Showing papers on "Grain boundary published in 1970"

Electrical-Resistivity Model for Polycrystalline Films: the Case of Arbitrary Reflection at External Surfaces

Abstract: In this paper, the total resistivity of a thin metal film is calculated from a model in which three types of electron scattering mechanisms are simultaneously operative: an isotropic background scattering (due to the combined effects of phonons and point defects), scattering due to a distribution of planar potentials (grain boundaries), and scattering due to the external surfaces. The intrinsic or bulk resistivity is obtained by solving a Boltzmann equation in which both grain-boundary and background scattering are accounted for. The total resistivity is obtained by imposing boundary conditions due to the external surfaces (as in the Fuchs theory) on this Boltzmann equation. Interpretation of published data on grain-boundary scattering in bulk materials in terms of the calculated intrinsic resistivity, and of thin-film data in terms of the calculated total resistivity suggests that (i) the grain-boundary reflection coefficient in Al is \ensuremath{\approx} 0.15, while it is somewhat higher in Cu; (ii) the observed thickness dependence of the resistivity in thin films is due to grain-boundary scattering as well as to the Fuchs size effect; and (iii) the common observation that single-crystal films possess lower resistivities than polycrystalline films may be accounted for by grain-boundary effects rather than by differences in the nature of surface scattering.

The creep strength of the Earth's mantle

Abstract: In this paper we show that it is probable that at stresses greater than about 10−2 bar creep in the earth's mantle is caused by dislocation motion rather than by the mass transport of atoms through diffusion from one grain boundary to another. The latter process leads to Nabarro-Herring creep. Only at very low stresses (<10−2 bar) should Nabarro-Herring creep be dominant. Dislocation creep equations (which are nonlinear in stress) are used to estimate the ‘effective viscosity,’ at a constant creep rate of 10−16 sec−1, of the moon, Mars, and the mantles of Venus and the earth. The effective viscosity of the mantles of Venus and the earth diminishes with increasing depth, goes through a minimum, and then increases continuously up to the mantle-core boundary. The effective viscosity in the lower mantle is much smaller than estimates derived from the Nabarro-Herring creep equation. The effective viscosity in the deep interior of the moon is approximately constant and does not increase appreciable with depth. The effective viscosity of Mars is intermediate in behavior between that of the earth and of the moon.

Quantitative observation of misfit dislocation arrays in low and high angle twist grain boundaries

Abstract: The fine structure of (001) twist boundaries in gold was systematically studied by transmission electron microscopy. About 200 such boundaries were prepared under controlled conditions by welding single crystal films together face-to-face at various twist angles Θ. An almost continuous study of the structure was then made over the entire range 0 ⋜ Θ⋜45°. Orthogonal grids of grain boundary misfit screw dislocations were found in the vicinities of critical angles Θc (Θc=0, 22–6, 28.1 and 36.9°). producing various high density coincidence site boundaries. Measured geometrical properties of the grids near each Θc (i.e. grid spacings, orientation and dislocation diffraction contrast) were completely consistent with those predicted for a boundary structure consisting of a suitable misfit dislocation grid embedded in the high density coincidence site interface corresponding to Θc. Fine structure was not detected in appreciable angular ranges lying between the Θc. This may have been due in part to the re...

Grain boundary sliding as a deformation mechanism during creep

Abstract: A model for grain boundary sliding is developed in which sliding occurs by the movement of dislocations along, or adjacent to, the boundary by a combination of climb and glide. Under these conditions the strain rate due to sliding is proportional to [sgrave]2/d, where [sgrave] is the applied stress and d is the average grain diameter. It is shown that reports in theliterature of enhanced creep rates at low stresses and/or small grain sizes may be explained by assuming that the various deformation mechanisms, including sliding, operate independently.

Reduction of electromigration in aluminum films by copper doping

Abstract: We have found that the lifetime of aluminum films subjected to high current densities at elevated temperatures can be increased by the addition of copper. Previous studies have indicated that the failure mechanism is a combination of electromigration-induced phenomena, including nucleation and growth of voids, which are gated primarily by material transport along grain boundaries. On the basis of the present study, it appears that the presence of copper causes an appreciable retardation in the rate at which this overall combination of processes takes place, thereby producing a considerable increase in lifetime.

The role of dislocations in the flow stress grain size relationships

Abstract: Calculations involving pile ups of dislocations, both analytical and numerical, using either discrete dislocations or continuous distribution of dislocations of infinitesimal Burgers vectors, are reviewed in the light of their effects on the relation between yield or flow stress and grain size. The limitations of the pileup models are discussed and some nonpileup theories of yielding are critically reviewed also. More critical experiments are still needed to reveal the fundamental mechanicm of yielding.

The role of oxide microstructure and growth stresses in the high-temperature scaling of nickel

Abstract: The oxidation of nickel near 1000°C is accompanied by the generation of stresses parallel with the metal-oxide interface and of magnitude (~1500 psi) sufficient to elongate nickel rod, increase sheet area, and sharpen the angle of bend of ells and helices. A primary cause of this stress is identified with the formation of layers of new nickel oxide upon boundaries of columnar grains where nickel, diffusing through the oxide crystals, meets oxygen, diffusing along grain boundaries. Classical parabolic growth of the scale gives way to a slower quasilinear rate when the major site of new oxide formation is abruptly shifted to a system of grain boundaries lying close to the metal surface and created by recrystallization of the oxide under the influence of stress and high temperature. Another source of stress in the scale arises from the constantly changing area of the metal-oxide interface when oxidation is occurring upon curved metal surfaces. This stress reinforces that generated by deposition of material at oxide grain boundaries when the surface is convex and opposes it when the surface is concave.

Dislocations and stacking faults

Abstract: The properties of linear defects in crystals (dislocation lines) and of planar defects (stacking faults) are important in almost every branch of solid state physics. This article is intended to give a comprehensive introduction to dislocation theory for the physicist who is not a specialist in crystal plasticity. It begins with a survey of the established theory relating to the geometrical and topological properties of dislocations, the elastic theory of dislocations in a continuum, the atomistic or core properties of dislocations, and the dynamics of moving dislocations. General methods for finding the elastic field of an arbitrary dislocation loop are outlined, and the results of some recent calculations using anisotropic elasticity are summarized. These include the prediction, partially confirmed by experiment, that dislocations in certain ranges of orientation may have negative line tension. The current importance of atomistic calculations of core structure and related problems is emphasized, and the methods available for these calculations are discussed. More detailed descriptions of dislocation and stacking fault configurations are given for some of the common crystal structures, and recent work on complex defects resulting from vacancy aggregation in close-packed structures is included. The experimental and theoretical evidence for the recent conclusion that screw dislocations in body-centred cubic metals have an asymmetric core is also reviewed. The rather controversial theory of thermally activated dislocation motion is described in a separate section, and examples are given of the application of this theory to various models of the obstacles encountered by moving dislocations. The final section is concerned with the theory of dislocations in grain boundaries and interphase boundaries, and includes the concept of the surface dislocation tensor.

The influence of polycrystal grain size on several mechanical properties of materials

Abstract: The ductile-brittle transition, hardness, fatigue, and creep behavior of polycrystalline materials are known to be influenced under certain conditions by the polycrystal grain size. These properties have been correlated, historically, with the material stress-strain behavior. The (Hall-Petch) stress-grain size relations are useful for describing the complete stress-strain behavior for polycrystals and, therefore, these relations provide a reference for understanding the manner in which these other properties should also depend on the grain size. In some cases, the grain size dependence of a particular property follows directly from this connection.

The surface energies of solid molybdenum, niobium, tantalum and tungsten

Abstract: The surface energies of solid molybdenum, niobium, tantalum, and tungsten at 1500 °C have been determined using the multi-phase equilibration technique The values obtained were 2050, 2550, 2680 and 2830 erg/cm2, respectively The grain boundary energy/surface energy ratios for the four metals varied from 028 to 038 with an average of 032

The Hall–Petch Relation and High-Temperature Subgrains

Abstract: Although originally proposed for high-angle boundaries, a relation of the Hall–Petch type has been applied by a number of authors to low-angle boundaries produced by high-temperature deformation. Investigations published to date include data on commercially pure Al and Fe and on silicon steel; in these studies room-temperature testing showed that the following relation applies: S = S 0′ + K′d−1/2. Here S represents the mechanical property being measured, d is the mean sub grain size, and S 0′ and K′ are empirical constants. However, this relation has previously been applied only to small ranges of sub grain size, and neither S 0′ nor K′ has any fundamental significance. A rationalization is proposed in which the published observations are reinterpreted in terms of sub-boundary strengths that depend on sub-boundary misorientation and perfection and therefore, indirectly, on sub grain size. According to this view, the relatively perfect sub-boundaries formed at creep strain rates have low strengths;...

Grain size effects in the strain hardening of polycrystals

Abstract: The degree to which the flow stress of a polycrystal is sensitive to grain size is discussed in terms of the distribution of slip and dislocation structure that develops in the vicinity of grain boundaries as deformation proceeds. The point of view is taken that the two principal classes of grain boundary hardening models, namely, those based on dislocation pile-ups and those based on dislocation density concepts respectively represent special cases of a single rationale developed in this paper. Grain boundary strengthening is intimately related to strain hardening which is affected by slip mode,i.e., the number of slip systems and the ability to cross slip. The effects of substitutional solute elements on grain boundary strengthenings is considered to be a consequence of their influence on slip modes rather than on their interaction with dislocation sources.

Grain boundaries as sinks for dislocations

Abstract: A thermal grooving technique has been used to measure the relative grain boundary energy of deformed and annealed copper. The relative grain boundary energy after annealing at 600°c is a function of amount of previous strain, but is always higher than that of material annealed at 1000°c. Annealing at 900°c leads to a return of the energy towards the equilibrium value. On the basis of the above results a mechanism is proposed for the action of grain boundaries as a sink for dislocations.

Neutron-irradiated molybdenum: relationship of microstructure to irradiation temperature.

Abstract: The microstructural defects produced in molybdenum by neutron irradiation in the temperature range 50 °C to 800 °C have been characterized by transmission electron microscopy. At a low irradiation temperature, 50 °C, a large number of small dislocation loops, presumably interstitial, form within a complex dislocation network. At intermediate temperatures, 400–600 °C, small interstitial loops agglomerate into rafts. At high temperatures, 600–800 °C, the small loops which comprise a raft are sufficiently mobile to form large loops which interact with each other to produce a coarse dislocation network. The migration of small loops through the lattice by a combination of prismatic glide and conservative climb accounts for the observed microstructures. Vacancy loops are the only identifiable vacancy defects at temperatures ≥ 500. Between 575–650 °C, both vacancy loops and voids exist. Above 650 °C to at least 800 °C, voids are the exclusive vacancy defect. Information on the effect of impurities and g...

Electromigration in single‐crystal aluminum films

Abstract: Electrical open circuits can be produced in current‐carrying polycrystalline aluminum thin film conductors as a result of electromigration phenomena. In this study, attempts have been made to induce such open circuits in comparable single‐crystal aluminum thin‐film conductors. It has not been possible to do so even after subjecting the latter to relatively high current densities for more than 10 000h. This observation adds strong support to the previous inference that the formation of electromigration‐induced open circuits in polycrystalline aluminum thin film conductors is caused predominantly by diffusion along grain boundaries.

Interfacial energy and structure in f.c.c. metals and alloys

Abstract: It is shown by transmission electron microscopy that a rather obvious distinction exists for the interfacial free energies of high-angle grain boundaries, low-angle grain boundaries, and twin bound...

Initiation of dendrites by crystal imperfections

Abstract: The development of dendrites from an initially flat, stationary solid/liquid interface in a transparent material was observed and photographed. It was found that the dendrites originated from preferred areas on the interface immediately adjacent to grain boundaries, subboundaries, and trapped foreign particles. The built-in large-amplitude distortions of the interface adjacent to these imperfections initiated dendritic growth under conditions which did not produce dendritic growth on imperfection-free regions of the interface. It is concluded that considerations of the stability of planar interfaces must take into account the influence of the imperfections which are present in almost all solids.

Structure and energy of grain boundaries: Application to symmetrical tilt boundaries around [100] in aluminium and copper

Abstract: On the basis of the classical assumption of interatomic central forces, a method is proposed for the computation of the structure and energy of a grain boundary: It is applied to the particular case of symmetrical tilt boundaries around [100] in Al and Cu. The resulting curve shows that the interfacial energy is almost independent of the angle θ except for values near 0° and 90° and for high density coincidence boundaries.