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The texture formation process, dislocation structures, and deformation bands observed in rolled and cross rolled [100] (001) oriented iron crystals have been interpreted from the viewpoint of fundamental dislocation behavior and the properties of low‐angle dislocation boundaries. Full agreement between theoretical expectations and published observations was obtained.

The prototype of all dislocation cells composed of dislocations with two mutually perpendicular Burgers vectors is the terminated quadrupole. It consists of two similar, mutually perpendicular, rectangular glide dislocation loops which interpenetrate such that their edge dislocation segments are parallel to each other and that each of the two pairs of like‐handed screw dislocation segments form a cross of fourfold symmetry. The stress components of the terminated quadrupole have been computed numerically and have been presented in the form of contour maps in, or parallel to, the midplane of the quadrupoles as well as in a cut parallel to the prism axis of the quadrupole. It is found that the intensity of the stresses falls with distance from the cell as 1/r5 for medium short or squat quadrupoles, and as 1/r4 for very elongated quadrupoles.

Infinitely tall dislocation cells such as may be constructed from assemblies of similar dislocation multipoles are investigated. The long‐range stress fields of these are shown to be the same as those of the corresponding dislocation multipoles, while the short‐range stress fields are those of the corresponding infinitely extended tilt walls, except for disturbances in the immediate vicinity of corners. It is shown that the stresses of a cell of given shape, cross‐sectional area, and angle of relative misorientation, decrease in magnitude the more closely the dislocations in its walls are spaced. In the limit of continuous dislocation distributions all cell stresses vanish identically. Terminated cells are briefly considered, and a method for the simple construction of two‐grid tilt boundaries, composed of parallel edge dislocations involving two arbitrarily oriented Burgers vectors, is presented.

Using moire fringe pattern techniques, elastic strains were measured in small gold nuclei (10–40 A in radius) prepared by evaporation in ultrahigh vacuum (10−8 Torr) onto MoS2 substrates. The variation of the elastic strain with the radius and angle of misalignment of the nuclei was found to be consistent with the theories of van der Merwe, Cabrera, and Jesser and Kuhlmann‐Wilsdorf.

An analysis of the experimental evidence in Part I of this paper clearly indicates that for the case of copper crystals, striations in low‐amplitude fatigue are suppressed by strong slip on intersecting slip planes, including the cross slip system, but are formed by interactions between dislocations on the primary glide system with dislocations on another glide system sharing the same slip plane. This observation is in obvious contradiction to any theory based on cross slip of the primary dislocations alone, since cross slip combined with glide and climb allows every conceivable rearrangement of the dislocations but cannot change the Burgers vectors. A model for the mechanism of striation formation is therefore developed which takes into account that dislocations with at least two different Burgers vectors on the primary slip plane cooperate, according to the experimental evidence. It is proposed that striations consist of sequences of ``cells,'' forming pairs of dense dislocation networks parallel to the primary slip plane, separated by narrow channels almost free of dislocations and debris. The networks consist of almost equal surplusses of dislocations with the three ½ 〈110〉 Burgers vectors in the active {111} slip plane, representing more or less well‐developed twist boundaries with a greater or smaller neutral filling of other dislocations and debris. Once striations are formed, glide becomes concentrated in them and hardening proceeds at a much slower rate or comes to saturation. Extrusions and intrusions can arise in at least three different ways and it is believed that these mechanisms act singly or in combination, depending on conditions. It is shown that the model is in good accord with previous evidence. In particular, dislocation structures associated with striations in fatigued copper, observed by Laufer and Roberts, are very close to those described. A few simple numerical relationships are derived from the model which could be employed to test the theory presented. Much of the theory is believed to be applicable also to dislocation behavior in unidirectional work hardening of fcc single crystals.

A theory for the effect of stresses on vacancy concentration in simple metals is presented in which the variation of mechanical energy, electronic energy, and vibration frequencies with stress is taken into account. The vacancy is treated as a point of dilatation and a local soft spot in the crystal with the result that the mechanical energy consists of a term representing the work done by the volume of relaxation against the internal pressure, plus an additional term which is quadratic in the stresses. The electronic energy term is computed from the quasifree electron model based on phase‐shift analysis, giving a term proportional to the dilatation. The variation of atomic frequencies with strain is treated by a generalized Gruneisen model which shows that the entropy of vacancy formation is proportional to the dilatation.The internal work and electronic terms in the energy of interaction of a vacancy with a stress field decreases the vacancy concentration in dilated regions and increases it in compresse...

Numerical data and curves for the shear stresses and energies of ½ 〈110〉, {111} edge dislocations in elastically anisotropic fcc and diamond‐type materials are presented, based on a previously published analytical solution, to supersede those contained in the earlier paper.The corrected data are compared with data by Foreman, by Van Hull and Weertman, and by Seeger and Wobser, and are shown to be reliable.

The theory developed in Part I is applied to the interaction energy between vacancies and dislocations for the case of elastic isotropy. In the elastic stress fields of dislocations, outside the dislocation cores, the vacancies are attracted into regions of compressional strain, as expected from the analogy with the Cottrell interaction between dislocations and substitutional atoms of a size smaller than the matrix atoms. Within dislocation cores, strains are much larger than in the elastic regions, but stresses are only moderately higher. Consequently, the two contributions to the binding energy which depend on normal strains rather than on normal stresses, namely, the electronic interaction energy and the change in the vibrational entropy, are much more important within cores than outside them and repel vacancies from regions of compressional strain. With the best possible estimates of core stresses and strains it is found that the electronic term is dominant in the cores at low temperatures, and the en...

Frank's vector formula defining low‐angle boundaries is rewritten into six independent scalar equations which can be represented in the form of three simple two‐dimensional vector diagrams. These diagrams facilitate the discussion and construction of low‐angle boundaries, and in particular allow to construct four‐grid boundaries due to glide dislocations on arbitrary planes.

The stresses of infinite edge dislocation multipoles are investigated with the aid of a B5500 computer, and contour maps are obtained using the line printer. These multipoles consist of infinitely long, parallel edge dislocations of same strength, arranged so as to define a prism whose cross section is a regular polygon and with their Burgers vectors in radial orientation. As will be shown in Part III, multipoles are the prototypes of dislocation cells containing the same Burgers vectors, independent of cell shape, in the same way that the quadrupole, discussed in Part I, is the prototype of all cells composed of dislocations involving two mutually perpendicular Burgers vectors. It is found that the stress fields of τrr, τφφ, and τrφ all exhibit 2N similar leaves of alternating sign for a multipole of Nth order, except that τφφ of the dipole has eight rather than the expected four leaves. The magnitude of the stresses falls as 1/rN at large distances, except that τφφ of the dipole falls as 1/r4. Lastly, t...

The results are reported of an investigation of quenched‐in prismatic dislocation loops in super‐purity aluminum. Some new effects have been observed: in particular, that loops tend to be grouped in clusters containing a surplus of loops of one orientation; that more than four loop orientations are realized; and that often pairs of similarly oriented and similarly shaped loops are present in the quenched material. It is concluded that vacancies aggregate into three dimensional clusters, containing from a few to a few hundred or even thousand vacancies, before being converted into prismatic loops.

Extending the investigations of Papers I–III, infinitely tall ``hybrid cells'', i.e., dislocation cells derivable from mixtures of different orders of multipoles, are considered. A symbolism is developed aiding in the analysis of such cells. It is shown that at different distances the stress fields of hybrid cells are dominated, in turn, by the multipoles composing them. For example, a cell that may be regarded as an assembly of dipoles, tripoles, and hexapoles exhibits a stress field that has dipole nature at the farthest distances, has tripole nature in an intermediate range, and has hexapole nature at the closest distance just beyond the true short‐range stress field of the cell walls. The latter is the same as that of the corresponding infinitely extended boundaries, as was shown in Paper III.

Analytic solutions for the shear stress and energy factors of three basic types of edge dislocations in cubic anisotropic crystals have been published previously based on the general solution of Eshelby, Read, and Shockley. Naming the slip plane and Burgers vector in order, the dislocation types referred to are {010}, 〈100〉; {110}, ½〈110〉; and {001}, ½〈110〉. The most important kind of edge dislocation in fcc metals and diamond‐type crystals, however, is of type {111}, ½〈110〉, belonging to by far the most important slip system. This problem has previously been considered by Seeger and Schock. In the present paper, analytic solutions are derived for the shear stresses and energy factors of the {111}, ½〈110〉 edge dislocation and are evaluated numerically for the cases of aluminum, α‐brass, copper, gold, lead, nickel, silver, thorium, diamond, germanium, and silicon. The results are compared to those obtained from isotropic elasticity theory and an approximation introduced by Aerts, Delavignette, Siems, a...

Gold and silver single-crystal foils of uniform thickness have been produced by electrolysis. The preparation of gold foils involves three steps: the evaporation of silver onto cleaved mica, the electrodeposition of gold on silver, and, lastly, the stripping of the gold foil by dissolving the intermediate layer of silver. Silver foils are prepared by (1) evaporating silver onto cleaved mica, (2) electrodepositing silver on silver, and (3) mechanically stripping the silver foil.