Three-dimensional computation of the interaction between a straight dislocation line and a particle

2005 ◽  
Vol 13 (7) ◽  
pp. 1163-1173 ◽  
Author(s):  
C Shin ◽  
M Fivel ◽  
W W Kim
Keyword(s):  
Dislocation Line ◽  
Three Dimensional ◽  
Straight Dislocation

ULTRASOUND AS A PROBE OF PLASTICITY? THE INTERACTION OF ELASTIC WAVES WITH DISLOCATIONS

2009 ◽  
Vol 19 (08) ◽  
pp. 2765-2781 ◽  
Author(s):  
AGNES MAUREL ◽  
VINCENT PAGNEUX ◽  
FELIPE BARRA ◽  
FERNANDO LUND
Keyword(s):  
Elastic Wave ◽  
Elastic Waves ◽  
Plane Waves ◽  
Dislocation Line ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Dislocation Segment ◽  
Plastic Behavior ◽  
Line Segments

An overview of recent work on the interaction of elastic waves with dislocations is given. The perspective is provided by the wish to develop nonintrusive tools to probe plastic behavior in materials. For simplicity, ideas and methods are first worked out in two dimensions, and the results in three dimensions are then described. These results explain a number of recent, hitherto unexplained, experimental findings. The latter include the frequency dependence of ultrasound attenuation in copper, the visualization of the scattering of surface elastic waves by isolated dislocations in LiNbO 3, and the ratio of longitudinal to transverse wave attenuation in a number of materials. Specific results reviewed include the scattering amplitude for the scattering of an elastic wave by a screw, as well as an edge, dislocation in two dimensions, the scattering amplitudes for an elastic wave by a pinned dislocation segment in an infinite elastic medium, and the wave scattering by a sub-surface dislocation in a semi-infinite medium. Also, using a multiple scattering formalism, expressions are given for the attenuation coefficient and the effective speed for coherent wave propagation in the cases of anti-plane waves propagating in a medium filled with many, randomly placed screw dislocations; in-plane waves in a medium similarly filled with randomly placed edge dislocations with randomly oriented Burgers vectors; elastic waves in a three-dimensional medium filled with randomly placed and oriented dislocation line segments, also with randomly oriented Burgers vectors; and elastic waves in a model three-dimensional polycrystal, with only low angle grain boundaries modeled as arrays of dislocation line segments.

Dislocation lines in the hyperbolic umbilic diffraction catastrophe

2006 ◽  
Vol 462 (2072) ◽  
pp. 2299-2313 ◽  
Author(s):  
J.F Nye
Keyword(s):  
Diffraction Pattern ◽  
Cross Section ◽  
Focal Plane ◽  
Dislocation Line ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Optical Vortices ◽  
Nodal Lines ◽  
Wave Interference ◽  
A Chain

The three-dimensional pattern of the hyperbolic umbilic diffraction catastrophe is computed from an integral representation. A detailed description is given of the geometrical arrangement of the wave dislocation lines (optical vortices) on which the diffraction pattern is based. From a crossed grid of nodal lines in the focal plane, two bundles of dislocation lines spring out symmetrically into the regions of 4-wave interference. Each dislocation line then follows a chain of curved segments which approximate successive steps along lattice vectors in the space group Fmmm . The result is a bundle of helices of non-circular cross-section that gradually straighten out until, far from the focal plane, they become the dislocations of the Pearcey diffraction pattern for the cusp catastrophe. A new phenomenon is the multiple puncturing of the caustic surface by a series of helical dislocations.

Identification of superfine precipitates and crystalline defects in silicon using TEM phase-contrast imaging

1989 ◽  
Vol 47 ◽  
pp. 600-601
Author(s):  
V. C. Kantian ◽  
M. L. Green ◽  
D. Brasen ◽  
H. S. Luftman ◽  
N. T. Ha
Keyword(s):  
Dislocation Loop ◽  
Phase Contrast ◽  
Dislocation Line ◽  
Phase Contrast Imaging ◽  
Contrast Imaging ◽  
Crystalline Defects ◽  
Large Loop ◽  
Image Characteristics ◽  
Small Loop ◽  
Straight Dislocation

Very large (≥1000Å in size) precipitates, and crystalline defects, such as dislocation loops or twins, can be identified in a straightforward manner using the conventional electron diffraction contrast in bright field/dark field (BF/DF) mode in a transmission electron microscope (TEM) On the other hand, superfine precipitates and crystallographic defects, whose sizes are ≤ 100Å, can be difficult to identify by the BF/DF technique. For example, the distinction between a small and a large dislocation loop (similar arguments hold for precipitates, too) is the way the elastic stress is distributed around the dislocation. The elastic stresses around a large loop have the same general form as that for a straight dislocation line. Hence, the BF and DF images of a large loop have the same general characteristics of the image of a straight dislocation line.[1] However, the image characteristics of a small dislocation loop are derived using the infinitesimal loop approximation of a dislocation line to describe the stress field of the small loop.[2] Hence, the image characteristics of a small loop can be complex with black/white or black/black dot contrast. In this article, we report a technique for distinguishing superfine precipitates and defects using the phase contrast imaging technique in the TEM without going through the time consuming and sometimes ambiguous BF/DF technique. This technique was applied to identify interfacial defects in homoepitaxial silicon films deposited by rapid thermal chemical vapor deposition (RTCVD).

A Variational Principle of Dislocations Kinetic in Crystals and a Toughening Mechanism of BCC or HCP Metals

2011 ◽  
Author(s):  
Su Hao ◽  
Hans Weertman
Keyword(s):  
Dislocation Line ◽  
Shear Bands ◽  
Three Dimensional ◽  
Variation Principle ◽  
Second Phase ◽  
Dislocation Loops ◽  
Line Energy ◽  
Other Point Defects ◽  
Stress States ◽  
Precipitate Strengthening

A dislocation kinetics-based analysis has been carried out on the toughening mechanisms of alloys. It is concluded that both improved strength and toughening can be achieved through adjusting the short range interatomic interactions between embedded solute atoms, or other point defects, that affect Peierls-Nabarro energy barrier, and the long range interactions between dislocation loops and heterogeneities such coherent precipitates, second phase particles, and crystallography; the latter determines dislocation loops’ patterns such as kink-jog formation. In order to quantify the effects of lattice heterogeneities, a variation principle that defines the energy minima of dislocation line configuration has been derived, which includes the effects of three-dimensional stress states and crystallography, instead of the conventional line energy-based Eular formulation that only considers the case under shear stress. This provides an analytical means and associated numerical tool to determine the favorite dislocation loop’s patterns in an alloy. The further analysis reveals that double-kinks within single slip-plane have limited effect on toughening while the corresponding bow-out solution may lead to a lower-bound estimate of precipitate strengthening. Therefore, a proposed strategy for toughening is to create dispersed softening centers in strengthened matrix that trap accumulated dislocation loops in the form of mixed double-kinks and jog-induced climbings, for example, helices. These kinds of dislocation patterns are able to spread out localized dislocations from single or close packed parallel slipping planes to many cross-over planes in multiple slip-systems, so as to delay the formation of shear bands while maximize the magnitude of bowing-out induced strengthening.

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

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