Systematic Absences

Definition

Systematic absences are specific reflections in a crystallographic diffraction pattern that are missing due to the symmetry and arrangement of the crystal lattice. These absences can reveal important information about the underlying space group and structural characteristics of a crystal, as they follow defined extinction rules that depend on the symmetry elements present in the crystal structure.

5 Must Know Facts For Your Next Test

1. Systematic absences occur due to specific symmetry elements, such as screw axes and glide planes, which dictate the allowed reflections in a crystal's diffraction pattern.
2. The presence of systematic absences can significantly narrow down the possible space groups for a crystal, guiding researchers in their structural analysis.
3. Absences can also be classified as either absolute or relative, where absolute absences are completely missing reflections, while relative absences might show reduced intensity but are not entirely absent.
4. When analyzing systematic absences, it's essential to compare observed data with theoretical predictions based on extinction rules to determine the correct space group.
5. In modulated structures, systematic absences may display unique patterns that indicate complex symmetry and variations in periodicity, providing insights into the crystal's organization.

Review Questions

• How do systematic absences help in identifying the space group of a crystal?
  • Systematic absences provide crucial clues about the symmetry elements present in a crystal structure. By examining which reflections are missing from the diffraction pattern, researchers can apply extinction rules to rule out certain space groups and narrow down possible candidates. The pattern of these absences correlates directly with specific symmetry operations, allowing for more accurate determination of the crystal's space group.
• Discuss how extinction rules relate to systematic absences and their impact on crystal structure analysis.
  • Extinction rules define which reflections will be systematically absent based on the symmetry of the crystal structure. These rules arise from the presence of symmetry elements like glide planes or screw axes. When performing crystal structure analysis, understanding these rules helps researchers anticipate which reflections should appear or be absent, guiding them to correct conclusions about the crystal's arrangement and aiding in accurate modeling of its atomic structure.
• Evaluate how systematic absences influence the interpretation of diffraction patterns in modulated structures compared to conventional crystals.
  • In modulated structures, systematic absences can exhibit distinct patterns that reflect additional complexities not seen in conventional crystals. This variation arises from changes in periodicity and symmetry due to modulation. As researchers analyze these diffraction patterns, they must consider both traditional extinction rules and new factors introduced by modulation. This multifaceted approach enables a deeper understanding of intricate structural behaviors and highlights how systematic absences serve as critical indicators of a material's unique properties.

Related terms

Extinction Rules:

Rules that predict which reflections will be absent in a diffraction pattern based on the symmetry of the crystal structure, helping to identify the space group.

Space Group:

A mathematical description of the symmetry of a crystal structure that defines how the points in the lattice repeat in three-dimensional space.

Structure Factor: A complex number representing the amplitude and phase of a diffracted beam, which is crucial for calculating the intensity of reflections in X-ray crystallography.