International Tables for Crystallography (2019). Vol. H. ch. 2.5, pp. 118-149
https://doi.org/10.1107/97809553602060000940

Chapter 2.5. Two-dimensional powder diffraction

Contents

  • 2.5. Two-dimensional powder diffraction  (pp. 118-149) | html | pdf | chapter contents |
    B. B. He
    • 2.5.1. Introduction  (pp. 118-119) | html | pdf |
      • 2.5.1.1. The diffraction pattern measured by an area detector  (p. 118) | html | pdf |
      • 2.5.1.2. Comparison between 2D-XRD and conventional XRD  (p. 118) | html | pdf |
      • 2.5.1.3. Advantages of two-dimensional X-ray diffraction  (pp. 118-119) | html | pdf |
    • 2.5.2. Fundamentals  (pp. 119-123) | html | pdf |
      • 2.5.2.1. Diffraction space and laboratory coordinates  (pp. 119-121) | html | pdf |
        • 2.5.2.1.1. Diffraction cones in laboratory coordinates  (pp. 119-120) | html | pdf |
        • 2.5.2.1.2. Diffraction-vector cones in laboratory coordinates  (pp. 120-121) | html | pdf |
      • 2.5.2.2. Detector space and pixel position  (pp. 121-122) | html | pdf |
        • 2.5.2.2.1. Detector position in the laboratory system  (p. 121) | html | pdf |
        • 2.5.2.2.2. Pixel position in diffraction space for a flat detector  (pp. 121-122) | html | pdf |
        • 2.5.2.2.3. Pixel position in diffraction space for a curved detector  (p. 122) | html | pdf |
      • 2.5.2.3. Sample space and goniometer geometry  (pp. 122-123) | html | pdf |
        • 2.5.2.3.1. Sample rotations and translations in Eulerian geometry  (pp. 122-123) | html | pdf |
      • 2.5.2.4. Diffraction-vector transformation  (p. 123) | html | pdf |
        • 2.5.2.4.1. Diffraction unit vector in diffraction space and sample space  (p. 123) | html | pdf |
        • 2.5.2.4.2. Transformation from diffraction space to sample space  (p. 123) | html | pdf |
        • 2.5.2.4.3. Transformation from detector space to reciprocal space  (p. 123) | html | pdf |
    • 2.5.3. Instrumentation  (pp. 123-132) | html | pdf |
      • 2.5.3.1. X-ray source and optics  (pp. 124-125) | html | pdf |
        • 2.5.3.1.1. Beam path in a diffractometer equipped with a 2D detector  (p. 124) | html | pdf |
        • 2.5.3.1.2. Liouville's theorem  (pp. 124-125) | html | pdf |
        • 2.5.3.1.3. X-ray source  (p. 125) | html | pdf |
        • 2.5.3.1.4. X-ray optics  (p. 125) | html | pdf |
      • 2.5.3.2. 2D detector  (pp. 125-128) | html | pdf |
        • 2.5.3.2.1. Active area and pixel size  (pp. 126-127) | html | pdf |
        • 2.5.3.2.2. Spatial resolution of area detectors  (p. 127) | html | pdf |
        • 2.5.3.2.3. Detective quantum efficiency and energy range  (pp. 127-128) | html | pdf |
        • 2.5.3.2.4. Detection limit and dynamic range  (p. 128) | html | pdf |
        • 2.5.3.2.5. Types of 2D detectors  (p. 128) | html | pdf |
      • 2.5.3.3. Data corrections and integration  (pp. 128-132) | html | pdf |
        • 2.5.3.3.1. Nonuniform response correction  (pp. 128-129) | html | pdf |
        • 2.5.3.3.2. Spatial correction  (pp. 129-130) | html | pdf |
        • 2.5.3.3.3. Frame integration  (p. 130) | html | pdf |
        • 2.5.3.3.4. Lorentz, polarization and absorption corrections  (pp. 130-131) | html | pdf |
        • 2.5.3.3.5. Air scatter  (pp. 131-132) | html | pdf |
        • 2.5.3.3.6. Sample absorption  (p. 132) | html | pdf |
    • 2.5.4. Applications  (pp. 132-147) | html | pdf |
      • 2.5.4.1. Phase identification  (pp. 133-136) | html | pdf |
        • 2.5.4.1.1. Relative intensity  (p. 133) | html | pdf |
        • 2.5.4.1.2. Detector distance and resolution  (pp. 133-134) | html | pdf |
        • 2.5.4.1.3. Defocusing effect  (p. 134) | html | pdf |
        • 2.5.4.1.4. Sampling statistics  (pp. 134-136) | html | pdf |
      • 2.5.4.2. Texture analysis  (pp. 136-140) | html | pdf |
        • 2.5.4.2.1. Pole density and pole figures  (p. 136) | html | pdf |
        • 2.5.4.2.2. Fundamental equations  (pp. 136-138) | html | pdf |
        • 2.5.4.2.3. Data-collection strategy  (p. 138) | html | pdf |
        • 2.5.4.2.4. Texture-data processing  (pp. 138-139) | html | pdf |
        • 2.5.4.2.5. Pole-figure interpolation and use of symmetry  (p. 139) | html | pdf |
        • 2.5.4.2.6. Orientation relationship  (pp. 139-140) | html | pdf |
      • 2.5.4.3. Stress measurement  (pp. 140-145) | html | pdf |
        • 2.5.4.3.1. Stress and strain relation  (pp. 140-141) | html | pdf |
        • 2.5.4.3.2. Fundamental equations  (pp. 141-142) | html | pdf |
        • 2.5.4.3.3. Equations for various stress states  (p. 142) | html | pdf |
        • 2.5.4.3.4. Data-collection strategy  (p. 143) | html | pdf |
        • 2.5.4.3.5. Data integration and peak evaluation  (pp. 143-144) | html | pdf |
        • 2.5.4.3.6. Stress calculation  (p. 144) | html | pdf |
        • 2.5.4.3.7. Comparison between the 2D method and the con­ventional method  (pp. 144-145) | html | pdf |
      • 2.5.4.4. Quantitative analysis  (pp. 145-147) | html | pdf |
        • 2.5.4.4.1. Crystallinity  (p. 145) | html | pdf |
        • 2.5.4.4.2. Crystallite size  (pp. 145-147) | html | pdf |
    • References | html | pdf |
    • Figures
      • Fig. 2.5.1. Diffraction patterns in 3D space from a powder sample and the diffractometer plane  (p. 118) | html | pdf |
      • Fig. 2.5.2. Diffraction pattern from a battery component containing multiple layers  (p. 119) | html | pdf |
      • Fig. 2.5.3. The diffraction cone and the corresponding diffraction-vector cone  (p. 120) | html | pdf |
      • Fig. 2.5.4. Detector positions in the laboratory-system coordinates  (p. 121) | html | pdf |
      • Fig. 2.5.5. Relationship between a pixel P and detector position in the laboratory coordinates  (p. 121) | html | pdf |
      • Fig. 2.5.6. Cylinder-shaped detector in vertical direction: (a) detector position in the laboratory coordinates; (b) pixel position in the flattened image  (p. 122) | html | pdf |
      • Fig. 2.5.7. Sample rotation and translation  (p. 122) | html | pdf |
      • Fig. 2.5.8. Unit diffraction vector in (a) the laboratory coordinates and (b) the sample coordinates  (p. 123) | html | pdf |
      • Fig. 2.5.9. X-ray beam path in a two-dimensional X-ray diffraction system  (p. 124) | html | pdf |
      • Fig. 2.5.10. Detector dimensions and maximum measurable 2θ  (p. 126) | html | pdf |
      • Fig. 2.5.11. Solid angle covered by each pixel and its location on the detector  (p. 126) | html | pdf |
      • Fig. 2.5.12. (a) Point-spread function (PSF) from a parallel point beam; (b) line-spread function (LSF) from a sharp line beam  (p. 127) | html | pdf |
      • Fig. 2.5.13. A 2D frame showing γ integration  (p. 130) | html | pdf |
      • Fig. 2.5.14. Geometric relationship between the monochromator and detector in the laboratory coordinates  (p. 131) | html | pdf |
      • Fig. 2.5.15. Absorption correction for a flat slab: (a) reflection; (b) transmission  (p. 132) | html | pdf |
      • Fig. 2.5.16. Diffraction pattern merged from four 2D frames collected from a battery material  (p. 134) | html | pdf |
      • Fig. 2.5.17. Defocusing effects: (a) cylindrical detector; (b) flat detector at various incident angles and detector swing angles; (c) comparison of defocusing factors  (p. 135) | html | pdf |
      • Fig. 2.5.18. Diffraction frame collected from a Cu film on an Si substrate showing intensity variation along γ due to texture  (p. 136) | html | pdf |
      • Fig. 2.5.19. (a) Definition of pole direction angles α and β; (b) stereographic projection in a pole figure  (p. 137) | html | pdf |
      • Fig. 2.5.20. Data-collection strategy: (a) 2D detector with D = 7 cm; (b) 2D detector with D = 10 cm; (c) point detector  (p. 138) | html | pdf |
      • Fig. 2.5.21. Pole-figure data processing: (a) a frame with the 2θ integration ranges for the (220) ring; (b) 2θ profile showing the background and peak; (c) integrated intensity distribution as a function of γ  (p. 139) | html | pdf |
      • Fig. 2.5.22. Pole-figure processing: (a) I(γ) mapped to the pole figure; (b) Pole figure after interpolation and symmetry processing  (p. 139) | html | pdf |
      • Fig. 2.5.23. Combined pole figure of a Cu (111) film on an Si (400) substrate: (a) regular 2D projection; (b) 3D surface plot  (p. 140) | html | pdf |
      • Fig. 2.5.24. Diffraction-cone distortion due to stresses  (p. 141) | html | pdf |
      • Fig. 2.5.25. Data-collection strategy schemes: (a) ω + φ scan; (b) ψ + φ scan  (p. 143) | html | pdf |
      • Fig. 2.5.26. Data integration for stress measurement  (p. 143) | html | pdf |
      • Fig. 2.5.27. Stress calculation with the 2D method and the [\sin ^2\psi ] method: (a) nine data points (abbreviated as pts) on the diffraction ring; (b) measured stress and standard deviation by different methods  (p. 145) | html | pdf |
      • Fig. 2.5.28. 2D diffraction pattern from an oriented polycrystalline polymer sample  (p. 146) | html | pdf |
      • Fig. 2.5.29. Crystallite-size analysis: (a) 2θ profile of a gold nanoparticle (grey) and regular gold metal (black); (b) γ profile of LaB6; (c) measurement range  (p. 146) | html | pdf |