Similarity operators and displacive transitions Application to the transition from the hexagonal NiAs to the orthorhombic MnP type1

E. F. Bertaut

doi:10.1524/zkri.1983.164.1-2.95

Similarity operators and displacive transitions Application to the transition from the hexagonal NiAs to the orthorhombic MnP type1

Zeitschrift für Kristallographie - Crystalline Materials ◽

10.1524/zkri.1983.164.1-2.95 ◽

1983 ◽

Vol 164 (1-2) ◽

Cited By ~ 2

Author(s):

E. F. Bertaut

Keyword(s):

Representation Theory ◽

Wave Vector ◽

Vector Group ◽

Similarity Operators

AbstractSimilarity operators are applied to the study of displacive transitions. The example considered is the transition from the hexagonal NiAs to the orthorhombic MnP type. The number of displacement modes is superior to that deduced from representation theory of the wave vector group.

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Densities of states in particles and crystals: characterization of bulk and surface properties

Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences ◽

10.1098/rsta.1986.0066 ◽

1986 ◽

Vol 318 (1541) ◽

pp. 127-134

Keyword(s):

Electronic Structure ◽

Surface Properties ◽

Wave Vector ◽

Local Symmetry ◽

Vector Group ◽

Densities Of States ◽

Local Symmetries ◽

Group Symmetries

This paper is concerned with the restrictions that local symmetry requirements impose on the structures of model clusters chosen for the reproduction of electronic structure, as densities of states, in metals. Simple techniques for the identification of such local symmetries from wave vector group symmetries are outlined. The theory is applied to iridium and comparisons are made between the calculated and measured dialectric function related to the reflectivity of the metal.

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Representation theory of an extension of a Chevalley group by a vector group

Journal of Algebra ◽

10.1016/0021-8693(81)90297-0 ◽

1981 ◽

Vol 72 (2) ◽

pp. 335-341 ◽

Cited By ~ 1

Author(s):

Joyce O'Halloran

Keyword(s):

Representation Theory ◽

Chevalley Group ◽

Vector Group

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Effects of Higher-Order Laue Zone reflections on structure images

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100148083 ◽

1993 ◽

Vol 51 ◽

pp. 450-451

Author(s):

H. S. Kim ◽

S. S. Sheinin

Keyword(s):

Wave Vector ◽

Theoretical Calculations ◽

Reciprocal Lattice ◽

Image Plane ◽

Bloch Wave ◽

Dynamical Theory ◽

Higher Order ◽

Lattice Image ◽

Lattice Vector ◽

Image Position

The importance of image simulation in interpreting experimental lattice images is well established. Normally, in carrying out the required theoretical calculations, only zero order Laue zone reflections are taken into account. In this paper we assess the conditions for which this procedure is valid and indicate circumstances in which higher order Laue zone reflections may be important. Our work is based on an analysis of the requirements for obtaining structure images i.e. images directly related to the projected potential. In the considerations to follow, the Bloch wave formulation of the dynamical theory has been used.The intensity in a lattice image can be obtained from the total wave function at the image plane is given by: where ϕg(z) is the diffracted beam amplitide given by In these equations,the z direction is perpendicular to the entrance surface, g is a reciprocal lattice vector, the Cg(i) are Fourier coefficients in the expression for a Bloch wave, b(i), X(i) is the Bloch wave excitation coefficient, ϒ(i)=k(i)-K, k(i) is a Bloch wave vector, K is the electron wave vector after correction for the mean inner potential of the crystal, T(q) and D(q) are the transfer function and damping function respectively, q is a scattering vector and the summation is over i=l,N where N is the number of beams taken into account.

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