Dynamical Theory of X-ray Diffraction
André Authier, Université de Pierre et Marie Curie,
Paris.
IUCr Monographs on Crystallography, Oxford University Press, 2001
Price: �95.00 (hardback)
ISBN 0-19-855960-7, xviii + 661 pages .
This book has been compiled with meticulous care and attention to detail. André Authier has been very active in the field of X-ray dynamical theory for more than 40 years, testing some of the conclusions through to the exploitation of the theory in topography. The theory is very relevant to the analysis of nearly perfect crystals and the design of high-resolution diffractometers and synchrotron beam lines.
The book is split into four sections; the first is concerned with the basics and the background. The first chapter is historical, explaining some of the conceptual thinking in the development of the theories. Chapter 2 introduces Maxwell�s equations, fundamental to all electromagnetic waves, and leads to the concept of polarisability in a crystal and introduces the Ewald and Laue theories; the former is based on a microscopic approach assuming the crystal is a series of dipoles, whereas the latter assumes a distribution of negative charges surrounding positively charged atoms. The geometrical (kinematical) theory is also derived in this section along with the application of the Fresnel equations, used extensively for specular scattering (reflectometry). This first section is more than 100 pages, and is well illustrated with diagrams of the dispersion surface construction and wave propagation.
Section II describes the theories in greater detail, with many more derivations leading to interesting consequences, from the deviations from Bragg�s law to the extreme conditions of back-reflection. These applications are especially relevant to the design of monochromators at synchrotrons. These properties of wave-fields are considered in transmission and reflection geometries and their combinations, and how they form standing waves. Thirty-five pages are devoted to the interesting condition when the exit or incident wave is almost parallel to the surface. The scattering profile is modified since several positions of the dispersion surface now have significant contributions to the scattering. When both waves are nearly parallel to the surface, scattering planes normal to the surface can be accessed; this is becoming an increasingly important technique for probing thin layers and the theory of the method is discussed in this section.
With monochromatic X-ray wavelengths, we generally assume the scattering comes from one set of crystal planes, but when several reflections can be excited simultaneously, fascinating effects occur. Authier has spared us much of the mathematical details but describes the boundary conditions for 3-beam dynamical theory and how it can lead to phase determination in structure determination. At page 249 the concept of spherical wave dynamical theory is introduced; basically the plane wave theory cannot model distorted structures. Kato's approach of creating a sum of plane waves is discussed first, with all its implications in various geometries, before the more generalised theory of Takagi, and its derivations, is covered in considerable detail. These descriptions are followed by the mathematics of ray tracing in perfect crystals, since the optics used to condition the X-rays will not create a pure plane of spherical wave. Experimental examples are given that illustrate these points.
Section III deals with imperfect crystals, working through the Eikonal approximation and the trajectories of the wave-fields in the plane and spherical wave theories. Twenty-eight pages are devoted to the propagation of waves in highly deformed crystals from the Tagaki theory and statistical dynamical theory. The latter is most relevant when the deformation becomes extreme and the wave coherence is disrupted.
The final section concentrates on applications of the dynamical theories. The description of X-ray optics is well illustrated with DuMond diagrams and the expected profile shapes determined by dynamical theory. The suppression of harmonic radiation and the controlling of the polarisation, focusing mirrors, Fresnel lenses, wave-guides and refractive lenses are all touched upon in this section. X-ray interferometry, developed by Bonse and Hart provides a very good illustration of dynamical theory leading to phase contrast imaging, Authier then extends this section to the increasing interest in phase contrast imaging by more direct methods. An important consequence of dynamical theory is the standing wave that is created which is periodic with the crystal lattice; it also extends outside the crystal and can be used for probing the atoms from their fluorescence yield. The formulae pertaining to these effects are presented for the diffraction condition and for the specular condition; the latter can probe longer length scales. This analysis becomes more complex with thin layers and is briefly discussed. The largest emphasis on the material applications of dynamical theory is on topography in its various forms, transmission (projection and section) and reflection, with a historical perspective of the important works of Berg and Lang, low and high resolution respectively, right up to the present day. This section is well illustrated with experimental and simulated images. The volume is rounded off with a list of useful formulae derived in the book and a transcript of a lecture given by Ewald in 1975.
This monograph covers a very important subject for today's X-ray scientists which has become a very large field with many applications from the electronics industry to the design of optics for synchrotron beam lines. It is full of references for further reading, and I for one am very pleased that André Authier has put into a print a lifetime of experience in this field. There will always be sections that one feels should also be included, for example the analysis of thin films, where dynamical theory is widely used; these aspects are, however, covered in other books. The real value of this monograph is that it brings up to date all the fundamental approaches and puts them together and explains them in a very good way.
Paul Fewster
Polymorphism in Molecular Crystals
Joel Bernstein,
Ben-Gurion University of the Negev, Beer Sheva, Israel
IUCr Monographs on Crystallography, Oxford University Press, 2002
Price: �75.00 (hardback)
ISBN 0-19-850605-8, xiv + 410 pages .
This book deals with a field that in the past forty years has grown from a curiosity to a major field of study. Joel Bernstein has been one of the main movers in this development, and the book he has produced is both an excellent resource book and a very good read - no small feat! The book makes extensive and relevant use of stereo diagrams. Readers who are unfortunate enough not to be able to focus directly on these should have a pair of spectacles at hand before starting to read.
The word "polymorph", literally meaning "multiform" or "many-shaped", is not easy to give a precise definition. Sometimes the word, which is used in many contexts, seems to describe its own definition! Bernstein adopts the definition of McCrone (1965) the a polymorph is "a solid crystalline phase of a given compound, resulting from the possibility of at least two different arrangements of the molecules of that compound in the solid state." Thus solvates fall outside the scope of the book as do such pairs as acetylene (C2H2) and benzene (C6H6) with the same chemical composition but different molecules. Crystals of molecules in different conformations are polymorphs, while those of geometrical isomers are not, and the same borderline cases arise as do in solution or the gas phase. A wide-ranging historical perspective is included, with particular reference to that still amazing mine of information, Groth's Chemische Kristallographie (1906-1919).
A chapter on "Fundamentals" includes thermodynamic and other characteristics of polymorphs, including the often confused distinction between crystal form and crystal habit. In the structural fundamentals, the valuable Etter graph sets are introduced. The development of these has been much due to Bernstein�s own use and active promotion of them.
Chapter 3 deals with the control of crystallisation and hence polymorph selection, insofar as this is possible. It includes the story of "disappearing polymorphs", which can no longer be made after once a more stable polymorph has been found. Chapter 4, the longest in the book, is a useful description of experimental techniques, headed by a splendid quote (from a baseball player) "You can observe a lot by just watching". In addition to a range of thermal methods and X-ray powder diffraction, solid state nuclear magnetic resonance (SSNMR) is included.
The next two chapters cover conformational polymorphism and structure-property relationships. The possibility of various molecular conformations, differing little in energy, explains the great difficulty in the prediction of crystal structures, and the failure, so far, of computer programs to predict structures of significant flexibility. A number of fascinating examples are given, including a six-polymorph system with a convenient range of colour and habit. The presence (or absence) of significant electrical and magnetic properties distinguishes some polymorphic crystals from one another, and Bernstein makes a distinction, which is useful but must sometimes be arbitrary, between differences in bulk and molecular properties.
There are three shorter chapters dealing specifically with the importance of polymorphism in pharmaceuticals, pigments and high-energy compounds. The text concludes with some fascinating accounts of the bizarre legal cases have been fought over polymorphs, particularly in the pharmaceutical industry.
The last chapter of the book is a really extensive bibliography, 92 pages in length, which covers literature up to the end of 2000, with a few entries for 2001.
All in all, this book can be recommended strongly both for content and interest. It is expensive. Perhaps it would be a good book to share with a friend?
Bob Gould
Crystal Structure Analysis - Principles and Practice
W. Clegg, A.J. Blake, R.O. Gould and P. Main
IUCr Texts on Crystallography, Oxford University Press, 2001
Price: �49.50 (hardback)
ISBN 0-19-850618-X, xiv + 265 pages .
Crystal Structure Analysis represents the compilation and publication of the material derived from the BCA Intensive Course in X-Ray Structure Analysis, taken largely from the 1999 Course for which the authors were the principal lecturers. The book is focused on the practical aspects of structure analysis, and the succinct introductory chapter advises readers at the outset that a certain level of prior knowledge is desirable. Hammond's earlier volume, The Basics of Crystallography and Diffraction, from the same IUCr series would seem to be an ideal companion. (Reviewed in September 2001 issue of 'Crystallography News') The present book follows essentially the path from obtaining crystals through to structure publication. The excellent Chapter 2, dealing with crystal growth and evaluation, is drawn unmistakably from genuine experience and gives the immediate impression that the authors are masters of their profession.
Chapters 3 and 4 provide the necessary conceptual framework for understanding crystal symmetry and the theory of data collection. The introductory sentence of Chapter 4 is beautifully understated: "Although many crystal structures are determined by people with little knowledge of the theory underlying the subject, success is more likely and problems will be better avoided by some understanding of the fundamental properties of the crystalline solid state, the nature of diffraction, and the relationships between a crystal structure and its diffraction pattern." Both chapters are necessarily brief, and are perhaps best considered as concise summaries of assumed prior knowledge. The discussion of symmetry is densely packed and may appear a little daunting on first sight. The section concerning data collection theory is somewhat less thorough and I was a little disappointed by the omission of the Ewald construction. My disappointment was rapidly tempered, however, by a clear discussion of the indexing process and orientation matrix.
Chapters 5 and 6 deal with data collection, using serial and area-detector instruments respectively. Although the discussion of area detectors has been augmented slightly from the original Course, the authors have perhaps failed to reflect the increasing prevalence of these instruments. The discussion of serial diffractometers is in itself excellent, and will be valuable for the still considerable number of four-circle users. The relative balance of Chapters 5 and 6, however, comprising eighteen and eight pages respectively, might be considered to lack vision. While the balance is distorted by initial discussions in Chapter 5 of fundamentals such as the number of independent data, data corrections, etc., which are not repeated in Chapter 6, it would be refreshing to see these issues addressed within a discussion of area-detector instruments. Equivalence of (hkl) and (h-kl) within the monoclinic system, for example, might be better illustrated by a wide-angle CCD frame taken from a monoclinic crystal oriented with the b axis perpendicular to the X-ray beam, rather than a reflection list from a serial instrument. I hope that the emphasis might be reconsidered for any subsequent editions of the book.
Chapters 7 - 10 deal with the fundamentals of Fourier syntheses and structure solution. The chapter on Fourier syntheses is masterful, with the 1-D FeS2 example providing excellent illustrations of the Fobs, Fcalc and difference syntheses, and of the effects of series termination. Any previous Course attendee will be pleased to see that ammonium oxalate monohydrate retains its rightful prominence in the 2-D examples! Chapter 8, dealing with Patterson techniques, is equally masterful and equally concise, with the introductory section on the nature of the Patterson function being particularly impressive. I would have been pleased to see both Chapters 7 and 8 expanded, but their brevity is consistent with the practical focus of the book as a whole. Chapter 9 deals with direct methods, in considerably greater depth than the previous chapters. The lucid discussion of the physical basis of direct methods gives genuine insight into what many of usthe book. The discussion of least-squares fitting in Chapter 11 is excellent and should prove generally valuable to a scientific audience much wider than the crystallographic community. Discussion of the effects of restraints and constraints on the least-squares procedure is particularly enlightening. Chapter 12 concentrates more specifically on crystal structure refinement and is filled with helpful practical advice; this chapter in conjunction with suitable example data sets would form the basis of an excellent refinement workshop. Chapters 13 and 14 describe the derivation of secondary results, their statistical significance, the effects of errors and the comparison of results with authority and a healthy realism. As the number of structure determinations performed by non-specialist crystallographers inevitably increases, Chapters 13 and 14 should become mandatory reading.
The closing chapters, dealing with the presentation of results, the CIF format and structure databases, are relatively lightweight in comparison with their predecessors, a reflection of the difficulties associated with presenting such topics in a traditional book format. Nonetheless, each provides a useful starting point and numerous sources of further information. The book also contains three Appendices: useful mathematical formulae, a brief crystallographic dictionary and the answers to Exercises present at the end of each chapter. Inclusion of the Exercises, no doubt remembered with affection by past students of the Course, is most welcome. I suspect that they may find extensive use in lecture courses - I am aware of at least one where that is already the case!
There is of course no question that the book is a valuable addition to the crystallographic literature, and it succeeds in communicating to the reader the extensive knowledge and experience of the authors. The chapters have been admirably edited into a coherent whole that provides an informative and enjoyable account of the practical aspects of the subject. Available initially only in hardback, the price may be intimidating to the average student, but the paperback release should be eagerly anticipated.
Andrew Bond
Structure Determination from Powder Diffraction Data
W.I.F. David, K. Shankland, L.B. McCusker and Ch. Baerlocher
Editors
IUCr Monographs on Crystallography, Oxford University Press, 2002
Price: �70.00 (hardback)
ISBN 0-19-850091-2, xvii + 337 pages .
It is probably best to start this review by declaring some American style First Amendment rights, in that the following is only the personal opinions of an individual reviewer. A reviewer who was less irritated by the promotional blurb and extremely high price would no doubt have very different options, and thus provide a very different review.
This book on structure determination from powder diffraction data is a worthy kindred spirit to the Rietveld book edited by Ray Young and published in 1995, both of which are part of the same series of IUCr Monographs on Crystallography. With the exceptions of peak profiling to obtain peak positions prior to indexing, a chapter on solving structures under extreme conditions, and information relating to structure validation and publication, there is a good spread of relevant topics. Examples of this are the inclusion of chapters on sample preparation and data collection, and using chemical information and intuition in solving structures from powders. However, it is disappointing there are no contributions by G.S. Pawley and Armel Le Bail, even if only in the form of reminiscences. It is their seminal contributions (Pawley in 1981 and Le Bail in 1988) that allowed solving structures from powder diffraction to start reaching escape velocity. Thanks also goes to Jeremy Cockcroft for observing that while crystallographers can now calculate the odds of solving structures from real space methods, they are not yet able to calculate the odds of the UK National Lottery (page 259): the real answer is 49!/(6!*(49-6)!) [1 in 13,983,816]. The reviewer would also be interested to hear if there are IUCr or OUP publishing policies relating to where possible conflicts of interest by authors need to be declared up front: for example, two of the authors already have a "software patent" that seems related to some of the ideas and information in the text (see International patent WO9906824 titled "Method and apparatus for determining molecular crystal structures" - http://l2.espacenet.com/espacenet/viewer?PN=WO9906824&CY=ep& LG=en&DB=EPD). Overall, there is nothing in the text itself to stop this becoming a standard text on crystallographers' shelves for the foreseeable future.
What might be considered a minor problem to some, though a major issue to this reviewer, is that of the book's blurb and the publisher's promotional webpages which give the impression that it is appropriate for guiding (http://www.oup-usa.org/isbn/0198500912.html) and http://www.oup.co.uk/isbn/0-19-850091-2 ). While appropriate and useful for experts and those seriously involved in powder diffraction, this text is not appropriate for guiding novices. Using the "Crystal Structure Determination" book my W. Massa as a benchmark text for comparison, the SDPD book suffers from having separate chapters written by separate authors. The reviewer cannot think of any text where sets of authors writing separate chapters has made a good teaching text or guide to novices. The quantity and quality of "hints" and useful rules of thumb vary from chapter to chapter. There is also no "novice friendly" worked example as available in the Massa book.
Furthermore, given the importance of software programs in a crystallographic text of this type, many of the chapters give the impression of being quite insular in not referring to any real world software tools. Some of these unmentioned programs are highly conspicuous by their absence, which a novice reader may not realise. Some chapters concentrate on the attributes of a certain software package, while others seem oblivious to available software. The most striking example of this is in the chapter on Le Bail and Pawley extraction which concludes: "well-developed computer programs based upon the Le Bail and Pawley methods are available for extracting integrated intensities from powder diffraction data". Yet it does not name any such programs or provide a relevant software bibliography and Internet resource list. There is also no helpful technical comparison between programs that novices would find helpful. The chapters on applying Patterson methods to extracted hkl data, while including references to SHELX, exclude any reference to DIRDIF ( http://www-xtal.sci.kun.nl/xtal/documents/software/dirdif.html ) and PATSEE ( http://www.org.chemie.uni-frankfurt.de/egert/html/patsee.html). This is despite at least one publication (uncited in the book) showing PATSEE to be effective in this role (Acta Cryst. A56 (Supplement), s24, 2000). Direct references to some important real-space programs are missing. These include ESPOIR by A. Le Bail (http://www.cristal.org/); FOX by V. Favre-Nicolin and R. Cerny (http://objcryst.sourceforge.net/) and ZEFSAII by M. Deem et al (http://www.mwdeem.rice.edu/zefsaII/). This is further compounded by an appendix listing of computer programs that is very incomplete and strangely not Internet aware. Given that programs can date or change quickly, there are also no general guides or advice in the Software Bibliography to assist the reader on building up a modern, relevant software toolset (e.g., using the IUCr's Crystallography World Wide or the IUCr's Sincris facility). These omissions may not seem that significant to those experienced in the field, but would be significant to novice readers.
Again, none of the above is fatal to this book becoming a standard text in powder diffraction for the foreseeable future. It is, however, my opinion that at �70, the cost is excessive. The pricing goes against technological advances in publishing that, in theory, should make this type of book cheaper, not priced in the stratosphere. To the young and impressionable, pricing of this type might in their minds justify the illegal use of a photocopier to make personal copies. An alternative for potential readers, institutes and libraries would be to make use of the Internet to find relevant up to date information on this topic. This Internet available information is plentiful (such as Armel Le Bail's website at http://www.cristal.org; the IUCr's Crystallography World Wide / Sincris at http://www.iucr.org; and the Structure Determination by Powder Diffractometry (SDPD) mailing list via http://www.yahoogroups.com/list/sdpd/). A revised price based in the reality of what is affordable to academics and students in both the developed and developing world might redeem this book and assist it in becoming a standard text in powder diffraction.
Lachlan M. D. Cranswick
Electron Microscopy & Analysis 2001,
Proceedings of the IOP Electron Microscopy & Analysis Group Conference,
Dundee 5-7 September 2001
M.Aindow and C.J.Kiely Editors
IOP Conference Series no. 168, Institute of Physics Publishing, 2001
Price �110 hardback
ISBN 07503 0812 5, 520 pages, Author and Subject index
EMAG conferences are biennial events organised by the Electron Microscopy and Analysis Group of the Institute of Physics in the UK. This volume is a conference proceedings arising from such a meeting in Dundee in 2001. 'Not much here for the crystallographer', I can hear you say, and in one sense you would be right - the book is hardly awash with crystal structures (I counted one in the entire volume), and most of the work is involved with the analysis of high resolution electron microscopy images and related methods. But, and it is an important 'but', as crystallographers deal with ever smaller crystalline samples, it is useful to have a current window on the world of nano-crystallography and associated materials, even within all the expected limitations of a book of conference proceedings based on electron microscopy.
There are 128 contributions in 11 sections; each contribution takes 4 pages. The ones that may interest crystallographers most are those on HREM and Electron Crystallography; Ferrous Metals and Intermetallics; Carbons, Ceramics and Composites; Catalysts, Sensors and Environmental Materials and Semiconductors, Superconductors and Magnetic Materials. This is more than half the book, although it must be said that the crystallography is dominated by HREM. There is also lot of material on EELS spectroscopy, and elemental mapping. In this context, I especially enjoyed a paper by Pike et al. on 'A Microscopy Station for Mars'. What about an X-ray diffractometer for Mars? - that would be exciting! Theory is not forgotten either: there are papers on image processing, image analysis, exit wave reconstructions in the electron microscope and tomography. Unlike many books of this sort, there is a uniformity of presentation that makes it easy to browse.
The crunch is: would I buy my own copy? The answer is 'no', but I might just persuade the university library to buy one.
Chris Gilmore
Valence Bond Methods - Theory and Applications
Gordon A. Gallup, University of Nebraska.
Cambridge University Press, 2002
Price: �65.00 (hardback)
ISBN 0-521-80392-6, xv + 238 pages .
Valence bond and ab initio molecular orbital theories were both developed in the 1920�s, but as the former is not so amenable for calculation of large molecules, molecular orbital theory has come to dominate the field. There are several problems, however, such as bond breaking/making or interpretation of molecular orbital plots, where valence bond theory has been shown to be the more appropriate method. It is therefore important that researchers and students of computational chemistry are aware of this alternative method.
Gallup�s book follows the tried and tested format for computational chemistry texts: part I is devoted to a discussion of the basic theory, whilst part II focuses on case studies for sets of related molecules. In addition the text also advertises the freeware program CRUNCH, available from the author�s website, from which most of the calculation results highlighted in the text were obtained.
The development of valence bond theory is comprehensively set out, starting with a general discussion on Schrodinger's equation, before moving on to the Heitler-London function and its subsequent extensions, and ending with the theory behind multi-configuration valence bond calculations. The hydrogen molecule is used as a simple two-electron illustration for many of the principles highlighted in the text. Special consideration is then paid to the treatment of three-electron doublet states, before an account of advanced methods, which are suitable for application to larger molecules, is presented. This section of the book also includes an extensive discussion on the symmetry grouping of wavefunctions. The author, however, does not give any indication of how large a �large molecule� is or state how the calculations scale with e.g. basis set description or the number of electronic configurations included in the calculation. The reader is thus left a little in limbo to know how tractable this style of calculation will be for a particular application they may have in mind.
The case studies presented in part II begin with four simple three-electron systems: the allyl radical, [He2]+, the valence orbitals of BeH and the Li atom. The reader is guided through multi-configurational and other valence bond theory methods, and for each system a consideration of the accuracy of the calculation (in terms of dissociation energies, geometries, vibrational frequencies, dipole moments, and energies) is discussed. The next set of compounds presented are the homonuclear diatomic molecules of the second row of the periodic table, before considering a set of isoelectronic second row heternuclear diatomics. The remainder of the book then focuses on organic examples, including small hydrocarbons, ring and aromatic compounds. Special consideration is given to the nature of resonance in benzene, which is perhaps the most well known example of where valence bond theory (supporting the Kekule/Dewar model) rates higher than molecular orbital theory (supporting the delocalised model).
In short, this book provides a comprehensive introduction to valence bond methods, and the complexity of equations presented is not too daunting for the mathematically timid.
Carole Morrison
Page last updated 15 Jan 2003
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