Reinhard B. Neder and Thomas Proffen
- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199233694
- eISBN:
- 9780191715563
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199233694.001.0001
- Subject:
- Physics, Crystallography: Physics
In recent years it has become apparent that merely knowing and understanding the average atomic structure is insufficient for comprehending material properties fully. Deviations from this average ...
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In recent years it has become apparent that merely knowing and understanding the average atomic structure is insufficient for comprehending material properties fully. Deviations from this average structure play an important role regarding these properties. To understand the defect or local structure one has to study diffuse scattering and go beyond the classic interpretation of Bragg intensities. Although there is an increasing interest in analysing disordered materials, as expressed by a number of recent text books, the practical aspects of this analysis are not yet widely known. A detailed step-by-step guide that explains how to simulate disordered materials has been missing. This book covers the full range; from basic steps such as how to build a computer model of the crystal to complex disorder models such as domains, stacking faults, and nanoparticles. It also explains how to use advanced refinement techniques to determine the parameters of a disordered structure. This book provides many examples of the simulation of disordered materials including the input files for DISCUS and explains the concepts and pitfalls encountered when simulating disordered materials.Less
In recent years it has become apparent that merely knowing and understanding the average atomic structure is insufficient for comprehending material properties fully. Deviations from this average structure play an important role regarding these properties. To understand the defect or local structure one has to study diffuse scattering and go beyond the classic interpretation of Bragg intensities. Although there is an increasing interest in analysing disordered materials, as expressed by a number of recent text books, the practical aspects of this analysis are not yet widely known. A detailed step-by-step guide that explains how to simulate disordered materials has been missing. This book covers the full range; from basic steps such as how to build a computer model of the crystal to complex disorder models such as domains, stacking faults, and nanoparticles. It also explains how to use advanced refinement techniques to determine the parameters of a disordered structure. This book provides many examples of the simulation of disordered materials including the input files for DISCUS and explains the concepts and pitfalls encountered when simulating disordered materials.
Reinhard B. Neder and Thomas Proffen
- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199233694
- eISBN:
- 9780191715563
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199233694.003.0011
- Subject:
- Physics, Crystallography: Physics
This chapter deals with the subject of refining the model of a disordered material based on diffraction data. Three different methods are presented: Reverse Monte Carlo (RMC), refinement of the PDF ...
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This chapter deals with the subject of refining the model of a disordered material based on diffraction data. Three different methods are presented: Reverse Monte Carlo (RMC), refinement of the PDF as a function of atom-atom distance, and the refinement of a set of parameters describing a defect structure using a differential evolutionary algorithm. The latter is the most powerful yet computer-hungry approach and two very detailed examples are given. The second example shows how to refine the powder diffraction pattern of a disordered nanoparticle. The refinement is based on a surprisingly small set of parameters needed to create these particles such as lattice parameters, particle diameter, and the stacking fault probability.Less
This chapter deals with the subject of refining the model of a disordered material based on diffraction data. Three different methods are presented: Reverse Monte Carlo (RMC), refinement of the PDF as a function of atom-atom distance, and the refinement of a set of parameters describing a defect structure using a differential evolutionary algorithm. The latter is the most powerful yet computer-hungry approach and two very detailed examples are given. The second example shows how to refine the powder diffraction pattern of a disordered nanoparticle. The refinement is based on a surprisingly small set of parameters needed to create these particles such as lattice parameters, particle diameter, and the stacking fault probability.
Dennis Sherwood and Jon Cooper
- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780199559046
- eISBN:
- 9780191595028
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199559046.001.0001
- Subject:
- Physics, Crystallography: Physics
This book presents a complete account of the theory of the diffraction of X-rays by crystals with particular reference to the processes of determining the structures of protein molecules. The book ...
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This book presents a complete account of the theory of the diffraction of X-rays by crystals with particular reference to the processes of determining the structures of protein molecules. The book develops from first principles all relevant mathematics, diffraction, and wave theory. The practical aspects of sample preparation and X-ray data collection using both laboratory and synchrotron sources are covered along with data analysis at both the theoretical and practical levels. The important role played by the Patterson function in structure analysis by both molecular replacement and experimental phasing approaches is covered, as are methods for improving the resulting electron density map. The theoretical basis of methods used in refinement of protein crystal structures are then covered in depth along with the crucial task of defining the binding sites of ligands and drug molecules. The complementary roles of other diffraction methods which reveal further detail of great functional importance in a crystal structure are outlined.Less
This book presents a complete account of the theory of the diffraction of X-rays by crystals with particular reference to the processes of determining the structures of protein molecules. The book develops from first principles all relevant mathematics, diffraction, and wave theory. The practical aspects of sample preparation and X-ray data collection using both laboratory and synchrotron sources are covered along with data analysis at both the theoretical and practical levels. The important role played by the Patterson function in structure analysis by both molecular replacement and experimental phasing approaches is covered, as are methods for improving the resulting electron density map. The theoretical basis of methods used in refinement of protein crystal structures are then covered in depth along with the crucial task of defining the binding sites of ligands and drug molecules. The complementary roles of other diffraction methods which reveal further detail of great functional importance in a crystal structure are outlined.
Peter Müller, Regine Herbst-Irmer, Anthony L. Spek, Thomas R. Schneider, and Michael R. Sawaya
- Published in print:
- 2006
- Published Online:
- September 2010
- ISBN:
- 9780198570769
- eISBN:
- 9780191718809
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570769.001.0001
- Subject:
- Physics, Crystallography: Physics
This book covers advanced aspects of practical crystal structure refinement, focusing on practical problems in the everyday life of a crystallographer. After an introduction to SHELXL in the first ...
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This book covers advanced aspects of practical crystal structure refinement, focusing on practical problems in the everyday life of a crystallographer. After an introduction to SHELXL in the first chapter, the second chapter provides a brief survey of crystal structure refinement. The next few chapters address the various aspects of structure refinement, from the treatment of hydrogen atoms to the assignment of atom types, to disorder, to non-crystallographic symmetry and twinning. One chapter is dedicated to the refinement of macromolecular structures and two shorter chapters deal with structure validation. In most chapters, the book gives refinement examples, based on the program SHELXL, describing every problem in detail.Less
This book covers advanced aspects of practical crystal structure refinement, focusing on practical problems in the everyday life of a crystallographer. After an introduction to SHELXL in the first chapter, the second chapter provides a brief survey of crystal structure refinement. The next few chapters address the various aspects of structure refinement, from the treatment of hydrogen atoms to the assignment of atom types, to disorder, to non-crystallographic symmetry and twinning. One chapter is dedicated to the refinement of macromolecular structures and two shorter chapters deal with structure validation. In most chapters, the book gives refinement examples, based on the program SHELXL, describing every problem in detail.
Robin Sowerby
- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780199286126
- eISBN:
- 9780191713873
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199286126.001.0001
- Subject:
- Literature, 18th-century Literature
Where previous studies of ‘Augustanism’ have concentrated largely upon political concerns, this book explores the translation of the Roman Augustan aesthetic into a vernacular equivalent by English ...
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Where previous studies of ‘Augustanism’ have concentrated largely upon political concerns, this book explores the translation of the Roman Augustan aesthetic into a vernacular equivalent by English neoclassical poets and does so through the analysis of translations. It has its genesis in the claim made implicitly by Dryden at the conclusion of his Virgil that he had given English poetry the kind of refinement in language and style that Virgil had given the Latin. The opening chapter explores the mediation of the Augustan aesthetic to the early Renaissance by way of the De Arte Poetica of the neo Latin Renaissance poet Vida, represented here in the Augustan version of Pitt. The second chapter charts early English engagements with the classical inheritance before moving on to its chief focus, Dryden's relation to his early predecessors in the refinement of the heroic couplet, Denham and Waller, and the establishment of the full Augustan aesthetic represented in Dryden's Virgil. The third and fourth chapters consider the effect of the Augustan aesthetic upon the translation of silver Latin poets, concentrating on Dryden's Persius and Juvenal, Rowe's Lucan and Pope's Statius and finally on the climactic Augustan achievement, Pope's Homer. The distinguishing strengths of Augustan poetic artistry are shown to advantage in a brief epilogue juxtaposing Augustan and modern versions.Less
Where previous studies of ‘Augustanism’ have concentrated largely upon political concerns, this book explores the translation of the Roman Augustan aesthetic into a vernacular equivalent by English neoclassical poets and does so through the analysis of translations. It has its genesis in the claim made implicitly by Dryden at the conclusion of his Virgil that he had given English poetry the kind of refinement in language and style that Virgil had given the Latin. The opening chapter explores the mediation of the Augustan aesthetic to the early Renaissance by way of the De Arte Poetica of the neo Latin Renaissance poet Vida, represented here in the Augustan version of Pitt. The second chapter charts early English engagements with the classical inheritance before moving on to its chief focus, Dryden's relation to his early predecessors in the refinement of the heroic couplet, Denham and Waller, and the establishment of the full Augustan aesthetic represented in Dryden's Virgil. The third and fourth chapters consider the effect of the Augustan aesthetic upon the translation of silver Latin poets, concentrating on Dryden's Persius and Juvenal, Rowe's Lucan and Pope's Statius and finally on the climactic Augustan achievement, Pope's Homer. The distinguishing strengths of Augustan poetic artistry are shown to advantage in a brief epilogue juxtaposing Augustan and modern versions.
Alex J. Bellamy
- Published in print:
- 2004
- Published Online:
- January 2005
- ISBN:
- 9780199265206
- eISBN:
- 9780191601866
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199265208.003.0001
- Subject:
- Political Science, International Relations and Politics
Starts by outlining the three broad ways that there are of thinking about the contribution of the English School of International Relations and international society approach to the study of ...
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Starts by outlining the three broad ways that there are of thinking about the contribution of the English School of International Relations and international society approach to the study of contemporary international relations. The first way is to follow Barry Buzan in arguing that the English School is an ‘underexploited resource’ and that ‘the time is ripe to develop and apply its historicist, and methodologically pluralist approach’ to the subject; the second, at the other end of the spectrum, calls for the School's closure, or indeed, argues that it no longer exists because it has been too much distorted by contemporary proponents who have eschewed some of its foundational ideas – such as the centrality of states, and the importance of power politics; the third perspective is somewhere between these two, and has arisen as a result of the increased dialogue between English School ideas and other theoretical perspectives – most notably realism and constructivism, which call for the further refinement of English School thinking to give it a theory that is capable of identifying the motors for change and lines of causation in world politics. The primary purpose of this book is to assess these three positions and question the utility of the English School and international society approach to world politics, and to contribute to the development of English School thinking by opening up avenues for theoretical dialogue with other perspectives and suggesting new lines of theoretically informed empirical analysis. Two further sections of the introduction look at international relations theory after the cold war, and discuss the central question of the relationship between the English School and the concept of international society. The final section summarizes the ground covered in each chapter of the book.Less
Starts by outlining the three broad ways that there are of thinking about the contribution of the English School of International Relations and international society approach to the study of contemporary international relations. The first way is to follow Barry Buzan in arguing that the English School is an ‘underexploited resource’ and that ‘the time is ripe to develop and apply its historicist, and methodologically pluralist approach’ to the subject; the second, at the other end of the spectrum, calls for the School's closure, or indeed, argues that it no longer exists because it has been too much distorted by contemporary proponents who have eschewed some of its foundational ideas – such as the centrality of states, and the importance of power politics; the third perspective is somewhere between these two, and has arisen as a result of the increased dialogue between English School ideas and other theoretical perspectives – most notably realism and constructivism, which call for the further refinement of English School thinking to give it a theory that is capable of identifying the motors for change and lines of causation in world politics. The primary purpose of this book is to assess these three positions and question the utility of the English School and international society approach to world politics, and to contribute to the development of English School thinking by opening up avenues for theoretical dialogue with other perspectives and suggesting new lines of theoretically informed empirical analysis. Two further sections of the introduction look at international relations theory after the cold war, and discuss the central question of the relationship between the English School and the concept of international society. The final section summarizes the ground covered in each chapter of the book.
Paul Crowther
- Published in print:
- 2007
- Published Online:
- May 2007
- ISBN:
- 9780199210688
- eISBN:
- 9780191705762
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199210688.003.0010
- Subject:
- Philosophy, Aesthetics
This chapter summarizes the central argument of the book as a whole and considers it in relation to some broader questions, most notably artistic value's deservedly high cultural status, and its ...
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This chapter summarizes the central argument of the book as a whole and considers it in relation to some broader questions, most notably artistic value's deservedly high cultural status, and its relation to controversies concerning the end of art. It is argued that each individual contribution to a medium offers a new way — however slight — of experiencing the world. When artistic refinement or innovation is of a fundamental kind, then one has the excitement of seeing highly significant new ways of configuring the medium and world flowing out of these. The artwork is always to some degree an inert material object; but in its style of imagery and originality it exemplifies the power and potential of freedom.Less
This chapter summarizes the central argument of the book as a whole and considers it in relation to some broader questions, most notably artistic value's deservedly high cultural status, and its relation to controversies concerning the end of art. It is argued that each individual contribution to a medium offers a new way — however slight — of experiencing the world. When artistic refinement or innovation is of a fundamental kind, then one has the excitement of seeing highly significant new ways of configuring the medium and world flowing out of these. The artwork is always to some degree an inert material object; but in its style of imagery and originality it exemplifies the power and potential of freedom.
Lisa D. Pearce and Melinda Lundquist Denton
- Published in print:
- 2011
- Published Online:
- January 2011
- ISBN:
- 9780199753895
- eISBN:
- 9780199894949
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199753895.003.0006
- Subject:
- Religion, Religion and Society
This chapter explores how three critical contexts of youth—family, peers, and religious institutions—can facilitate or pose barriers for religious refinement in adolescence. What appears to be the ...
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This chapter explores how three critical contexts of youth—family, peers, and religious institutions—can facilitate or pose barriers for religious refinement in adolescence. What appears to be the most positive model is reminiscent of what other scholars have called “social scaffolding.” Scaffolding is providing support around the learning or development of youth, but leaving just enough space between the foundational scaffolding and where youth are in the process of developing their own religiosity. When youth know the support is there, but that they are free to further refine their faith relatively autonomously, they are more confident and happy in their religious and spiritual lives. When parents, peers, or religious institutions under- or over-scaffold, youth sense they are being misunderstood and often disengage from the process of religious refinement.Less
This chapter explores how three critical contexts of youth—family, peers, and religious institutions—can facilitate or pose barriers for religious refinement in adolescence. What appears to be the most positive model is reminiscent of what other scholars have called “social scaffolding.” Scaffolding is providing support around the learning or development of youth, but leaving just enough space between the foundational scaffolding and where youth are in the process of developing their own religiosity. When youth know the support is there, but that they are free to further refine their faith relatively autonomously, they are more confident and happy in their religious and spiritual lives. When parents, peers, or religious institutions under- or over-scaffold, youth sense they are being misunderstood and often disengage from the process of religious refinement.
James Bergin
- Published in print:
- 2005
- Published Online:
- July 2005
- ISBN:
- 9780199280292
- eISBN:
- 9780191602498
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199280290.003.0010
- Subject:
- Economics and Finance, Microeconomics
Equilibrium in extensive form games is considered. Covers Nash equilibrium, perfect equilibrium, sequential equilibrium, and perfect Bayesian equilibrium. The classic chain store paradox example is ...
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Equilibrium in extensive form games is considered. Covers Nash equilibrium, perfect equilibrium, sequential equilibrium, and perfect Bayesian equilibrium. The classic chain store paradox example is discussed to illustrate.Less
Equilibrium in extensive form games is considered. Covers Nash equilibrium, perfect equilibrium, sequential equilibrium, and perfect Bayesian equilibrium. The classic chain store paradox example is discussed to illustrate.
Achi Brandt
- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199233854
- eISBN:
- 9780191715532
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199233854.003.0007
- Subject:
- Mathematics, Applied Mathematics
Building on the complementary advantages of Renormalization Group (RG) and multigrid (MG) methods, Systematic Upscaling (SU) comprises rigorous procedures for deriving suitable variables and ...
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Building on the complementary advantages of Renormalization Group (RG) and multigrid (MG) methods, Systematic Upscaling (SU) comprises rigorous procedures for deriving suitable variables and corresponding numerical equations (or statistical relations) that describe a given physical system at progressively larger scales, starting at some fine scale where the physical laws are known (in the form of a partial differential system, or a statistical-mechanics Hamiltonian, or Newton laws for moving particles, etc.). Unlike RG, the SU algorithms include repeated coarse-to-fine transitions, which are essential for (1) testing the adequacy of the set of coarse-level variables (thus providing a general tool for constructing that set); (2) accelerating the finer-level simulations; and, most importantly (3) confining those simulations to small representative subdomains. No substantial scale separation is assumed; as in MG, small scale ratio between successive levels is in fact important to ensure slowdown-free simulations at all scales. Detailed examples are given in terms of local-interaction systems at equilibrium, and extensions are briefly discussed to long-range interactions, dynamic systems, low temperatures, and more.Less
Building on the complementary advantages of Renormalization Group (RG) and multigrid (MG) methods, Systematic Upscaling (SU) comprises rigorous procedures for deriving suitable variables and corresponding numerical equations (or statistical relations) that describe a given physical system at progressively larger scales, starting at some fine scale where the physical laws are known (in the form of a partial differential system, or a statistical-mechanics Hamiltonian, or Newton laws for moving particles, etc.). Unlike RG, the SU algorithms include repeated coarse-to-fine transitions, which are essential for (1) testing the adequacy of the set of coarse-level variables (thus providing a general tool for constructing that set); (2) accelerating the finer-level simulations; and, most importantly (3) confining those simulations to small representative subdomains. No substantial scale separation is assumed; as in MG, small scale ratio between successive levels is in fact important to ensure slowdown-free simulations at all scales. Detailed examples are given in terms of local-interaction systems at equilibrium, and extensions are briefly discussed to long-range interactions, dynamic systems, low temperatures, and more.
Karsten Urban
- Published in print:
- 2008
- Published Online:
- May 2009
- ISBN:
- 9780198526056
- eISBN:
- 9780191712340
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198526056.003.0008
- Subject:
- Mathematics, Applied Mathematics, Mathematical Finance
The construction of wavelets on general domains is performed in three steps. This chapter starts by introducing the construction of scaling functions and wavelets on bounded univariate intervals. ...
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The construction of wavelets on general domains is performed in three steps. This chapter starts by introducing the construction of scaling functions and wavelets on bounded univariate intervals. Next, building tensor products allows constructing wavelets on rectangular domains. Finally, the Wavelet Element Method (WEM) is introduced. Using non-overlapping domain decomposition and mapping to the unit cube the WEM matches scaling functions and wavelets across the interfaces of the subdomains in order to obtain a globally continuous basis. The realization of the construction in terms of software is shown as well how to use this software.Less
The construction of wavelets on general domains is performed in three steps. This chapter starts by introducing the construction of scaling functions and wavelets on bounded univariate intervals. Next, building tensor products allows constructing wavelets on rectangular domains. Finally, the Wavelet Element Method (WEM) is introduced. Using non-overlapping domain decomposition and mapping to the unit cube the WEM matches scaling functions and wavelets across the interfaces of the subdomains in order to obtain a globally continuous basis. The realization of the construction in terms of software is shown as well how to use this software.
Benjamin L. Carp
- Published in print:
- 2007
- Published Online:
- September 2007
- ISBN:
- 9780195304022
- eISBN:
- 9780199788606
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195304022.003.0005
- Subject:
- History, American History: early to 18th Century
Urban townhouses framed many important aspects of urban life, including consumption, gender and race relations, and paternal authority. The wealthiest Charleston residents sat atop the pyramid of ...
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Urban townhouses framed many important aspects of urban life, including consumption, gender and race relations, and paternal authority. The wealthiest Charleston residents sat atop the pyramid of colonial patriarchal society, and they built grand houses that bespoke their mastery and refinement. Wealthy elite masters like Henry Laurens clung to traditional notions of patriarchal regulation to keep their houses and cities in order. These elite city dwellers found it difficult to maintain rigid, patriarchal domination and social control when rioters might pressure their neighbors who supported obnoxious British policies, when slaves might revolt or run away, and when women asserted their decision‐making power. The imperial crisis caused social unrest that gave the urban gentry several reasons to feel less secure about their households. As the revolutionary movement spread, Charlestonians negotiated with one another about the proper arrangement of their households and the appropriate limits of mobilization.Less
Urban townhouses framed many important aspects of urban life, including consumption, gender and race relations, and paternal authority. The wealthiest Charleston residents sat atop the pyramid of colonial patriarchal society, and they built grand houses that bespoke their mastery and refinement. Wealthy elite masters like Henry Laurens clung to traditional notions of patriarchal regulation to keep their houses and cities in order. These elite city dwellers found it difficult to maintain rigid, patriarchal domination and social control when rioters might pressure their neighbors who supported obnoxious British policies, when slaves might revolt or run away, and when women asserted their decision‐making power. The imperial crisis caused social unrest that gave the urban gentry several reasons to feel less secure about their households. As the revolutionary movement spread, Charlestonians negotiated with one another about the proper arrangement of their households and the appropriate limits of mobilization.
Fernando Vega‐Redondo
- Published in print:
- 1996
- Published Online:
- November 2003
- ISBN:
- 9780198774723
- eISBN:
- 9780191596971
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198774729.003.0002
- Subject:
- Economics and Finance, Microeconomics
Presents the basic theoretical framework and introduces the key notion of Evolutionarily Stable Strategy (ESS). The chapter addresses the issue of existence of ESS, the relationship of ESS to the ...
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Presents the basic theoretical framework and introduces the key notion of Evolutionarily Stable Strategy (ESS). The chapter addresses the issue of existence of ESS, the relationship of ESS to the standard game‐theoretic equilibrium concepts (such as Nash Equilibrium), the considerations arising in asymmetric contexts, or the implications of finite populations. It closes with an example on the evolution of cheap talk.Less
Presents the basic theoretical framework and introduces the key notion of Evolutionarily Stable Strategy (ESS). The chapter addresses the issue of existence of ESS, the relationship of ESS to the standard game‐theoretic equilibrium concepts (such as Nash Equilibrium), the considerations arising in asymmetric contexts, or the implications of finite populations. It closes with an example on the evolution of cheap talk.
Erich H. Kisi and Christopher J. Howard
- 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 ...
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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 indexing, intensity extraction, space group determination, structure solution, and structure refinement are described. Indexing methods such as zone indexing, exhaustive methods or recently developed whole pattern methods, and the use of a figure of merit (M20) are presented. Intensity extraction is shown to be reasonably straightforward but for the problem of peak overlap that occurs in powder patterns. The phase problem makes structure solution more difficult: Fourier and Patterson methods, direct methods, or global optimization methods (simulated annealing, genetic algorithms) are brought to bear. The chapter concludes with a section on advanced refinement techniques, including the interpretation of displacement and site occupancy parameters, and the use of constraints. The discussion is illustrated by frequent reference to structure solution for the Ruddlesden-Popper compound Ca3Ti2O7.Less
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 indexing, intensity extraction, space group determination, structure solution, and structure refinement are described. Indexing methods such as zone indexing, exhaustive methods or recently developed whole pattern methods, and the use of a figure of merit (M20) are presented. Intensity extraction is shown to be reasonably straightforward but for the problem of peak overlap that occurs in powder patterns. The phase problem makes structure solution more difficult: Fourier and Patterson methods, direct methods, or global optimization methods (simulated annealing, genetic algorithms) are brought to bear. The chapter concludes with a section on advanced refinement techniques, including the interpretation of displacement and site occupancy parameters, and the use of constraints. The discussion is illustrated by frequent reference to structure solution for the Ruddlesden-Popper compound Ca3Ti2O7.
David M. Kreps
- Published in print:
- 1990
- Published Online:
- November 2003
- ISBN:
- 9780198283812
- eISBN:
- 9780191596568
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198283814.003.0005
- Subject:
- Economics and Finance, Microeconomics
The weaknesses of game theory for purposes of economic modelling are discussed: the theory requires that protocols for interaction are precise (whereas in the real world they are often ambiguous). ...
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The weaknesses of game theory for purposes of economic modelling are discussed: the theory requires that protocols for interaction are precise (whereas in the real world they are often ambiguous). The theory often provides many equilibria and no way to choose among them. Despite work on so‐called refinements of equilibrium, the theory fails to help us understand how individuals react to counter‐theoreticals in dynamic interactions. Equilibria are often very delicate, depending on states of nature that have very small probability a priori. The theory fails to explain how the rules of a particular game got to be what they are.Less
The weaknesses of game theory for purposes of economic modelling are discussed: the theory requires that protocols for interaction are precise (whereas in the real world they are often ambiguous). The theory often provides many equilibria and no way to choose among them. Despite work on so‐called refinements of equilibrium, the theory fails to help us understand how individuals react to counter‐theoreticals in dynamic interactions. Equilibria are often very delicate, depending on states of nature that have very small probability a priori. The theory fails to explain how the rules of a particular game got to be what they are.
Sander Van Smaalen
- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780198570820
- eISBN:
- 9780191718762
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570820.003.0007
- Subject:
- Physics, Crystallography: Physics
This chapter provides a complete account of the method of structure refinement of incommensurately modulated structures and incommensurate composite crystals. Modulation functions for displacive ...
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This chapter provides a complete account of the method of structure refinement of incommensurately modulated structures and incommensurate composite crystals. Modulation functions for displacive modulation, for occupational modulation, and for modulation of anisotropic displacement parameters (ADPs; temperature parameters) are described by truncated Fourier series, thus providing the Fourier amplitudes as parameters of the structure model. Constraints and restraints on the structural parameters are discussed, including the use of rigid bodies and non-crystallographic site symmetries. The block-wave (crenel) function and the saw-tooth function are presented as special modulation functions that may be alternatives to Fourier series. Next to structure refinements against single-crystal diffraction data, refinements of incommensurate structures against powder diffraction data (Rietveld refinement) are presented.Less
This chapter provides a complete account of the method of structure refinement of incommensurately modulated structures and incommensurate composite crystals. Modulation functions for displacive modulation, for occupational modulation, and for modulation of anisotropic displacement parameters (ADPs; temperature parameters) are described by truncated Fourier series, thus providing the Fourier amplitudes as parameters of the structure model. Constraints and restraints on the structural parameters are discussed, including the use of rigid bodies and non-crystallographic site symmetries. The block-wave (crenel) function and the saw-tooth function are presented as special modulation functions that may be alternatives to Fourier series. Next to structure refinements against single-crystal diffraction data, refinements of incommensurate structures against powder diffraction data (Rietveld refinement) are presented.
Dennis Sherwood and Jon Cooper
- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780199559046
- eISBN:
- 9780191595028
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199559046.003.0016
- Subject:
- Physics, Crystallography: Physics
Many of the biological functions of proteins depend on hydrogen atoms, or protons. Whilst the X-ray diffraction data obtained from most protein crystals do not allow the positions of hydrogen atoms ...
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Many of the biological functions of proteins depend on hydrogen atoms, or protons. Whilst the X-ray diffraction data obtained from most protein crystals do not allow the positions of hydrogen atoms to be determined experimentally, some crystals diffract to atomic resolution and these allow the electron density for individual hydrogen atoms to be seen. A more powerful means for defining hydrogen atom positions is to use neutrons, rather than X-rays, in a diffraction experiment, although this generally relies on the availability of large crystals. Neutrons are much more sensitive to hydrogen atoms than X-rays and the visibility of hydrogens can be further enhanced by replacing them with the isotope deuterium, either by soaking the crystals or by special expression methods (known as perdeuteration). This chapter discusses the essential physical properties of neutrons, the basis of neutron production and diffraction, and the practical aspects of data collection and analysis. It also describes X-ray methods for analysing short-lived reaction intermediates that rely on extremely rapid data collection (the Laue method).Less
Many of the biological functions of proteins depend on hydrogen atoms, or protons. Whilst the X-ray diffraction data obtained from most protein crystals do not allow the positions of hydrogen atoms to be determined experimentally, some crystals diffract to atomic resolution and these allow the electron density for individual hydrogen atoms to be seen. A more powerful means for defining hydrogen atom positions is to use neutrons, rather than X-rays, in a diffraction experiment, although this generally relies on the availability of large crystals. Neutrons are much more sensitive to hydrogen atoms than X-rays and the visibility of hydrogens can be further enhanced by replacing them with the isotope deuterium, either by soaking the crystals or by special expression methods (known as perdeuteration). This chapter discusses the essential physical properties of neutrons, the basis of neutron production and diffraction, and the practical aspects of data collection and analysis. It also describes X-ray methods for analysing short-lived reaction intermediates that rely on extremely rapid data collection (the Laue method).
Peter Müller
- Published in print:
- 2006
- Published Online:
- September 2010
- ISBN:
- 9780198570769
- eISBN:
- 9780191718809
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570769.003.0002
- Subject:
- Physics, Crystallography: Physics
The determination of a crystal structure consists of several steps of which refinement comes towards the end. After crystal growth, data collection, data reduction, absorption correction, and ...
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The determination of a crystal structure consists of several steps of which refinement comes towards the end. After crystal growth, data collection, data reduction, absorption correction, and solution of the phase problem, the crystallographer has obtained atomic coordinates for some or all non-hydrogen atoms. Frequently, the atom types assigned to some of these coordinates are incorrect or no atom types have been assigned at all. In addition, the coordinates in the first solution are usually not very accurate and many details of the structure are yet to be determined. The way to get from the first solution to the final accurate and publishable model is called refinement. This chapter explains how structure refinement is performed by SHELXL. This includes the concept of constraints, restraints, and free variables as well as calculating structural parameters such as bond lengths and angles.Less
The determination of a crystal structure consists of several steps of which refinement comes towards the end. After crystal growth, data collection, data reduction, absorption correction, and solution of the phase problem, the crystallographer has obtained atomic coordinates for some or all non-hydrogen atoms. Frequently, the atom types assigned to some of these coordinates are incorrect or no atom types have been assigned at all. In addition, the coordinates in the first solution are usually not very accurate and many details of the structure are yet to be determined. The way to get from the first solution to the final accurate and publishable model is called refinement. This chapter explains how structure refinement is performed by SHELXL. This includes the concept of constraints, restraints, and free variables as well as calculating structural parameters such as bond lengths and angles.
Peter Müller
- Published in print:
- 2006
- Published Online:
- September 2010
- ISBN:
- 9780198570769
- eISBN:
- 9780191718809
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570769.003.0012
- Subject:
- Physics, Crystallography: Physics
This chapter contains general advice and illustrates several points that are important enough to be mentioned but did not quite fit into the context of the previous chapters, such as how many ...
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This chapter contains general advice and illustrates several points that are important enough to be mentioned but did not quite fit into the context of the previous chapters, such as how many refinement cycles are necessary or what to do with ‘non-positive definite’ atoms, or how many restraints may be used in a structure. In addition, the chapter contains tables giving typical coordination geometries for common metal ions and standard single-, double- and triple-bond lengths for common elements as well as 2Θ versus resolution tables for molybdenum and copper radiation.Less
This chapter contains general advice and illustrates several points that are important enough to be mentioned but did not quite fit into the context of the previous chapters, such as how many refinement cycles are necessary or what to do with ‘non-positive definite’ atoms, or how many restraints may be used in a structure. In addition, the chapter contains tables giving typical coordination geometries for common metal ions and standard single-, double- and triple-bond lengths for common elements as well as 2Θ versus resolution tables for molybdenum and copper radiation.
Klaus Böhmer
- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780199577040
- eISBN:
- 9780191595172
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199577040.003.0006
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
Chapter 6 describes the idea of a posteriori error estimation and adaptive mesh refinement. The main points are the description of the adaptive finite element algorithm, its convergence and a sketch ...
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Chapter 6 describes the idea of a posteriori error estimation and adaptive mesh refinement. The main points are the description of the adaptive finite element algorithm, its convergence and a sketch of the optimal complexity of this algorithm with respect to an approximation class of solutions. As in the last chapter the relations between the strong and weak form of the equations are the key for deriving upper and lower a posteriori error estimates. Quantities of interest are estimated.Less
Chapter 6 describes the idea of a posteriori error estimation and adaptive mesh refinement. The main points are the description of the adaptive finite element algorithm, its convergence and a sketch of the optimal complexity of this algorithm with respect to an approximation class of solutions. As in the last chapter the relations between the strong and weak form of the equations are the key for deriving upper and lower a posteriori error estimates. Quantities of interest are estimated.
