T. Spreng, J. B. Vander Sande, and J. Weertman, SP317, pp. 71-82 (Dec. 1970).

Key words: Dislocation dynamics; interface dislocations; supersonic dislocation.

This paper examines the problem of a dislocation moving on an interface separating two isotropic elastic media that have differing elastic constants and densities. This problem has application to the phenomenon of diffusionless transformations. Solutions are found for moving screw dislocations, gliding edge dislocations, and climbing edge dislocations. It is assumed that the dislocation velocity lies in either the subsonic, the transonic, or the supersonic velocity region. We have generalized the analysis that was used in a study of the elastic displacements and stress field of subsonic, transonic, and supersonic dislocations moving in an ordinary elastic medium. The results given in the present paper are formally identical to those obtained in that simpler analysis.

Internal stress and the incompatibility problem in infinite anisotropic elasticity, J. A. Simmons and R. Bullough, SP317, pp. 89-124 (Dec. 1970).

Key words: Anisotropic elasticity; dislocations; Green's tensor; incompatibility; internal stress; source kernels; stress functions.

Using the language of integral projection operators, the linear elastic distortion field of an infinite anisotropic body is decomposed into its internal and external components. The kernel of the external projection operator is identified as the elastic field due to force dipoles while that of the internal field corresponds to internal distortion fields due to displacement dipoles.

By integration of the projection operator for the internal distortion field, an alternative description for internal distortion fields in terms of dislocations is given. The Mura-Willis formula as well as the distortion field due to a rational dislocation element (in the sense of Eshelby and Laub) for an anisotropic body are then obtained as integrals of the basic displacement dipole kernel for internal distortions.

Further integration of the displacement dipole kernel provides a description of the internal distortion field due to a rational incompatibility element. The general formula for the stress function due to an incompatibility distribution in a general infinite anisotropic body is then given and shown to reduce to the formulation of Kröner for isotropic bodies.

Finally, explicit methods to compute kernels for internal distortions due to incompatibilities are given and discussed. Series representations of the elastic Green's tensor for cubic media, D. M. Barnett, SP317, pp. 125-134 (Dec. 1970).

Key words: Anisotropy; cubic materials; elasticity; Green's tensor.

Two representations for the cubic Green's tensor components as power series in the anisotropy factor w=1 – (C11 C12)2C44 are developed, and first order corrections of anisotropy to the Green's tensor and to the interaction energy between two "mechanical" point defects are calculated. It is shown that the best successive approximation scheme is that which constructs the zeroth order (isotropic) approximation to the Green's tensor by identifying the Lamé constants A and μ as λ=C12,MC44.

Some problems involving linear dislocation arrays, N. Louat, SP317, pp. 135-146 (Dec. 1970).

Key words: Dislocation pileups; dislocations-elasticity; phase boundaries.

Muskhelishvili's inversion formulae for singular integral

equations are shown to be special cases of a more general result which is then employed to deal with two types of problems. In the first we consider the distribution of dislocations in a double periodic array of screw pile-ups in an arbitrary stress field. The second type is concerned with screw pile-ups terminating at phase boundaries, again for arbitrary stress fields.

Some recent results on dislocation pileups, J. C. M. Li, SP317, pp. 147-150 (Dec. 1970).

Key words: Dislocation pileups; Moutier cycle; stress concentrations.

A few results intended to illustrate the usefulness of orthogonal polynomials and singular integral equations for the problem of dislocation pileups are described. A simple method of solving a few special integral equations is suggested. The usefulness of a Moutier cycle for the calculation of stress concentration is shown.

The behavior of an elastic solid containing distributions of free and fixed dislocations, E. Smith, SP317, pp. 151-162 (Dec. 1970).

Key words: Crack nucleation; dislocations-elasticity; internal stresses.

There are many situations in metal physics where the stresses acting on fixed dislocations have an important bearing on a physical phenomenon, and the paper derives a general expression relating these stresses when fixed edge dislocations are contained within an infinite elastic solid in which there are also free edge dislocations that occupy equilibrium positions.

Special cases are considered in detail, particular attention being given to the situation where all the dislocations are of the same type, the free ones having identical Burgers vectors b while there are two fixed dislocations with Burgers vectors pb and qb; all the dislocations lie in the same plane within an infinite solid. This is the most general model for which the stresses on each dislocation and also the equilibrium positions of the free dislocations may be determined analytically. It is indicated how the model degenerates into all the others that have been discussed analytically in terms of classic polynomial functions.

The results are briefly discussed in relation to the problem of cleavage crack nucleation in crystalline solids. The elastic interaction between grain boundaries and screw dislocation pile-ups, M. O. Tucker, SP317, pp. 163-171 (Dec. 1970).

Key words: Anisotropic elasticity; dislocation pileups; dislocations-elasticity; grain boundaries.

The configuration of an array of parallel infinitive straight screw dislocations, in equilibrium under a constant applied stress, and piled-up on a plane inclined to a grain boundary at an arbitrary angle is considered. The model used for the grain boundary is the plane interface between two elastically anisotropic half-spaces welded together. Using this approximation of a continuous distribution of infintesimal dislocations the integral equation expressing the equilibrium conditions is solved using a Wiener-Hopf technique and approximate expressions are presented for the stresses near to the tip of the array when the dislocations are parallel to orthotropic symmetry axes in each half-crystal.

One-electron theories of cohesion on ion-pair potentials in metals, N. W. Ashcroft, SP317, pp. 179-200 (Dec. 1970).

Key words: Band structure; cohesion; core-core interactions; electron density; inter-atomie; one-electron potentials; pseudopotentials.

The single particle picture of cohesion in metals is briefly reviewed in the light of modern knowledge of their band structures. Periodic components in the electron density distributions (intimately connected with the same band structures) are important in the determination of the effective potential between ions.

In simple metals, defined to be those with tightly bound core states, the net binding of the metallic state is basically a remnant of a competition between kinetic (Pauli principle) and Madelung energies of ostensibly free conduction electrons. Various corrections (for correlation, for exchange, etc.) must be included, and the Madelung energy (which is normally appropriate to a uniform electron gas in a Coulomb lattice of point ions) can be modified as necessary for departures from Coulomb's law. Terms in the total energy also arise from periodic variations in conduction electron density; for perfect lattices these are naturally dependent on the ionic arrangement and will vary in importance from crystal structure to crystal structure. Electronic density variations arising from disorder (e.g. distributions of defects) also introduce corrections into total energy.

The structurally dependent terms in the total energy can be evaluated to second order in the pseudopotential: to this same order the total energy may be written as a sum over pair potentials between ions whose form is quite straight forward to evaluate. As with many inter-atomic potentials, the ion-ion potentials demonstrate "hard-core" effects at small separation, and are rather weak at large distances.

Extending the simple theory to transition metals or metals exhibiting additional band structure more akin to itinerant narrow-band behavior, can be carried through by incorporating Born-Mayer interactions between tight binding atomic states. This procedure is, of course, only valid in situations where the Block method itself is applicable. While the core-core exchange term approximated by the BornMayer interaction is quite small in the simple metals it is appreciable for metals like Cu, Ag and Au, and in fact is basically responsible for fixing the equilibrium density. Its addition to the otherwise “simple-metal” like ion pair potentials modifies the behavior at short range.

Localized vibration modes associated with screw dislocations, A. A. Maradudin, SP317, pp. 205-217 (Dec. 1970).

Key words: Dislocation-phonon interactions; dispersion relations; lattice of dynamics; localized modes.

The dispersion relation for the one-dimensional continuum of localized modes associated with a screw dislocation is obtained in the long wavelength limit, as a function of the wave vector parallel to the dislocation line. The result has the form w2(q)=s2q2—wo2 exp(-const./q) where s is the speed of sound for transverse acoustic waves, and wo is a typical Brillouin zone boundary frequency.

The method of lattice statics, J. W. Flocken and J. R. Hardy, SP317, pp. 219-245 (Dec. 1970).

Key words: Computer simulation; Kansaki method; lattice statics; point defects; Schottky pairs.

The formalism of the method of lattice statics for treating the lattice distortions and the formation and interaction energies associated with a defect in a crystal is presented in detail. This approach is based on the Fourier transformation of the set of direct space equilibrium equations to reciprocal space. This results in a set of decoupled equations which can be explicitly solved for the Fourier amplitudes of the displacement field which can then be found by Fourier inversion. A similar approach is used to obtain Fourier trans

formed expressions for the relaxation and interaction energies associated with the defect.

The solution of the equations of lattice statics for the Fourier amplitudes in the limit of small wave vectors gives expressions for the displacement field identical to those obtained from the theory of continuum elasticity.

Results are presented of recent applications of the method of lattice statics to find the formation energies of Schottky. pairs in certain alkali halides. Strain field displacements, relaxation energies and interaction energies associated with vacancies in Na and K are given.

Lattice statics in its asymptotic form has been used to find the displacement field far from cubic point defects and double force defects in a number of metals. Displacement profiles about vacancies in Na and K and about a double force defect in Cu are shown. A comparison of the exact lattice statics results to asymptotic results along a (111) direction in K shows that the elastic limit is only attained at about the 19th or 20th neighbor position from the defect. Effect of zero-point motion on Peierls stress, H. Suzuki, SP317, pp. 253-272 (Dec. 1970).

Key words: Anharmonicity; dislocations in lattices; Peierls stress; zero point motion.

Calculations of the Peierls stress hitherto made are criticized and the following conclusions are obtained. The significant difference in Peierls stress between different materials arises mainly from the difference in crystal structures. The Peierls stress is necessarily high in a rectangular lattice where atoms just above and below the slip plane face each other, while in the lattices where the atoms face alternately along the slip plane it is of the order of one percent of that in the rectangular lattice. The Peierls stress in the body-centered cubic crystal is, however, rather high for a screw dislocation owing to the screw structure of this crystal with the axes parallel to [111] direction. The calculated Peierls stresses are several times of those expected from experiments. The zero-point motion decreases the calculated Peierls stress through two mechanisms. The one is the difference in frequency spectrum of a dislocation line at the bottom of the potential valley and at the top of the potential hill. The other is due to the change in spring constants of atom pairs around the dislocation through anharmonicity.

Point defects and dislocations in copper, A. Englert, H. Tompa, and R. Bullough, SP317, pp. 273-283 (Dec. 1970). Key words: Computer simulation; copper; dislocation structure; pair-potential; point defects.

A new pair potential for copper has been constructed from a set of ten interpolated cubic polynomials. The form of the potential is such that at short range it agrees with the usual Born-Mayer repulsive potential and is in satisfactory agreement with the available phonon dispersion data and the observed stacking fault energy and vacancy formation energy for copper. The potential has been used to study the atomic configuration associated with various point and line defects in copper. In particular, because of its fit to the stacking fault energy, it provides a consistent result for the degree and nature of the dissociation to be expected for an edge dislocation in copper.

Atomistic calculations of dislocations in solid krypton, M. Doyama and R. M. J. Cotterill, SP317, pp. 285-289 (Dec. 1970).

Key words: Atomic calculation; interatomic potential; kryp

ton.

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The elastic continuum theory treatment usually fails near the core of dislocations. Atomic calculations of edge and screw dislocations in solid krypton were carried out using a pairwise potential. In rare gases, the electron redistribution of the electron density is small, thus, this method is useful in studying the properties of dislocation cores.

A lattice theory model for Peierls-energy calculations, A. Hölzler and R. Siems, SP317, pp. 291-298 (Dec. 1970).

Key words: Computer simulation; Green's tensors; interatomic potential; lattice studies; Peierl's energy; screw dislocation.

A lattice theory model for a screw dislocation is discussed which is similar to that of Maradudin. For the forces between neighbouring rows of atoms, however, a sinusoidal, not a linear, dependence of their relative displacements is assumed throughout the whole lattice. The displacements are expanded about the elastic theory values. The conditions of equilibrium then yield a system of linear equations for the deviations of the displacements from the elastic theory values, which is solved by an iteration procedure making use of Green's Function for a plane square lattice. For a number of points in the vicinity of the source point and for points in certain symmetry directions simple exact analytical expressions for the latter are derived, for points at larger distances an asymptotic expansion is given. The displacements thus obtained are then used to calculate the energies of the dislocation at the position of minimum energy and at the saddle point and their difference, the Peierls energy, by direct summation of the interaction energies of neighbouring pairs of atoms.

The interaction between a screw dislocation and carbon in body-centered cubic iron according to an atomic model, R. Chang, SP317, pp. 299-303 (Dec. 1970).

Key words: Carbon in iron; computer simulation; dislocation-interstitial interaction; interatomic potentials; lattice defects.

The interaction energy between carbon and a screw dislocation in body-centered cubic iron near the core regions of the dislocation was calculated atomistically using a pairwise interatomic potential matching the elastic properties of the material. In order to avoid the use of the iron-carbon potential, it was assumed that the iron-carbon octahedron of the Johnson configuration (2 iron atoms separated by 1.225 ao in the [100] direction and 4 iron atoms separated by 0.958 ao in the (100) plane, a, being the lattice parameter) remains undistorted whether it is present in a perfect or a defective lattice. Our first calculations yield, depending on site location, binding energies varying from 0.04 to 0.55 eV.

The structure of the (111) screw dislocation in iron, P. C. Gehlen, G. T. Hahn, and A. R. Rosenfield, SP317, pp. 305308 (Dec. 1970).

Key words: Computer simulation; dislocation core structure; interatomic potentials; iron.

The concept of a dissociated a/2 (111) screw dislocation has been invoked to explain the slip behavior in b.c.c. materials and particularly the asymmetry of the critical resolved shear stress. No direct experimental evidence of dissociation has been obtained, but the idea has received some albeit conflicting support from discrete lattice calculations of the atomic positions in the core. Chang, using isotropic elasticity for a-iron, found that the dislocation core has three very narrow intrinsic faults. These three faults are symmetric with respect to the screw axis. Bullough and Perrin, on the other hand, found that the screw is split with

faults on two {112} planes belonging to the zone of the screw axis. The misfit is spread over a distance of about 3b. On the third {112} plane no splitting was found to occur.

In view of these discrepancies, the calculations were repeated for anisotropic and isotropic elastic boundary conditions and with different interatomic potentials. Excellent agreement was found with Chang's configuration even though a volume expansion term was added to the displacements associated with the dislocation.

It was shown that the final configuration is strongly dependent on the position of the dislocation line with respect to the lattice and at least two metastable positions were found. Even though the atomic arrangement is quite different, their energy is not more than 0.1 eV larger than the energy of the stable one.

Using the Johnson potential unmodified for long-range electronic effects, the dislocation was found to have the following characteristics: core radius, 4-5.5 A; core energy, 0.20-0.25 eV per atomic plane; and an effective hole radius of 1.35 Å.

It was shown that the final configurations are rather insensitive to the model size and to the boundary conditions used. Eigenfrequencies in a dislocated crystal, T. Ninomiya, SP317, pp. 315-357 (Dec. 1970).

Key words: Dislocation-phonon interactions; dislocation vibration; internal friction; localized modes.

Dynamical theories of dislocation vibration and interactions with phonons are surveyed. Eigenfrequencies of lattice vibrations in a crystal containing a straight dislocation are calculated by using Lagrangian formalism. It is found that there is one eigenfrequency of dislocation vibration (wave number κ) in each of the intervals of the normal mode frequencies of k2 = k in a perfect lattice. It is also found that there is a band of localized dislocation vibration below the phonon band. The mean squared amplitude of the dislocation vibration is determined by the localized mode for an edge dislocation and by the resonance modes for a screw dislocation. Phonon scattering by the fluttering mechanism is next treated by using the above results and the conditions of resonance scattering is given. Finally, the effect of the Peierls potential and the vibration of a dislocation dipole are discussed. In the Appendices the problem of quantization of dislocation vibration and the extension of the above theories to a case of translational motion are briefly described.

Phonon scattering by dislocations and its influence on the lattice thermal conductivity and on the dislocation mobility at low temperatures, P. P. Gruner, SP317, pp. 363-389 (Dec. 1970). Key words: Dislocation mobility; dislocation-phonon interactions; nonlinear elasticity; phonons; thermal conductivity.

On account of the large strains associated with dislocations, the superposition principle is violated. The resulting scattering of phonons limits the lattice thermal conductivity and leads to a friction force which acts on moving dislocations. The phonon-dislocation interaction is treated with nonlinear continuum theory. Terms up to the third order in the strains are retained in the Taylor expansion of the elastic energy density. These third order terms contain the phonondislocation interaction and the normal three-phonon interactions. In the case of thermal conductivity, the transport problem is solved with the variational method which leads to a system of linear equations for the phonon occupation numbers. The coefficients of this system of equations contain all the information on the scattering mechanisms. The

influence on the thermal conductivity of special dislocation configurations such as piled-up dislocations and dislocation dipoles will be discussed.

It will be shown that the friction force which acts on moving dislocations on account of the anharmonicity can be obtained from quantities that are known from the calculations of the phonon conductivity. A one to one correspondence between friction force and thermal resistance exists, however, only if the dislocation velocity is small compared with the sound velocity and if all parts of the dislocation move with the same velocity.

Phonon scattering by Cottrell atmospheres, P. G. Klemens, SP317, pp. 391-394 (Dec. 1970).

Key words: Cottrell atmospheres; mechanical properties; phonon scattering; thermal resistivity.

The formation of Cottrell atmospheres can change the scattering of phonons by dislocations and in some cases substantially enhance the lattice thermal resistivity due to dislocations. The strength of the atmospheres can be changed by annealing. This changes thermal conductivity values at high temperatures first, since diffusion through shorter distances is involved. The diffusion coefficient can be determined by means of such annealing studies.

Dragging forces on moving defects by strain-field phonon scattering, A. Seeger and H. Engelke, SP317, pp. 397-401 (Dec. 1970).

Key words: Dislocation drag; dislocation-phonon interactions; electroresistivity; kink motion; phonon scattering.

An expression for the dragging force on a uniformly moving defect by scattering of phonons at its strain-field has been derived using nonlinear elasticity theory. The quantization procedures and the formulation of the master equation for the phonon distribution follow the techniques developed in the theory of heat conductivity. Numerical calculations have been performed for kinks in screw dislocations in copper. A comparison with numerical results obtained in the theory of heat conductivity shows quite good agreement. The formalism developed should prove useful also for calculations of the electron drag on dislocations in metals.

Thermal energy trapping by moving dislocations, J. H. Weiner, SP317, pp. 403-414 (Dec. 1970).

Key words: Computer simulation; dislocation-phonon interaction; Frenkel-Kontorowa model.

The steady motion of a dislocation along a piece-wise harmonic Frenkel-Kontorowa model is considered For suitable model parameters there is one localized mode associated with either the stable or unstable dislocation configuration and the remaining modes are nonlocalized or extended. Because of the piece-wise harmonic character of the model, the set of normal modes of the system changes at discrete instants of time, referred to as transition times, as the dislocation moves along the chain. In particular, the localized modes must move along with the dislocation position and we refer to the localized mode momentum and energy as the dislocation momentum and energy respectively. The particle momentum and energy due to the sum of the extended modes is termed thermal.

At the transition times, it is necessary to expand atomic velocities in terms of the new set of modes appropriate to the forthcoming state of the crystal. It is found that a coordination effect exists between the transition times and the thermal motion such that on the average over many transi

tions, thermal momentum in the direction of the dislocation motion is transferred to the dislocation momentum.

Dislocation resonance, J. A. Garber and A. V. Granato, SP317, pp. 419-421 (Dec. 1970).

Key words: Dislocation damping; dislocation resonance; internal friction.

At low temperatures in insulators and superconductors, only reradiation of elastic waves should limit dislocation resonance. This effect has been calculated using Eshelby's expression for the reradiation. It is found that the resonance is very sharp, and still persists even when a random distribution of dislocation segment lengths is assumed.

Dislocation radiation, R. O. Schwenker and A. V. Granato, SP317, pp. 423-426 (Dec. 1970).

Key words: Dislocation radiation; dispersion relations; internal friction.

Thin walls of mobile dislocations have been produced. These can be excited to emit macroscopic plane sound waves. Calculations have been made to predict the properties of the reradiated waves on the basis of a vibrating string model which neglects dislocation interactions. Measurements of the relative modulus change AG/G and the decrement ▲ (real and imaginary part of the response) as a function of frequency permit a check of the Kramers-Kronig dispersion relations. In addition, measurements of the amplitude of the reradiated wave provide another check since the amplitude is proportional to [(AG/G)2+(A/π)2] 1/2. The anharmonic properties of vibrating dislocations, C. Elbaum and A. Hikata, SP317, pp. 427-445 (Dec. 1970). Key words: Anharmonic properties; dislocation dynamics; ultrasonics.

The anharmonic properties of vibrating dislocations are discussed in terms of the nonlinear stress-strain relation and of the higher harmonics of an ultrasonic wave generated when an initially sinusoidal wave propagates in a solid containing (mobile) dislocations. The treatment takes account of both lattice and dislocation contributions to the anharmonic behavior of the solid.

Estimates of the amplitude of the harmonics (these estimates have been confirmed experimentally) indicate that the lattice and dislocation components are comparable for the second harmonic and that the dislocation component is much larger than the lattice component for the third harmonic. Therefore, by investigating the third harmonic, it is possible to obtain detailed information on dislocation dynamics, without the complications of the lattice contribution.

A source of dissipation that produces an internal friction independent of the frequency, W. P. Mason, SP317, pp. 447-458 (Dec. 1970).

Key words: Internal friction; kink motion; Peierl's stress.

Many measurements of the internal friction of metals and other materials such as the earth's crust show that there is a component at low frequencies which produces a value independent of the frequency. It has been shown that this component is associated with dislocation motion.

Using a model for which dislocation motion results from the motion of kinks, it is shown that such a loss can be associated with the energy dissipated when kinks cross Peierls barriers. Theoretical calculations have shown that the energy dissipated in mechanical vibrations requires a dissipative force equal to from 0.01 to 0.1 of the Peierls stress to replace the energy lost. At the low stresses used in internal

friction measurements, it requires a thermal activation to cause motions of the kinks. The lag of the motion behind the applied' stress produces a drag coefficient B proportional to the temperature. The energy due to kink dissipation produces an internal friction to modulus change ratio ß, equal to the ratio of the dynamic to the static kink stress. Measurements in copper and in the alloy Ti-6Al-4V indicate that this ratio is about 0.03, in agreement with calculations.

The meaning of dislocations in crystalline interfaces, W. Bollmann, SP317, pp. 465-477 (Dec. 1970).

Key words: Dislocations; grain boundaries; interfaces; twinning.

The extension of the dislocation concept to arbitrary crystalline interfaces is discussed. It is shown that invariance and continuity of the Burgers vector can be conserved and that in high angle boundaries the function of the standard or primary dislocation is the delimitation of ranges of coordination between the two crystals. In certain relative orientations where the superposition of the two crystals forms a highly periodic pattern (which is energetically favorable such that the crystal tends to conserve it) a slight deviation from that optimum pattern is corrected by a network of secondary dislocations. There is complete balance between the Burgers vectors of primary as well as secondary dislocations.

Structural and elastic properties of zonal twin dislocations in anisotropic crystals, M. H. Yoo and B. T. M. Loh, SP317, pp. 479-493 (Dec. 1970).

Key words: Dislocation geometry; twinning; zonal dislocations.

A descriptive definition of zonal twin dislocations for compound twin systems is given based on the well established rational crystallographic elements. Geometric characteristics of zonal twin dislocations in double lattice structures are thoroughly discussed. Equilibrium shapes of an incoherent twin boundary have been analyzed by using the anisotropic elastic properties of edge dislocations. Shortranged structural properties of zonal twin dislocations are discussed based on a Peierls-Nabarro model. It is found that the "anisotropic parameter," KeS66, correctly predicts the active mode of crystallographically nonequivalent conjugate twin systems.

Non-planar dissociations of dislocations, S. Mendelson, SP317, pp. 495-529 (Dec. 1970).

Key words: Dislocation dissociation; lattice shuffling; partial dislocations; twinning; zonal dislocations.

Non-planar dissociations of dislocations are studied in hcp, fcc, bcc, diamond lattice, tetragonal and orthorhombic crystal structures. The geometric and energetic conditions are shown to be favorable for various dissociations in each crystal structure. A general equation is formulated for dissociations into partials which are glissile on various twin planes of a common zone. The Burgers vector of the twinning dislocations are expressed in terms of orthogonal unit vectors which lie in the "plane of shear" of the twin mode. The twinning dislocations are generally of the "zonal" type, chosen to be consistent with minimum shearstrain and simple atomic shuffling criteria for twinning, and applied in derivations of the twinning elements and shearstrains for various twin modes. The sign of the shear-strain determines the "stress sense" characteristics for dislocation resistance and twinning and are shown to be consistent with behavior in various hcp and bcc metals. The maximum repulsive force on the twinning partials ym is computed using anisotropic elasticity, and compared with evaluations of twin lamella energies y. In many cases it is found that ym/y > 1, leading to an increase in dislocation resistance, locking,

or twinning at lower temperatures. In the cases where 0 < Ym/y1 the partialized dislocation model reduces to the "modified pseudo-Peierls-Nabarro model" for dislocation resistance.

Among various effects, the dissociations account for all twin modes in hcp metals and for the extreme difference in the flow behavior of Cd and Zn on one hand and Ti and Zr on the other. The stress dependent activation energies for motion of dissociated 60° dislocations in germanium are computed and compare favorably with the data of Kabler. A "lock" for kinks on 60° dislocations is described which can account for dragging points in the model of Celli et al.

Propagation of glide through internal boundaries, M. J. Marcinkowski, SP317, pp. 531-545 (Dec. 1970).

Key words: Boundary dislocations; glide propagation; grain boundaries; virtual dislocations.

It has been shown that when an internal boundary such as a grain boundary is cut by a crystal glide dislocation, a disturbance is left at the boundary. This disturbance closely resembles that about a crystal dislocation with the exception that (a) there is no extra half plane associated with the dislocation and (b) the Burgers vector associated with this disturbance is a variable which depends on the nature of the internal boundary. These boundary dislocations have been termed virtual dislocations.

The nature of the virtual boundary dislocations has been treated in detail for the symmetrical tilt boundary. Both homogeneous and heterogeneous type glide across these boundaries have in turn been applied to grain boundary crack formation and propagation, grain boundary rotation, preferred orientation, etc.

Kinks, vacancies, and screw dislocations, R. M. Thomson, SP317, pp. 563-576 (Dec. 1970).

Key words: Dislocation geometry; dislocations; kinks; pipe diffusion; vacancies in dislocations.

A vacancy on a nonsplit pure screw dislocation can dissociate into a set of kinks. This dissociation is demonstrated geometrically for the NaCl lattice, showing that no geometrical constraints are violated by the dissociation. The kinks thus generated also splinter and spread the charge of the vacancy along the line. The effective vacancy association energy on the line is thus much higher than has been supposed hitherto, and is partly due to the delocalization of the charge singularity of the point defect and partly due to the delocalization of elastic singularity. When the Peierls energy is low, the vacancy will always dissociate, while if it is high, the dissociation will occur only when the total kink energy is less than the vacancy energy. Vacancy contributions to both climb and pipe diffusion are discussed in terms of the kink dissociation process. Results are that interstitial pipe diffusion is entirely symmetric to vacancy pipe diffusion, no motion energy is needed, and the formation energy for diffusion is related to the Peierls energy.

Topological restriction on the distribution of defects in surface crystals and possible biophysical application, W. F. Harris, SP317, pp. 579-592 (Dec. 1970).

Key words: Dislocations in biophysics; protein structure; surface crystals; surface dislocations.

Many thin biological structures such as some plasma membranes and virus capsids appear to be made up of units packed in two-dimensional lattices. Such structures are termed surface crystals. Dislocations and disclinations are observable in some of these crystals. The perfect surface crystal is described by a pair of basis vectors and the conventional crystal by a triplet of basis vectors; both are re