The quantum theory of lattice dynamics. IV

1969 ◽  
Vol 310 (1500) ◽  
pp. 111-119 ◽  
Keyword(s):  
Lattice Dynamics ◽  
Equilibrium Configuration ◽  
Real Space ◽  
Electronic Energy ◽  
Nuclear Potential ◽  
Bravais Lattice ◽  
Hartree Fock ◽  
Total Electronic Energy ◽  
The Many ◽  
Condensed Systems

The total electronic energy for condensed systems is examined as a function of nuclear displacements from the equilibrium configuration. The expansion is derived to all orders both for the exact solutions to the many-electron Schrödinger equation and for the approximate Hartree-Fock solutions. The results are shown to be translationally invariant to all orders. Expressions are derived for the electronic contributions to the force-constant tensors in real space and it is shown that the effective nuclear potential has a simple two-body form for a Bravais lattice.

The quantum theory of lattice dynamics. Il

1969 ◽  
Vol 310 (1500) ◽  
pp. 89-99 ◽  
Keyword(s):  
Quantum Theory ◽  
Total Energy ◽  
Ground State ◽  
Lattice Dynamics ◽  
Equilibrium Configuration ◽  
Third Order ◽  
Hartree Fock

Expressions are derived for the expansion of the total energy of the electrons in their ground state in a crystal in powers of displacements of the nuclei from their equilibrium configuration. The expansion is taken up to third order on the basis of the coupled Hartree-Fock equations and thus one obtains expressions for the electronic contributions to the dynamical and anharmonic tensors.

The quantum theory of lattice dynamics. I

1969 ◽  
Vol 310 (1500) ◽  
pp. 79-87 ◽  
Keyword(s):  
Quantum Theory ◽  
Potential Energy ◽  
Lattice Dynamics ◽  
Adiabatic Approximation ◽  
Nuclear Potential ◽  
Body Interaction ◽  
Hartree Fock ◽  
Nuclear Interactions ◽  
Rigid Ion Model

The dynamics of a crystal is examined on the basis of the adiabatic approximation. In part I we examine the form of the dynamical and anharmonic tensors on the assumption that the effective nuclear potential energy can be represented as a simple two-body interaction. In part II we derive expressions for the electronic contributions on the basis of the Hartree-Fock approximation and show that these electron-nuclear interactions are more complex than a simple two-body interaction. In part III we examine these interactions in more detail and find that the two-body approximation is equivalent to a rigid-ion model and that this approximation becomes exact in the limit q = 0.

A Simple Real-Space Channelling Theory for Electron Diffraction and HREM

1990 ◽  
Vol 48 (1) ◽  
pp. 64-65
Author(s):  
D. Van Dyck
Keyword(s):  
High Resolution ◽  
Electron Diffraction ◽  
Direct Method ◽  
Real Space ◽  
Zone Axis ◽  
Phase Object ◽  
High Resolution Images ◽  
The Many ◽  
Analytical Expressions ◽  
Electron Wavefunction

The computation of the many beam dynamical electron diffraction amplitudes or high resolution images can only be done numerically by using rather sophisticated computer programs so that the physical insight in the diffraction progress is often lost. Furthermore, it is not likely that in this way the inverse problem can be solved exactly, i.e. to reconstruct the structure of the object from the knowledge of the wavefunction at its exit face, as is needed for a direct method [1]. For this purpose, analytical expressions for the electron wavefunction in real or reciprocal space are much more useful. However, the analytical expressions available at present are relatively poor approximations of the dynamical scattering which are only valid either for thin objects ((weak) phase object approximation, thick phase object approximation, kinematical theory) or when the number of beams is very limited (2 or 3). Both requirements are usually invalid for HREM of crystals. There is a need for an analytical expression of the dynamical electron wavefunction which applies for many beam diffraction in thicker crystals. It is well known that, when a crystal is viewed along a zone axis, i.e. parallel to the atom columns, the high resolution images often show a one-to-one correspondence with the configuration of columns provided the distance between the columns is large enough and the resolution of the instrument is sufficient. This is for instance the case in ordered alloys with a column structure [2,3]. From this, it can be suggested that, for a crystal viewed along a zone axis with sufficient separation between the columns, the wave function at the exit face does mainly depend on the projected structure, i.e. on the type of atom columns. Hence, the classical picture of electrons traversing the crystal as plane-like waves in the directions of the Bragg beams which historically stems from the X-ray diffraction picture, is in fact misleading.

scholarly journals Deriving the skyrmion Hall angle from skyrmion lattice dynamics

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
R. Brearton ◽  
L. A. Turnbull ◽  
J. A. T. Verezhak ◽  
G. Balakrishnan ◽  
P. D. Hatton ◽  
...  
Keyword(s):  
High Efficiency ◽  
Magnetic Field Gradient ◽  
Real Space ◽  
Magnetic Multilayer ◽  
Multilayer Systems ◽  
Space Technique ◽  
Hall Angle ◽  
Lattice State ◽  
The Many ◽  
Magnetic Skyrmions

AbstractMagnetic skyrmions are topologically non-trivial, swirling magnetization textures that form lattices in helimagnetic materials. These magnetic nanoparticles show promise as high efficiency next-generation information carriers, with dynamics that are governed by their topology. Among the many unusual properties of skyrmions is the tendency of their direction of motion to deviate from that of a driving force; the angle by which they diverge is a materials constant, known as the skyrmion Hall angle. In magnetic multilayer systems, where skyrmions often appear individually, not arranging themselves in a lattice, this deflection angle can be easily measured by tracing the real space motion of individual skyrmions. Here we describe a reciprocal space technique which can be used to determine the skyrmion Hall angle in the skyrmion lattice state, leveraging the properties of the skyrmion lattice under a shear drive. We demonstrate this procedure to yield a quantitative measurement of the skyrmion Hall angle in the room-temperature skyrmion system FeGe, shearing the skyrmion lattice with the magnetic field gradient generated by a single turn Oersted wire.

scholarly journals THE METHOD OF INCREMENTS — A WAVEFUNCTION-BASED AB-INITIO CORRELATION METHOD FOR SOLIDS

2007 ◽  
Vol 21 (13n14) ◽  
pp. 2204-2214 ◽  
Author(s):  
BEATE PAULUS
Keyword(s):  
Experimental Data ◽  
Ab Initio ◽  
Ground State ◽  
Infinite System ◽  
Correlation Energy ◽  
Correlation Method ◽  
Many Body ◽  
Hartree Fock ◽  
The Many ◽  
Good Agreement

The method of increments is a wavefunction-based ab initio correlation method for solids, which explicitly calculates the many-body wavefunction of the system. After a Hartree-Fock treatment of the infinite system the correlation energy of the solid is expanded in terms of localised orbitals or of a group of localised orbitals. The method of increments has been applied to a great variety of materials with a band gap, but in this paper the extension to metals is described. The application to solid mercury is presented, where we achieve very good agreement of the calculated ground-state properties with the experimental data.

Dynamics of Silicon Nanostructures Under Laser Irradiation Studied Quantum Mechanically

2004 ◽  
Vol 850 ◽  
Author(s):  
A.M. Mazzone ◽  
M. Bianconi
Keyword(s):  
Electronic Devices ◽  
Finite Size ◽  
Laser Pulses ◽  
Real Space ◽  
Atomic Scale ◽  
Silicon Nanostructures ◽  
Hartree Fock ◽  
Nuclear Subsystem ◽  
Short Laser Pulses ◽  
Small Clusters

ABSTRACTThis study is motivated by recent applications of ultra-short laser pulses to the manipulation of structures on the atomic scale. It describes the energies and the time-scale needed to induce and to observe such changes. The structures adopted to this purpose are taken from the field of silicon nanotechnology and consist on monotaomic wires and small clusters of a columnar shape. These last ones are covered on both sides with an aluminum overlayer and can be regarded as the finite-size analogous of macroscopic electronic devices. The effect of laser is simply described as an increase of the kinetic energy in the nuclear subsystem. The calculations are based on real-time, real-space implementation of the semiempirical Hartree-Fock theory. The results show the occurrence of phenomena similar to recristallization and melting in the bulk and illustrate the dependence of these effects on the energy input and on the cluster size and composition.

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