Calculation of crystal truncation rod structure factors for arbitrary rational surface terminations

2002 ◽  
Vol 35 (6) ◽  
pp. 696-701 ◽  
Author(s):  
Thomas P. Trainor ◽  
Peter J. Eng ◽  
Ian K. Robinson
Keyword(s):  
Coordinate System ◽  
Reciprocal Lattice ◽  
Rational Surface ◽  
Cell Geometry ◽  
System A ◽  
Surfaces And Interfaces ◽  
Crystal Truncation Rod ◽  
Structure Factors ◽  
Rational Plane ◽  
Crystalline Surfaces

The technique of crystal truncation rod (CTR) diffraction is widely used for studying the structure of crystalline surfaces and interfaces. The theory and experimental details of the technique are well established; however, published methods for structure-factor calculations are typically based on a simple surface cell geometry. A method is presented for determining a surface coordinate system which results in a reciprocal lattice that is simply defined in terms of the surface termination. Based on this surface coordinate system, a general formalism for the calculation of CTR structure factors is re-derived, which may be easily applied to any surface that can be represented as a rational plane of a bulk crystal system.

scholarly journals Zur exakten Behandlung von kollektiven Rotationen Teil A: Theorie / On the Exact Treatment of Collective Rotations Part A: Theory

1973 ◽  
Vol 28 (2) ◽  
pp. 206-215
Author(s):  
Hanns Ruder
Keyword(s):  
Coordinate System ◽  
Perturbation Expansion ◽  
Rotational Energy ◽  
The Body ◽  
System A ◽  
N Body Problem ◽  
Definition Of ◽  
Fixed System ◽  
Body Fixed Coordinate System ◽  
Groundstate Energy

Basic in the treatment of collective rotations is the definition of a body-fixed coordinate system. A kinematical method is derived to obtain the Hamiltonian of a n-body problem for a given definition of the body-fixed system. From this exact Hamiltonian, a consequent perturbation expansion in terms of the total angular momentum leads to two exact expressions: one for the collective rotational energy which has to be added to the groundstate energy in this order of perturbation and a second one for the effective inertia tensor in the groundstate. The discussion of these results leads to two criteria how to define the best body-fixed coordinate system, namely a differential equation and a variational principle. The equivalence of both is shown.

scholarly journals Coverage dependent adsorption sites in the K/Cu(100) system: A crystal truncation rod analysis

1993 ◽  
Vol 208 (1) ◽  
Author(s):  
H. L. Meyerheim ◽  
I. K. Robinson ◽  
V. Jahns ◽  
P. J. Eng ◽  
W. Moritz
Keyword(s):  
Crystal Surface ◽  
High Coverage ◽  
Adsorption Sites ◽  
System A ◽  
Crystal Truncation Rod ◽  
Surface Crystal

AbstractThe analysis of the intensity along the diffraction rods normal to the crystal surface (crystal truncation rods) has been used to analyse the adsorption sites of potassium atoms adsorbed atAt high coverage (

Crystal truncation rod X-ray scattering: exact dynamical calculation

2008 ◽  
Vol 41 (1) ◽  
pp. 18-26 ◽  
Author(s):  
Václav Holý ◽  
Paul F. Fewster
Keyword(s):  
Reciprocal Lattice ◽  
Dynamical Theory ◽  
Lattice Points ◽  
Space Distribution ◽  
Matrix Formalism ◽  
X Ray ◽  
Transmission Coefficients ◽  
X Ray Scattering ◽  
Crystal Truncation Rod ◽  
Scattering Geometry

A new method is presented for a calculation of the reciprocal-space distribution of X-ray diffracted intensity along a crystal truncation rod. In contrast to usual kinematical or dynamical approaches, the method is correct both in the reciprocal-lattice points and between them. In the method, the crystal is divided into a sequence of very thin slabs parallel to the surface; in contrast to the well known Darwin dynamical theory, the electron density in the slabs is constant along the surface normal. The diffracted intensity is calculated by a matrix formalism based on the Fresnel reflection and transmission coefficients. The method is applicable for any polarization of the primary beam and also in a non-coplanar scattering geometry.

SOLVING SPATIAL CONSTRAINTS WITH GLOBAL DISTANCE COORDINATE SYSTEM

2006 ◽  
Vol 16 (05n06) ◽  
pp. 533-547 ◽  
Author(s):  
LU YANG
Keyword(s):  
Coordinate System ◽  
Systematic Approach ◽  
Distance Geometry ◽  
Spatial Constraints ◽  
Constraint Equations ◽  
System A ◽  
Short Program ◽  
Complete Set ◽  
Point Line ◽  
Made In

A systematic approach making use of distance geometry to solve spatial constraints is introduced. We demonstrate how to create the constraint equations by means of a relevant distance coordinate system. A short program is made (in Maple) which implements the algorithm producing automatically a complete set of constraint equations for a given point-plane configuration. The point-line-plane configurations are converted into point-plane ones beforehand.

scholarly journals Pepinsky's Machine: an interactive graphics-based Fourier synthesis program with applications in teaching and research

1999 ◽  
Vol 32 (4) ◽  
pp. 821-823 ◽  
Author(s):  
Nicholas M. Glykos
Keyword(s):  
Electron Density ◽  
Reciprocal Lattice ◽  
Interactive Graphics ◽  
Lattice Plane ◽  
Fourier Synthesis ◽  
Teaching And Research ◽  
Electron Density Function ◽  
Density Maps ◽  
Structure Factors ◽  
Plane Group

A computer program has been developed which, given a set of structure-factor amplitudes for any centrosymmetric plane group, displays the amplitude-weighted reciprocal-lattice plane and allows the user interactively to assign and modify the phases of the structure factors, while observing the effect of these changes on the corresponding electron density function. The program has the added feature of being able to calculate and interactively display the electron density maps corresponding to all phase combinations of a user-defined subset of structure factors. Applications of the program in both crystallographic teaching and research are discussed.

Lattice-Fringe Fingerprinting: Structural identification of nanocrystals by HRTEM

2007 ◽  
Vol 1026 ◽  
Author(s):  
Moeck Peter ◽  
Ruben Bjorge
Keyword(s):  
Structural Information ◽  
Reciprocal Lattice ◽  
Chemical Information ◽  
Fourier Synthesis ◽  
Transmission Electron ◽  
Structure Factors ◽  
Lattice Geometry ◽  
Group A ◽  
Experimental Side ◽  
Novel Method

AbstractA novel method for the structurally identification of a nanocrystal from a single high resolution (HR) transmission electron microscopy (TEM) micrograph is described. Components of this method are demonstrated on both experimental and simulated HRTEM images. On the experimental side, the structural information that can be extracted from a HRTEM image is the projected reciprocal lattice geometry, the plane symmetry group, a few structure factor amplitudes and phases, and an outline of the projected atomic structure to the limited resolution of the HRTEM (via a Fourier synthesis of the structure factors). Searching for this information in a comprehensive database and matching it with high figures of merit to that of candidate structures should allow for highly discriminatory identifications of nanocrystals, even without additional chemical information as obtainable in analytical TEMs.

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