Modern Diffraction Methods

[BOOK DESCRIPTION]

The role of diffraction methods for the solid-state sciences has been pivotal to determining the (micro)structure of a material. Particularly, the expanding activities in materials science have led to the development of new methods for analysis by diffraction. This book offers an authoritative overview of the new developments in the field of analysis of matter by (in particular X-ray, electron and neutron) diffraction. It is composed of chapters written by leading experts on 'modern diffraction methods'. The focus in the various chapters of this book is on the current forefront of research on and applications for diffraction methods. This unique book provides descriptions of the 'state of the art' and, at the same time, identifies avenues for future research. The book assumes only a basic knowledge of solid-state physics and allows the application of the described methods by the readers of the book (either graduate students or mature scientists).

[TABLE OF CONTENTS]

Preface                                            xv
About the Editors                                  xxi
        List of Contributors                       xxiii
  Part I Structure Determination                   1    (86)
    1 Structure Determination of Single Crystals   3    (24)
          Sander van Smaalen
      1.1 Introduction                             3    (2)
      1.2 The Electron Density                     5    (3)
      1.3 Diffraction and the Phase Problem        8    (2)
      1.4 Fourier Cycling and Difference           10   (1)
      Fourier Maps
      1.5 Statistical Properties of Diffracted     11   (4)
      Intensities
      1.6 The Patterson Function                   15   (3)
      1.7 Patterson Search Methods                 18   (1)
      1.8 Direct Methods                           19   (2)
      1.9 Charge Flipping and Low-Density          21   (3)
      Elimination
      1.10 Outlook and Summary                     24   (3)
        References                                 25   (2)
    2 Modern Rietveld Refinement, a Practical      27   (34)
    Guide
          Robert Dinnebier
          Melanie Muller
      2.1 The Peak Intensity                       29   (1)
      2.2 The Peak Position                        30   (1)
      2.3 The Peak Profile                         31   (7)
      2.4 The Background                           38   (1)
      2.5 The Mathematical Procedure               39   (1)
      2.6 Agreement Factors                        39   (2)
      2.7 Global Optimization Method of            41   (3)
      Simulated Annealing
      2.8 Rigid Bodies                             44   (2)
      2.9 Introduction of Penalty Functions        46   (1)
      2.10 Parametric Rietveld Refinement          47   (14)
        2.10.1 Parameterization of the Scale       49   (1)
        Factor Depending on Time for Kinetic
        Analysis
        2.10.2 Parameterization of the Lattice     50   (3)
        Parameters Depending on Pressure for
        Determination of the Equations of State
        2.10.3 Parameterization of Symmetry        53   (5)
        Modes Depending on Temperature for
        Determination of Order Parameters
        References                                 58   (3)
    3 Structure of Nanoparticles from Total        61   (26)
    Scattering
          Katharine L. Page
          Thomas Proffen
          Reinhard B. Neder
      3.1 Introduction                             61   (3)
      3.2 Total Scattering Experiments             64   (5)
        3.2.1 Using X-Rays                         66   (1)
        3.2.2 Using Neutrons                       67   (2)
      3.3 Structure Modeling and Refinement        69   (5)
        3.3.1 Using a Particle Form Factor         69   (1)
        3.3.2 Modeling Finite Nanoparticles        70   (4)
      3.4 Examples                                 74   (8)
        3.4.1 BaTiO3                               74   (4)
        3.4.2 CdSe/ZnS Core-Shell Particles        78   (4)
      3.5 Outlook                                  82   (5)
        References                                 83   (4)
  Part II Analysis of the Microstructure           87   (196)
    4 Diffraction Line-Profile Analysis            89   (38)
          Eric J. Mittemeijer
          Udo Welzel
      4.1 Introduction                             89   (1)
      4.2 Instrumental Broadening                  90   (4)
        4.2.1 Determination of the Instrumental    92   (1)
        Profile Using a Reference (Standard)
        Specimen
        4.2.2 Determination of the Instrumental    92   (1)
        Profile by Calculus
        4.2.3 Subtraction/Incorporation of the     93   (1)
        Instrumental Broadening
      4.3 Structural, Specimen Broadening          94   (17)
        4.3.1 Measures of Line Broadening:         94   (2)
        Fourier Series Representation of
        Diffraction Lines
        4.3.2 Column Length/Crystallite Size       96   (2)
        and Column-Length/Crystallite-Size
        Distribution
        4.3.3 Microstrain Broadening               98   (1)
        4.3.3.1 Assumptions in Integral-Breadth    99   (1)
        Methods
        4.3.3.2 Assumptions in Fourier Methods     100  (1)
        4.3.3.3 Microstrain-Broadening             101  (3)
        Descriptions Derived from a
        Microstructural Model
        4.3.4 Anisotropic Size and                 104  (2)
        Microstrain(-Like) Diffraction-Line
        Broadening
        4.3.5 Macroscopic Anisotropy               106  (1)
        4.3.6 Crystallite Size and Coherency of    106  (5)
        Diffraction
      4.4 Practical Application of Line-Profile    111  (11)
      Analysis
        4.4.1 Line-Profile Decomposition           111  (1)
        4.4.1.1 Breadth Methods                    111  (4)
        4.4.1.2 Fourier Methods                    115  (1)
        4.4.1.3 Whole Powder-Pattern Fitting       116  (1)
        4.4.2 Line-Profile Synthesis               116  (1)
        4.4.2.1 General Strain-Field Method        117  (1)
        4.4.2.2 Specific Microstructural           118  (2)
        Models: Whole Powder-Pattern Modeling
        (WPPM) and Multiple Whole-Profile
        Modeling/Fitting (MWP)
        4.4.2.3 General Atomistic Structure:       120  (2)
        the Debye Scattering Function
      4.5 Conclusions                              122  (5)
        References                                 123  (4)
    5 Residual Stress Analysis by X-Ray            127  (28)
    Diffraction Methods
          Christoph Genzel
          Ingwer A. Denks
          Manuela Klaus
      5.1 Introduction                             127  (2)
      5.2 Principles of Near-Surface X-Ray         129  (12)
      Residual Stress Analysis
        5.2.1 Fundamental Relations                129  (1)
        5.2.2 Concepts of Diffraction Data         130  (1)
        Acquisition: Angle-Dispersive and
        Energy-Dispersive Modes
        5.2.3 Concepts of Strain Depth             131  (1)
        Profiling: LAPLACE and Real Space
        Approach
        5.2.3.1 Definition of the Information      131  (2)
        Depth
        5.2.3.2 Depth Profiling in the LAPLACE     133  (3)
        Space
        5.2.3.3 Depth Profiling in Real Space      136  (3)
        5.2.3.4 "Fixed" versus "Variable Depth"    139  (2)
        Methods
      5.3 Near-Surface X-Ray Residual Stress       141  (10)
      Analysis by Advanced and Complementary
      Methods
        5.3.1 Residual Stress Depth Profiling      141  (1)
        in Multilayered Coating Systems
        5.3.1.1 The "Equivalence Thickness"        141  (3)
        Concept
        5.3.1.2 The "Stress Scanning" Method       144  (3)
        5.3.2 Residual Stress Gradient             147
        Evaluation in Surface-Treated Bulk
        Samples
        5.3.2.1 Fixed Depth Analysis in the        142  (7)
        Real Space: Direct Access to σ (z)
        5.3.2.2 Residual Stress Evaluation in      149  (2)
        the LAPLACE Space: From σ (τ)
        to σ (z)
      5.4 Final Remarks                            151  (4)
        References                                 153  (2)
    6 Stress Analysis by Neutron Diffraction       155  (18)
          Lothar Pintschovius
          Michael Hofmann
      6.1 Introductory Remarks                     155  (1)
      6.2 Fundamentals of the Technique            155  (4)
        6.2.1 The d0-Problem                       156  (1)
        6.2.2 Macrostrains versus Microstrains     157  (1)
        6.2.3 Strain Tensors                       158  (1)
        6.2.4 Reflection Line Broadenings          158  (1)
      6.3 Instrumentation                          159  (5)
        6.3.1 Angle-Dispersive Instruments         159  (1)
        6.3.1.1 Monochromators                     159  (1)
        6.3.1.2 Beam-Defining Optics               160  (1)
        6.3.1.3 Detectors                          161  (1)
        6.3.1.4 Auxiliaries                        162  (1)
        6.3.2 Time-of-Flight Instruments           162  (2)
        6.3.3 Special Instruments                  164  (1)
      6.4 Capabilities                             164  (2)
        6.4.1 Types of Materials                   164  (1)
        6.4.2 Spatial Resolution                   164  (1)
        6.4.3 Penetration Depth                    165  (1)
        6.4.4 Accuracy                             166  (1)
        6.4.5 Throughput                           166  (1)
      6.5 Examples                                 166  (7)
        6.5.1 Railway Rail                         166  (101)
        6.5.2 Weldments                            267
        6.5.3 Ceramics                             168  (2)
        6.5.4 Composite Materials                  170  (1)
        References                                 170  (3)
    7 Texture Analysis by Advanced Diffraction     173  (48)
    Methods
          Hans-Rudolf Wenk
      7.1 Introduction and Background              173  (4)
      7.2 Synchrotron X-Rays                       177  (13)
        7.2.1 General Approach                     177  (1)
        7.2.2 Hard Synchrotron X-Rays              178  (2)
        7.2.3 In situ High-Pressure Experiments    180  (3)
        7.2.4 From Diffraction Images to           183  (5)
        Orientation Distribution
        7.2.5 Opportunities with the Laue          188  (1)
        Technique
        7.2.6 Synchrotron Applications             188  (2)
      7.3 Neutron Diffraction                      190  (14)
        7.3.1 General Comments                     190  (3)
        7.3.2 Monochromatic Neutrons               193  (1)
        7.3.3 Polychromatic Time-of-Flight         194  (3)
        (TOF) Neutrons
        7.3.4 Special Techniques                   197  (1)
        7.3.5 Data Analysis for TOF Neutrons       198  (4)
        7.3.6 Neutron Applications                 202  (1)
        7.3.6.1 Grain Statistics                   202  (1)
        7.3.6.2 Polymineralic Rocks                202  (1)
        7.3.6.3 In situ Experiments and Phase      203  (1)
        Transformations
        7.3.6.4 Magnetic Textures                  204  (1)
      7.4 Electron Diffraction                     204  (8)
        7.4.1 Transmission Electron Microscope     204  (1)
        7.4.2 Scanning Electron Microscope (SEM)   205  (4)
        7.4.3 EBSD Applications                    209  (1)
        7.4.3.1 Misorientations                    209  (1)
        7.4.3.2 In situ Heating                    209  (1)
        7.4.3.3 In situ Deformation                210  (1)
        7.4.3.4 3D Mapping                         211  (1)
        7.4.3.5 Residual Strain Analysis           211  (1)
      7.5 Comparison of Methods                    212  (1)
      7.6 Conclusions                              213  (8)
        Acknowledgments                            214  (1)
        References                                 214  (7)
    8 Surface-Sensitive X-Ray Diffraction          221  (38)
    Methods
          Andreas Stierle
          Elias Vlieg
      8.1 Introduction                             221  (3)
        8.1.1 Structure Determination by X-Ray     223  (1)
        Diffraction
      8.2 X-Ray Reflectivity                       224  (3)
      8.3 Bragg Scattering in Reduced              227  (22)
      Dimensions (Crystal Truncation Rod
      Scattering)
        8.3.1 Thin-Film Diffraction                227  (3)
        8.3.2 Surface Diffraction from             230  (2)
        Half-Infinite Systems
        8.3.2.1 Surface Relaxations                232  (2)
        8.3.2.2 Surface Reconstructions and        234  (3)
        Fourier Methods
        8.3.2.3 Surface Roughness                  237  (2)
        8.3.2.4 Vicinal Surfaces                   239  (1)
        8.3.2.5 Two-Layer Roughness Model for      240  (5)
        Growth Studies
        8.3.2.6 Interface Diffraction              245  (2)
        8.3.2.7 The Specular Rod                   247  (2)
      8.4 Grazing Incidence X-Ray Diffraction      249  (3)
      8.5 Experimental Geometries                  252  (2)
      8.6 Trends                                   254  (5)
        Acknowledgments                            255  (1)
        References                                 255  (4)
    9 The Micro- and Nanostructure of Imperfect    259  (24)
    Oxide Epitaxial Films
          Alexandre Boulle
          Florine Conchon
          Rene Guinchretiere
      9.1 The Diffracted Amplitude and Intensity   260  (2)
        9.1.1 Diffracted Amplitude                 260  (1)
        9.1.2 Diffracted Intensity                 261  (1)
      9.2 The Correlation Volume                   262  (7)
        9.2.1 Crystallite Size and Shape           262  (3)
        9.2.2 Crystallite Size Fluctuations        265  (2)
        9.2.3 Crystallite Shape Fluctuations       267  (2)
      9.3 Lattice Strain                           269  (5)
        9.3.1 Statistical Properties               269  (3)
        9.3.2 Spatial Properties                   272  (2)
      9.4 Example                                  274  (3)
      9.5 Strain Gradients                         277  (2)
        9.5.1 Background                           277  (1)
        9.5.2 Strain Profile Retrieval             277  (1)
        9.5.3 Example                              278  (1)
      9.6 Conclusions                              279  (4)
        References                                 281  (2)
  Part III Phase Analysis and Phase                283  (76)
  Transformations
    10 Quantitative Phase Analysis Using the       285  (36)
    Rietveld Method
          Ian C. Madsen
          Nicola V.Y. Scarlett
          Daniel P. Riley
          Mark D. Raven
      10.1 Introduction                            285  (1)
      10.2 Mathematical Basis                      286  (9)
        10.2.1 Rietveld-Based Methods              286  (4)
        10.2.2 Improving Accuracy                  290  (2)
        10.2.3 Correlation with Thermal            292  (3)
        Parameters
      10.3 Applications in Minerals and            295  (23)
      Materials Research
        10.3.1 Crystallization from                295  (3)
        Hydrothermal Solutions
        10.3.2 Energy-Dispersive Diffraction       298  (3)
        10.3.2.1 Application of EDD to the         301  (3)
        Study of Inert Anodes for Light Metal
        Production
        10.3.3 Quantitative Phase Analysis in      304  (2)
        Mineral Exploration
        10.3.3.1 Particle Statistics               306  (1)
        10.3.3.2 Preferred Orientation             306  (1)
        10.3.3.3 Microabsorption                   306  (1)
        10.3.3.4 Identification of Mineral         307  (1)
        Types and Polytypes
        10.3.3.5 Element Substitution and Solid    307  (1)
        Solution
        10.3.3.6 Severe Peak Overlap               308  (1)
        10.3.3.7 Poorly Crystalline Components     309  (1)
        10.3.3.8 Clay and Disordered Structures    309  (1)
        10.3.4 The Reynolds Cup                    310  (2)
        10.3.5 Use of QPA-Derived Kinetics in      312  (1)
        the Design of Novel Materials
        10.3.5.1 Methodologies for Synthesis       312  (1)
        Optimization Using QPA
        10.3.5.2 Design and Synthesis              312  (4)
        Optimization of Novel Materials:
        Mn+1AXn Phases
        10.3.5.3 In situ Differential Thermal      316  (2)
        Analysis (DTA) Using QPA
      10.4 Summary                                 318  (3)
        Acknowledgments                            318  (1)
        References                                 318  (3)
    11 Kinetics of Phase Transformations and of    321  (38)
    Other Time-Dependent Processes in Solids
    Analyzed by Powder Diffraction
          Andreas Leineweber
          Eric J. Mittemeijer
      11.1 Introduction                            321  (2)
      11.2 Kinetic Concepts                        323  (14)
        11.2.1 Process Rates                       323  (4)
        11.2.2 The Temperature Dependence of       327  (1)
        the Process Rate
        11.2.2.1 Arrhenius-Type Temperature        327  (1)
        Dependence of the Rate Constant k(T)
        11.2.2.2 Non-Arrhenius-Type Process        328  (2)
        Kinetics
        11.2.3 Rate Laws for Isothermally          330  (1)
        Conducted Processes
        11.2.3.1 mth-Order Kinetics of             330  (1)
        Homogeneous Processes
        11.2.3.2 Johnson-Mehl-Avrami-Kolmogorov    331  (1)
        Kinetics of Heterogeneous Phase
        Transformations
        11.2.3.3 Grain Growth and Ostwald          332  (1)
        Ripening
        11.2.3.4 Volume-Diffusion-Controlled       333  (1)
        Processes
        11.2.3.5 Order-Disorder-Related            333  (3)
        Processes
        11.2.4 Rate Laws for Nonisothermally       336  (1)
        Conducted Processes
      11.3 Tracing the Process Kinetics by         337  (2)
      Powder Diffraction
      11.4 Mode of Measurement: In Situ versus     339  (3)
      Ex Situ Methods
      11.5 Types of Kinetic Processes and          342  (12)
      Examples
        11.5.1 Local Composition in Solid is       342  (1)
        Retained
        11.5.1.1 Reconstructive, Polymorphic       342  (4)
        Transformations α → β
        11.5.1.2 Polymorphic Transformations of    346  (1)
        Order-Disorder Character and Related
        Processes
        11.5.1.3 Polymorphic Transformations of    347  (2)
        Polytypic Character
        11.5.1.4 Grain Growth                      349  (1)
        11.5.2 Local Concentration Variations      350  (1)
        within Isolated Solid Systems
        11.5.2.1 Precipitation Processes           350  (1)
        11.5.2.2 Solid-State Reaction between      351  (1)
        Different Phases
        11.5.3 Composition Changes in Solids by    352  (2)
        Reaction with Fluid Matter
      11.6 Concluding Remarks                      354  (5)
        References                                 354  (5)
  Part IV Diffraction Methods and                  359  (160)
  Instrumentation
    12 Laboratory Instrumentation for X-Ray        361  (38)
    Powder Diffraction: Developments and
    Examples
          Udo Welzel
          Eric J. Mittemeijer
      12.1 Introduction: Historical Sketch         361  (4)
      12.2 Laboratory X-Ray Powder Diffraction:    365  (23)
      Instrumentation
        12.2.1 Overview                            365  (1)
        12.2.2 Laboratory X-Ray Sources;           365  (1)
        Monochromatization
        12.2.2.1 X-Ray Sources                     365  (3)
        12.2.2.2 Monochromatization/Filtering      368  (2)
        12.2.3 Debye-Scherrer (-Hull) Geometry     370  (1)
        12.2.4 Monochromatic Pinhole Techniques    371  (1)
        12.2.5 (Para-)Focusing Geometries          371  (1)
        12.2.5.1 Seemann-Bohlin Geometry           372  (1)
        12.2.5.2 Bragg-Brentano Geometry           373  (3)
        12.2.6 Instrumental Aberrations of         376  (1)
        (Para-)Focusing Geometries
        12.2.7 Parallel-Beam Geometry              377  (1)
        12.2.7.1 Polycapillary Collimators         378  (1)
        12.2.7.2 X-Ray Mirrors                     379  (2)
        12.2.7.3 X-Ray Mirrors versus X-Ray        381  (2)
        Lenses; Comparative Discussion
        12.2.7.4 Instrumental Aberrations of       383  (1)
        Parallel-Beam Geometry
        12.2.8 Further, Recent Developments        384  (1)
        12.2.8.1 Two-Dimensional Detectors         384  (3)
        12.2.8.2 Microdiffraction                  387  (1)
        12.2.8.3 Energy-Dispersive Diffraction     388  (1)
      12.3 Examples                                388  (11)
        12.3.1 Parallel-Beam Diffraction Methods   388  (1)
        12.3.1.1 High Brilliance, Parallel-Beam    388  (1)
        Laboratory X-Ray Source
        12.3.1.2 Applications                      389  (2)
        12.3.2 Two-Dimensional Diffraction         391  (3)
        Methods
        Acknowledgments                            394  (1)
        References                                 394  (5)
    13 The Calibration of Laboratory X-Ray         399  (40)
    Diffraction Equipment Using NIST Standard
    Reference Materials
          James P. Cline
          David Black
          Donald Windover
          Albert Henins
      13.1 Introduction                            399  (1)
      13.2 The Instrument Profile Function         400  (11)
      13.3 SRMs, Instrumentation, and Data         411  (7)
      Collection Procedures
      13.4 Data Analysis Methods                   418  (5)
      13.5 Instrument Qualification and            423  (13)
      Validation
      13.6 Conclusions                             436  (3)
        References                                 437  (2)
    14 Synchrotron Diffraction: Capabilities,      439  (30)
    Instrumentation, and Examples
          Gene E. Ice
      14.1 Introduction                            439  (2)
      14.2 The Underlying Physics of               441  (4)
      Synchrotron Sources
        14.2.1 Storage Ring Sources                441  (4)
        14.2.2 Free-Electron Lasers and Other      445  (1)
        Emerging X-Ray Sources
      14.3 Diffraction Applications Exploiting     445  (11)
      High Source Brilliance
        14.3.1 Microdiffraction                    446  (3)
        14.3.1.1 Microdiffraction Example 1:       449  (2)
        Stress-Driven Sn Whisker Growth
        14.3.1.2 Microdiffraction Example 2:       451  (1)
        Damage in Ion-Implanted Si
        14.3.1.3 Other Microdiffraction            452  (1)
        Applications
        14.3.2 Surface and Interface Diffraction   452  (1)
        14.3.2.1 Surface Diffraction Example 1:    453  (2)
        Truncation Rod Scattering (TRS)
        14.3.2.2 Surface Diffraction Example 2:    455  (1)
        Surface Studies of Phase
        Transformations in Langmuir-Blodgett
        Films
      14.4 High Q-Resolution Measurements          456  (1)
      14.5 Applications of Tunability: Resonant    456  (9)
      Scattering
        14.5.1 Resonant Scattering Example 1:      458  (3)
        Multiple Anomalous Diffraction, MAD
        14.5.2 Resonant Scattering Example 2: 3    461  (3)
        λ Determination of Local
        Short-Range Correlation in Binary Alloys
        14.5.3 Resonant Scattering Example 3:      464  (1)
        Determination of Magnetic Structure and
        Correlation Lengths
      14.6 Future: Ultrafast Science and           465  (4)
      Coherence
        14.6.1 Coherent Diffraction                466  (1)
        14.6.2 Ultrafast Diffraction               466  (1)
        References                                 467  (2)
    15 High-Energy Electron Diffraction:           469  (22)
    Capabilities, Instrumentation, and Examples
          Christoph T. Koch
      15.1 Introduction                            469  (1)
      15.2 Instrumentation                         470  (4)
        15.2.1 Fundamentals                        470  (2)
        15.2.2 Diffraction Modes in a TEM          472  (2)
        15.2.3 Femtosecond Electron Diffraction    474  (1)
      15.3 Electron Diffraction Methods in the     474  (12)
      TEM
        15.3.1 Precession Electron Diffraction     474  (2)
        (PED)
        15.3.2 Quantitative Convergent-Beam        476  (1)
        Electron Diffraction (QCBED)
        15.3.3 Large-Angle Convergent-Beam         477  (1)
        Electron Diffraction (LACBED)
        15.3.4 Large-Angle Rocking-Beam            478  (4)
        Electron Diffraction (LARBED)
        15.3.5 Diffraction Tomography              482  (1)
        15.3.6 Real-Space Crystallography          482  (1)
        15.3.7 Coherent Diffractive Imaging        483  (2)
        (CDI) with Electrons
        15.3.8 Mapping Strain by Electron          485  (1)
        Diffraction
      15.4 Summary and Outlook                     486  (5)
        Acknowledgment                             486  (1)
        References                                 486  (5)
    16 In Situ Diffraction Measurements:           491  (28)
    Challenges, Instrumentation, and Examples
          Helmut Ehrenberg
          Anatoliy Senyshyn
          Manuel Hinterstein
          Hartmut Fuess
      16.1 Introduction                            491  (1)
      16.2 Instrumentation and Experimental        492  (5)
      Challenges
        16.2.1 General Considerations              492  (1)
        16.2.2 Absorption                          493  (1)
        16.2.3 Detection Challenges                494  (3)
      16.3 Examples                                497  (22)
        16.3.1 Electrochemical In Situ Studies     497  (5)
        of Electrode Materials and In Operando
        Investigations of Li-Ion Batteries
        16.3.2 In situ Studies of Piezoceramics    502  (13)
        in Electric Fields
        Acknowledgment                             515  (1)
        References                                 515  (4)
Index                                              519