1 A Bonding Parameter

I -

Jesse Elson Delowore Volley College

Doylestown, Pennsylvania 18901 11, Rock salt and cesium. chloride

I crystal structures

At ordinary temperature and pressure 17 of the 20 alkali halogenides crystallize with the rock salt structure with coordination number (CN) of 6, while the other three (CsC1, CsBr, CsI) assume the cesium chloride structure with CN of 8. Cesium halo- genides also crystallize with CN of 6 when deposited from the vapor on cleavage surface of other crystals (I,$), while RhBr with CN of 8 can be grown from solu- tion on oriented silver films (3).

The change from CN of 8 to that of 6 also occurs on heating CsCl to 469' C, but neither CsBr nor CsI un- dergoes this transformation a t least up to temperatures within a few degrees of their melting points (4, 5). In contrast, a low temperature causes RbCl to crystallize with a CN of 8 (6).

The cesium chloride structure is more dense (for a given halogenide) than the rock salt structure, so that a change should be expected to take place under pressure. This happens for rubidium halogenides (except fluoride) a t 5,000 kg/cmz (7-ii), and for potassium salts (except fluoride) a t 20,000 kg/cm2 (IS), while lithium and so- dium salts do not change even under a pressure of 50,000 kg/cm% (15). Crystal density and compressibility will be compared with respect to the two crystal forms.

The stability of rock salt and cesium chloride struc- tures is usually related to crystal energies and radius- ratio effects. However, calculations of the crystal energies for the two possible structures for any salt show little difference in stability between the two. While correlation of radius ratio with CN is in general satis- factory for many ionic crystals, the alkali halogenides do not fit into the groupings as required by the limiting radius-ratio values. According to the simple theory the rock salt structure should be stable within the range 0.414 5 raa/rx 5 0.732. Thus LiCl (0.33), LiBr (0.31), and LiI (0.28) should have tetrahedrally coordinated structures, while K F (0.98), RbF (1.09), and CsF (1.24) should have CN of 8 or 12. These deviations indicate that the criterion of ion size should be re-examined in its relation to the crystal forms.

It is the purpose of this study to compare the rock salt and cesium chloride structures of the alkali halo- genides by relating theoretical and experimental data to the Ab value' of the 1LI-X bond (14) calculated by

' The Ab value is derived:

BE/BD = 10" (1)

where B E (single band energy) is in ergj/moleeule, BD (bond distance) is in cm, and b is the bonding parameter.

AbiAB) = NAB) - [biAd + b(BJ112 (2)

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eqn. (2). In Figures 1 and 2 the individual values of crystal energy (Born), of observed inter-nuclear dis- tance, of volume compressibility, and of crystal density are plotted against the Ab value of the M-X bond. In Figure 4 the dipole moments are similarly plotted.

Crystal Energy and inter-Nuclear Distance

The plots for crystal energy and inter-nuclear dis- tance in Figure 1A and 1B are mirror inversions of each other, which would be expected because of the depen- dence of the former on the latter. However, the larger inter-nuclear distance range for the cesium salts with CN of 8 is not reflected in crystal energy. This is also shown in Figure 3, where the range in data for each alkali halogenidc sequence is plotted as a function of the alkali's ionic radius.

The large range in crystal energy for the lithium salts correlates with a large range in their Ab values. A sim- ilar correspondence was shown for the boiling point (bp) and melting point (mp) ranges for the lithium salts. However, while the sodium halogenides have smaller

2.3

2.0

0.4 0.5 0.6 0.7 0.8 0.9 10

Ab VALUE OF M-X BOND

Figure 1. A, crystoi energy; B, intemucteor dirtonce of okoli hologenide crystals plotted against Ab wlus of the M-X bond.

A b VALUE OF M - X BOND

Figure 2. A, volume compressibility; 8, density of olkoli hologenide ~rystals plowed ogointt A6 value d lhe M-X bond.

A b VALUE OF H-X OR M-X BOND

Figure 3. Dipole moments of diotomic molecules planed against Ab value of the H-X or M-X bond.

crystal energies than those of lithium, the former salts have larger bp's and mp's. It was previously pointed out (14) that the sodium salts have the smallest Ab values of all the alkalies.

It would he expected that inter-nuclear distance (which partly depends on ion size) and Ab value would be inversely related, and Figure 1B shows such an agree- ment in each alkali sequence as a function of anion size. However, a comparison between sequences (except sodium whose odd behavior was already mentioned), shows that for any anion the Ab value increases with cation size. As a result the cesium salts have the larg- est Ab values.

Volume Compressibility and Crystal Density

A comparison between volume compressibility and crystal density in Figure 2A and 2B indicates that CsF

0.6 08 1.0 1.2 1.4 1.6 1 s

IohllC RADIUS OF ALKALI x Figure 4. Range in A, crystal energy; B, internuclear distance; C, volume compressibility for each alkali halogenide sequence plotted against ionic radius of alkoli.

with CN of 6 is denser hut more compressible than RbF or IW. However, the other cesium salts with CN of 8 are denser but less compressihle than comparable rubidium or potassium salts. Also compare Figure 3C. The smaller compressibility of the cesium salts (CN of 8) would appear to be a consequence of their crystal structure for there would he greater electrostatic repul- sion opposing compression among the ions surrounding a cubically coordinated ion than one octahedrally co- ordinated.

Evidently, for a stable structure with a CN of 8, the hond between the central ion and the coordinated ions must be able to offset the repulsive forces among the latter ions. The Ab values show that the cesium salts have the largest values followed in turn by rubidium, potassium, lithium, and sodium. The nature of the hond is not obvious, but is apparently related to bond polarity (dipole moment) as will be discussed in the next section.

In CsF the repulsion between fluoride ions restricts the crystal to CN of 6. Similarly, RhF and ICE' cannot he compressed into the cesium chloride structure which happens for other rubidium and potassium salts. The iodides of sodium and lithium have compressibilities comparable with some of the rubidium and potassium salts, but the former (as well as other sodium and lith- ium salts) do not assume a CN of 8 even under a pres- sure of 50,000 kg/cm2. This is perhaps associated with their small sizes and small bond polarities.

Dipole Moments and Ab Values

It is considered that the crystal is held together by electrostatic ion attractions, which are not all central forces, so that the presence of one ion near another af- fects the forces of interaction with a third ion (15). However, the central field model forms a good first ap- proximation for ionic crystals, so that no great error is introduced in relating dipole moments (bond polarities) of diatomic molecules to the structures of the alkali halogenides.

Volume 46 Number I , knuory 1969 / 29

In Figure 4 the dipole moments are plotted as a func- tion cf the Ab values of the bond. The hydrogen halo- genidcs are included as a comparison. It should be understood that the dipole moment is not used to in- dicate the ionic character of the bond, because there is doubt about such use of the dipole moment (16).

It is recognized that polarizability, or the ratio of dipole moment to the field producing it, is a measure of how easily the atom or ion is distorted, and that polarizability is proportional to the volume of the atom with large atoms being easily polarized. The hydrogen and alkali halogenides have permanent dipole moments, which result from the mutual interaction of the cation and anion in each molecule. It would therefore be ex- pected that the combination of different cations with the same anions would reveal a size effect.

Examination of the halogenide sequences in order from hydrogen to cesium shows a definite cation size effect, resulting in increased polarizability of the mole- cules containing large anions when associated with large cations. As a result the cesium halogenides with CN of 8 have large dipole moments, which correlate with their large Ab values.

Crystal Siruciures of Other Salts

The ammonium halogenides (except fluoride) behave similarly to the alkalies, with the ammonium salts crys- tallizing in the cesium chloride structure below a tran- sition temperature, above which they assume the rock salt structure. Ammonium fluoride crystallizes in the

wurzite structure with the nitrogen atom forming N- H-F bonds to its four neighbors arranged tetragonally around it (17). Ordinary ice has essentially the same structure.

The rock salt structure is also found in silver halo- genides, and in oxides and sulfides of the alkaline earths, and many other divalent metal ions, oftcn with radius ratios far outside the predicted limits. Whether or not the present concept is applicable to these crystals is not known since experimental data are not yet available to calculate the Ab values of the 14-X bonds.

Literature Cited

(1) SCHULZ, L. G., J . C h m . Phys., 18, 996 (1950). (2) SCHULZ, L. G., A d a Cryst., 4, 487 (19.51). (3) Sc~ur.z, L. G., J. Chem. Phgs., 19, 504 (1952). (4) WIGST, C. D., 2. Krist., 88, 94 (1934). (.5) JOHNSON, J. W., el al., J . Am. Chem. Soe., 77, 2734 (1955). (6) Wn~xr.:n, G., AND LIPPERT, L., Z. Phys. Chem. B, 33, 297

,,"?C, \.I,Y",. SLITISX, J. C., Phys. Rm., 23, 488 (1924). ~ R I D G M A N , P. W., Z. z<risl., 67, 363 (1927). PAULING, L., Z. Krist., 69, 35 (1928). Jncons, R . R., P h p . Rev. 53, 930 (1938). Jacom, R . R., Phljs. Reti., 54, 468 (1938). BRIDGMAN, P. W., P h y ~ . Rev. 55, 237 (1940). WELLS, A. F., "S1ru~twa.I Inorganic Chemistry," (3rd ed.),

Oxford Universit,y Press, London, 1962, p. 336. ELSON, J., J. CHI:M. EDUC., 45, 564 (1968). S I . . \ T F ~ , J. C., "Quantum Theory of Mxtlcr," MeGraw-

Hill, New York, 1951, p 233. WISLLS, A. F., op. ci l . , p. 33. PLUMI~, 1:. C. A N D HOIINIG, I). F., J . Chem Phg~. , 33, 947

(1955).

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