crystals, but also in free

zero valence. The physical characteristic of stable groupings derived by him from the model of the atom of Lord Kelvin–Thomson cannot be retained at the present time. Soon after Thomson, P. Drude [²], adhering to Abegg’s theory of valence, likewise explained positive valence by the number of loosely bound electrons in the atom, and negative valence by its ability to attach electrons.

molecules of an ideal ionic bond, we shall ask ourselves what properties it leads us to expect and to what extent they are actually observed in real substances. These questions are discussed in detail in two papers by Kossel, of 1916 and 1920.

a. Influence of the charge and size of the ions.

If the forces binding atoms in the molecules and crystals of salt-like compounds are interpreted as the electrostatic attraction of ions, then one can predict their dependence on the properties of the ions. Kossel, who in his first paper, which touched upon this new field, for quite understandable reasons tried to get by with the simplest possible assumptions, takes into account two properties of ions, considered as impenetrable spheres: charge and radius. Application of Coulomb’s law indicates that the electrostatic action of an ion increases, on the one hand, with the increase of charge, and on the other hand—with the decrease of the radius of the ion. Using the method of electron impacts and certain firmly established numerical data, one can determine the energy liberated in the formation of the crystalline lattice of a salt from free gaseous ions, the so-called lattice energy, a new important thermochemical quantity introduced by M. Born (1919) [4]. And indeed it turns out (see Fig. 1) that this lattice energy \(U\) is the greater, the smaller the size of the ions composing the lattice. Thus, for example,

Fig. 1. Lattice energies of several halide compounds.

\[ U_{\mathrm{NaCl}} > U_{\mathrm{NaBr}} > U_{\mathrm{KBr}} \]

in accordance with the order of ionic radii (see Fig. 11)

\[ r_{\mathrm{Cl}^{-}} < r_{\mathrm{Br}^{-}} \quad \text{and} \quad r_{\mathrm{Na}^{+}} < r_{\mathrm{K}^{+}} . \]

Quantitatively, the experimentally determined lattice energy of the halide salts of the alkali metals agrees satisfactorily with that calculated from electrostatic theory [5].

The electrostatic action of ions also manifests itself in the dissolution of gaseous ions in water. In this process a considerable amount of energy is liberated, the heat of hydration, which arises because the dipoles of water orient themselves and are attracted by the dissolved ions. Here too the amount of energy increases,

respectively, mainly to its electrostatic origin, with increasing charge and decreasing radius of the dissolved ion [6].

For the transition from such new and unusual properties as lattice energy and the heat of hydration of ions to those better known to the experimenter, let us first consider volatility. The evaporation of a solid salt means the removal of individual molecules from the lattice. From the point of view of the simple theory of vapor-like ions, this requires overcoming part of those forces which bind the free ions into a crystal. According to these ideas, the heat of sublimation of solid salts of a definite lattice type must constitute a definite part of the total lattice energy [7], or in any case must change in the same direction. With increasing heat of sublimation, volatility falls. It might therefore be expected that substances consisting of two ions with double charges would be far less volatile than those containing singly charged ions, since in the former case the forces between the ions (and also between the molecules) are 4 times greater than in the latter. And indeed this requirement of electrostatic theory is justified, at least qualitatively: thus, for example, sodium fluoride \((\mathrm{Na}^+, \mathrm{F}^-)\) boils at approximately \(1700^\circ\), whereas the boiling point of \(\mathrm{MgO}\) \((\mathrm{Mg}^{++}, \mathrm{O}^{--})\) lies above \(2800^\circ\). In the halide compounds of the alkali metals one can trace a more subtle dependence of the heat of sublimation of salts on the radius of the ions composing them. Instead of the heats of sublimation of these salts, which are not yet known with sufficient accuracy, we shall consider here their boiling points, directly determined by von Wartenberg [8] in the molten state. For such a closely related group of substances as the halide compounds of the alkali metals, one may expect, at least qualitatively, the same course of boiling points as for the heats of evaporation or the heats of sublimation, which differ little from them. As is seen from Fig. 2, the course of the boiling points of the halide compounds of Na, K, Rb, and Li, each taken separately, is the same as the course of the lattice energies. This is precisely what would be expected according to the theory of the ideal ionic bond. With increasing radius of the halide ions, the boiling points decrease, i.e., the forces acting between the molecules diminish. On the other hand, significant deviations from the simplest theory are also noticeable. Caesium fluoride boils

Fig. 2. Boiling points of halide compounds of alkali metals, according to von Wartenberg.

DEFORMATION OF ELECTRON SHELLS

lower than the chloride; among the iodides the Na salt boils lower than the K salt and even lower than the Rb salt, and the line corresponding to the smallest cation, lithium, which ought to lie above the lines of the other cations, intersects them.

Something similar is also seen in Fig. 3, which depicts the melting points1; the theory of these, to be sure, has been little developed, but they nevertheless should stand in close relation to the forces acting in the solid and in the liquid phase. This is confirmed by Fig. 3, which shows, for the melting points of these compounds, in general outline, the same course as Fig. 2 for the boiling points. Here we also find the NaJ line below the KJ line, and the lithium salts likewise disturb the general order.

Thus, if one restricts oneself to compounds of the light metals, it may be said that the theory of spherical ions is, in its broad outlines, justified, but is not capable of conveying all the details. The circumstances become still more confused if one considers the halide compounds of heavy metals, for example silver. The distances between ions in the lattice of silver chloride are, by chance, almost exactly equal to the distances in the NaCl lattice. Therefore, if only the charge and size of the ions determined their behavior, AgCl and NaCl would have to have identical properties. Instead, the former melts at more than 300° lower than the latter, and the order of melting points among the silver halide salts is irregular and quite different from that among the halide salts of the alkali metals.

Fig. 3. Melting points of the halide compounds of alkali metals and silver.

b. Influence of the structure of the outer electron shell.

As is known, elements belonging to different subgroups of one and the same group of the periodic system differ from one another in many respects. Thanks to the new theory of the periodic system, given by Bohr, it is known that the ions of these elements, at the same charge and size, may differ in a very important property, namely the structure of the surface, i.e. the number and arrangement of the electrons in the outer—

electron shell. For example, whereas the metals of the first subgroup, according to W. Kossel and G. N. Lewis [9], have, in the form of ions, the configuration of the noble gases, i.e. an outer shell of eight electrons, the majority of the cations of the second subgroup also have a stable configuration, but one differing from that of the noble gases, namely a configuration with 18 outer electrons.

8 outer electrons:

\[ \mathrm{N}^{3-}\quad \mathrm{O}^{2-}\quad \mathrm{F}^{-}\quad \mathrm{Ne}\quad \mathrm{Na}^{+}\quad \mathrm{Mg}^{2+}\quad \mathrm{Al}^{3+}\quad \mathrm{Si}^{4+}\quad \mathrm{P}^{5+}\quad \mathrm{S}^{+6}\quad \mathrm{Cl}^{7+} \]

18 outer electrons:

\[ \mathrm{Ag}^{+}\quad \mathrm{Cd}^{2+}\quad \mathrm{In}^{3+}\quad \mathrm{Sn}^{4+}\quad \mathrm{Sb}^{5+}\quad \mathrm{Te}^{6+}\quad \mathrm{J}^{7+}. \]

For other ions not similar to the noble gases, such as \(\mathrm{Cu}^{++}\), \(\mathrm{Ni}^{++}\), \(\mathrm{Fe}^{++}\), etc., the arrangement of the electron shells is different.

According to Bohr, the structure of the electron shell has a decisive influence on the physical and chemical properties of the atom. Therefore one could have expected in advance that the properties of chemical compounds containing ions of different structure would also be different. And indeed, Grimm (H. G. Grimm) [5], from consideration of a whole series of properties, found that one can obtain a quite satisfactory classification of compounds built from different ions if, in addition to the charge and size of the ions taken into account by Kossel, one also takes into consideration the structure of their electron shell. Let us give an example: in Fig. 1, in addition to the lattice energies of the halide compounds of the alkali metals, numbers are given for the halide compounds of the ions \(\mathrm{Ag}^{+}\) and \(\mathrm{Cu}^{+}\), which possess 18 outer electrons. For these cations the lattice energy also decreases with increasing radius of the halide ion. Further, it may be noted that the values for the smaller cuprous ion are much greater than for the more bulky \(\mathrm{Ag}\) ion\(^1\). At the same time, the quantitative relations between the lattice energies, manifested in the slope of the individual segments of the broken line, are different for ions with 18 electrons than for salts of the noble-gas type. Thus the decrease in lattice energy from fluoride to iodide in the silver salts is considerably smaller than in the sodium salts. In this way it may be said that the lattice energy of these compounds is a function of the charge, size, and structure of the ions. Purely formally, the above-mentioned “strange” values of the boiling and melting points of the lithium salts can be explained by the fact that the \(\mathrm{Li}\) ion possesses only two electrons, whereas the other ions of the alkali metals have shells of eight electrons.

The question arises whether this influence of the structure of ions cannot be approached from the point of view of physics. In this direction the lattice theory of Born–Landé [4] proves useful. In this theory the ions are not regarded as spheres that can approach one another up to contact—

\(^1\) On the relative sizes of these ions see Niggli (P. Niggli) [10].

colliding with their impermeable shells, but attention is paid to the structure of the outer electron shells, consisting of a limited number of negative electrons, and to those repulsive forces that act between negatively charged shells. It turns out that these repulsive forces, against which the attractive forces must do work, depend on the structure of the shells. Grimm pointed out that this circumstance can, to a certain extent, explain the difference between the values of the lattice energy of the salts of the alkali metals and silver. It is possible that this view will prove fruitful when the theory of repulsive forces, at present only outlined \[26\], receives further development. However, even now it can be said that the difference in the repulsive forces, depending on the structure of the electron shell, cannot prove sufficient for a complete explanation of the difference between sodium and silver salts. This factor also gives no explanation of those deviations from the theory of spherical ions with which we became acquainted in the halide salts of ions of similar structure, for example for the boiling points of KJ and NaJ.

3. Deformation of ions.

These difficulties, at least in part, depend on the fact that the picture of the structure of salt-like compounds presented above idealizes reality too much: at the basis of all the views set forth so far lies the assumption that, upon combination into a molecule or into a crystal, the ions remain unchanged. However, already Kossel, in his first work, pointed out that the electrostatic field of a cation must exert a deforming action on an anion in the sense that the cation draws toward itself the electron shell of the anion, which, according to the state of Bohr’s theory at that time, was imagined in the form of a ring. Different degrees of this displacement of the electron ring make it possible to explain transitional forms between molecules with an ideal ionic bond and nonpolar compounds. In his detailed analysis of the properties of compounds, Kossel, however, did not take this circumstance into account and operated exclusively with undeformed (starr) ions. Therefore very important was the consequence of the deformability of ions found by Haber (1919) \[7\]: he showed that the energy liberated upon combination of the hydrogen nucleus with a halide ion into a hydrogen halide molecule is much greater (by approximately 100 large calories) than could have been expected if undeformed ions were assumed. Haber interpreted this in terms of displacement of the nucleus of the halide ion relative to its electron shell, and Reiss \[12\], on this basis, connected the special properties of hydrogen compounds with the strong deforming action of the hydrogen nucleus.

Independently of this, Born [13] came to the conviction that, in order to explain the physical properties (residual rays, elastic and piezoelectric constants) of certain crystals, it is necessary to take into account the deformability of ions. The most vivid indication of the mutual deformation of ions in salt-like compounds was given by Meisenheimer (I. Meisenheimer, 1921) [14], who explained the color of certain salts by the distortion (deformation) of ions. Since many lead salts and many iodides are colorless, free ions of lead and iodine must be regarded as colorless. And from the fact that lead iodide is intensely yellow in color, it must be concluded that in this compound the electron shell of at least one of the ions has undergone a change under the influence of the other. Many such examples can be cited. Indications of ion deformation may be found in Langmuir and in the monograph of G. N. Lewis [9]. It is also necessary to mention Weigert’s (F. Weigert) [15] general considerations on the mutual influence and deformation of the electron shells of atoms and on the effect of deformation on the optical and photochemical properties of complex systems.

Finally, of some relevance to what follows is Debye’s (1920) [16] reduction of the van der Waals forces to the mutual polarization of molecules, whereby the electric moment (quadrupole moment) of molecules is ascribed a polarizing action on neighboring molecules, and their molecular refraction is regarded as a measure of polarizability.

Recently, the influence of deformation of ions and molecules on the properties of chemical compounds has been subjected to systematic study. On the basis of a photochemical investigation carried out by the author together with Franckenburger [17], he, in collaboration with Beutler (H. Beutler), Holstamm (A. Holstamm), Joos (G. Joos), and Scott (A. Scott) [18], explained many properties of salt-like compounds from the point of view of the deformation of electron shells, and certain relationships among them were established. Shortly thereafter Born and Heisenberg (W. Heisenberg) [19], as well as Hund (F. Hund), subjected the problem of ion deformation to quantitative study, at least for the simplest cases. The results obtained so far will be briefly set forth here.

a. Unilateral polarization of ions in a homogeneous and nonhomogeneous field.

It may be asserted that every neutral atom is polarized in an electric field. In the simplest case of a homogeneous field, one can picture the effect without considering more closely the structure of the electron shell. It is enough to replace it by a negatively charged circumference (or sphere).

In a free atom (see Fig. 4a) let us imagine the positively charged atomic nucleus at the center of a circle, with which the electric center of gravity of the negative charge also coincides. The atom will then be electrically neutral with respect to the surrounding space. But if such a system is situated between the plates of a capacitor (Fig. 4b), then the negative circle is attracted to the positive plate of the capacitor, the positive nucleus to the negative one; the centers of gravity of the positive and negative charges separate, and a dipole arises. The atom is deformed or, to speak more precisely physically, is polarized. If now the atom described is introduced not into a capacitor but into a light ray, then, according to the electromagnetic theory of light, the atom undergoes in the electric field of the light waves a polarization analogous to that described. In this process the velocity of propagation of the wave changes, i.e. the light ray undergoes refraction. As Lorentz and Lorenz have shown (Lorentz und Lorenz), between the constant \(a\), serving as a measure of the polarizability of the particle, and the refractive index \(n\) (for light of infinitely great wavelength) there exists the relation \([^{16}]\):

Fig. 4a.            Fig. 4b

Polarization (deformation) of a neutral atom in an electric field.

\[ a=\frac{3}{4\pi N}\times\left(\frac{n^{2}-1}{n^{2}+2}\times V\right)=\frac{3}{4\pi N}\cdot R, \]

where \(V\) is equal to the volume containing one gram-mole (\(N=6.06\cdot 10^{23}\)) of the corresponding particles. The expression in parentheses is called the molar refraction (\(R\))\(^{1}\). Thus the molar refraction, which is calculated from the easily and very accurately measurable quantities \(n\) and \(V\), can serve as a measure of polarizability. In a homogeneous electric field of strength \(E\), as a consequence of polarization, an electric moment \(p\) arises. It is determined by the following equation, introduced into the theory of molecular forces by Debye \([^{16}]\) and repeatedly used in calcula—

\(^{1}\) In what follows we shall use the term molar refraction irrespective of whether the matter concerns a mole of molecules, atoms, atomes, or complex ions.

according to Born’s and Heisenberg’s conceptions: \(p=\alpha E\). The moment \(p\), as is known, is determined by the relation \(p=e \times l\), where \(e\) denotes the charge of both poles of the dipole, and \(l\) the distance between them (see Fig. 4b).

What has been said here about the neutral atom also applies to an ion, which differs from the atom only in that the total charge of its nucleus is not equal to the charge of the electron shell. Here too, in an electric field, a displacement of the centers of gravity of the positive and negative charges takes place, and the refraction of the whole ion may serve as a measure of its polarizability.

Much more complicated than this case of deformation in a homogeneous electric field is the case when an ion enters the inhomogeneous electric field of neighboring ions. Here we must not only consider in greater detail the structure of the electron shell, but also take into account whether interaction between ions occurs within a free molecule or in a crystal lattice.

Fig. 5. Electron orbits in an argon atom according to Bohr1.

As regards the structure of such ions, we shall assume, together with Bohr, that individual electrons describe circular or, as is the case in the majority of instances, elliptical orbits around the nucleus (see Fig. 5).

If a positive ion combines with a negative one into a free molecule, then all the orbits of the anion are attracted toward the positive charge of the cation, and here too the ion as a whole is polarized; but it is clear that those electron orbits of the anion which pass closer to the cation are, generally speaking, deformed more strongly than the more distant ones. Thus the various orbits experience the Stark effect with different strengths. The constant \(\alpha\), or the molar refraction \(R\) of the whole ion, can therefore serve, in quantitative calculations, only as an approximate measure of deformability. It is, however, quite sufficient in many cases where, as in what follows, the question is mainly one of a qualitative comparison of the behavior of ions of identical structure under similar conditions.

b. Deformation of electron orbits in the lattice.

The circumstances are different if an anion in a crystal lattice, as for example in common salt, is symmetrically surrounded on different sides by cations. Here, of course, no one-sided polarization of the whole anion occurs; nevertheless, the individual elliptical orbits are one-sidedly deformed by the stronger action of the nearer—

...the ions closest to it (see Fig. 9), so that in this case as well one may speak of deformation and use the molar refraction of the entire ion as a measure of the deformability of the electron orbits.

The behavior of cations under the influence of the deforming field of negative ions must be the same; only here the electron shell or electron orbits of the cation are not attracted to the deforming anion, but experience repulsion from it.

In all the cases indicated, we must expect the deformation of ions to affect the known, for example optical, properties of ions. And indeed, this can be demonstrated quite convincingly, above all in the example of the molar refraction of ions.

4. Molar Refraction and Deformation.

The investigations of Wasastjerna[^20], Fajans and Joos, and Born and Heisenberg gave us the possibility1 of determining the molar refraction of free gaseous ions. Fig. 6, borrowed from the work of Fajans and Joos, gives an idea of the values of the refraction of noble gases and of ions of the noble-gas type2. When considering the noble gases, it is striking how strongly (from 1.00 to 10.42) the refraction (and, together with it, the polarizability and deformability) increases with increasing atomic number (and atomic size), from neon through argon and krypton to xenon. The same is observed when comparing other similar ions from different periods, for example, among the ions of halogens, alkali and alkaline-earth metals. As with many other properties studied by Grimm, the transition from an ion of the type

argon to the krypton type causes the smallest change in refraction, as is readily seen from the inclination of the corresponding segments of the broken lines.

It is especially interesting to compare ions of identical structure, for example ions of the neon type:

\[ \mathrm{O}^{--},\ \mathrm{F}^{-},\ \mathrm{Ne},\ \mathrm{Na}^{+},\ \mathrm{Mg}^{++}. \]

The strong decrease of refraction observed in this series is quite understandable. All these ions possess the same number of electrons as the corresponding noble gas, and, according to the basic assumption of Kossel and Lewis, the structure of their electronic systems should also be similar.

Fig. 6. Molar refractions of gases and gaseous ions.

The difference between these ions consists only in the fact that identically constructed electron shells are under the attractive influence of positive nuclei whose charge increases in this series by one unit with each member. The more strongly the shell is bound to the nucleus, the more difficult it is to displace it relative to the nucleus, and the smaller, consequently, the polarizability and the molar refraction of the ion must become. This requirement is also fulfilled by ions of the argon, krypton, and xenon types, as was first shown by Wasastjerna.

Thus one may picture, for example, the transition from the chlorine ion to the argon atom as follows: the positive elementary charge enters from outside into the nucleus of the chlorine ion, whereby the electron shell of the ion is contracted and strengthened. A point positive charge can be attached to the chlorine ion in another way as well: by joining it with a hydrogen nucleus into the molecule of hydrogen chloride (HCl)

and thereby forming a chemical compound from free ions. A very interesting question is how the refraction of the chlorine ion changes in this process.

As was mentioned at the beginning, attempts were usually made to compose the molar refraction of compounds additively from the molar refractions of their constituent parts. According to this, one might have expected that when a hydrogen nucleus, deprived of electrons and therefore possessing a refraction equal to zero, is joined to a halide ion, the refraction of the halide would remain unchanged. We would arrive at the same result if, in the combination of the chlorine ion with the hydrogen nucleus, it were a question of the formation of a strictly polar compound with undeformed ions. Even if one were to admit that, upon the attachment of the H-nucleus, the Cl-ion is polarized, i.e. that the nucleus of the Cl-ion is displaced with respect to its undistorted electron shell (cf. Fig. 4), then, with a quasi-elastic bond between the nucleus and the shell of the Cl-ion, no change in its refraction can be expected upon the formation of the HCl molecule. This case of nuclear displacement was considered in greater detail by Tabor for the hydrogen halides from the energetic point of view, and Born and Heisenberg likewise carry out their new calculations of the deformation effect on the assumption that the polarizability (i.e. the constant \(\alpha\), or the refraction \(R\)) does not change under polarization.

Using Fig. 6, one can compare the values of the refraction of the halide ions with the values of the refraction of the gaseous hydrogen halides corresponding to the same abscissae. It turns out that the latter are significantly smaller than the former. Hence it follows that the polarization of a halide ion by a hydrogen nucleus is accompanied by a change in the electron shell. This is fully consistent with the assumption expressed above that, when two ions unite into a molecule, the individual electronic orbits of the ion are deformed with different strengths, as a result of which the entire electron shell undergoes distortion.

In the same way, in other cases where, upon the combination of ions, the molar refraction of the resulting molecules or crystals differs from the sum of the refractions of the constituent parts, one may conclude that deformation phenomena occur in the process of combination. Born quite correctly pointed out that in the deductive quantitative theory of the polar bond, the calculation of attractive forces between the excess charges of the ions may be regarded as a first approximation, the introduction of one-sided polarization under the assumption of constant polarizability as a second approximation, and the consideration of the change in polarizability due to the bond between ions as a third approximation.

The more inductive method of the author and his collaborators, who attempt, by studying various properties of substances, to obtain information about the phenomena—

tions of deformation, i.e., to all changes which ions undergo when combining with other ions, thus corresponds to the second and third approximations. The study of refraction thereby acquires especially important significance: since in the mutual interaction of ions there are always inhomogeneous fields, any unilateral polarization of ions is accompanied by a greater or lesser distortion of their electron shell and, because of this, by a corresponding change in refraction. Therefore, in many cases an accurately measurable refraction is the best means of establishing that deformation has occurred in the process of bonding. Further, from the magnitude of the resulting change in refraction one can, in similar cases, estimate the relative strength of the deformation. Finally, as was already indicated earlier, even in an inhomogeneous field refraction may be regarded as an approximate measure of deformability.

5. Deformation by hydrogen nuclei.

Before proceeding to apply these points of view to more complex systems, let us consider once more Fig. 6. In ions of the neon type the upward-concave form of the broken line connecting the individual values allows one to conclude that the decrease in refraction with increasing nuclear charge does not proceed linearly, but gradually slows down.

Fig. 7. Influence of the H-nucleus on molar refraction.

This means that the change in the electron shell caused by each new charge joining the nucleus, and measured by the decrease in refraction, is the smaller, the smaller the deformability (refraction). This fully agrees with the propositions set forth above. Something similar is also obtained when comparing the changes in refraction occurring in the formation of the three hydrogen halides. The deformability (refraction) of the halide ions increases in the series Cl, Br, J, and accordingly it turns out that the decrease in refraction (the force of deformation) caused by the addition of an H-nucleus increases in the same order. This is evident from the lengths of the vertical distances Cl⁻—HCl, Br⁻—HBr, J⁻—HJ in Fig. 6, or from the slope

corresponding lines in Fig. 7, is nevertheless even clearer from Table I¹), in which the refraction values are given for the halide ions \((X^-)\), for the hydrogen halides \((HX)\), and for the difference between them \((\Delta)\).

TABLE I.

Molar refractions (for the \(D\) line) of halide ions
and gaseous hydrogen halides.

\(X\)	F	Cl	Br	J
\(R_{x^-}\)	2.50	9.00	12.67	19.24
\(R_{HX}\)	(1.90)	6.668	9.142	13.74
\(\Delta\)	(0.60)	2.33	3.53	5.50

The results presented in this table may be formulated as follows: the hydrogen nucleus, which upon combination with a halide ion remains in its outer electron shell, by its attractive action on the electrons strengthens the shell the more, the looser it had been.

A very illustrative comparison, carried out by Born and Heisenberg, is that between the refraction values obtained by the system \(\mathrm{Cl^- + H^+}\) for three different relative positions of its constituent parts. When they are infinitely far removed from one another, the refraction of the system is equal to the refraction of the \(\mathrm{Cl}\)-ion; when the H-nucleus penetrates into the Cl nucleus, an argon atom is obtained; and when it remains in an intermediate position, namely in the outer electron shell of the \(\mathrm{Cl}\)-ion, an HCl molecule is obtained. Accordingly, the refraction of HCl lies between the values for \(\mathrm{Cl^-}\) and for Ar (cf. Fig. 6):

\(\mathrm{Cl^-}\)	HCl	Ar
9.00	6.67	4.20

This strengthening influence of the H-nucleus can also be established in many other cases of its attachment to acid anions. In Fig. 7 it appears not only in ions (e.g. \(\mathrm{Cl^-}\) and \(\mathrm{Br^-}\)), but also upon attachment of the H-nucleus to the neutral ammonia molecule \((\mathrm{NH_3})\), which, as is evident, undergoes a strong deformation in forming the \(\mathrm{NH_4}\) ion.

¹) The value for HF, placed in parentheses and not entirely reliable, is not shown in Figs. 6 and 7. For details see [18c].

Of particular interest is the decrease of refraction in the series \( \mathrm{O}^{--}, \mathrm{OH}^{-}, \mathrm{OH}_{2}, \mathrm{OH}_{3}^{+} \) ^1), from which it is evident that with each addition of one H-nucleus there occurs a strengthening of the electron shell, and that the decrease of refraction is the smaller, the smaller the value it had before, i.e., the smaller its deformability.

6. Deformation by Other Ions.

The results obtained for the H-nucleus can be extended to other cases. The study of the refraction of complex systems has shown that in all cases in which ions combine into molecules or into crystals, the electronic systems of the ions undergo a more or less considerable change. In particular, it has been possible to establish the following regularities: cations act on anions in the sense of decreasing their refraction (strengthening). The decrease is the more considerable, the greater the deformability of the anion and the stronger the electric field of the cation; here it must be remembered that the strength of this field in cations of identical structure increases with increasing charge and with decreasing radius of the cation. The influence of anions on cations is in general weaker than the reverse action, partly because the deformability of cations is considerably smaller than that of the corresponding anions (cf., for example, in Fig. 6 \( \mathrm{K}^{+} \) and \( \mathrm{Cl}^{-} \)), and partly because the radius of anions, generally speaking, is greater than that of most of the monatomic cations considered.

If, however, in a molecule the anion is larger than the cation, then the excess positive charge situated at the center of the cation approaches the nearest electronic orbits of the anion more closely than the excess charge of the anion approaches the electronic orbits of the cation. The deforming action of anions has so far been established only in a few cases; it amounts to a loosening ^2) (an increase of refraction) owing to the repulsion which the electrons of the cation experience from the anion.

Dissolved ions also influence the refraction of the water molecules surrounding them; moreover, cations likewise act in a strengthening manner, i.e., decrease the refraction, while anions, as is evident, act in a loosening manner, i.e., increase the refraction.

To illustrate these propositions we shall give several examples. Consideration of Fig. 8 shows that deformation phenomena must be taken into account even for understanding the properties of solid halide compounds of the alkali metals, although here the deforming

^1) Physical and chemical methods agree in indicating that the formation of the complex ion \( \mathrm{H}_{3}\mathrm{O}^{+} \) may be regarded as the first stage of hydration of the H-nucleus \([^{48}]\).

^2) The loosening action of anions on a cation was revealed especially clearly in measurements of the refraction of \( \mathrm{SrF}_{2} \) and \( \mathrm{BaF}_{2} \), carried out by Goldstam \([^{18}]\).

effect is produced by relatively large singly charged ions. This is all the more remarkable since oppositely charged ions in the lattice surround one another symmetrically on all sides, so that one might expect not a one-sided deformation of the entire shell, but only of individual orbits.

In Fig. 8 the ordinates are the differences between the sum of the molar refractions of the free gaseous ions, as they are obtained from Fig. 6, and the molar refraction of crystalline salts according to the compilation of Shpanenberg [20].

Thus, for example, for NaJ one obtains:

\[ R_{\mathrm{Na}^+}+R_{\mathrm{J}^-}=0.50+19.24=19.74;\quad R_{\mathrm{NaJ}}=17.07, \]

whence

\[ R_{\mathrm{free\ ions}}-R_{\mathrm{solid\ salt}}=19.74-17.07=2.67. \]

This value, 2.67, and the corresponding values for other salts are given in Fig. 8. If the free ions remained unchanged upon their combination into a crystal, all these differences would have to be equal to zero. True, the interaction of free ions with light, manifested in the refraction of light, must change in the presence of other (identical or different) ions¹), even if the ions undergo no change upon combination. But the Lorentz–Lorenz formula takes this circumstance into account, especially for crystals of the regular system. Therefore a significant deviation of the molar refraction of a salt from additivity must be regarded as an indication of deformation of the electronic orbits of ions by neighboring ions.

Fig. 8. Mutual influence of the refraction of ions of alkali metals and halides in a crystalline lattice.

For the nearest interpretation of Fig. 8 it must be borne in mind that in the halide salts of the alkali metals, as in all other salts of polar structure, according to what was said above, one may expect, on the one hand, an influence of the cations on the anions, expressed in the strengthening of the latter, and, on the other hand, the reverse action, connected with the loosening of the electronic orbits. Since the first effect causes a decrease, and the second an increase, of the refraction of ions in the lattice, the values \(R_{\mathrm{free\ ions}}-R_{\mathrm{solid\ salt}}\) represent the result of two factors acting in opposite directions. The fact that most of the values in Fig. 8 are positive confirms our

¹) Cf., for example, the interesting works of Bragg (W. L. Bragg) [23], who explains by this factor the double refraction of certain crystals.

the supposition that the action of cations on anions is stronger than the reverse effect. Further, a definite increase of these positive values in the series F, Cl, Br, J and Rb, K, Na, Li quite satisfies the requirement that the deformation (change of refraction) should be the greater, the greater the deformability of the anion and the smaller the radius of the deforming cation. Only for two salts, KF and RbF, are the differences under consideration negative, since only in them does the action of the anion on the cations prove stronger than the opposite effect. It is quite understandable that this is observed precisely in these salts, since they contain the F-ion, the smallest of the anions, which therefore produces the strongest field action and is least deformed, and the positive ions of potassium and rubidium, the largest and most easily deformed among the cations1. Thus the data of Fig. 8, at least from the qualitative side, are quite explicable.

If already in the lattices of the halide salts of the alkali metals, consisting of singly charged ions, such strong deformation effects are observed (the change of refraction of the iodine ion in LiJ is equal to \(3.46/19.24 = 18\%\)), it is not surprising that in the oxides of the alkaline-earth metals with doubly charged ions the oxygen ion undergoes still stronger change. This is evident from the fact that the O-ion, which in the free state has a molar refraction of about 7, has in MgO a molar refraction of 4.2, and in the oxide of the still smaller \(\mathrm{Be}^{++}\)—only 3.2. Thus in BeO the refraction of \(\mathrm{O}^{--}\) is less than half of the same value in the free state.

The fact that the oxygen ion in the crystal lattice of MgO differs so much optically from the free O-ion in no way contradicts the X-ray result obtained by Gerlach and Pauli [^24], according to which this lattice consists of ions. Indeed, the X-ray method used by them indicates only that the equilibrium position of the oxygen nucleus in the lattice is at the same time the electric center of gravity of the shell consisting of 10 electrons; this is not contradicted by the symmetrical structure of the free O-ion either. On the other hand, the idea of deformation may be illustrated by the schematic Fig. 92, in which the dashed lines depict the electron orbits of the free oxygen ion, and the solid lines—the position of the orbits in the lattice, where the O-ion is symmetrically surrounded on all sides by deforming positively charged Mg-ions. Thus—

DEFORMATION OF ELECTRON SHELLS

... the center of gravity of the electron shell does not change during its deformation. This explains why, at present, X-ray analysis of crystals still does not make it possible to detect all the subtleties of structure revealed by refraction1.

The circumstances are quite different in the case when one is dealing not with a crystal lattice, but with free molecules. Thus, one may picture the formation of the molecule \(\mathrm{CO}_2\) from the ion \(\mathrm{C}^{4+}\) and \(2\mathrm{O}^{--}\). As might have been expected, the O-ions undergo very strong deformation on the side of the small C-ion with four charges. This is evident from the fact that the refraction \(6.68\) of the entire \(\mathrm{CO}_2\) molecule is less than that of the free O-ion (\(R_0 = \sim 7\)) and, thus, the share of the O-ion in \(\mathrm{CO}_2\) has the maximum value \(3.34\). Here, however, the strong lowering of the refraction occurs in a different way than in the lattice of \(\mathrm{MgO}\) or \(\mathrm{BeO}\), since, under the one-sided influence on O in \(\mathrm{CO}_2\), the electron orbitals nearest to the \(\mathrm{C}^{4+}\) originally present there are deformed and strengthened much more than the more distant ones, so that the entire ion undergoes a one-sided distortion. At the same time, on the basis of approximate calculations that will be published elsewhere, it appears very probable that individual \(\mathrm{O}^{--}\) orbitals are so strongly attracted in the direction toward \(\mathrm{C}^{4+}\) that they can hardly be regarded as belonging only to a single O nucleus, and \(\mathrm{CO}_2\) cannot be regarded as consisting of closed ions.

Fig. 9. Deformation of the electron orbits of the anion in the lattice.

The same applies also to the complex ions of Table II.

K. Fajans

TABLE II.

Complex ion . . . . . .	$\mathrm{PO_4^{3-}}$	$\mathrm{SO_4^{2-}}$	$\mathrm{ClO_4^-}$
“Central ion” . . . . .	$\mathrm{P^{5+}}$	$\mathrm{S^{6+}}$	$\mathrm{Cl^{7+}}$
$R$ for each O atom . . .	4.05	3.65	3.32

Together with Kossel we may imagine that these ions have arisen from atom-ions—from cations of the neon type, given in the second row of the table, and from four O-ions, for example,

$\mathrm{ClO_4^- = Cl^{7+}(O^{--})_4}$.

However, upon combination these atom-ions obviously undergo very strong changes, since for the refraction of the O-ion in these complexes the values given in the third row of the table are obtained. These values differ greatly from the values for the free O-ion: they are the smaller—i.e. $\mathrm{O^{--}}$ is changed the more strongly under the influence of the “central cation”—the higher the charge of the latter. This is in full accord with our conception of deformation.

Since in the formation of these complexes, just as in $\mathrm{CO_2}$, a one-sided action on the $\mathrm{O^{--}}$ ions takes place, here too the existence of separate (independent) atom-ions within the finished complex anions must be regarded as very improbable. The values of the refraction of the O atom in $\mathrm{CO_2}$ and in $\mathrm{ClO_4^-}$ are approximately equal, which indicates a similar mode of binding of O in both molecules. This conclusion was questioned (Kossel) on the grounds that in solid $\mathrm{BeO}$, in which in his opinion the existence of ions is beyond doubt, $R_0$ has almost the same value—3.2. However, a crystalline lattice cannot simply be compared with a free molecule, in view of the completely different character of the deformation phenomena occurring in the one and the other system. On the other hand, recently Aminoff (G. Aminoff) [38] has shown by X-ray analysis that in $\mathrm{BeO}$ the existence of neutral atoms is more probable than that of $\mathrm{Be^{++}}$ and $\mathrm{O^{--}}$ ions, as a result of which a strong transfer of electrons from $\mathrm{O^{--}}$ to $\mathrm{Be^{++}}$ may be considered proved.

Many more examples could be adduced, but from what has been said it is already clear what great significance deformation phenomena have when ions combine with one another and with neutral molecules. It is also clear how, with the aid of the idea of deformation, it became possible to reduce to a coherent whole a large body of numerical material relating to the refraction of light in inorganic compounds, and why this could be done only in a very imperfect form so long as one proceeded from the usual assumption of the additivity of refraction.

The notion of deformation also proved fruitful in considering the refraction of organic compounds (in the author’s work with Knorr [¹⁸⁴]), since it made it possible to find certain new dependences, accessible to physical interpretation, in a system constructed on the assumption of additivity and formally quite satisfactory.

7. Fluidity of Halide Salts of Alkali Metals from the Point of View of the Notion of Deformation.

The frequently mentioned differences between the phenomena of deformation in the crystal lattice, on the one hand, and in the free molecule of a salt, on the other, make it possible to explain the deviations (see Fig. 2) of the boiling points of halide salts of alkali metals from what one might have expected on the assumption of undeformed ions. Let us first imagine that in a molecule isolated from the lattice all the electron orbits of both ions are situated exactly as in the lattice. In that case the heats of sublimation of salts of similar structure would have to constitute equal fractions of the lattice energy (for the halide salts of alkali metals, according to Reiss, —0.32), irrespective of whether these orbits are deformed in comparison with the free ions or not. After this separation of the molecule, which should be accompanied by an expenditure of energy, there in fact still occurs a spontaneous process, i.e. one associated with the release of energy: the process of one-sided deformation of the ionic shells.

This energy of deformation diminishes the heat of sublimation, initially proportional to the lattice energy, and does so the more strongly, the greater the mutual deformation of the two ions. On the basis of the assumptions set forth in § 2a, one may expect that the course of the boiling points of the alkali-halide salts will show the same deviation from the course of the lattice energies, and that the boiling points will be situated relatively the lower, the more strongly the given ions are deformed in the molecule. The degree of one-sided deformation in molecules of various alkali-halide salts must, according to the propositions repeatedly mentioned, show the same trend as that observed in Fig. 8 for the deformation of orbits in the lattice.

This supposition is justified by the data presented in Fig. 2. At first we do not consider the lithium salts and the fluorides: then, to a first approximation, one may confine oneself to considering the deformation of anions by cations; its degree increases in the series Cl, Br, J and Cs, Rb, K, Na. In this connection, in comparison with undeformed ions, the boiling points should be lowered most strongly for the salts of Na and the iodides, and most weakly for the salts of Cs and the chlorides. That this is justified is easiest to verify by comparing the differences between the boiling temperatures

of analogous salts (see Fig. 2 and Table III). In this way the negative difference between the boiling temperatures of NaJ and KJ, which until now has been especially striking, is most easily explained. Although the lattice energy of NaJ is greater than that of KJ (see Fig. 1), the deformation energy of the NaJ molecule evidently exceeds the deformation energy of KJ to such an extent that for the boiling temperature (heat of sublimation) we find the opposite relation. In the same way one may explain a certain decline of the differences between the salts of Na and K and of Rb and Cs on going from chloride to iodide, or, among the chlorides, bromides, and iodides, from Na to Cs.

Whereas among the chlorides the difference between the boiling points of the Na and Cs salts is \(128^\circ\), and among the iodides \(20^\circ\), among the fluorides it is \(444^\circ\). This large value for the fluorides is explained, first, by the fact that the deformation of the fluorine ion by the cations is relatively small, and, second, by the fact that here, undoubtedly, the deformation of the cations by the fluorine ion plays a role, increasing in the series Na, K, Rb, Cs. For the last three cations it is already manifested in the optical properties of the lattice (see Fig. 8). This lowers the boiling point of CsF especially strongly1: it lies \(52^\circ\) below the boiling point of CsCl2.

The anomaly in the boiling points of lithium salts, inexplicable from the standpoint of sphere-like ions, may be explained by the strong deforming action of the small Li ion. Finally, let us again compare

...the boiling point of MgO (about \(2800^\circ\text{ C} = 3100^\circ\) absolute) with the boiling point of NaF (\(1693^\circ\text{ C} = 1968^\circ\) absolute). Here there is qualitative agreement of experiment with the theory of undeformed ions. Quantitatively, however, from the point of view of this theory, we should have expected that the lattice energy of MgO would be approximately 4.4 times greater than that of NaF, since in the former substance the ions carry a double charge, and their distances in the former lattice are 10% smaller than in the latter. The heat of sublimation and the absolute boiling point of MgO should likewise have been about four times greater than those of NaF. In reality, however, the ratio of the boiling temperatures is only \((3100 : 1968 =) 1.5\), which again can be partly explained by the fact that the energy liberated

TABLE III.

Boiling points of the halide salts of the alkali metals in degrees C (at 760 mm).

	\(F\)	\(\Delta\)	\(Cl\)	\(\Delta\)	\(Br\)	\(\Delta\)	\(J\)
\(Li\)	1676	294	1332	72	1310	140	1170
\(\Delta\)	\(-19\)		\(-59\)		\(-83\)		\(-130\)
\(Na\)	1695	259	1441	48	1393	93	1300
\(\Delta\)	190		24		12		\(-31\)
\(K\)	1505	88	1417	36	1381	50	1331
\(\Delta\)	95		34		30		26
\(Rb\)	1410	27	1383	22	1351	46	1305
\(\Delta\)	149		80		51		25
\(Cs\)	1251	\(-52\)	1303	3	1300	20	1280

upon the one-sided deformation of the ions in the molecules arising during evaporation is, in MgO, absolutely and relatively much greater than in NaF.

Thus the conception of deformation makes the relations between the character of the bonding of ions, on the one hand in crystals and on the other in free molecules of salt-like compounds, much more intelligible. Only a quantitative investigation will show whether a complete explanation can be achieved in this way. An important step forward in this direction was the work of Born and Heisenberg, who calculated the energy liberated in the union of gaseous ions into vapor molecules. In doing so they applied the same principles which Born had introduced for calculating lattice energy, with the difference that in the molecule the one-sided polarization of the ions is taken...

taken into account in the following form, which considerably simplifies the true relations.

In the same way as in Fig. 4, the shell is regarded as a whole, and its polarizability is characterized by an unchanging polarization constant $\alpha$, while the field of the deforming ions is taken to be homogeneous. On the basis of these assumptions the structure of the molecule and of the crystal can be represented by the following scheme: let Fig. 10a depict the mutual arrangement of two oppositely charged ions in the crystal; then Fig. 10b will be a representation of the same ions in a free molecule. Here both ions are polarized1. The dipoles that arise give rise to attractive forces, added to the action of the excess charges of the unpolarized ions. Owing to this, the release of energy when the ions approach up to equilibrium between the forces of attraction and repulsion becomes greater than for undeformed ions. In this way the above-mentioned “deformation energy,” which diminishes the heat of sublimation, becomes accessible to calculation.

Fig. 10. Cation and anion in the crystal (a) and in the free molecule (b).

To carry out the calculation, one must make one further simplifying assumption: that the repulsive forces, whose theory for the crystal also cannot be considered elucidated [26], may for the molecule be taken into consideration in the same form as for the crystal, despite the distortion which the ions undergo in it. The heat of formation ($V$) of molecules from free ions, calculated under these assumptions, can be compared with experiment, since the expression holds:

\[ V = U - S, \]

where $U$ denotes the energy of formation of the crystal from free ions, i.e. is equal to the already known (see Fig. 1) lattice energy, and $S$ is also the approximately known heat of sublimation.

Born and Heisenberg obtained good agreement with experiment; this agreement, however, becomes somewhat worse if, instead of the full heat of evaporation of liquid alkali-metal halide salts erroneously used by them, as determined by F. Wartenberg at high temperatures, one uses the internal heat of sublimation of solid salts at $T = 0^\circ$ abs., exceeding the former by approximately 10 large calories.

However, it is very likely that, when molecules evaporate from the lattice of alkali halide salts, owing to the resulting one-sided deformation of the ions, an amount of energy is released equal to 10–15 cal. It is also of interest that in the molecule the ions approach one another more closely than in the crystal (as in Fig. 10), which was already shown by Reiss \[7\] on the basis of the Born–Landé theory, under the assumption of nondeformable ions. This effect, however, is strengthened if deformation is taken into account.

8. Absorption of light and deformation of electron orbits.

As was shown above using the example of one of the simplest physico-chemical processes—the evaporation of solid halide compounds of the alkali metals—these salts behave, in general outline, as though their molecules and crystals consisted of nondeformable (starr) ions.\[^1\]

On the other hand, indisputable deviations of the boiling points of these salts (according to the new measurements of Wartenberg \[8\]) from the values that could have been expected for salts of such a structure were pointed out. These deviations were explained, at least qualitatively, by the fact that the electron shells, or electron orbits, of the ions composing these salts undergo deformations in the electric field of neighboring ions, especially in vapor molecules. Starting from the molar refraction of crystalline halide salts of the alkali metals, the existence of such deformations was undoubtedly demonstrated even in the case of the latter, which represent the closest approximation to an ideal ionic bond. A considerable influence of deformation on the properties of these compounds was established. To confirm the information about deformation that we obtain from refraction data, examples were also given for substances of other composition.

The facts cited above, and many other facts from the field of refraction, may at present be regarded as the most direct proof that, in order to understand the properties of salt-like compounds, it is necessary to take into account the deformation of the electron orbits of the ions composing the salt. Conversely, the concept of deformation has proved useful in interpreting refraction data for inorganic and organic compounds \[18c,d\]. But, in addition to refraction, there exists a whole series of other physical and chemical properties of salt-like compounds which it has first become possible to connect and make more accessible to understanding precisely from the standpoint of the theory of deformation \[18a\]. Here we shall give a brief survey of them.

\[^1\]: This had earlier been pointed out by Kossel \[3b\] and Reiss \[7\].

The deformation of the electronic orbits of free ions when they combine into molecules or crystals must manifest itself especially strongly, besides the phenomena of refraction, also in the absorption of light. Unfortunately, the experimental material relating to the absorption of light in simple compounds is far too insufficient for one to be able to derive simple regularities of a quantitative character. However, a number of qualitative observations on the color of salt-like compounds can undoubtedly be connected with the idea of deformation.

Already in § 3, in the example of lead iodide, mention was made of the interpretation, first given by Meisenheimer, of the coloration of certain compounds as the result of the mutual distortion of ions upon combination. This author also drew attention to the intensification of the coloration of certain inorganic and organic compounds observed with increasing atomic weight of the haloid. Especially instructive examples may be provided by the salts of nickel and copper:

NiF$_2$	NiCl$_2$	NiBr$_2$	NiJ$_2$
yellowish	yellow-brown	dark-brown	black

CuF$_2$	CuCl$_2$	CuBr$_2$	(CuJ$_2$)
colorless	yellow-brown	brownish-black	unstable

The fact that CuF$_2$1, like CuSO$_4$, is colorless in the anhydrous state shows that the free gaseous ion Cu$^{++}$ must be colorless, and that the intense blue color of aqueous solutions of copper salts belongs to the hydrated Cu ion, i.e. to the complex Cu(4H$_2$O)$^{++}$. The green color of solutions of nickel salts likewise cannot be explained by the color of the free Ni ion, since the anhydrous NiF$_2$, NiSO$_4$, and Ni(ClO$_4$)$_2$ are colored a faint yellowish color [18f], so that the free gaseous Ni ion, if colored at all, is yellow. If, however, the chloride, bromide, and iodide of nickel exhibit a coloration that changes greatly in depth and intensity in the order indicated, this may be regarded as an indication of deformation of the electronic orbits of the haloid ions by the nickel ion. The intensification of the color can be explained by the strong increase, known to us on the basis of refraction data, in the deformability of the ions from F$^-$ to J$^-$.

From this point of view one can also explain the coloration of other salts of copper and nickel; for example, why CuSO$_4$ (and also Cu(NO$_3$)$_2$) or NiSO$_4$ and NiClO$_4$ behave like the corresponding fluorides, whereas the oxides are colored much more darkly: CuO is black, NiO dark green. In the oxides, ions O$^{--}$ are in contact with the metal ions; in other salts, complex ions are.

We have no right to compare the refraction of \(O^{--}\) with the refraction of a complex ion as a measure of the deformability sought: both in the \(O^{--}\) ion and in the more complex anion, the appearance of color is explained by the deformation of a few electron orbits of the anion nearest to the metal ion. Thus the matter reduces to the deformability of individual electron orbits. It is therefore best to compare the refraction for the same number of electrons, i.e. the refraction of \(O^{--}\) in the case of oxides with the refraction of each individual oxygen octet in complex ions.

Whereas the refraction of the free \(O^{--}\) ion is equal to 7, the \(O^{--}\) ions in the complex ion are so strongly deformed and strengthened\(^1\) by the central ion (e.g., \(S^{6+}\) in \(SO_4^{--}\)) that their refraction (cf. Table II) is only 3.65 in \(SO_4^{--}\) and 3.32 in \(ClO_4^{-}\).\(^2\) The electron orbits in these complexes are thus deformed much less than in free \(O^{--}\) ions, which explains the much darker color of oxides in comparison with sulfates and perchlorates.

The deformation of ions manifested in the cases named by the appearance of color we shall conceive, from the point of view of the views expressed in § 3b, as a stretching of the electron orbits of the anion in the direction toward the cation. In complete agreement with this conception is the behavior of the halide compounds (oxide) of copper; already \(Br^{-}\) in \(CuBr_2\) is very strongly deformed, as is clear from the black color of the compound and from its strongly expressed tendency toward complex formation in concentrated solutions [cf. § 13].

The electrons of the still more easily deformable ion \(J^{-}\) are so strongly attracted in the direction toward \(Cu^{++}\) that stable common electron orbits can no longer form at all between \(Cu^{++}\) and \(2J^{-}\), and one electron passes completely to the complex with the formation of \(CuJ\) and \(J\): as is known, \(CuJ_2\) is not capable of existing at ordinary temperature.

The indicated changes in color (absorption of light) upon the combination of ions, which can be illustrated by a whole series of other examples, are just as unambiguous a sign of a change in the electron orbits as are the experimental data cited above from the field of refraction. However, whereas the sign of the change in refraction (decrease of the refraction of anions under the influence of cations, and conversely) admits of a simple explanation, the phenomena of absorption are more

\(^1\) Cf. § 6.

\(^2\) This method of considering whole octets is also only a first and very rough approximation, since the individual orbits of the O-octets in free \(O^{--}\) ions and especially in complex anions are not equally firmly bound [cf. 18d]; therefore one would have to pass to consideration of each electron orbit separately.

entangled. In some of the cases described (e.g., for PbJ₂, § 3), as well as in many others, upon deformation of anions under the influence of cations there occurs a displacement of absorption from the ultraviolet region (in general, from the region of shorter oscillations) into the visible (the region of longer oscillations), i.e., in the spirit of the terminology proposed by Stark (J. Stark) [²⁸], a “weakening of the bond” (Lockerung) of the electronic orbits, or a “liberation” of the electrons, whereas from the point of view of refraction the electronic orbits of the anions undergo a “strengthening” (Verfestigung), and the anions become more firmly bound in the field of the cations. This contradiction between the indications of refraction and absorption is, however, only apparent. Indeed, according to Bohr’s theory of the absorption of light, a shift of the absorption of the ion J⁻ into the region of longer waves under the influence of the ion Pb⁺⁺ means that less energy is required to transfer an electron in the ion J⁻ to a higher quantum orbit when J⁻ is in the field of Pb⁺⁺ than when it is free. In other words, the difference in energy between two quantum orbits decreases under the action of the field of Pb⁺⁺. It follows from this that at least one of these orbits, and possibly both, have undergone deformation¹). However, the displacement of absorption into the region of longer oscillations says nothing about the sign of the change of each individual orbit. The change in refraction, on the other hand, pertains precisely to the state of the normal quantum orbit. Therefore it is necessary strictly to distinguish the concepts of the “strength” (Festigkeit) of an orbit “in the sense of absorption” and the “strength of an orbit in the sense of refraction.” Unfortunately, only for a few simple compounds are there simultaneously accurate measurements of refraction and absorption [²⁹], so that at present it is not yet possible to establish more general relations between changes in these two optical properties upon the union of ions.

It may be said that the phenomena of deformation, studied in greater detail up to now on the basis of data on refraction, relate for the most part to the action of cations constructed according to the type of the noble gases, whereas the strong changes in absorption, manifested in changes of color, must be ascribed to the influence of cations not possessing the structure of the noble gases.

How great the difference is between cations of the one and the other type, in their ability to deform anions to the point of producing color, is evident from a comparison of sodium and silver salts. Whereas all sodium salts with colorless anions are colorless (cf. Table IV), AgBr and AgJ are yellow, and Ag₂O and Ag₂S are black. Hence it follows that the anions Br⁻,

¹) The possibility is not excluded that, under the influence of an external electric field, the difference in energy of two quantum orbits may change while the form of these orbits remains unchanged. However, the appearance of color indicates the action of a particularly strong field, which always produces a corresponding strong geometrical deformation. Therefore the appearance of color may be regarded as a sign of such deformation.

I\(^-\), O\(^{--}\), and S\(^{--}\) are deformed under the action of Ag\(^+\) up to the appearance of color\(^1\).

Obviously, in this strong deforming influence of ions that do not belong to the noble-gas type lies the cause of the difference in the properties of compounds of cations of different types (see § 2b). We shall show this by comparing certain properties of salts of both types, chiefly the salts of Na and Ag.

9. Distances between ions and lattice energy.

Especially indicative in this respect is the course of the distances between ions in the crystal lattice of silver halide salts. As is seen in Fig. 11, the distances between the centers of oppositely charged ions in the crystal lattice of the halide salts of Na and K, if not entirely exactly, then at any rate approximately, are additive. As a first approximation for these salts one may assume that the corresponding ions are undeformable (rigid) and impenetrable spheres of definite radius, brought together in the lattice until their surfaces touch, whereby

\[ r_{\mathrm{K}^{+}} > r_{\mathrm{Na}^{+}} \]

and

\[ r_{\mathrm{J}^{-}} > r_{\mathrm{Br}^{-}} > r_{\mathrm{Cl}^{-}} > r_{\mathrm{F}^{-}} . \]

Fig. 11.

If we now turn to the silver halide salts, this representation proves inapplicable. Indeed, from a comparison of the fluorides it would follow that the Ag\(^+\) ion is larger than Na\(^+\); in comparing the chlorides the ratio changes only slightly, in the bromides very clearly, while in the iodides the distances between the ion centers for the silver salt are considerably smaller than for the sodium salt. This can be explained, at least qualitatively, from the standpoint of the idea of deformation. It is clear that the stretching of the electronic orbits of the anion in the direction toward the cation will bring the entire anion closer to the cati-

\(^1\) The fact that Ag\(_2\)O is more intensely colored than AgJ, i.e. that O\(^{--}\) is deformed more strongly than J\(^-\), although the refraction of J\(^-\) (19.2) is considerably greater than that of O\(^{--}\) (7), should not be regarded as contradicting the views expressed. This is explained by the fact that the O ion, with two charges, owing to the stronger attraction, approaches closer to Ag\(^+\) and therefore is deformed more strongly than J\(^-\) with one charge.

it more than would be possible in the case of nondeformable ions. If, however, one takes into account that the deformation in silver salts is stronger than in sodium salts, and that it is much greater in iodides than in fluorides, the relations shown in Fig. 11 become entirely understandable.

The different course of the lattice energies for sodium and silver salts, shown in Fig. 1 and considered in § 2b, obviously also depends on deformation phenomena. The very fact that the lattice energy of AgCl is considerably greater than that of NaCl, although the lattice constants, i.e., the distances between ions, are very similar in these two salts of the same structure, shows1 that here one cannot make do with a difference in the repulsive forces between the halide anions, on the one hand, and \( \mathrm{Na}^+ \) and \( \mathrm{Ag}^+ \), on the other, as Grimm assumed (see § 2b). It must be accepted that, in the value of the lattice energy of silver salts, besides the positive work of the attractive forces of the excess ionic charges and the negative work that must be expended against the repulsive forces of the electron shells, there enters still another positive term—the “deformation energy,” associated with the spontaneous process of approach of the deformed electron orbits of the anion to the cation. The lattice-energy values of AgBr and AgJ likewise include “deformation energy.” The circumstance that the energy decreases much less from chloride to iodide in silver salts (by only 12 large calories) than in sodium salts (24 large calories) depends chiefly on the fact that the distance between ions in NaJ (see Fig. 11) is much greater (by \(0.42\,\text{\AA}\)) than in NaCl, and, in connection with this, the work of the excess charges is smaller. In the corresponding silver salts the difference between the distances in the lattice is extremely small (\(0.05\,\text{\AA}\)). Since we have related the latter circumstance to deformation, the different decrease of the lattice energy in the two cases must also be regarded as a consequence of deformation phenomena.

The relation of the lattice energies of the halide salts of Na and Ag shown in Fig. 1 can be expressed as follows: the lattice energy of an Ag salt exceeds the lattice energy of the Na salt by the more, the more readily the halide ion is deformed. As the author has shown together with Scott (A. Scott) [18a], this proposition can be generalized, since in rough outline the following rule is justified: the lattice energy of a salt of a heavy metal exceeds the lattice energy of a salt whose cation (with the same number of charges) belongs to the noble-gas type by the more, the more strongly the anion is deformed. As an example we shall give here only a comparison of the series of Ag and Na salts. In Table IV, for the series of anions given in the first row, the second row shows by how many large calories per 1 gram-equivalent the lattice energy of the corresponding Ag salt exceeds the lattice energy of the Na salt; the third row gives

refraction, as a measure of the deformability of the anion. From the considerations indicated in the discussion of the coloration of compounds (§ 8), for complex ions not their total refraction is given, but only that part of the refraction which belongs to the O-octet contained in the complex ion.

TABLE IV.

X	F⁻	NO₃⁻	1/2 SO₄--	1/2 CO₃--	Cl⁻	Br⁻	J⁻	1/2 O--	1/2 S--	1/2 Se--
\(U_{\mathrm{Ag}X}-U_{\mathrm{Na}X}\) in g. calories	9.3	10.5	11.5	17.9	25.6	31.4	39.1	45	49.8	63.6
R.	2.5	3.66	3.65	4.03	9.0	12.7	19.2	7	20	25
Color of Ag salt	?	white	white	white	white	yellow	yellow	black	black	black

As is evident from this table, in comparable cases, i.e., for example, for \(\mathrm{SO_4^{--}}\) and \(\mathrm{CO_3^{--}}\), or for the halides, and also for the ions of the oxygen group, the difference between the lattice energies \(U_{\mathrm{Ag}X}-U_{\mathrm{Na}X}\) does in fact increase with the refraction (deformability) of the electron orbits of the anion. Since the lattice structure of the corresponding compounds is known only in part, it is impossible here to determine more precisely, as in the case of the halide salts, what role in these regularities is played, on the one hand, by the influence of deformation on the lattice constant, and, on the other hand, by the appearance of deformation energy. However, if attention is also paid to the parallelism between the increase in the values of \(U_{\mathrm{Ag}X}-U_{\mathrm{Na}X}\) and the intensification of the coloration of the silver salts, the total influence of deformation on these values becomes beyond doubt. The fact that oxide shows a higher value of \(U_{\mathrm{Ag}X}-U_{\mathrm{Na}X}\) than iodide, despite the lower refraction of \(\mathrm{O^{--}}\) in comparison with \(\mathrm{J^-}\), can be explained in the same way as the coloration—by the double charge of \(\mathrm{O^{--}}\) and, consequently, by its stronger attraction to the cation. In Table IV the anions are arranged in the order of increasing values of \(U_{\mathrm{Ag}X}-U_{\mathrm{Na}X}\). For the increase in the difference between the lattice energies of salts of other heavy metals in comparison with the salts of cations of the noble-gas type, the same series of anions is obtained, with only small changes. This cannot be explained by chance. The deeper reason for this must be sought in the fact that, in this series, the influence which the deformation of ions exerts on the properties of the corresponding salts increases.

10. Photoelectric conductivity of salts.

This conception has received interesting confirmation, thanks to the observations of Gudden and Pohl (B. Gudden und R. Pohl) \([31]\) in an entirely different field, namely, in the photoelectric conductivity of salts. This property can be explained as follows: under the action of light, electrons are split off from the constituent parts of the salt and become

therefore capable of transport in an electric field. There can be no doubt that the action of light on salt-like compounds manifests itself on the electrons of the anion. This was first shown in the example of the photochemical decomposition of silver halide salts [7]. Consequently, photoelectric conductivity in various salts will be observed to the greater extent the more easily electrons can be split off from their anions. It may be assumed that the strengthening of light absorption, observed in many cases, or its shift toward longer wavelengths when anions are deformed by cations in salt-like compounds, is a general phenomenon. On the other hand, one may make the plausible assumption that the ability of electrons to absorb light is parallel to the ease with which they are split off from the anion in the salt. Then one may predict that photoelectric conductivity will increase with increasing deformation of the anions in the crystal lattice. From this point of view one may expect, first, that photoelectric conductivity will be considerably greater in salts of heavy metals than in salts of light metals, and, secondly, that for salts with different anions it will increase in the order indicated in Table IV. As Gudden and Pohl pointed out soon after the publication of this series of anions, their investigations fully confirm the consequences derived here; this is readily seen from consideration of Table V, which requires no further explanation.

TABLE V.

Photoelectric conductivity according to Gudden and Pohl.

Increasing deformability.

Cation type	Cation	F⁻	NO₃⁻	SO₄²⁻	CO₃²⁻	Cl⁻	Br⁻	J⁻	O²⁻	S²⁻
Cations of the type of noble gases.	K⁺	−	−	−	−	−	−	−
Cations of the type of noble gases.	Na⁺	−	−	−	−	−	−	−
Cations of the type of noble gases.	Ba²⁺	−	−	−	−	−				+
Cations of the type of noble gases.	Sr²⁺	−	−	−	−	−				+
Cations of the type of noble gases.	Ca²⁺	−	−	−	−	−				+
Cations unlike noble gases.	Tl⁺		+	−	+	+	+	+	+	+
Cations unlike noble gases.	Ag⁺		−	−		+	+	+	+	+
Cations unlike noble gases.	Pb²⁺		−	−		+	+	+	+	+
Cations unlike noble gases.	Cu²⁺							+	+	+
Cations unlike noble gases.	Hg²⁺							+	+	+

+ photoelectric conductivity is observed.
− “ ” is not observed.

11. Solubility of salts and deformation.

If, in this way (see § 9), the increase in the difference in lattice energy between the silver and sodium salts in the given series of anions depends on the deformation of the anions by the ion Ag, then one more essential difference between the silver and sodium salts may be reduced to the same phenomena of deformation, namely: the difference in their solubilities. The process of dissolving a salt in water may be represented as follows [6]: first the solid lattice, with expenditure of lattice energy, is split into free gaseous ions, which then dissolve in water with liberation of the heat of hydration. The heat of solution \(L\) is thus the difference between the sum of the heats of hydration of the anion \((W_A)\) and the cation \((W_K)\) and the lattice energy \(U_{AK}\).

\[ L = W_A + W_K - U_{AK}. \]

Solubility, especially in sparingly soluble salts, is connected with the heat of solution in the following way: a salt, generally speaking, is the more difficultly soluble the more negative its heat of solution. Thus, the heat of solution of readily soluble NaJ or AgF is positive, whereas the heat of solution of very difficultly soluble AgJ is equal to \(-26\) b. cal.

In considering the Ag- and Na-salts of the series of anions given in Table IV, one may draw the following conclusions regarding the difference in heats of solution and, hence, their relative solubility:

\[ L_{\mathrm{Ag}X'} = W_{\mathrm{Ag}^+} + W_{X'} - U_{\mathrm{Ag}X'}, \]

\[ L_{\mathrm{Na}X'} = W_{\mathrm{Na}^+} + W_{X'} - U_{\mathrm{Na}X'}, \]

\[ L_{\mathrm{Ag}X'} - L_{\mathrm{Na}X'} = (W_{\mathrm{Ag}^+} - W_{\mathrm{Na}^+}) - (U_{\mathrm{Ag}X'} - U_{\mathrm{Na}X'}), \]

and correspondingly for another anion \(X''\)

\[ L_{\mathrm{Ag}X''} - L_{\mathrm{Na}X''} = (W_{\mathrm{Ag}^+} - W_{\mathrm{Na}^+}) - (U_{\mathrm{Ag}X''} - U_{\mathrm{Na}X''}). \]

Thus the difference in heats of solution between the silver and sodium salts is determined, independently of the anion, by the difference \(W_{\mathrm{Ag}^+} - W_{\mathrm{Na}^+} = \Delta W\) of the heats of hydration of the free ions Ag\(^+\) and Na\(^+\), and by the difference in lattice energy given in Table IV. \(\Delta W\) is approximately equal to 10 b. cal.; if therefore we consider the nitrates, for which \(U_{\mathrm{Ag}X} - U_{\mathrm{Na}X}\) also approaches 10 b. cal., we obtain \(L_{\mathrm{AgNO_3}} - L_{\mathrm{NaNO_3}}\) close to zero, i.e. AgNO\(_3\) and NaNO\(_3\) have approximately equal heats of solution (about 5 b. cal.). In accordance with this, we find very similar solubilities (about 10 moles per liter)—they are both very readily soluble. The larger the value of \(U_{\mathrm{Ag}X} - U_{\mathrm{Na}X}\) becomes, the more negative \(L_{\mathrm{Ag}X}\) becomes

in comparison with \(L_{\mathrm{NaX}}\), and the silver salt should become less soluble in comparison with the sodium salt. This is indeed confirmed for the series of anions in Table IV, as is seen in Fig. 12. Here on the abscissae are plotted the values \(U_{\mathrm{AgX}} - U_{\mathrm{NaX}}\), i.e. the anions are arranged in the same sequence—by increasing deformability—as in Table IV. On the ordinates are the logarithms of the solubility of the Na and Ag salts. As can be seen from the diagram, the solubility of the sodium salts, all of which dissolve well, varies within narrow limits, differing in the extreme cases by only a little more than a factor of 10 (\(\mathrm{NaF}\)—1 mole/liter, \(\mathrm{NaJ}\)—18 moles/liter). In accordance with this, parallel to the strong increase in the values \(U_{\mathrm{AgX}} - U_{\mathrm{NaX}}\), in our series there is observed a strong decrease in the solubility of the silver salts, down to the vanishingly small value \(10^{-16}\) mole/liter for \(\mathrm{Ag_2S}\). Thus, one may say that silver sulfide is so extraordinarily sparingly soluble because, when \(\mathrm{Ag}^{+}\) combines with the \(\mathrm{S}^{--}\) ion, the electron orbits of the sulfur ion are very deeply drawn in by the silver ions, and this determines a large deformation energy and a large lattice energy. The hydration force proves insufficient to perform the work that must be expended in order to liberate the ions from the lattice.

Fig. 12.

12. “Loosening” of the Crystal Lattice

In conclusion let us consider one more property of salt-like compounds which can likewise be brought into close correspondence with the ideas set forth in this article, namely—the electrical conductivity of salts in the solid state, associated with the transport of ions. It has recently been studied by Tubandt (C. Tubandt et al.) \([32]\) in a series of valuable investigations. Whereas various molten salts have electrical conductivities of one order of magnitude, in solid salts very much larger differences are observed in this respect. In order, for purposes of comparing different salts, to eliminate as far as possible the influence of temperature, which is strongly reflected

DEFORMATION OF ELECTRON SHELLS

on the absolute values of electrical conductivity, we shall take, together with Hevesy (G. v. Hevesy) [32], the ratios of the electrical conductivities in the molten and in the solid state, near the melting point.

TABLE VI.

Electrical conductivity \((\sigma)\) near the melting point.

	\(\dfrac{\sigma\ \text{above}}{\sigma\ \text{below}}\) the melting point	Solubility in mol/liter
KNO\(_3\)	20000	Readily soluble.
LiNO\(_3\)	10000	Readily soluble.
KCl	9000	Readily soluble.
NaCl	3000	Readily soluble.
TlCl	160	\(1.2 \cdot 10^{-2}\)
TlBr	130	\(1.4 \cdot 10^{-3}\)
TlJ	100	\(1.5 \cdot 10^{-4}\)
AgCl	30	\(0.9 \cdot 10^{-5}\)
AgBr	5	\(4.5 \cdot 10^{-7}\)
AgJ	0.9	\(1 \cdot 10^{-8}\)

As is seen from the second column of Table VI, the ratio \(\dfrac{\sigma\ \text{above}}{\sigma\ \text{below}}\) the melting point varies for the salts listed over an enormous range, from 20000 to 0.9. Thus, whereas, for example, in KNO\(_3\) the electrical conductivity in the solid state is quite negligible in comparison with that of the molten salt, in AgJ the crystal conducts 10% better than the molten salt. Thus in solid AgJ the ions are extraordinarily mobile; the lattice is, as it were, “loosened,” in Hevesy’s expression.

It may be expected that, along with other factors, the deformation of the electron orbits will strongly affect this “loosening” of the lattice. At absolute zero an ion in the lattice, being more or less symmetrically surrounded by oppositely charged ions, exerts electrostatic actions (attraction) on them and is itself held by these forces in its equilibrium position. When, as the temperature rises, the ions enter into thermal motion, at a certain moment some part of the ions occupy positions removed from their equilibrium positions; for example, a cation approaches some anion more closely than its other neighbors. Under such a strong asymmetric approach, the deformation of the anion by the cation is considerably intensified; the electron orbits of the anion are drawn toward the cation, and the polar opposition of the ions is more or less erased, in de-

dependence on the deformability of the anion and on the field strength of the cation. Such a site in the lattice, in which the anion and the neighboring cation have approached the state of a neutral atom, exerts a weaker electrostatic attraction on the surrounding ions than do the normal parts of the lattice. Therefore the ions surrounding such a site become more mobile, and the crystal at this site is “loosened.”1 In favor of this conception is the circumstance, indicated by Hevesy, that various salts show the greater tendency to “loosen” the lattice the more easily electrons are detached from the anion and the greater the cation’s affinity for the electron, i.e., the more readily the transition of an electron from anion to cation can occur. This transition, however, need not be complete, as is assumed, for example, in the photochemical decomposition of salts; for the weakening of the field and the “loosening,” a more or less strong deformation of the electron orbits is sufficient.

In order to show the connection of “loosening” with deformation phenomena, Table VI also gives the solubility of the salts, which, as was indicated above, in sparingly soluble salts depends on the degree of deformation. As is seen from the table, in readily soluble salts of the alkali metals, for which on various grounds we assume only weak deformation effects, the ratios in the second column are very large, i.e., the loosening is weak. Conversely, the halide salts of Tl and Ag cations, which do not belong to the noble-gas type and in which deformation phenomena play a large role, are strongly loosened, and the “loosening” increases in the Tl and Ag salts from chloride to iodide. Parallel with the fall of the values in the second column, for all six salts there is a decrease in solubility. In the group of soluble salts the solubility values are not given, since here the course of solubility cannot stand in a simple relation to the deformation of the ions. However, if the fall of the coefficient from $\mathrm{KNO}_3$ to $\mathrm{NaCl}$ were real, then in these salts too the “loosening” would change parallel to deformation, since $\mathrm{Li}^+$ and $\mathrm{Na}^+$ deform more strongly than $\mathrm{K}^+$, and $\mathrm{Cl}^-$ is deformed more strongly than $\mathrm{NO}_3^-$.

It should also be mentioned that the sequence of melting points of the silver halide salts given in § 2a, which differs strongly from that observed for the alkali-metal halide salts (Fig. 3), indicates the “loosening” of these salts and, at least in part, can be explained by deformation phenomena. Thus we see that many properties of silver salts, by which they differ so markedly from alkali-metal salts, for example, the absorption of light

(color), and at the same time the photochemical sensitivity and photoelectric conductivity, further—the ionic conductivity in the solid salt, the lattice energy, and the solubility, can be brought into connection with the strong deformation which the silver ion causes in the anions.

13. Structure of the electron shell and deformation.

In considering a number of properties of salt-like compounds from the standpoint of the structure of atoms, or more precisely, the structure of ions, the influence of the following features of ionic structure was taken into account: the charge and size of the ions, the arrangement of their outer surface (the distinction between ions of the noble-gas type and ions not belonging to this type was especially emphasized), and the deformability of the ions. If, on this simple basis, it proved possible to explain qualitatively a number of properties of salts, it would be a mistake to think that these factors are sufficient for a full understanding of all the physical and chemical properties of salts. In order to understand them more deeply, it is necessary first of all to pay attention to the structure of the outer electron shell. Above we limited ourselves to distinguishing cations belonging and not belonging to the noble-gas type, the former being ascribed a relatively weak ability to deform anions, and the latter a relatively strong one. However, this division proves insufficient when, from the silver ion that has been considered, we pass to other ions differing in structure from the noble gases. Thus, for example, salts of the ions of (cuprous) copper and mercury, which likewise do not belong to the noble-gas type, behave, with respect to solubility and color, not as silver salts do. It is true that CuO and CuS, HgO and HgS are sparingly soluble, in accordance with the strong deformation of their anions, manifested in their intense coloration. In the halide salts, however, we encounter substantial differences. White AgCl and yellow AgBr are very sparingly soluble; white HgCl₂ and HgBr₂ have moderate solubility; intensely colored CuCl₂ and CuBr₂ dissolve very readily.

In any case, concentrated solutions, for example of CuBr₂, unlike solutions of the halide salts of the alkali metals, are not dissociated predominantly into the atomic ions Cu++ and Br−, but, as is shown by their dark-brown color and by experiments on ion transfer [33], contain, along with the cations Cu++, complex anions (for example, CuBr₃− or CuBr₄−−). The formation of these concentrated solutions is therefore not an indication that the hydration forces overcome especially easily the bond between the ions in the solid salt. Indeed, in the formation of these solutions only part of the Cu++ ions separate from the bromine ions, whereas another part, belonging to the complex anion, draws the bromine ions to itself even closer than in the lattice,

as a consequence of the one-sided bond with them and, accordingly, of the stronger deformation. Nevertheless, the dissolution of CuBr₂ with the formation of separate atom-ions proceeds incomparably more readily than that of silver bromide: whereas the solubility of AgBr is \(10^{-7}\) mol/liter, a solution of CuBr₂ at a concentration of 0.1 mol/liter already has the normal blue color of the cupric ion and, according to data obtained from electrolytic transport, does not reveal the presence of complex ions in any appreciable quantity. In any case, the forces of hydration, in comparison with the forces acting in the lattice, manifest themselves in CuBr₂ much more strongly than in AgBr.

A comparison of the salts of silver and copper with other anions leads to an analogous result. Here one cannot yet see an expression of the difference in the structure of the electron shells of \(Ag^+\) and \(Cu^{++}\), since very often, on passing from salts of monovalent cations to salts of polyvalent cations, the heat of solution becomes more positive, i.e. the heat of hydration of the ions increases more strongly than the lattice energy. However, mercuric halide compounds behave in a peculiar manner in this respect. In these salts we must also take into account certain effects of deformation. This is expressed in the fact that, although \(HgCl_2\) and \(HgBr_2\) are colorless, \(HgJ_2\) is intensely colored both in the solid state and in organic solvents, in which it dissolves in the form of undissociated molecules. In terms of solubility, the mercuric halide compounds lie between the extremely sparingly soluble silver halide salts and the very readily soluble cupric halide salts. However, the state of solutions—for example, of \(HgBr_2\)—differs from that of \(CuBr_2\). Whereas the latter, at high concentrations, gives, as was indicated, complex anions, and at a concentration of 0.1 N practically decomposes completely into ions, a 0.01 N solution of \(HgBr_2\) is dissociated by only 1% and contains almost all the salt in the form of \(HBr_2\) molecules. Undoubtedly this circumstance too is connected with the strong deformation of the \(Br\)-ion in \(HgBr_2\), but this deformation manifests itself here differently than in sparingly soluble AgBr or than in \(CuBr_2\), which forms complex ions. This difference indicates that, in mercury halide compounds, in the transition from the lattice to the molecule, a special role is played by the strengthening of deformation mentioned in § 7 and by the liberation of deformation energy as a result of the one-sided attraction of the ions. This directly explains the relatively easy volatility, i.e. the low heat of evaporation of sublimate and its homologues, as well as the good solubility of these salts in organic solvents.

However, these subtle differences in the magnitude of deformation in the lattice and in the molecule are connected with the question of the stability of electron orbits, about which at present we know very little. Directly connected with this question is also the circumstance that \(AgJ\)

I\(^-\) and HgJ\(_2\) are very stable compounds, whereas the strong deformation of the J\(^-\)-ion by the Cu\(^{++}\)-ion leads to the instability of CuJ\(_2\). In this special case the explanation must be sought in the fact that, according to Bohr and others, Ag\(^+\), Hg\(^{++}\), and Cu\(^+\) form symmetric closed electron shells with 18 outer electrons, whereas Cu\(^{++}\) has an incomplete shell, which tends to completion to Cu\(^+\) by the removal of one electron from J\(^-\). In many other individual cases one should assume a connection with the fine structure of the electron shell.

Thus, Ladenburg (R. Ladenburg) [34] and Bohr connected the color and paramagnetic properties of the salts of the elements of group VIII and their neighbors with the incompleteness of their electron groups, which, according to Bohr’s theory of the periodic system, characterizes the ions of these “transition elements.” To explain coloration, however, one must approach this conception with a certain caution. Indeed, we know that the Cu\(^{++}\) ion, despite its incomplete electron shell in the free state and in salts with an anion that is difficult to deform, gives no coloration, and that, on the other hand, the symmetric ions Ag\(^+\) or Hg\(^{++}\) in combination with easily deformable anions give colored salts.

Thus in these cases color is not a specific property of the cation, but depends on the anion. Still, it cannot be denied that, in general, in salts and especially in hydrates and other complexes formed by cations with incomplete electron groups, coloration appears more often than in compounds containing only ions with stable electron groups. Roughly, the matter may be represented in such a way that the electrons of the anions and neutral molecules surrounding the cation and deformed by it, especially readily (under the action of visible light), make quantum jumps into the “holes” of cations with incomplete electron groups.

14. Continuous and Discontinuous Deformation.

For the further study of the deformation which, in the formation of complex systems, the electron orbits of their components undergo, apart from the immediate consideration of the structure of the corresponding electronic systems, the following question acquires special importance.

According to Bohr’s theory, a change in an electron orbit under the influence of external factors may occur in two ways. On the one hand, there may occur a continuous change in the form of the orbit, without a change in the quantum numbers characterizing the orbit. This kind of deformation of the orbit is experienced in an ordinary electric field, for example in the Stark effect. On the other hand, under the action of light, electrons produce quantum jumps (transitions), in which the numbers,

characterizing the quantum state change by jumps1). One asks to which of these two kinds one should assign the deformations of electronic orbits that occur when atomic systems combine. Although what is involved here is the influence of electric fields, it must be borne in mind that the electronic orbit of one of the combining atoms (or atomic groups) comes into the closest connection with the nuclei of the other, and therefore one must allow for the possibility of a sudden, discontinuous (sprunghaft) change of the quantum state of the orbit. In the preceding exposition we did not touch upon the question of the category to which the corresponding deformations belong, and implicitly considered the deformations as more or less continuous, since in most of the cases examined the question of interest to us here did not admit of an unambiguous solution, and its solution would not have greatly altered our previous arguments.

However, there are cases in which one can establish a change in the quantum state of the components during the formation of complex systems. Thus, on the basis of spectroscopic data that served as the foundation for the new scheme of electron distribution in the atoms of various elements, given by Main Smith (J. D. Main Smith) and Stoner (E. C. Stoner) [35], the four valence electrons of a free carbon atom are not equivalent: two electrons are in the quantum state 2, 1, 1, and the other two—in the quantum state 2, 2, 1.

Since, on the other hand, it must be regarded as beyond doubt that in symmetrical carbon compounds, such as, for example, diamond, CH$_4$, or CCl$_4$, all four carbon electrons are in the same state, one has to assume that, when a C atom combines with atoms like itself or with H or Cl atoms, the quantum state of at least two electrons undergoes a change. In the combination of ions, too, one can establish a change in the quantum state of the electrons. A sign of this may be taken to be the circumstance that many sulfides, such as, for example, Ag$_2$S, PbS, or CuS, already at ordinary temperature and without any illumination possess electronic conductivity, i.e. some of the electrons in them are “free.” In the sense of the considerations set forth above, this must be regarded as a sign of an extremely strong deformation of the electronic orbits under the influence of the cation, leading to the complete separation of the electron from the sulfur ion. The black color of these sulfides also points to the same thing. When this electron is liberated, naturally, a change in its quantum state takes place.

A much more important criterion of a discontinuous change of the quantum state is paramagnetism. According to modern views, the magnetic moment of paramagnetic substances changes by jumps—

...by whole quanta, by Bohr magnetons. The number of these magnetons is connected with the internal quantum number [36]. A strong change in the magnetic moment must therefore be regarded as a consequence of a change in the quantum state. Such a change can be established, as Fayans and Joos [18c] have shown, in the process

\[ \mathrm{Fe}^{++} + 6(\mathrm{CN})^- = \mathrm{Fe}(\mathrm{CN})_6^{4-}. \]

The very change in color that occurs shows that, in this case of the combination of a cation with anions leading to the formation of a complex, phenomena of deformation take part. The magnetic properties of the components, however, are more instructive. The ferrous ion in aqueous solution, in many salts and, consequently, in the free state, is strongly paramagnetic; the cyanide ion is weakly diamagnetic, so that the complex ion should, according to the rule of additivity, be paramagnetic. Since in reality it is diamagnetic, it is necessary to assume a quantum change of the electron orbits when the ferrous ion combines with cyanide ions.

For the present, nothing more can be said with certainty about the character of this change. We shall point out, however, one view that often plays a role in the discussion of chemical phenomena from the standpoint of atomic structure. Just as the tendency of many elements to form ions was reduced by Kossel and Lewis to the tendency to form certain stable electron configurations—for example, with 8 outer electrons, as in the noble gases, or with 18 outer electrons—so also Lewis, Langmuir [9], and others expressed the view that, in the formation of complex molecules, there is likewise manifested a tendency to form certain preferred electron configurations. Thus, for example, in the formation of chlorine molecules the 14 outer electrons of two chlorine atoms are distributed between the two chlorine nuclei in such a way that each of them obtains a stable group of 8 electrons, forming a noble-gas shell, while 2 electrons in the molecule belong simultaneously to both nuclei. The idea that the chemical bond between two atoms is effected by two shared electrons plays a large role in many other investigations of the structure of molecules possessing no strongly pronounced polarity. From this point of view, together with Sidgwick (N. V. Sidgwick) [37]¹, one could explain the origin of the complex ion \(\mathrm{Fe}(\mathrm{CN})_6^{4-}\) in such a way that two electron orbits of each of the six CN-groups are so strongly drawn toward the iron by the deforming action of the \(\mathrm{Fe}^{++}\) ion that they may be considered as also belonging to the electron system of the iron. The latter possesses in such a—

¹ The author advises, however, that this explanation be treated with some caution.

case, in addition to the 24 electrons of \(\mathrm{Fe}^{++}\)¹), also 12 electrons shared with the CN groups, i.e. 36 electrons in all. This number of electrons is characteristic of the noble gas krypton, i.e. it forms an especially stable and symmetrical system; in this is to be found the explanation both of the tendency toward the formation of such a complex and of the disappearance of the paramagnetic moment of the \(\mathrm{Fe}^{++}\) ion.

LITERATURE.

1. Cf., for example, N. Bohr. Zeitschr. f. Physik 9, 1 (1922) and the volume of Die Naturwissenschaften devoted to Bohr’s theory, vol. 11, July 1923. A. Sommerfeld, Atombau und Spektrallinien, IV. Aufl. (1924).

2. J. J. Thomson, Phil. Mag. 7, 237 (1904). Die Korpuskulartheorie der Materie, vol. 6, Sammlung Wissenschaft (1908). Cf. also P. Drude, Ann. d. Physik, 14, 715 (1904).

3. W. Kossel, a) Ann. d. Phys. 49, 229 (1916), b) Zeitschr. f. Phys. 1, 395 (1920). Cf. also Naturwissenschaften 7, 339, 360 (1919), Zeitschr. f. Elektrochem. 26, 314 (1920).

4. a) M. Born, Verh. d. D. phys. Ges. 21, 13 (1919), b) M. Born und A. Landé, ibid., 20, 210 (1918). Cf. also M. Born, Atomtheorie des festen Zustandes, Leipzig, 1923.

5. H. G. Grimm, a) Zeitschr. f. phys. Chem. 102, 113, 141, 504 (1922), b) ibid., 98, 353 (1921).

6. K. Fajans, Verh. d. D. phys. Ges. 21, 549, 709, 714 (1919); Naturwissenschaften 9, 729 (1921). M. Born, Zeitschr. f. Physik 1, 45 (1920).

7. A. Reis, Zeitschr. f. Physik, 1, 294 (1920).

8. H. v. Wartenberg mit Ph. Albrecht, Zeitschr. f. Elektrochem. 27, 162 (1921); mit H. Schulz, ibid., 568. Cf. also O. Ruff, ibid., 30, 356 (1924).

9. G. N. Lewis, Journ. Am. Chem. Soc. 38, 762 (1916); Valence and the Structure of Atoms and Molecules, Amer. Chem. Soc. Monograph Series (1923). Cf. also: General Discussion of the Faraday Soc., The Electronic Theory of Valency (July 1923) and Trans. Faraday Soc. 19, 462 (1923) with works by various English and American investigators. Further I. Langmuir, Journ. Am. Chem. Soc. 41, 868 (1919).

10. P. Niggli, Zeitschr. f. Kristall. 56, 12, 167 (1921), 60, 249 (1924). Lehrbuch der Mineralogie. 2. Aufl. I. B 571 (1924).

11. F. Haber, Verh. d. D. phys. Ges. 21, 750 (1919).

12. A. Reis, Zeitschr. f. Physik, 1, 309 (1920); Zeitschr. f. Elektrochem. 26, 408, 507 (1920).

13. M. Born, Phys. Zeitschr. 19, 539 (1918). M. Born und E. Bormann, Ann. d. Physik, 62, 218 (1920).

14. J. Meisenheimer, Zeitschr. f. phys. Chem. 97, 304 (1921).

15. F. Weigert, Zeitschr. f. Elektrochem. 23, 357 (1917); Zeitschr. f. phys. Chem. 101, 414 (1922); Zeitschr. f. Phys. 14, 408 (1923).

16. P. Debye, Phys. Zeitschr. 21, 178 (1920); cf. also M. Polanyi, Zeitschr. f. Elektrochem. 26, 374 (1920).

17. K. Fajans, Zeitschr. f. Elektrochem. 28, 499 (1922); W. Frankenburger, Zeitschr. f. phys. Chem. 105, 273 (1923).

18. a) K. Fajans, Naturwissenschaften, 11, 165 (1923); b) with O. Hassel, Zeitschr. f. Elektrochem. 29, 495 (1923); c) with G. Joos, Zeitschr. f. Phys. 23, 1 (1924); d) with C. A. Knorr, Ber. d. D. Chem. Ges. 1926, cf. Chem. Ztg. 48, 403 (1924); e) K. Fajans, Zeitschr. f. Kristall. 61, 18 (1925); f) A. Holstamm, Dissertation München (1924), Chemiker Ztg. (1925).

¹) The nuclear charge of (neutral) Fe is 26.

1. a) M. Born and W. Heisenberg, Zeitschr. f. Phys. 23, 388 (1924).
   b) M. Born, Zeitschr. f. Elektrochem. 30, 382 (1924). c) W. Heisenberg, Zeitschr. f. Phys. 26, 196 (1924); H. Kornfeld, ibid., 205. d) F. Hund, ibid. 31, 81, 32, 1 (1925).

2. J. A. Wasastjerna, Zeitschr. f. phys. Chem. 101, 193 (1922); Soc. Scient. Fennica Commentationes Physico-Mathemat. I, 37, 38 (1923). Cf. also K. Spangenberg, Zeitschr. f. Kristall. 57, 494 (1923).

3. Cf. the review in A. Heydweiller, Physik. Zeitschr. 26, 526 (1925).

4. D. R. Hartree, Proc. Roy. Soc. A. 106, 552 (1924). E. Schrödinger, Ann. Phys. 77, 43 (1925).

5. W. L. Bragg, Proc. Roy. Soc. London, A. 105, 370; 106, 346, 369 (1924).

6. W. Gerlach and O. Pauli, Zeitschr. f. Physik 7, 116 (1921).

7. D. Coster, Zeitschr. f. Phys. 25, 83 (1924); O. Stelling, Zeitschr. f. phys. Chem. 117, 175 (1925).

8. Cf. the verification of Born–Landé’s theory of repulsive forces in J. C. Slater, Phys. Rev. 23, 488 (1924).

9. E. Widmer, Zeitschr. f. Kristall. 60, 181 (1924).

10. J. Stark, Jahrb. d. Rad. u. Elektron. 5, 124 (1908); Phys. Zeitschr. 9, 85 (1918). W. Biltz, Zeitschr. f. anorg. Chem. 127, 169 (1923).

11. Cf., e.g., H. v. Halban, Zeitschr. f. Elektrochem. 29, 434 (1923); H. v. Halban and L. Ebert, Zeitschr. f. phys. Chem. 112, 321 (1924); G. F. Hüttig and M. Keller, Zeitschr. f. Elektroch. 31, 390 (1925).

12. To be published shortly in Zeitschr. f. Physik.

13. B. Gudden and R. Pohl, Zeitschr. f. Phys. 16, 42 (1923).

14. C. Tubandt and S. Eggert, Zeitschr. anorg. Chem. 110, 196 (1920). C. Tubandt and H. Reinhold, Zeitschr. f. Elektrochem. 31, 84 (1925). G. v. Hevesy, Zeitschr. f. phys. Chem. 101, 337 (1922).

15. Denham, Zeitschr. f. phys. Chem. 65, 641 (1909).

16. R. Ladenburg, Naturwissenschaften 8, 5 (1920).

17. J. D. Main Smith, Chemistry and Industry (1924); Chemistry and Atomic Structure, London, 1924. E. C. Stoner, Phil. Mag. 48, 719 (1924). A. Sommerfeld, Phys. Zeitschr. 26, 70 (1925).

18. Cf., e.g., A. Sommerfeld, Zeitschr. f. Phys. 19, 221 (1923); W. Gerlach, Ergebnisse der exakten Naturwissenschaften, vol. II (1923).

19. N. V. Sidgwick, Journ. Chem. Soc. 123, 725 (1923).

20. G. Aminoff, Zeitschr. f. Kristall. 62, 113 (1925). Cf. also the article soon to appear in print: A. Sommerfeld and H. Grimm, Zeitschr. f. Physik (1926).

1. At present it is necessary to distinguish at least three kinds of quantum numbers: the so-called principal quantum number, the azimuthal, and the inner quantum numbers. ↩↩↩↩↩↩↩↩↩↩↩↩↩

2. It should be pointed out that, in view of the smallness of the temperature differences considered, one cannot assert with certainty that the heats of sublimation must in all details have the same course as the boiling points. Indeed, the latter depend, besides the heats of sublimation, also on heats of fusion, heat capacities, and chemical constants. However, the above-noted agreement of the course of the boiling points with the concept of deformation nevertheless has, in general outline, a real significance: in those cases where the differences between the heats of evaporation are so large that they can be compared for different alkali-halide salts on the basis of Wartenberg’s measurements, they show, like the boiling points, deviations from the simplest theory of undeformable ions, which the concept of deformation requires. Thus, the heats of evaporation of all four iodides of the alkali metals are almost equal (34 large calories), although the lattice energy increases from CsJ to NaJ by 20 large cal. (more than 10% of the absolute value). The heat of evaporation of CsF is 3 large cal. less than that of CsCl, and not greater, as one might expect from the course of the lattice energies. ↩↩↩