Keen DA

English

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This is the author’s final, peer-reviewed manuscript as accepted for publication (AAM). The version presented here may differ from the published version, or version of record, available through the publisher’s website. This version does not track changes, errata, or withdrawals on the publisher’s site. Published version information Citation: DA Keen. Introduction to crystallography. Crystallogr Rev (2021) DOI: 10.1080/0889311X.2021.1971660 This is an Accepted Manuscript version of the above article, accepted for publication in Crystallography Reviews. It is deposited under the terms of the Creative Commons Attribution-Non-commercial License (http://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited.  This version is made available in accordance with publisher policies. Please cite only the published version using the reference above. This is the citation assigned by the publisher at the time of issuing the AAM. Please check the publisher’s website for any updates.  This item was retrieved from ePubs, the Open Access archive of the Science and Technology Facilities Council, UK. Please contact epublications@stfc.ac.uk or go to http://epubs.stfc.ac.uk/ for further information and policies.  Introduction to crystallography David A. Keen BOOK REVIEWIntroduction to Crystallography, by Frank Hoffmann. SpringerInternational Publishing, Switzerland, 1st Ed. 2020, 319pp,ISBN-13:978-3030351090, Hardcover. Price GBP 56.18David A. KeenaaISIS Facility, Rutherford Appleton Laboratory, Harwell Campus, Didcot, Oxfordshire OX110QX, UKARTICLE HISTORYCompiled August 12, 2021I have a confession: although I have read biographies of crystallographers this is thefirst book on crystallography that I have read from cover to cover. I am one of thosecrystallographers who has ‘learnt on the job’ (or more accurately who is still learning onthe job) and was never taught crystallography as a student in any depth. I expect thatthis is now the situation for most researchers who use crystallography as a means tounderstand their materials. We use the readily available crystallographic tools, whetherthey be programs for Rietveld refinement or single crystal structure determination orsimple structure plotting, and we dip in and out of text books and online resources asneeded to make sense of these tools, most of which do the crystallographic ‘hard work’for us. The danger with this approach of course is that we can place our structuralresearch on flaky foundations that, although usually sufficient, might at some pointlimit our ability to develop our crystallographic understanding fully. We might comeunstuck when tackling a tricky sample or phase transition or fail to describe our resultsas effectively as we might with better understanding of the basics of crystallography.As an example, the first structure I studied in my PhD was rocksalt-structuredsilver bromide, space group Fm3̄m, a structure covered in some detail in Hoffmann’sbook. I could manipulate the structure, calculate correlation functions and structurefactors and look for ways that atoms might move within the structure (one of thethemes of my thesis), but it was only several years later that I properly understoodthe full meaning of “Fm3̄m”. At the time, for example, it was not necessary to knowwhich viewing directions corresponded to the m, 3̄ and m of the space group symbol.Now, many more years later, I know that I would not have been alone in only havinga fuzzy understanding of such key pieces of crystallographic knowledge.In his preface to this English translation of his original German work ‘FaszinationKristalle und Symmetrie’, Hoffmann says, “the most important thing is to try tomake the basic concepts of a subject clear.” He goes on to say that this is so “thequasi-natural curiosity of the learners is preserved as long as possible”. In this he hassucceeded; I stayed with him for almost all of the book, and it was only in the finalchapter that my attention wandered a little (more on this later). The basic conceptsare clearly and gently introduced and explained, each chapter building on previousCONTACT D. A. Keen. Email: david.keen@stfc.ac.ukones, and the text is well-linked to excellent diagrams and relevant sections elsewherein the book.The book’s chapters are well-organised and bring the reader on a journey fromsimple observations about crystals and symmetry to space groups and the IUCr Inter-national Tables for Crystallography. This is followed by descriptions of a small numberof pertinent crystal structures (using the knowledge gained in the previous chapters)and discussions of some of the non-standard behaviour seen in crystals. In Chapter1, Hoffmann introduces us to crystals in the general sense, what they are and howbig they can be, how observing their sizes and shapes might help us understand theirsymmetry and how the concepts of a lattice and a unit cell give rise to the sevencrystal systems. Chapter 2 goes into more detail about crystal shapes and how theyarise from the lattice symmetry even if at first this is not obvious. Miller indices areintroduced in the context of labelling the faces of a crystal, as are the fourteen Bravaislattices in the context of unit cell centring (and indeed why there are only fourteen).Face- and body- etc. centring naturally leads to the idea of atoms within the unit cellhaving fractional coordinates and hence how a crystal structure is described. Usefullythis is done with reference to the crystallographic information file (CIF) and the freelyavailable crystal structure drawing software VESTA. The final section of the chapterdeals with the apparently awkward behaviour of the hexagonal crystal system.Chapter 3 is the symmetry chapter, where symmetry elements are introduced andhow they help us understand crystal shapes. The 32 crystal classes are described. It isalso where a toy locomotive first appears in the book as a structure motif. Chapter 4,by returning to discussions of planar symmetry, may seem like a backward step. Butthis helps establish the symmetry of glide planes through its links to patterns in artand ancient culture – and wallpaper. The next two chapters, Chapters 5 and 6, dealwith translational symmetry elements in crystals, glide planes and screw axes, andhow these combine with the already established symmetry elements to build up the230 space groups. Some of the nomenclature is introduced in Chapter 5 and then theway that this is codified within the IUCr International Tables for Crystallography isexplained in some detail in Chapter 6, using a small number of examples. The helpfultoy locomotive is also still much in evidence. Chapter 7 gives some helpful examples.Chapter 8 looks at ways that the ‘forbidden’ symmetry within quasicrystals may beunderstood by going to higher dimensions and Chapter 9 discusses how some crystalsmight be understood using ideas about topology and networks.Two things that mark this book out against older introductions to crystallographyare the links to resources on the author’s web-pages and the suggestions for using spe-cific pieces of software to demonstrate the crystallographic concepts throughout thebook. Both of these are really helpful enhancements that complement the excellentdiagrams throughout the text; there is no real substitute for creating physical crystalmodels and/or being able to rotate and otherwise manipulate structures on the com-puter screen. It is also very well written. Initially I was unsure of the writing style asit started a little clunkily to my way of reading but it quickly improved—or I happilybecame used to it—and I enjoyed the clear descriptions, the care to cover the odditiesand to explain the apparent exceptions, and the interesting and useful asides alongthe way.There were other things that I was less sure about. I didn’t entirely understandthe rationale for including the final chapter in the book. It seemed somewhat out ofplace in the context of the rest of the work and this was the only part of the bookthat I skimmed through. Instead I would have preferred a discussion of how we under-stand crystals which are imperfect. There was a passing discussion of incommensurate2structures in Chapter 8, but no discussion of the effect of temperature or other disor-dering effects. Indeed the author discusses the phase transitions of BaTiO3 in Chapter7 in terms of symmetry changes to the TiO6 octahedra, whereas it is becoming moreaccepted that these octahedra remain in their low-symmetry form, with the centraltitanium ion always offset towards an octahedral face at all temperatures. On heatingeach titanium ion can displace towards an increasing number of such faces, thus pro-gressively raising the average symmetry (which in turn leads to a misunderstandingof the local structure). This would have been an ideal place to introduce concepts ofdisorder. I also think that a stronger link to diffraction, and the reciprocal lattice,would be expected in a book with this title. Instead it is mostly only discussed in thecontext of quasicrystals. I realise that this would probably have necessitated a greateramount of mathematics but crystallography is so dependent on the way that crystalstructures are measured that the book would have been improved with a chapter onthis. But maybe the very general title of the English version of the book gave me falseexpectations; had a literal translation of the German title been used I might not haveanticipated such a chapter.So who might gain most benefit from this book? It would be an excellent companionto undergraduate-level crystallography courses as it is very accessible to the differentdisciplines which have crystallographic content. Although many of the examples havea mineralogical bias—largely because of the easy access to good specimens displayingclear crystal morphologies—researchers in other fields should not be put off by this.The links to other areas of science and culture would also make it suitable to those witha general, or even only passing, interest in crystallography; it is certainly very readableand easily followed and, as the author intended, contains hardly any mathematics.I also feel that—maybe because this was the approach I was thinking about whenreading it—it can help firm up the basic understanding of those researchers who usecrystallography as tool; those who have become expert in crystallographic methodswill find their work further enriched by this book. In this context did I learn anythingnew and fill in some more crystallographic gaps? A few, yes, particularly about crystalmorphology which I have never needed to consider before. And did my foundationalunderstanding become more firmly embedded? Definitely.3

Introduction to crystallography, by Frank Hoffmann

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Introduction to crystallography, by Frank Hoffmann

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