Patterson map

Definition

A Patterson map is a mathematical tool used in crystallography that visualizes the distribution of interatomic vectors within a crystal structure, derived from the Patterson function. It is essential for analyzing the arrangement of atoms in a crystal by providing insights into distances between pairs of atoms, aiding in the determination of crystal structures. By transforming diffraction data into real space, Patterson maps serve as a foundational method for solving structures, especially when direct methods are challenging.

5 Must Know Facts For Your Next Test

1. Patterson maps are particularly useful when the phase information is unavailable due to the phase problem, allowing researchers to infer atomic positions based solely on intensity data.
2. Each peak in a Patterson map corresponds to an interatomic vector, representing the distance and direction between pairs of atoms, which can reveal symmetry and structural information.
3. Patterson maps can be generated from experimental X-ray or neutron diffraction data, making them versatile for various types of crystal analyses.
4. The resolution of a Patterson map is dependent on the quality and completeness of the diffraction data collected, influencing its usefulness in structure determination.
5. While Patterson maps provide valuable insights into atomic arrangement, they may not uniquely define a structure due to potential overlap and ambiguity in interpreting peaks.

Review Questions

• How does a Patterson map help solve the phase problem in crystallography?
  • A Patterson map helps solve the phase problem by allowing researchers to visualize interatomic vectors without needing direct phase information. The map displays peaks that correspond to distances and directions between pairs of atoms based on intensity data from diffraction patterns. This approach provides a means to deduce atomic positions indirectly, making it especially valuable when traditional methods are not applicable.
• Discuss the significance of each peak in a Patterson map and how it relates to atomic arrangement.
  • Each peak in a Patterson map represents an interatomic vector, indicating both the distance and orientation between pairs of atoms within the crystal. These peaks can reveal crucial information about symmetry, connectivity, and relative positions of atoms. Analyzing these peaks helps crystallographers build a model of the atomic arrangement, guiding further refinement and verification of crystal structures.
• Evaluate how the quality of diffraction data affects the interpretation and utility of Patterson maps in determining crystal structures.
  • The quality of diffraction data directly impacts the clarity and resolution of Patterson maps. High-quality data leads to well-defined peaks, allowing for more accurate interpretations of atomic arrangements. Conversely, poor data may produce overlapping or ambiguous peaks, complicating structure determination. Understanding this relationship emphasizes the importance of collecting precise diffraction data to maximize the effectiveness of Patterson maps in crystallographic analysis.

Related terms

Patterson function: A mathematical function that generates a three-dimensional representation of the distribution of atomic pairs in a crystal, forming the basis for creating Patterson maps.

Fourier transform: A mathematical technique used to convert data from real space to reciprocal space and vice versa, which is crucial in crystallography for analyzing diffraction patterns.

Phase problem: A challenge in crystallography where the phases of diffracted waves are not directly measurable, complicating the reconstruction of electron density maps from diffraction data.