Dipole Loops Research Articles

Scattering by Dipole Loops near Interfaces

We calculate the resistivity due to scattering by dipole loops parallel and by dipole lines perpendicular to the interface of a conducting film on a dielectric substrate. This model may serve as a rough description of scattering by certain types of dislocations and corresponding misfit geometries. We give a number of general rules for the choice of materials to minimize this contribution to the total resistivity.

On the formation mechanism of faulted dipolar loops in gamma -TiAl

] Some new geometrical features of 1/6<112] faulted dipolar loops have been observed in a Ti-52 at.% Al alloy deformed at 77 K. It was observed that the 1/6<112] dipole could switch its alignment from <101] to <011] directions, and vice versa; also the loops in alignment along both <101] and <011] could be created by the same parent superdislocation along its line and, on further movement of the parent dislocation, the two loops could attach to one another at the meeting point. No extra dislocation debris or segments were created at either the turning point or the attachment site. These particular features have been discussed on the basis of the available models for the formation mechanism of the dipoles. It is predicted that the particular features can be created only under a favourable stress and no such features are expected for 1/3<211]faulted dipolar loops.

On the sweeping of dipolar loops by gliding dislocations

To analyse the formation of dislocation patterns during the early stages of monotonic and cyclic deformation, the sweeping of edge dipolar loops by gliding dislocations has been examined by three different approaches. Dynamic simulations show the efficiency of this mechanism, particularly when it leads to the formation of a mobile tripolar configuration, as well as its propensity to induce the formation of organised structures. The critical condition for the formation of a tripole configuration is further studied by simplified numerical and analytical methods, leading to the concept of a critical character or angle of the gliding dislocation.

The model of formation and disintegration of vein dislocation structure

A qualitative, one dimensional model of dislocation structure evolution during cycling is treated as a process of self-organization. The main mechanisms of the dislocation structure development are a generation of dipolar loops, their sweeping by glide dislocations to high dislocation density regions and their annihilation. The model is described by the system of three equations: The balance law for the density of dipolar loops, the local yield condition governing the motion of glide dislocations and the equation controlling the local stress. The results of the numerical solution of the system simulate the formation of the dislocation vein structure, its disintegration and formation of dipolar walls in agreement with the available electron microscopic observations.

Room-temperature deformation behavior of a directionally solidified β (B2)-(Ni-Fe-Al) intermetallic alloy

The room-temperature mechanical behavior of a directionally solidified columnar-grained, single-phase β (B2)-(Ni-20 at. pct Fe-30 at. pct A1) intermetallic alloy deformed along the “hard” 〈001〉 direction has been characterized. The 0.2 pct offset compressive yield stress was found to be comparable to that of 〈001〉 single crystals of stoichiometric NiAl. The dislocation substructure consisted of a preponderance of long, straight a〈111〉 screw dislocations on {112} planes, with cross-slip on {123} and {110} planes. The superpartials were not resolved by weak-beam imaging conditions, indicating that the antiphase boundary (APB) energy of NiAl is not reduced significantly by the Fe addition. The dislocation substructure was analyzed as a function of strain and compared to the dislocation substructure in 〈001〉 NiAl and body-centered cubic (bcc) metals deformed at low homologous temperatures. The debris left behind by a〈111〉 screw dislocations consisted of prismatic edge dipole loops 5 to 25 nm in diameter.

Glide dislocation shapes and long-range internal stresses in dislocation wall structures

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Configuration of loop patch at low strain amplitude in polycrystalline copper

Abstract The loop patch structure produced in polycrystalline copper, fatigued at low strain amplitudes below the quasiplateau region of the cyclic stress strain curves, reveals three types of configuration: cylindrical, irregular and cellular shapes. It is identified that the cylindrical loop patches consist of edge dipolar debris with primary Burgers vector and are formed from the deposition of edge segments by sweeping screw dislocations. The irregular loop patches are developed predominantly from stacking of two kinds of dislocation dipolar debris and loops in the grains oriented with double slip. The cellular loop patches are formed from the interaction of four types of dislocation in the grain oriented with multislip. In addition, cubic sessile dislocations are found to coexist with the irregular loop patches and the cellular loop patches. These cubic sessile dislocations are formed from the reaction between edge dislocations and screw dislocations which are perpendicular to each other. It is explai...

On the dynamic origin of dislocation structures in deformed solids

The formation of dislocation structures seems to be governed by two types of instability transitions. In the first type of transition the uniform distribution of dislocations stored in ductile solids becomes unstable, forming dipolar dislocation structures. Stored dislocations, mostly in the form of elongated dipolar loops, are swept by gliding dislocations or drifted by stress gradients into dense regions (clusters, braids, veins, dipolar walls). When the dislocation density in the dense regions reaches a critical value, stored dislocations start to annihilate, causing dynamic recovery. The second type of instability transition is of non-linear continuum mechanics origin. In plasticity deformed solids, this instability leads to the formation of a microshear band and to misorientation of the crystal lattice accompanied by the formation of geometrically necessary bipolar dislocation structures (dislocation sheets, walls of misoriented cells, subgrain boundaries). The proposed continuum mechanics approach indicates that the observed plastic phenomena are the consequences of competition between the two instability processes. These processes can be understood as a trend towards minimizing the internal energy of the solid under dynamic conditions, where the synergetics of dislocations and the applied and internal stresses play a decisive role.

Dislocation pattern formation and strain hardening in solids

At the microscale plastically deformed solid behaves as a strongly nonlinear system governed by instability transitions. According to the model proposed for cell forming materials the stored dislocations, mostly in the form of dipolar loops, are arranged into a characteristic pattern of tangles, veins or walls giving rise to strain hardening. Annihilation of stored dislocations in the high density regions changes the wavelength and profile of the pattern. The process tends to reach a steady state, in which the generation and annihilations of stored dislocations are balanced. The geometry of stabilized cell walls derived for single, double and multi slip corresponds well to observed deformation microstructures. However, the dislocation cell formation may be seriously interfered by geometrical instability. The internal bending type instability causes transformation of cell walls into subgrain boundaries or formation of dislocation grids. The second type of geometrical instability triggers strain localization into shear bands or persistent slip bands destroying the original dislocation structure and forming the new one.

Loop patch orientations in the matrix structure of cyclically deformed copper

A detailed analysis was performed of two regions of matrix or loop patch structure of cyclically deformed copper, each containing a single orientation of persistent slip bands (PSBs). Each loop patch orientation identified agreed with a wall geometrically predicted from a dipole-loop-stacking model for the occurrence of primary slip in combination with a slip system involving a secondary Burgers vector. The wall orientations identified were mechanistically favoured, based on dislocation-sweeping angle considerations, and also were those best able to accommodate excess primary slip dipole loops. The occurrence of {135} walls emphasized the importance of mechanistic considerations in determining wall orientations. The loop patch orientations identified generally contained 〈112〉 parallel to the primary edge dislocations, permitting a high percentage of walls and loop patches to coincide at PSB interfaces. The same geometrical condition enables us to understand wall rotations within PSBs. Additional evidence was obtained related to the influence of dislocation-sweeping angles on wall spacing and on dipolar structures in the immediate vicinity of twin boundaries.

Loop patch orientations in the matrix structure of cyclically deformed copper

A detailed analysis was performed of two regions of matrix or loop patch structure of cyclically deformed copper, each containing a single orientation of persistent slip bands (PSBs). Each loop patch orientation identified agreed with a wall geometrically predicted from a dipole-loop-stacking model for the occurrence of primary slip in combination with a slip system involving a secondary Burgers vector. The wall orientations identified were mechanistically favoured, based on dislocation-sweeping angle considerations, and also were those best able to accommodate excess primary slip dipole loops. The occurrence of {135} walls emphasized the importance of mechanistic considerations in determining wall orientations. The loop patch orientations identified generally contained 〈112〉 parallel to the primary edge dislocations, permitting a high percentage of walls and loop patches to coincide at PSB interfaces. The same geometrical condition enables us to understand wall rotations within PSBs. Additional evidence was obtained related to the influence of dislocation-sweeping angles on wall spacing and on dipolar structures in the immediate vicinity of twin boundaries.

The occurrence of dislocation-free zones at grain boundaries and free surfaces during cyclic deformation

Dislocation-free zones at some grain boundaries and free surfaces can be produced when cyclic deformation results in dipolar dislocations structures. These zones are similar to channels between dipolar walls and result when the dipole loops are swept to these internal or external surfaces at sufficiently large dislocation sweeping angles.

The three-dimensional shape of loop patches produced by cyclic deformation

Loop patches produced by cyclic deformation often have an elongated shape. The elongation aspects inferred from observations in the literature on f.c.c. single crystals and the elongation direction identified for h.c.p. titanium and zirconium are shown to be consistent with recent proposals to explain the orientations of dislocation structures consisting of dipole loops.

LEDS: Properties and effects of low energy dislocation structures

Not only epitaxy and phenomena in connection with solid transformations, but also the static mechanical properties of crystalline materials can be understood via Low Energy Dislocation Structures (LEDS). They are characterized by areas of high dislocation density embedded in, or interspersed with, almost dislocation-free areas. LEDS include misfit boundaries, low angle dislocation boundaries, the Taylor lattice (formed either from interacting pile-ups of alternating sign or from accumulations of dipolar dislocation loops), dipolar dislocation walls (as in “deformation bands” formed in unidirectional deformation, or in the “ladder structure” as well as in the “maze structure” formed in fatigue) and the “mosaic block” structure of old, now recognized to be indentical with the dislocation cell structure. By means of LEDS the empirical rules of (1) the parabolic dependence of shear stress on dislocation density and (2) the decrease of the dislocation cell size with increasing stress are readily understood, as is (3) the three-stage work-hardening curve. The quoted inverse dependence of dislocation cell diameter on flow stress can be used to deduce the stress distribution which caused the cell structure, e.g. after shock loading, about crack tips or underneath wear scars. “Recovery” is the removal of jogs and kinks in LEDS, while the mild stress dependence of flow stress on strain rate is explained through the increase in the fraction of the dislocations which move at any given moment.

Geometrical factors influencing the orientations of dipolar dislocation structures produced by cyclic deformation of f.c.c. metals

A recently proposed geometrical model to explain the orientations of labyrinth dipolar walls produced by cyclic deformation of f.c.c. metals is extended to explain the orientations of loop patches, channels within the matrix structure, and dipolar walls within persistent slip bands. The model is based on determining favourable stacking arrangements for dipolar loops involving one or two Burgers vectors and slip systems and on determining the directions in which stacking should be limited. The stacking of dipolar loops into regular networks results evidently in low energy dislocation structures. The dipolar loops are assumed to be swept into the dipolar dislocation arrangements by edge dislocations. When excess dipolar loops of one slip system are present, the ability of the dipolar arrangements to accommodate these becomes important. Good agreement is found between the predictions of this model and the available experimental evidence.

An explanation of labyrinth walls in fatigued f.c.c. metals

The occurrence of labyrinth dipolar walls in fatigued f.c.c. metals is explained as resulting from double pseudo-polygonization (DPP) arrangements of dipole loops essentially edge in character. From the orientations of the edge dislocations of two Burgers vectors on any two slip systems, a three-dimensional regular stacking network of dipole loops can be constructed from which a dipolar wall is obtained by restricting stacking in one of two directions, since the third possible stacking direction appears to be mechanistically favoured. The experimentally demonstrated {100} and {210} walls are shown to be obtained from the same dipole networks. Some experimental evidence also exists suggesting the presence of geometrically predicted {110}, {111} and {211} and/or {311} DPP walls. The present model for f.c.c. metals explains the main aspects of the existing experimental evidence on the orientations of labyrinth walls and also appears to explain that on walls produced at intersections of persistent slip bands. Apparent rotations of simple polygonization {100} walls and the occasional presence of dipolar walls along persistent slip band interfaces can also be rationalized by this model.

The identification of labyrinth wall orientations in cyclically deformed AISI-SAE 316 stainless steel

Labyrinth walls observed in a grain of cyclically deformed AISI-SAE 316 stainless steel were identified as having orientations intermediate between (001) and (01̄2) and between (100) and (21̄0). The principal Burgers vectors were identified as [1̄01] and [101]. Labyrinth walls of these {100} and {210} orientations can be predicted for this pair of Burgers vectors by considering a Taylor's network arrangement of the dipole loops in the walls. Walls of intermediate orientations can be considered to consist of segments of a pair of {100} and {210} orientations.

Influence of Inhomogeneities in a Stratified Ground on the Field of a Circular Loop Antenna

This paper extends earlier works on three-dimensional scattering from a finite obstacle in a stratified halfspace, treated by means of the T-matrix method. In this paper we consider a general source configuration above the ground, that excites the subsurface medium and its inhomogeneity. Explicit expressions are given for the magnetic dipole, the circular, and rectangular antenna loops. Numerical examples, which show the effect of an extended source on the ground, are given for the circular antenna loop.

The electromagnetic field in a layered earth induced by an arbitrary stationary current distribution

The subject of this paper is to calculate the fields in a layered earth induced by a current distribution. A general formulation is presented, which contains very few restrictions of the current distribution. For the simplest current distributions (dipole, circular, and rectangular loops) we derive expressions for the fields, which contain a single integral (Sommerfeld type). Numerical computations are presented for the above mentioned sources, and some techniques for increasing the rate of convergence are discussed.

Radio Wavelength Observations: Structure, Strength and Variability of Magnetic Fields in the Transition Region and the Solar Corona

The 6 cm radiation of solar active regions marks the legs of dipolar loops which have their footpoints in lower-lying sunspots. The temperatures T ≈ 106K and longitudinal magnetic field strengths Hℓ ≈ 600 Gauss at heights h ≈ 4 × 109 cm above sunspot umbrae. The circularly polarized emission at 6 cm delineates the magnetic structure above sunspot penumbrae. The 20 cm radiation of solar active regions delineates the ubiquitous coronal loops previously detected at X-ray wavelengths. We infer semilengths L ≈ 5 × 109cm, maximum electron temperatures Te(max) ≈ 3 × 106K, emission measures and electron densities Ne ≈ 109cm−3 for the 20 cm bremsstrahlung. Future V.L.A. observations at 20 cm may be used to determine the magnetic field strength of coronal loops. Changes in temperature and magnetic structure before and during solar bursts are briefly discussed.