Elastic wave surfaces for the (111) plane of cubic crystals

ABSTRACTConsideration of the direction of the normal at any point on a continuous sheet of a surface yields a sufficient condition for the existence of parabolic points on that sheet. This condition has been used to derive some simple inequalities between elastic constants, whose fulfilment determines the existence of parabolic points upon the inverse surfaces of media of orthorhombic, tetragonal, cubic or hexagonal symmetry; in virtue of the polar reciprocal relation between inverse and wave surfaces, the existence of cusp points on the latter is thereby simultaneously established. It is also pointed out that conditions for external conical refraction may prevail in hexagonal media.

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Measurement of the Displacement Across a Coincidence Grain Boundary

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100078213 ◽

1977 ◽

Vol 35 ◽

pp. 124-125

Author(s):

J. W. Matthews ◽

W. M. Stobbs

Keyword(s):

Grain Boundary ◽

Grain Boundaries ◽

Stacking Fault ◽

The Other ◽

Measuring Technique ◽

High Angle ◽

Twin Boundaries ◽

Rigid Displacement ◽

Cubic Crystals ◽

Lattice Displacement

Many high-angle grain boundaries in cubic crystals are thought to be either coincidence boundaries (1) or coincidence boundaries to which grain boundary dislocations have been added (1,2). Calculations of the arrangement of atoms inside coincidence boundaries suggest that the coincidence lattice will usually not be continuous across a coincidence boundary (3). There will usually be a rigid displacement of the lattice on one side of the boundary relative to that on the other. This displacement gives rise to a stacking fault in the coincidence lattice.Recently, Pond (4) and Smith (5) have measured the lattice displacement at coincidence boundaries in aluminum. We have developed (6) an alternative to the measuring technique used by them, and have used it to find two of the three components of the displacement at {112} lateral twin boundaries in gold. This paper describes our method and presents a brief account of the results we have obtained.

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Microtwinning Evidence For The Apparent Five-Fold Symmetry in T2(Al6Li3Cu)

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100125178 ◽

1987 ◽

Vol 45 ◽

pp. 24-25

Author(s):

Kenneth S. Vecchio ◽

David B. Williams

Keyword(s):

Stable Equilibrium ◽

Equilibrium Phase ◽

Convergent Beam Electron Diffraction ◽

Icosahedral Structure ◽

Cubic Crystals ◽

Icosahedral Phases ◽

Heat Treated ◽

Zero Layer ◽

Convergent Beam ◽

Zr Alloy

Since the discovery in 1984 by Shechtman et al. of crystals which display apparent five-fold symmetry, extensive effort has been given to establishing a theoretical basis for the existence of icosahedral phases (eg.2.). Several other investigations have been centered on explaining these observations based on twinning of cubic crystals (eg.3.). Recently, the existence of a stable, equilibrium phase T2Al6 Li3Cu) possessing an icosahedral structure has been reported in the Al-Li-Cu system(4-6).In the present study an Al-2.6wt.%Li-l.5wt.%Cu-0.lwt.%Zr alloy was heat treated at 300°C for 100hrs. to produce large T2 precipitates. Convergent Beam Electron Diffraction (CBED) patterns were obtained from two-fold, three-fold, and apparent five-fold axes of T2 particles. Figure 1 shows the five-fold symmetric zero layer CBED pattern obtained from T2 particles.

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