The generalized Mackenzie distribution: Disorientation angle distributions for arbitrary textures

Plastic deformation creates orientation differences in grains of originally uniform orientation. These disorientations are caused by a local excess of dislocations having the same sign of the Burgers vector. Their increase with increasing plastic strain is modeled by dislocation dynamics taking into account different storage mechanisms. The predicted average disorientation angles across different types of boundaries are in close agreement with experimental data for small and moderate plastic strains. At large plastic strains after severe plastic deformation, saturation of the measured average disorientation angle is observed. This saturation is explained as an immediate consequence of the restriction of experimentally measured disorientation angles to angles below a certain maximum value imposed by crystalline symmetry. Taking into account the restrictions from crystalline symmetry for modeled disorientation angles does not only lead to an excellent agreement with experimental findings on Ni after high pressure torsion, but also rationalizes the work-hardening behavior at large plastic strains as well as a saturation of the flow stress.

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The energy dependence of the {111} and {100} tilt grain boundaries on disorientation angle in Ni3Al

Russian Physics Journal ◽

10.1007/s11182-007-0161-x ◽

2007 ◽

Vol 50 (11) ◽

pp. 1101-1103

Author(s):

D. V. Sinyaev ◽

G. M. Poletaev ◽

M. D. Starostenkov ◽

A. I. Potekaev

Keyword(s):

Grain Boundaries ◽

Energy Dependence ◽

Disorientation Angle

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Disorientation angle distribution of primary particles in potash alum aggregates

Journal of Crystal Growth ◽

10.1016/j.jcrysgro.2017.03.026 ◽

2017 ◽

Vol 467 ◽

pp. 93-106 ◽

Cited By ~ 6

Author(s):

Tijana Kovačević ◽

Viktoria Wiedmeyer ◽

Jonathan Schock ◽

Andreas Voigt ◽

Franz Pfeiffer ◽

...

Keyword(s):

Angle Distribution ◽

Primary Particles ◽

Disorientation Angle

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Investigation of boundary structure of copper phthalocyanine crystal grains in resolving crystallographic planes

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100109306 ◽

1978 ◽

Vol 36 (1) ◽

pp. 432-433

Author(s):

G.I. Natsvlishvili

Keyword(s):

Copper Phthalocyanine ◽

Large Angle ◽

Boundary Structure ◽

Good Resolution ◽

Dislocation Boundary ◽

Perfect Lattice ◽

Elastic Fields ◽

Disorientation Angle ◽

Crystallographic Planes ◽

The Right

Deformed crystals of copper phtalocyanine have been investigated. The crystals were deformed in the process of grinding. Large angle grain boundaries with good resolution of dislocations and crystallographic planes (001) have been detected in the electron microscope JEM-100 C.Fig1 shows the grain dislocation boundary with disorientation angles ≈ll.5°.Attention should be paid to the asymmetry of the boundary. The boundary for the left side grain is almost parallel to the plane (100), while the atomic planes of the right side grain break off at the boundary at a distance of ≈65 Å from each other. The measured Burgers vector (b=12.6 Å) and the distance between the dislocations in the wall correspond to the measured disorientation angle.If the image of the region of ‘perfect’ lattice is projected from the same negative under the photographic enlarger on the printed photograph, it will be easy to see that the elastic fields of dislocation forming the boundary given in fig. 1 are also asymmetric.

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X-ray scattering by crystals with local lattice rotation fields

Journal of Applied Crystallography ◽

10.1107/s0021889899010237 ◽

1999 ◽

Vol 32 (6) ◽

pp. 1050-1059 ◽

Cited By ~ 23

Author(s):

R. I. Barabash ◽

P. Klimanek

Keyword(s):

Intensity Distribution ◽

Reciprocal Lattice ◽

Diffraction Theory ◽

Lattice Rotation ◽

Scattering Intensity ◽

X Ray ◽

Lattice Space ◽

Local Lattice ◽

Disorientation Angle ◽

Dislocation Walls

X-ray (or neutron) scattering by crystals with local rotation fields arising from dislocations is treated on the basis of the formalism of the kinematical diffraction theory. Such fields mostly change the intensity distribution of reflections in the azimuthal plane. Scattering intensity in the azimuthal plane for crystals with one or two sets of different-type dislocation walls, causing local rotations in the lattice, is analysed. In this case the intensity distribution is close to Lorentzian in the radial direction and to Gaussian in the azimuthal direction. The expressions for the scattering intensity are valid when averaging over a large statistical ensemble of defects. If this condition is not fulfilled, the intensity distribution in the azimuthal plane will split into several spikes. The mean distance between these spikes in the reciprocal-lattice space is connected with the disorientation between the walls. The conditions necessary for such splitting of the reflection into spikes are considered. The values of the limiting disorientation angle for some common scattering volumes and distances between dislocation walls are evaluated.

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Maximum disorientation angles between crystals of any point groups and their corresponding rotation axes

Journal of Applied Crystallography ◽

10.1107/s0021889808016373 ◽

2008 ◽

Vol 41 (4) ◽

pp. 803-807 ◽

Cited By ~ 4

Author(s):

Youliang He ◽

John J. Jonas

Keyword(s):

Computer Program ◽

Input Data ◽

Quaternion Algebra ◽

Stereographic Projection ◽

The Other ◽

Vertex Enumeration ◽

Rotation Axes ◽

Symmetry Operators ◽

Point Groups ◽

Disorientation Angle

The symmetry-reduced misorientation,i.e.disorientation, between two crystals is represented in the angle–axis format, and the maximum disorientation angle between any two lattices of the 32 point groups is obtained by constructing the fundamental zone of the associated misorientation space (i.e.Rodrigues–Frank space) using quaternion algebra. A computer program based on vertex enumeration was designed to automatically calculate the vertices of these fundamental zones and to seek the maximum disorientation angles and respective rotation axes. Of the C_{32}^2 = 528 possible combinations of any two crystals, 129 pairs give rise to incompletely bounded fundamental zones (i.e.zones having at least one unbounded direction inR3); these correspond to a maximum disorientation angle of 180° (the trivial value). The other 399 pairs produce fully bounded fundamental zones that lead to nine different nontrivial maximum disorientation angles; these are 56.60, 61.86, 62.80, 90, 90.98, 93.84, 98.42, 104.48 and 120°. The associated rotation axes were obtained and are plotted in stereographic projection. These angles and axes are solely determined by the symmetries of the point groups under consideration, and the only input data needed are the symmetry operators of the lattices.

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