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Incommensurate Crystallography

Sander van Smaalen

Published in print:
2007
Published Online:
January 2008
ISBN:
9780198570820
eISBN:
9780191718762
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570820.001.0001
Subject:
Physics, Crystallography: Physics

Aperiodic crystals are crystalline materials with atomic structures that lack translational symmetry. This book gives a comprehensive account of the superspace theory for the description of the ... More


Ab initio structure solution

Erich H. Kisi and Christopher J. Howard

in Applications of Neutron Powder Diffraction

Published in print:
2008
Published Online:
January 2009
ISBN:
9780198515944
eISBN:
9780191705663
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198515944.003.0006
Subject:
Physics, Condensed Matter Physics / Materials

This chapter describes general approaches to the ab initio solution of crystal structures from X-ray or neutron powder diffraction data. The steps in the process, unit cell determination and ... More


METHODS OF STRUCTURE SOLUTION

Sander Van Smaalen

in Incommensurate Crystallography

Published in print:
2007
Published Online:
January 2008
ISBN:
9780198570820
eISBN:
9780191718762
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570820.003.0010
Subject:
Physics, Crystallography: Physics

This chapter provides an overview of the methods of structure solution of incommensurately modulated crystals and composite crystals. Assuming the periodic average structure is known, it is shown ... More


An introduction to maximum entropy

Peter Main

in Crystal Structure Analysis: Principles and Practice

Published in print:
2009
Published Online:
September 2009
ISBN:
9780199219469
eISBN:
9780191722516
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199219469.003.0011
Subject:
Physics, Crystallography: Physics

Maximum entropy methods are used in crystallography for estimating reflection phases among other applications. This chapter explains the basic concepts behind maximum entropy, including entropy ... More


INTRODUCTION

Andrea Braides

in Gamma-Convergence for Beginners

Published in print:
2002
Published Online:
September 2007
ISBN:
9780198507840
eISBN:
9780191709890
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507840.003.0001
Subject:
Mathematics, Applied Mathematics

The idea of a variational convergence is introduced as an equality of upper and lower bounds for families of variational problems. Examples are given that illustrate some of the main applications of ... More


Solving crystal structures from ED data

Xiaodong Zou, Sven Hovmöller, and Peter Oleynikov

in Electron Crystallography: Electron Microscopy and Electron Diffraction

Published in print:
2011
Published Online:
January 2012
ISBN:
9780199580200
eISBN:
9780191731211
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199580200.003.0009
Subject:
Physics, Crystallography: Physics

The principles of how to solve crystal structures from electron diffraction (ED) data are described. Recording and quantification of ED data is not trivial, considering the sharp diffraction spots ... More


Direct methods of crystal-structure determination

Peter Main

in Crystal Structure Analysis: Principles and Practice

Published in print:
2009
Published Online:
September 2009
ISBN:
9780199219469
eISBN:
9780191722516
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199219469.003.0010
Subject:
Physics, Crystallography: Physics

Reflection phases are essential for crystal structure solution but are not available experimentally. They can be estimated from probability and other relationships derived from known or assumed ... More


Global optimization strategies

Kenneth Shankland and William I. F. David

in Structure Determination from Powder Diffraction Data

Published in print:
2006
Published Online:
January 2010
ISBN:
9780199205530
eISBN:
9780191718076
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199205530.003.0015
Subject:
Physics, Condensed Matter Physics / Materials

Global optimisation methods that involve the assessment of multiple trial crystal structures against measured diffraction data offer a powerful alternative to Direct methods of structure solution. ... More


Direct methods in powder diffraction—basic concepts

Rene Peschar, Anke Etz, Jouk Jansen, and Hendrick Schenk

in Structure Determination from Powder Diffraction Data

Published in print:
2006
Published Online:
January 2010
ISBN:
9780199205530
eISBN:
9780191718076
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199205530.003.0010
Subject:
Physics, Condensed Matter Physics / Materials

Direct methods are ab initio structure determination techniques that handle the crystallographic phase problem starting from only the observed intensities. They are undoubtedly responsible for the ... More


Direct methods in powder diffraction—applications

Carmelo Giacovazzo, Angela Altomare, Maria Cristina Burla, Benedetta Carrozzini, Giovanni Luca Cascarano, Antonietta Guagliardi, Anna Grazia G. Moliterni, Giampiero Polidori, and Rosanna Rizzi

in Structure Determination from Powder Diffraction Data

Published in print:
2006
Published Online:
January 2010
ISBN:
9780199205530
eISBN:
9780191718076
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199205530.003.0011
Subject:
Physics, Condensed Matter Physics / Materials

This chapter focuses on the performance of a particular software package, EXPO, against a wide range of test datasets. In EXPO, the intensity extraction and Direct methods stages are intimately ... More


Solution of Patterson-type syntheses with the Direct methods sum function

Jordi Rius

in Structure Determination from Powder Diffraction Data

Published in print:
2006
Published Online:
January 2010
ISBN:
9780199205530
eISBN:
9780191718076
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199205530.003.0013
Subject:
Physics, Condensed Matter Physics / Materials

This chapter provides a detailed mathematical definition of the Direct methods modulus sum function and its associated tangent formula (S' – TF). The latter appears to be especially well-suited to ... More


The Analytical Method of Fluxions

Niccolò Guicciardini

in Isaac Newton on Mathematical Certainty and Method

Published in print:
2009
Published Online:
August 2013
ISBN:
9780262013178
eISBN:
9780262258869
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262013178.003.0008
Subject:
History, History of Science, Technology, and Medicine

This chapter explores the analytical method of fluxions, as stated in De Methodis. Newton’s method of fluxions can be divided into two parts: The direct and the inverse. Newton considered the ... More


Drawing Inferences from Average Seismic Parameters

Sarbani Basu and William J. Chaplin

in Asteroseismic Data Analysis: Foundations and Techniques

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691162928
eISBN:
9781400888207
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691162928.003.0007
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter determines stellar properties from seismic data. It discusses how the average seismic properties discussed in the previous chapters are used in determining the mass and radius of a star. ... More


The derivation of trial structures. I. Analytical methods for direct phase determination

Jenny Pickworth Glusker and Kenneth N. Trueblood

in Crystal Structure Analysis: A Primer

Published in print:
2010
Published Online:
November 2020
ISBN:
9780199576340
eISBN:
9780191917905
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199576340.003.0017
Subject:
Chemistry, Crystallography: Chemistry

As indicated at the start of Chapter 4, after the diffraction pattern has been recorded and measured, the next stage in a crystal structure determination ... More


Optimal Control

David J. N. Limebeer and Matteo Massaro

in Dynamics and Optimal Control of Road Vehicles

Published in print:
2018
Published Online:
April 2019
ISBN:
9780198825715
eISBN:
9780191864636
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198825715.003.0008
Subject:
Physics, Condensed Matter Physics / Materials

Chapter 8 focuses on nonlinear optimal control and its applications. The chapter begins by introducing the fundamentals of optimal control and prototypical problem formulations. This is followed by ... More


The Making of The Blair Witch Project

Peter Turner

in The Blair Witch Project

Published in print:
2015
Published Online:
February 2021
ISBN:
9781906733841
eISBN:
9781800342163
Item type:
chapter
Publisher:
Liverpool University Press
DOI:
10.3828/liverpool/9781906733841.003.0002
Subject:
Film, Television and Radio, Film

This chapter details the making of The Blair Witch Project (1999). The stories that surround the production of The Blair Witch Project are as fascinating as the final product. The circumstances of ... More


Hedonic Imputation versus Time Dummy Hedonic Indexes

W. Erwin Diewert, Saeed Heravi, and Mick Silver (eds)

in Price Index Concepts and Measurement

Published in print:
2010
Published Online:
February 2013
ISBN:
9780226148557
eISBN:
9780226148571
Item type:
chapter
Publisher:
University of Chicago Press
DOI:
10.7208/chicago/9780226148571.003.0005
Subject:
Economics and Finance, Econometrics

This chapter deals with the “direct characteristics method” approach, in which the index change between two periods is computed using separate hedonic functions estimated for each period. It compares ... More


The Finite-Element Method—Part II

Shiro Kobayashi, Soo-Ik Oh, and Taylan Altan

in Metal Forming and the Finite-Element Method

Published in print:
1989
Published Online:
November 2020
ISBN:
9780195044027
eISBN:
9780197560006
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195044027.003.0010
Subject:
Chemistry, Materials Chemistry

Numerical integration is an important part of the finite-element technique. As seen in Section 6.5 of Chap. 6, volume integrations as well as surface integrations ... More


Correlation Methods

Kenneth G. Dyall and Knut Faegri

in Introduction to Relativistic Quantum Chemistry

Published in print:
2007
Published Online:
November 2020
ISBN:
9780195140866
eISBN:
9780197561744
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195140866.003.0018
Subject:
Chemistry, Quantum and Theoretical Chemistry

It is well known from nonrelativistic quantum chemistry that mean-field methods, such as the Hartree–Fock (HF) model, provide mainly qualitative insights ... More


An Introduction to Finite Differencing

T. N. Krishnamurti, H. S. Bedi, and V. M. Hardiker

in Title Pages

Published in print:
1998
Published Online:
November 2020
ISBN:
9780195094732
eISBN:
9780197560761
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195094732.003.0004
Subject:
Earth Sciences and Geography, Meteorology and Climatology

This chapter on finite differencing appears oddly placed in the early part of a text on spectral modeling. Finite differences are still traditionally used for vertical ... More


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