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246 PHILIPS TECYNICAL REVIEW VOL." 15, No. 8-9
LATTICE IMPERFECTIONS AND PLASTIC DEFORMATION IN METALS
1. NATURE AND CHARACTERISTICS OF LATTICE IMPERFECTIONS,NOTABLY DISLOCATIONS.
by H. ,G. van BUEREN
. Not more than 30 or 40 years ago our knowledge of the physical properties of metals was basedalmost entirely on experience. After the first world war a change come.brought about by agradual expansion in the s,tudy of the physics of metals, the object of which was to justifytheoreticallv the observed characteristics. Recently, much progress has been made in the fieldof plastic properties of metals. The new conception, that the plastic d~for1]lationof materials isintimately connected with the occurrence and concentration of imperfections in the regularstructure ofthe atoms, that is, oflattice imperfections, has beenfound to be very fruitful. It canbe applied not only to metals, but also to other materials.
At the beginning of this century it was still thegeneral belief that the more important physicalproperties of crystalline substances could heexplained exclusively in terms of the periodicarrangement of the component atoms. It wasgenerally thought that any defects in that structure(irregularities in the crystal lattice) had but littlebearing on the characteristics, and these irregu-larities were accordingly disregarded; the crystallattices were held to he perfect.
Although this standpoint originally met with con-siderable success, e.g. in the explanation of X-raydiffraction patterns and in the theories of cohesionbetween the atoms in crystals, it was soon foundthat there were many phenomena which woulddefinitely not answer to theoretical considerationson that basis. Particularly in the study of transportphenomena such as the conduction of heat andelectricity and diffusion, insurmountable diffi-culties were encountered.The first and most important step towards a
better understanding of, these phenomena can besaid to have been the recognition of thermallatticevibrations. The atoms at the lattice points of a,crystal vibrate, practically as harmonic oscillators,about their position of equilibrium, and the energywith which they do this, and hence the ~mplitudes,increase considerably with the temperature.
Although this conception led to important addit-ions to the theory of certain transport phenomena,many effects were still without any satisfactoryexplanation, in particular, those which relate tothe mechanical properties of crystals. Ultimately, 'therefore, it was found necessary to take into con-sideration other imperfections in the crystalstructure. To enter into a general discussion on the
influences of lattice imperfections upon the phy-sical and chemical properties of crystals, would notbe practicable within the scope of this article. Weshall therefore limit our discussion to two articlesdealing with some of the phenomena connectedwith the plastic deformation of metals. For a reviewof the many other domains in which lattice defectsare of interest, the reader may refer to a recentarticle in this Review by G. W. H.athenau 1), andto the comprehensive survey by F. Seitz 2).
Some phenomena related to the plastic deformationofmetals
Microscopie examination of the surface of metalswhich have been polished and subsequently de-formed, usually reveals a pattern of fine, more orless straight lines (fig. la). The more the metal isdeformed, the more clearly these so-called slip linesbecome visible and the greater is their number. Theorientation of these lines appears almost invariablyto correspond to the planes in the crystal in whichthe atoms are most closely packed. This relationshipis found to be the most marked in metals with theclosest packed crystal structure. In metals havingbody-centred cubic lattices which are not packedas closely as possible, the slip lines are somewhatirregular, . but the relationship between the sliplines and the crystal planes still remains.
Examination ofthe slip lines under high magnifica-tion by means of the electron microscope, shows thatwhat appear to he single lines when seen with lowermagnification, are in many cases groups of some
1) G. W. Rathenau, Philips tech. Rev. 15, 105-113, 1953(No. 4).
2) F. Seitz. Imperfections in nearly perfect crystals. JohnWiley, New York, 1952, p. 3-76.
FEBRUARY-MARCH 1954 LATTICE IMPERFECTIONS IN METALS 247
Fig.1.a) Micrograph of the polished surface of a metal single crystal subjected to 7%deformation. Magnification approx. 200 X (R. \V. Cahn, J. Inst. Metals 79,129-158,1951).b) Slip band on the surface of a polished, deformed crystal as seen under the electronmicroscope. Magnification 25,000 X (A. F. Brown, Advances in Physics, 1, 421-479, 1952,No.4).
tens to hundreds of adjacent lines (fig. Ib), whichmay be termed slip bands. Single lines are seen aswell, however.A study of the slip lines or bands has revealed the
fact that these are in effect "steps" in the surfaceof the metal, of which the height may vary fromsome tens to some thousands of times the atomicspacing. The conclusion to be drawn is clear, viz.that in the deformed metal, translations take placealong certain crystallographic planes whose orien-tation corresponds to the direction of the slip line.
_1 77977Fig. 2. Diagrammatic representation, on a highly exaggeratedscale, of slip in a metal crystal. g slip planes; T shear stress.
This mechanism is sketched in jig. 2, which refersto simple slip lines and is, of course, drawn on anexaggerated scale. This deformation mechanism,which appears to be of a very universal nature, isknown as gliding or slip; the lattice plane alongwhich the slip takes place is termed the slip plane,
and the direction of the translation, the slip direction.The slip plane and direction together constitute theslip system.The theoretical critical shear stress Tcr, that is, theminimum shear stress necessary to produce a sliptranslation of this kind, is of the order of 0.1 G,where G is the modulus of rigidity, or torsionalmodulus of the material.
This result is obtained in the following manner (videFren keI 3.
Take the case of two neighbouring rows of atoms in a simplecrystal. Let a denote the spacing of the atoms in theundistorted condition. The force required to move the oncrowan infinitesimal distance over the other depends upon thedisplacement that both rows have already undergone. In theundeformed state, which is the state of equilibrium, this forceis zero. Each time the rows are displaced an integral numberof times a/2 from the undeformed state, an equilibrium stateis restored, as a symmetrical configuration of the lattice isagain reached. It would appear to be a reasonable assumptionthat the relationship between the shear .stress (T) and therelative displacement (x) might be approximated by a simpleperiodic function:
T = k sin 2nx .a
With only a small displacement this becomes T = k.2nx/a.In this case also Hooke's law applies, which states that:
T = Cx],
From this, k = G/2n; hence:
G . 2nxT = 2n S111 -;;-
If T is larger than G/2n, it follows from this formula that thedisplacement x of the atoms is unrestricted and slip will occur.Closer investigation yields a value for the theoretical criticalshear stress slightly lower than G/2n, although still of the orderof 0.1 G.
3) .J. Frenkel, Z. Physik. 37, 572, 1926.
24,8 PHILIPS' TECHNICAL REVIEW VOL. 15, No. 8-9
For most metals, G lies between some thousandsand some ten-thousands of kilograms/mm, fromwhich a theoretical critical shear stress of a fewhundreds or a few thousands of kilograms/mm''follows. It is a well-known fact, however, that metalscan be very much more easily deformed than wouldappear from these values. The ,observed criticalshear stress of well-annealed single crystal occursbetween 0.1 and 10 kgfmm2;' annealed polycrystall-ine metals yield somewhat higher values but stillvery much less than the theoretical shear stress.
To explain this ease of deformation, it was postu-lated that a particular kind of lattice defect, namelydislocations, occur very frequently in every crystal.It was very soon apparent that such dislocationsdo play a, dominant rle in the process of deforma-tion of a metal.
We have referred above to the critical shear stressof well-annealed materials. The annealing mini-:mizes the, consequences of any previous deforms-tions which would otherwise manifest themselves,for example, by the increase which occurs in thestress required to deform a metal as the deformationitself increases (fig. 3). This effect is known as workhardening (it does' not occur in all materials;substances such as pitch, for example, undergo nowork hardening). A severely deformed and un-annealed metal may have a critical shear 'stressmany tens of times higher than that in the annealedstate.
Fig. 3. Diagram showing the relationship between the defor-mation 6 and the shear stress -c in a pure metal. The straightpart at the commencement of the curve represents the elasticdeformation. When the critical shear stress -Ccris exceeded,plastic dformation sets in, this being accompanied by strainhardening, as. a result of which the characteristic assumes aparabolic form (in cubic metals). In practiee, irregular curvesare often encountered, but the general form remains the same.
As we shall see presently, work hardening inmetals is attributable mainly to the mutual inter-action of the dislocations associated with the defor-mation.The extent to which a metal can be deformed is
dependent not only on the previous deformation;
variations in the temperature, will also affectthe ductility, albeit to a relatively small degree.Thus, materials which are brittle when cold arenearly always ductile at elevated temperatures.Fo