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## Über dieses Buch

I was highly flattered when I was asked by Mark Ladd and Rex Palmer if I would write the Foreword to this Fourth Edition of their book. "Ladd & Palmer" is such a well-known and classic book on the subject of crystal structure determination, one of the standards in the field: I did feel daunted by the prospect, and wondered if I could do justice to it. The determination of crystal structures by X-ray crystallography has come a long way since the 1912 discoveries of von Laue and the Braggs. In the intervening years great advances have been made, so that today it is almost taken for granted that crystal structures can be determined in which hundreds, if not thousands, of sepa­ rate atomic positions can be found with apparent ease. In the early years the struc­ tures of relatively simple materials, such as the alkali halides, were often argued over and even disputed, whereas today we routinely see published structures of most complex molecular crystals, including the structures of viruses and proteins.

## Inhaltsverzeichnis

### 1. Crystal Morphology and Crystal Symmetry

Abstract
Crystallography grew up empirically as a branch of mineralogy. It was supported by laws deduced from observations, such as the law of constancy of interfacial angles and the law of rational intercepts, and involved mainly the recognition, description, and classification of naturally occurring crystal species, that is, it was a study of the morphology, or external form, of crystals. By the end of the 19th century, it was believed that crystals were composed of orderly arrays of atoms and molecules and, on this basis, Federov, Schönflies, and Barlow, independently, concluded that there were only 230 ordered spatial patterns, or space groups, based on the 14 crystal lattices deduced earlier by Bravais.

### 2. Lattices and Space-Group Theory

Abstract
In this chapter, we continue our study of crystals by investigating the internal arrangements of crystalline materials. Crystals are characterized by periodicities in three dimensions. An atomic grouping, or pattern motif, which, itself, may or may not be symmetrical, is repeated over and over again by a certain symmetry mechanism that corresponds to the space group of the crystal. Altogether, there are 230 space groups, and each crystalline substance will belong to one or other of them. In its simplest form, a space group may be derived from repeating the pattern motif by the translations of a lattice, as discussed below. It can be developed further by incorporating additional symmetry elements, as demonstrated through Problem 2.1. We now enlarge on these ideas, starting with an examination of lattices.

### 3. I X-rays, X-ray Diffraction, and Structure Factors

II Intensities and Intensity Statistics
Abstract
X-rays are an electromagnetic radiation of short wavelength, and can be produced by the sudden deceleration of rapidly moving electrons at a target material. If an electron falls through a potential difference of V volt, it acquires an energy of eV electron-volt (eV), where e is the charge on an electron. This energy may be expressed as quanta of x-rays of wavelength λ, where each quantum is given by
$$\lambda = hc/(eV)$$
(3.1)
h being Planck’s constant and c the speed of light in vacuum. Substitution of numerical values into (3.1) leads to
$$\lambda = 12.4/V$$
(3.2)
where V is measured in kilovolt and λ is given in Ångström units (Å). The wavelength range of x-rays is approximately 0.1-100 Å, but for the purposes of practical x-ray crystallography, the range used is approximately 0.6–3.0 Å.

### 4. I Optical and X-ray Examination of Crystals

II Measurement of Intensity Data from Single Crystals
Abstract
The optical examination of crystals is interesting in its own right. However, in structure determinations with modern equipment, it is not uncommon to proceed immediately with x-ray studies. In many cases, the technique is straightforward, particularly with the single-crystal x-ray diffractometer (Section 4.7), and the desired results are readily obtained. There are other situations though, where complications arise because of an unusual habit (Section 4.3.3), pseudosymmetry (Section 6.4.4) or twinning (Section 4.11). In such cases, it may be possible to extract useful information from an optical examination of a crystal before using the more detailed x-ray methods.

### 5. Fourier Series and Fourier Transforms

Abstract
In Chapter 3, we touched upon the analogy between the diffraction of x-rays and that of visible light. Here, we extend that discussion and consider some aspects of Fourier series and Fourier transforms.

### 6. Fourier Techniques in X-ray Structure Determination

Abstract
We have reached the stage where we can consider how to attack the solving of a crystal structure. After the earliest trial and error determinations in the 1920s with very simple and highly symmetrical structures, it was found that the application of Fourier series, initially in one dimension, led to the electron density function, in which peaks of density corresponded to atomic positions. As we have seen in the previous chapters, it is necessary to have the phases of the structure factors for this synthesis to be carried out meaningfully. One way in which phase information is obtained is through the Patterson function of vector density, a function of interatomic vectors in the crystal structure.

### 7. Direct Methods and Refinement

Abstract
In this chapter, we consider direct methods, also known as phase probability methods, of solving the phase problem, together with Patterson search techniques, least-squares refinement, and other important procedures that are usually involved in the overall investigation of crystal and molecular structure are also discussed.

### 8. Examples of Crystal Structure Determination

Abstract
In this chapter we wish to draw together, by means of actual examples, material presented earlier in the book. It may be desirable for the reader to refer back to the previous chapters for descriptions of the techniques used, since we shall present here mainly the results obtained at each stage.

### 9. X-ray Structure Determination with Powders

Abstract
Since the earlier editions of this book, developments have taken place with the x-ray examination of polycrystalline materials that have led to complete structure determinations of medium-sized molecules, with up to 60 atoms in the asymmetric unit. It is appropriate, therefore, to include a short account of this topic in the present edition. Further, more detailed discussions of powder methods can be found in the literature.a,b,c

### 10. Proteins and Macromolecular X-ray Analysis

Abstract
In this chapter, we take a more detailed look at methods of x-ray analysis that are particularly applicable to large biological molecules. It will involve some useful reiteration of concepts and ideas discussed in previous chapters. We would also like to remind readers that although there are definite distinctions between large and small molecules in the crystallographic arena, there is no reason to exclude one from the other, and in fact, there are many advantages in being familiar with both. The major differences should become clearer as you progress through this chapter. It follows that while we mainly deal here with macromolecules, much of the information provided in this chapter is applicable to all areas of crystal structure analysis.

### 11. Computer-Aided Crystallography

Abstract
The title of this chapter emphasizes the need for the pre-knowledge gained from a study of the earlier chapters of this book. The programs supplied on the CD and described here are complementary to that work and designed to enable the reader to gain practical experience of the concepts and methods in x-ray structure analysis.

### Backmatter

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