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107 In this way the absolute values of the structure factors may be found, not the phases (6. 8). The problem to find these phases is the phase problem. The present article will treat the following topics. At first the description of the ideal crystal will be given in Chap. B. The underlying principles of this description are the concepts of reciprocal lattice, FOURIER synthesis and sym­ metry. The evaluation of the intensity will then follow in Chap. C and D. Chap. E is concerned with the phase problem and related topics. Though this article treats the analysis of crystal structures, the fundamental concepts for other structures will here be found too. But these topics, and the experimental methods, will l find their place elsewhere . B. Description of the crystalline state. I. Lattice theory. a) The direct lattice. 8. Introduction. In Sect. 3, a description of the ideal crystal was given: The space, occupied by a crystal, is divided into congruent parallelepipeds, each with the same orientation. This parallelepiped is defined by the three basic vectors, a, band c, drawn from an origin 0 (Fig. 2), and is called the primitive cell. This cell is filled with atoms (or ions), and the same configuration of atoms is repeated in space. It has been aptly called a three-dimensional wallpaper, as on a wallpaper the same pattern is repeated again and again.

Inhalts verzeichnis.- Les méthodes expérimentales des déterminations de structures cristallines par rayons X.- A. Les apparails de la radiocristallographie.- I. Les diagrammes de diffraction d’un cristal unique.- II. Les diagrammes de diffraction des poudres cristallines.- B. Du diagramme au réseau réciproque.- I. Cas du cristal unique.- II. Cas des poudres cristallines.- C. Du réseau réciproque à la structure.- I. Méthodes.- a) Préparation des données expérimentales.- b) Ebauche de la structure.- c) L’amélioration des résultats.- II. Techniques.- a) Séries de Fourier.- b) Calcul des facteurs de structure.- D. Applications des méthodes radiocristallographiques.- I. Déterminations de la cristallinité d’une substance.- II. Etude de la texture d’un solide.- III. Textures d’échantillons polycristallins.- IV. L’analyse radiocristallographique.- V. Application de la mesure précise des paramètres du cristal.- Bibliographie générale.- Theoretical Principles of Structural Research X-rays.- A. Fundamental concepts in structure analysis.- B. Description of the crystalline state.- I. Lattice theory.- a) The direct lattice.- b) The reciprocal lattice.- II. The electron density.- III. Symmetry of structures.- C. The fundamental concepts in X-ray scattering.- D. The intensity of the diffracted X-rays.- I. The diffraction by small crystals.- II. The dynamical theory, extinction and absorption.- III. Lattice distortions and temperature factor.- E. Problems of structure analysis.- General references.- Etude de la structure des fluides et des substances amorphes au moyen de la diffusion des rayons X.- A. Théorie de la diffusion des rayons X par les fluides.- I. Diffusion des rayons X par une particule.- a) Diffusion des rayons X par une particule fixe.- b) Diffusion des rayons X par une particule mobile.- II. Diffusion des rayons X par un fluide composé d’une seule espèce de particules.- a) Cas des particules à symétrie sphérique.- b) Diffusion des rayons X par un fluide composé de particules identiques de nature quelconque.- III. Diffusion des rayons X par un fluide composé de plusieurs espèces de particules.- B. Etude expérimentale de la diffusion des rayons X par les fluides.- I. Les montages expérimentaux.- II. Etude des gaz peu comprimés.- III. Etude des fluides denses.- IV. Etude des solutions.- V. Interprétation générale de la présence d’un maximum dans une courbe de diffusion.- C. Etude des substances amorphes.- Bibliographie générale.- Size of Particles and Lattice Defects.- A. Size and shape of particles from small angle x-ray scattering.- I. Theory.- a) Scattering by single particles.- b) Scattering by a group of particles.- II. Analysis of data.- III. Experimental equipment.- IV. Applications.- a) Dilute solutions of proteins and viruses.- b) Concentrated solutions of colloidal particles.- c) Finely divided solids.- B. Lattice defects.- I. Formal treatment of scattering by an imperfect crystal.- a) Review of results for the perfect crystal.- b) The finite crystal.- c) The disordered crystal.- II. Survey of important lattice defects.- a) The mosaic crystal.- b) One-dimensioisal disorders.- c) Three-dimensional substitutional disorder.- d) Point defects.- III. The interpretation of Debye-Scherrer line shapes.- IV. Special techniques.- a) Qualitative investigation of substructure in metals.- b) Microbeam experiments.- c) Small angle scattering from cold worked metals.- Elektroneninterferenzen.- I. Aufbau von Interferenzapparaturen.- a) Aufbau einer normalen Anordnung.- b) Verschiedene Zusatzeinrichtungen.- c) Feinstrahlanordnungen.- d) Erwärmung des bestrahlten Objektes.- II. Die Interferenzen der Elektronenwellen.- a) Elementare Darstellung der Interferenzen an Kristallen.- b) Begründung der elementaren Darstellung.- c) Spezielle Interferenzerscheinungen.- d) Interferenzen sehr harter und sehr weicher Elektronenwellen.- e) Elektroneninterferometrie.- f) Interferenzen an nichtidealen Kristallgittern.- g) Interferenzerscheinungen an nichtkristallinen Stoffen.- III. Anwendung der Elektroneninterferenzmethode auf spezielle Probleme.- a) Über die Struktur elektrolytisch polierter Metalloberflächen.- b) Über die Struktur mechanisch bearbeiteter Oberflächen.- c) Der Aufbau dünner Schichten.- IV. Beugung der Elektronenwellen.- Zusammenfassende Darstellungen.- Neutron Diffraction and Interference.- I. Introduction.- II. Theory of the scattering of thermal neutrons.- a) Scattering by single nuclei.- b) Scattering by non-magnetic crystals.- c) Additions to the simple diffraction theory.- III. Experimental techniques.- a) Sources of thermal neutrons.- b) Monochromators and spectrometers.- c) Detectors.- d) Neutron diffraction methods.- e) Miscellaneous techniques.- IV. Measurement of nuclear properties by use of neutron optics.- V. Determination of the structures of non-magnetic materials by neutron diffraction and refraction.- a) Studies of the positions of hydrogen atoms, without Fourier syntheses.- b) Studies of hydrogen atom positions by Fourier synthesis methods.- c) General structural studies of non-magnetic materials by neutron diffraction and refraction.- VI. Studies of magnetic materials by neutron diffraction and refraction.- a) Magnetic scattering and polarization.- b) Studies of the structure of magnetic materials.- c) Special topics in magnetic scattering.- General references.- Sachverzeichnis (Deutsch-Englisch).- Subject Index (English-German).- Table des matières (Français).