3) In contrast to the ccp pattern, the bcc stlucture is concentrated on the left side of Tahle 2. This means the bonding makes use mainly of d and s orbitals with little p orbital involvement. 4) The hcp structure is scattered in Tahle 2. The most prominent groups having this structure are Sc and Ti families configurations). Two Sets of Directed Hybrid Orbitals. Both Pauling (86, 40) and Ganzhorn (41) have suggested a correlation between the crystal structures and some properties of the hybrids which can he formed from the available orbitals in the metals. Several results of this latter type suggest that the metallic bond has more definite directional properties than is usually imagined. This suggests a directional character of the bonding in which, apart from the neighbors in its own layer, an atom has six neighbors at the corners of a trigonal prism in the hop structure, and a t the corners of a trigonal antiprism in the ccp structure. Of the three typical metallic structures, the ccp and bcc structures have a centrosymmetric arrangement of closest neighbors around a given atom. In the hcp structure, the six close neighbors of an atom in the basal plane are arranged ceutrosymmetrically, but the remaining six neighbors in the up-down direction occupy the corners of a trigonal prism, and are not centrosymmetric. In viewing close packing, two types of directional character can therefore he assumed. One is in the plane of the packing layers, the so-called basal plane. The other is toward the neighbors of the planes above and below the basal plane. If the bond type used in these two directional sets are the same, normal ccp or hcp structures should be obtained. Otherwise, deviation from those normal structures would be observed. For instance, in the hop structure of zinc, its axial ratio differs from 1.633, the "ideal" value, by more than 10%. I n interpreting this abnormal phenomenon, Wallace (48) proposed that there is a system of covalent bonds in the basal plane resulting from dp2hybrids orbitals. Value of a B r w d View of Close Packing
The structures of the elements, using the PTOT notation, are summarized in Table 2. Many of these structures are close-packed in the strict sense, but even many metals would he excluded without hroadening the concept to include the 3.2PTOT (hcc) structure. This broadening of the concept includes the uncommon
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simple cubic (3PO) structure. Further extensions are useful to include distorted structures (3P1, 6P01, etc.) and the unusual double layer structures 2ID, 2IP, and 3IP. It is instructive to note the changes in structure or in the extent of distortion within a periodic family as indications of changes in bonding. The broader views of close packing make it possible to visualize comparisons even though there are changes of structural types. literature Cited (1) (2) (3) (4)
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(.5.)
. . (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23) (24) (25) (26) (271 (28) (29) (30) (31)
DONOHUE. J . . CARON. A,.
ond do". 1964.. HOLTGREN. R., AND WARREN. B.E.. Phya. RN.. 4 7 , 8 0 8 (1935). S ~ o x nH.. . 2 . Anow. Allg. Chem., 242,138 (1939). Hum. A. W., Phys. Rcu.. 20, 113 (1922). HABBEL. O..ANDMAR=,H.. Z.Phys., 25,317 (1924). B E ~ N A S . J. D.. P r o e . ~ o y .or.. A106:749 ( 1 9 2 4 ) . BACON. G. E.. A d a Cwstalloyr.. 3 , 3 2 0 (1950): 4 . 5 5 8 (19511. BOTENKERK. H. P., BUNDY, F. P., HAG'. H. T..STBOW.,H. M., *ND WENTORP,R. H. J ~ . . N a t u r e184,1094 , (19591. Enaun. 8..A N D ALEXANDER, L. E.. Natwa. 195,765 (1962). B u ~ o rF. . P.. J . Chcm.Phus..38.631 (1963). S~no~o H., M . , AND H A N N ~ X A R. N , E., J . Chem. Phys., 4 6 , 3668 (1967). D E C K ~ B. R , F., A N D KABPER.J. 8.. Acts Cry8lallogr.. 12, 503 (1959). G n ~ n ~3u .., Moons. A,, AND RATNOR.G . V . , J . Inat. Melala, 8 4 . 86 (1955). WYOROPP. R . w. Q., "Crystal Structures" (2nd e d . ) . Intemaienoe, New York, 1963, Yol. I. B ~ n n ~ Cn. 8.. . Phys. Rm.. 110,1071 (1958). P A ~ L I IN ,.,~J . Amer. Chem. Soe., 6 9 , 5 4 2 (1947). Pm'mo. L., PVOC. Roy. S0c..A196.343 (1949). HUME-ROTAERT, W.. Ann. Rep. Chcm.Soc.. 46.42 (1949). ALTMAN, S. L., COULSON.C. A,. AND HUME-ROTRERI, W., P I G ROY. Soc.. AZ40.145 (19571. Z=nsa.C.,Phva. R N . , 81.440 (1951). Consrss. .4. J.,Ndurc. 211,512 (1966). Sau~r,.C . G . . A N D W A ~ A N E.. 0.. in "Solid State Physica" (Edilora: SEITZ,F.. a m T u n u x m ~ D , . ) . Academic Press, New York, 1956,
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V",
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( 3 2 ) Exom. N.. Powdm Mat. Bull.. 7 . 8 (1954). (33) BREWER,L., in "Phase Stability in Metala and Alloya" (Editors: Ronm N . P.. ~ T R I N G E R .J.. A N D JAFIEE. R. I.),MeGrsw-Hill.New York,
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Ewam~.N.. Acta M d . . 15,557 (1967). H n x ~ - R o ~ m sW u ,. .Pwgr. Mate?. Sci.. 13. 229 (1967). BREWER, L.,Acta Met.. 15,553 (19671. Bnrwm. L..Science. 161,115 (19681. BREWER, L., "Prediction of High Temperature Metsllio Phaae Diagrarna" in "High-strength Materials" (Editor: Z*cnnr, V.) John Wiley, New York. 1965. HUME-RO~HERY. W., Act. Met.. 13,1039 (1965). P n u ~ m aL., . Phys. Rm., 54,899 (19381. GANZHORN. K.. 2. N d ~ v / o v 9 ~ h8 A . . , 3 3 0 (1953). WAI.LICE.W. E., J . Chem.Phya., 23,2281 (19551.
