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X-ray and neutron scattering studies of surfaces and interfaces have become increasingly popular over that last few year due to the recent developments in both scattering techniques and high intensity sources, particularly synchrotron x-ray sources. Although detailed characterization of any interface requires understanding of scattering both at small angles and in the (wide angle) Bragg reflection regime, as shall restrict ourselves here to discussing only the small angle region. Despite fundamental differences in the basic interactions between x-rays (or neutrons) with atoms, most of the analysis of our x-ray scattering results presented here can be used for neutron studies, with minor modifications. Although it should be mentioned here that current synchrotron x-ray sources are several orders of magnitude more intense than neutron sources and as a result for relatively smooth solid surface specular reflectivity can be measured down to 10−9 with x-rays where as for neutrons this value is (approximately) 10−6 before the measured intensity is buried with diffuse scattering and other background. As we shall discuss, this reduces the resolution with which one can determine density profile at an interface. The plan of this talk is as follows. After giving a brief outline of this method, we shall discuss out results on liquid surfaces first, and then we shall analyze specular and diffuse scattering data of multilayer interfaces. Finally we demonstrate a new method of anomalous reflectivity to determine electron density profiles of thin films in a model independent way.
ways in which the magnetic interaction between neutrons and magnetic moments can yield information on the magnetization densities of thin ?lms and multilayers. I commend the organizers for having organized a group of expert lecturers to present this subject in a detailed but clear fashion, as the importance of the subject deserves. Argonne, IL S. K. Sinha Contents 1 The Interaction of X-Rays (and Neutrons) with Matter . . . . . . . . . . . . . . 1 F. de Bergevin 1. 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. 2 Generalities and De?nitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1. 3 From the Scattering by an Object to the Propagation in a Medium . 14 1. 4 X-Rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 1. 5 X-Rays: Anisotropic Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 1. A Appendix: the Born Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . 54 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 2 Statistical Aspects of Wave Scattering at Rough Surfaces . . . . . . . . . . . . 59 A. Sentenac and J. Daillant 2. 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 2. 2 Description of Randomly Rough Surfaces . . . . . . . . . . . . . . . . . . . . . 60 2. 3 Description of a Surface Scattering Experiment, Coherence Domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 2. 4 Statistical Formulation of the Diffraction Problem . . . . . . . . . . . . . . 72 2. 5 Statistical Formulation of the Scattered Intensity Under the Born Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 3 Specular Re?ectivity from Smooth and Rough Surfaces . . . . . . . . . . . . . 85 A. Gibaud and G. Vignaud 3. 1 The Re?ected Intensity from an Ideally Flat Surface . . . . . . . . . . . . 85 3. 2 X-Ray Re?ectivity in Strati?ed Media . . . . . . . . . . . . . . . . . . . . . . . . 98 3. 3 From Dynamical to Kinematical Theory . . . . . . . . . . . . . . . . . . . . . . 107 3. 4 In?uence of the Roughness on the Matrix Coef?cients . . . . . . . . . . 111 3. A Appendix: The Treatment of Roughness in Specular Re?ectivity . . 113 3. B Appendix: Inversion of re?ectivity data . . . . . . . . . . . . . . . . . . . . . . .
The reflection of and neutrons from surfaces has existed as an x-rays exp- imental for almost it is in the last technique fifty Nevertheless, only years. decade that these methods have become as of enormously popular probes This the surfaces and interfaces. to be due to of several appears convergence of intense different circumstances. These include the more n- availability be measured orders tron and sources that can over (so reflectivity x-ray many of and the much weaker surface diffuse can now also be magnitude scattering of thin films and studied in some the detail); growing importance multil- basic the realization of the ers in both and technology research; important which in the of surfaces and and role roughness plays properties interfaces; the of statistical models to characterize the of finally development topology its and its characterization from on roughness, dependence growth processes The of and to surface scattering experiments. ability x-rays neutro4s study four five orders of in scale of surfaces over to magnitude length regardless their and also their to ability probe environment, temperature, pressure, etc. , makes these the choice for buried interfaces often probes preferred obtaining information about the microstructure of often in statistical a global surfaces, the local This is manner to complementary imaging microscopy techniques, of such studies in the literature witnessed the veritable by explosion published the last few Thus these lectures will useful for over a resource years.
The availability of synchrotron x-ray sources and the subsequent developments described in this book have led to substantial progress in our understanding of molecular ordering at liquid interfaces. This practical guide enables graduate students and researchers working in physics, chemistry, biology and materials science to understand and carry out experimental investigations into the basic physical and chemical properties of liquid surfaces and interfaces. The book examines the surfaces of bulk liquids, thin wetting films and buried liquid-liquid interfaces. It discusses experiments on simple and complex fluids, including pure water and organic liquids, liquid crystals, liquid metals, electrified liquid-liquid interfaces and interfacial monolayers of amphiphiles, nanoparticles, polymers and biomolecules. A detailed description of the apparatus and techniques required for these experiments is provided, and theoretical approaches to data analysis are described, including approximate methods such as the Master formula, the Born approximation, Parratt's algorithm and the Distorted Wave Approximation.
Owing to the increased availability of synchrotron sources, surface X-ray scattering is a rapidly expanding technique with important applications to surface structures and surface phase transitions, roughening of surfaces and interfaces, and the structure of liquid surfaces, including polymers, liquid crystals, and organic films. Surface studies with neutrons, on the other hand provide important information on liquid andmagnetic films. The contributions to this volume, written by active researchers in the field, provide an up-to-date overview of the highly sophisticated techniques and their applications.
In what is an extremely practical and applicable new work, experts provide concise explanations, with examples and illustrations, of the key techniques in this important field. In each case, after basic principles have been reviewed, applications of the experimental techniques are discussed and illustrated with specific examples. Scientists and engineers in research and development will benefit from an application-oriented book that helps them to find solutions to both fundamental and applied problems. They will know that the surfaces and interfaces of polymers play an important role in most of the application areas of polymers, from moulds, foils, and composites, to biomaterials and applications in micro- and nanotechnology.
A practical guide for graduate students and researchers on all aspects of x-ray scattering experiments on liquid surfaces and interfaces.
X-ray scattering is used extensively to provide detailed structural information about materials. Semiconductors have benefited from X-ray scattering techniques as an essential feedback method for crystal growth, including compositional and thickness determination of thin layers. The methods have been developed to reveal very detailed structural information concerning material quality, interface structure, relaxation, defects, surface damage, etc.This book provides a thorough description of the techniques involved in obtaining that information, including X-ray diffractometers and their associated instrument functions, data collection methods, and the simulation of the diffraction patterns observed. Also presented are examples and procedures for interpreting the data to build a picture of the sample, much of which will be common to materials other than semiconductors./a