PLBSTICITY OF S I S G L E (‘RYPTALS’ BY WHEELER P. D B T E Y
Plasticity, as applied t o single crl-stals has to do with the slipping of planes of atoiiis upon adjacent planes. It ia related t o ductility, for in ordw to he ductile. a substance must he plastic in addition to having sufficient strength to keep it frofii breaking froin the strain of pulling it through a die. The following discussion is strictly liinitetl to the plasticity of single crystalq, thus avoiding those complications incident to grain size which make the properties of polycr? stalline materials 40 often different from those of the corresponding single crystals. The results of esperiiiient may he generalized by the statement that the plastic. ductile. and malleable inetals such a s copper, silver. gold aluniinnni, et?., have face-centered cubic structures, 2nd that the metals which are relatively non-plastic, such as chromiiini and tungsten, have body-centerec I cubic structures. This rule is not, however, of universal application, for iron is reasonabl?- plastic and has a hod\--centered cubic structure. The reason for this exception is not known-it may be caused by some peculiar configuration of the valence electronq of iron. Single crystals of metals, such a $ zinc, which are ductile in the cold only in certain directions through the crystal, have a “hemponal close-packed” structure. The work of I I a r k , Polyani and Schniid? and others makes it appear that, other experimental conditions being strictly the same, mechanical working of the metal causes slip along those planes in the crystal which have the maximum atomic population. It is a characteristic of the geometry of crystal structure that the planes of inasiriiuin atomic population are those which art’ furthest apart froin each other. This means not only that the atoins in an individual plane are packed so closely together that they can hold to each other quite strongly. so that these individual planes of atoms are quite strong, but also that, because of the distance from any one of these planes t o its nmrest similar plane, the interlocking of atoms from plane t o plane is relatively weak, so that each plane can glide over its neighbor. I n the face-centered cube. the I I I (octahedral) planes are those of greatest atomic population. There are four families of I I I planes symmetricall?placed about 7 o . j degrees from each other. Each atom is symmetrically placed with respect t o six other atoms in adjacent I I I planes, for there are three atoms which form an equilateral triangle in the plane immediatel>above, and three which forni an equilateral triangle in the plane immediately helow. This ineans that each atom is directly below the center of a triangle of atonis of the 111 plane nest above it and is directly above the center of a Paper presented a t the Plasticity Symposium, Lafayette College, Oct. 17 (1924). ‘ Z . Physlk. 12, j8 (1922).
triangle of atoms of the I I I plane nest below it,. This close packing prevents loss of cohesion during slip. Thp I O O planes have nearly as large an atoniic population and are, therefore, almost as far apart f r m each ot,her as the I I I planes. There are three faniilies of I O O (cube face) planes mutually 90 ticg e e s t o each other. Each atom in the I O O plane is equally spaced from four atoms in the adjacent plane below. The face-centered cube is, therefore, well supplied with both primary and secondary Flip planes. and since both of these families of planes have high orders of symmetry, a face-centered cutie can hardly escape being plastic in almost any orientation.
If the axial ratio of a hexagonal close-packed crystal is preater than 1.7~3.; the 00.1planes are the planes of greatest nt,oInic population and should. therefore, be the planes of primary slip. This is the case with zinc, whose axial ratio is 1.86. Each atom in an 0 0 . I plane is equally spaced from three atoiiis jn the t8woadjacent planes much as in the case of the face-centered cube. R u t the 00.1planes are the basal planes of the hesagonal prisms. There is, therefore, only one direction through a zinc crystal which is the opt'iniuni direction for mechanical worliing. The planes of nest highest atomic population in zinc are the 10.0planes. These are the faces of the hesagonal prisms. There are three families of 10.0planes. all parallel to the z-axis and all 1 2 0 degrees from each other. The atomic arrangement is not as favorable t o slip without loss of cohesion as in the case of the 00.1 planes. for a given atom is equally spaced between four atoins in t,he adjacent on one side of it. and between only two atoms in t8headjacent, plane on the other side of it. There will be! therefore, greater loss in cohesion during slip along the 10.0 planes of zinc. \Ye should expect that, cont.rary t o the common opinion, slip along the 10.0planes of ziiic will show different characteristics from slip along the 00.1 planes. Iiistead of nearly every plane sliding over its neighbors we should expect t,he 10.0planes t o slip in tilocks. If a single crystal of zinc is stretched beyond its elast,ic h i i t we should expect the etch figures to show block-slip along the 10.0planes t o a very much preater extent than along the 00.1 planes. I n a private communication some time ago to Dr. S.L. Hoyt of this laboratory. 0. E. Koiiiig reported t,hat he has found this t o be actually the case. I t is a pleasure t o acknowledge N r . Kornig's permission t o mention his esperiinental results which coincide so well with the theoretical deductions. If the axial ratio of a hexagonal close-packed c tal is less thaii 1 . 7 3 5 (as is t,he case with magnesiuni) t8heatomic populatioii of the 10.0planes will he higher t8hanthat of the 00.1 planes. Primary slip will, therefore, occur along the 10.0 planes. Since t,here are three families of 10.0 planes polycryst'alline magnesium should be a little more plastic than zinc. Becaus: of the unfavorable arrangement of atoms in t,he 10.0 planes of the hexagonal closepacked lattice, and since it has only three fanlilies of planes for primary slip and one for secondary slip, magnesiuiii should be iiiuch less plastic than facecentered cubic metals like copper or aluininuni, which haye a favorable ar-
PLASTICITY O F b I S G L E CRTSTALY
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rangement of atoms, anti four families of planes for primary slip, and three for secondary slip. These conclusions are in accord with the results of practical experience. I n this connection cobalt is of peculiar interest. Pure cobalt is of only iiioderate ductility, and therefore of only moderate plasticity. while cobalt containing traces of impurities is fairly ductile. Hull' showed that pure cobalt may contain some face-centered cubic crystals, but that it usually crystallizes in a hexagonal close-packed lattice. Traces of impiirities alTvays make cobalt take the face-centered cubic structure, trhw giving a rational explan:+ tion of the ductility of impure cobalt. ;1 consideration of the body-centered cubic ]attic? shows it to hr an inherently non-plastic structure. The planes of highest atomic population, anti. therefore, those which are furthest apart. are the I I O planes. The atomic arrangement is such that each atom in a I I O plane is equally spxcccl from t u o atoms in the adjacent plane a h o w it and from two other ntoin- in the adjarent plane below it. This means that slip along the I I O planes is ~ i c c c s ~ i r i l y accompanied by very p e a t loss in cohesion. The crystal n-ill tend to crack during mechanical working. The planes of liest hig1ieF.t atoinic population are the 100 planes. Thc atomic arrangement, is here more favorable to slip. for each atom is equally spaced between four atom. on each side of it. but it is of little use to have planes of secondary slip with good cohesion if cracking occurs along the planes of primary slip. The outstanding exception to all this is iron. Iron is body-centered cubic, and yet it is rczsonably ductilt.. Rut this is not the only way in which iron is an exceptional metal. Its iiiapiietic properties ?re such as t o give rise t o the term "ferro-iiiagIietic," I t is the only knonn metal which, when suficiently heated, changes froin a tmdj centered to a face-centered cubic lattice. I t is quite likely that tho cxceptional behavior of iron during mechanical working is tied up in soinc way with the underlying causes of its other exceptional properties. Substances which crystallize with a simple cubic structure have prartically no plasticity. An example of this sort of structure is ordinary SaC'l. The rhombohedron of calcite has the same sort of structure except that the "cube" is deformed in the direction of its body-diagonal. I n the siiiiple cuhic crystal the 100 plane (cube face) is the plane of highest atomic population, and is therefore the plane of primary slip. I n these planes. each atom can only hold to one atom in the plane above it and one in the plane below it. The I I O plane (the dodecahedral plane) is the plane of second highest atomic population. Here too, each atom can only hold t o one atom above and one below. The simple cubic structure, therefore, tends t o crack apart upon the application of very small forces,-it is the least plastic of all the structures we have considered. It is said that the only way a sodium chloride crystal can be deformed at room temperature is t o bend it while it is immersed in fresh water. Then if the bending is done so slowly that the rate of propapa' P h y s . Rev.
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W H E E L E R P. D A \ X T
tion of the cracks is less than the rate of solution in the water, the crystals may he successfully bent It ~ o u l c seem l froin the ahove that the plasticity of single crystals is intiinetely connected n i t h the rriarshalling of their atoms in space. and that, iii gener: ', the relative plasticities of two cr:.qtalb may he precticte,l from a consideration of their crystal s t t u c t r m . K f o e n i r h L o h i a f t i il Grne7al Elect) i c C ' o r i i i ( i r i y S'cheriectndy, ,\-el( I 0 1 i,
