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Determination of Crystal Structures

Determination of Crystal Structures

In the late 1800s, the revelation that light extended beyond visible wavelengths led to the discovery of X-rays by Wilhelm Roentgen. Recognized as high-energy electromagnetic radiation with short wavelengths, X-rays prompted exploration into their interaction with crystals. Max von Laue proposed in 1912 that the periodic arrangement of atoms, ions, or molecules in crystals would cause them to diffract X-rays, a hypothesis confirmed through experiments with copper sulfate and zinc sulfide...

X-ray Crystallography

X-ray Crystallography

The size of the unit cell and the arrangement of atoms in a crystal may be determined from measurements of the diffraction of X-rays by the crystal, termed X-ray crystallography.
Diffraction
Diffraction is the change in the direction of travel experienced by an electromagnetic wave when it encounters a physical barrier whose dimensions are comparable to those of the wavelength of the light. X-rays are electromagnetic radiation with wavelengths about as long as the distance between neighboring...

Crystallographic Point Groups

Crystallographic Point Groups

Crystallographic point groups represent the various symmetry operations that can occur within crystals. They are unique in that at least one point will always remain unchanged during these actions. For instance, consider the triclinic system. This system, devoid of any axis or plane of symmetry, aligns with the C1 and Ci point groups.where Cᵢ is characterized solely by a center of inversion.Contrastingly, the monoclinic system introduces an element of symmetry. This system with one plane...

The Seven Crystal Systems: Overview

The Seven Crystal Systems: Overview

Crystals with various point group symmetries belong to different crystal classes, which are synonymous terms. Despite being in the same class, crystals may have distinct shapes, like cubes and octahedra. There are 32 three-dimensional point groups, all of which are systematically divided into seven crystal systems.The basic cubic crystal system, exemplified by NaCl, features orthogonal vectors (α = β = �� = 90°) of equal lengths (a = b = c). When specific...

Unit Cells

Unit Cells

A crystal's internal structure is an orderly array of atoms, ions, or molecules, and the details of this array significantly influence the solid's properties. In a crystal, periodically repeating 'structural motifs' - which could be atoms, molecules, or groups thereof - create a 'space lattice.' This is essentially a three-dimensional, infinite array of points, each surrounded by its neighbors in an identical way, forming the basic structure of the crystal.A 'unit cell' is a theoretical...

Crystal Field Theory - Tetrahedral and Square Planar Complexes

Crystal Field Theory - Tetrahedral and Square Planar Complexes

Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than...

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Related Experiment Video

Updated: Apr 19, 2026

X-Ray Crystallography to Study the Oligomeric State Transition of the Thermotoga maritima M42 Aminopeptidase TmPep1050

X-Ray Crystallography to Study the Oligomeric State Transition of the Thermotoga maritima M42 Aminopeptidase TmPep1050

Published on: May 13, 2020

SHELXT - integrated space-group and crystal-structure determination.

George M Sheldrick¹

¹Department of Structural Chemistry, Georg-August Universität Göttingen, Tammannstrasse 4, Göttingen, 37077, Germany.

Acta Crystallographica. Section A, Foundations and Advances

|December 25, 2014

Summary

SHELXT is a new program that solves crystal structures using a dual-space algorithm. It efficiently determines atomic positions from diffraction data, enabling rapid structure solution.

Keywords:

Patterson superposition direct methods dual-space recycling element assignment space-group determination

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Last Updated: Apr 19, 2026

X-Ray Crystallography to Study the Oligomeric State Transition of the Thermotoga maritima M42 Aminopeptidase TmPep1050

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Area of Science:

Crystallography
Computational Chemistry
Materials Science

Background:

Solving the phase problem is crucial for determining crystal structures from diffraction data.
Existing methods may struggle with incomplete or low-resolution data.

Purpose of the Study:

To introduce SHELXT, a novel program for solving the crystal structure phase problem.
To present a new dual-space algorithm for efficient structure determination.

Main Methods:

Employs a dual-space algorithm for single-crystal reflection data.
Handles missing data and extends resolution as needed.
Tests all space groups for consistency with P1 phases and applies symmetry.

Main Results:

Successfully solved thousands of structures with a high success rate.
Optimized for multiprocessor computers for faster computation.
Assigns elements and refines structures, including Flack parameter calculation.

Conclusions:

SHELXT provides an efficient and successful method for solving crystal structures.
The program is well-suited for routine structure determination from diffraction data.
Limitations include unsuitability for severely disordered or twinned structures.