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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.
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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...

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...

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...

Crystal Field Theory - Octahedral Complexes

Crystal Field Theory - Octahedral Complexes

Crystal Field Theory
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...

Crystal Field Theory - Tetrahedral and Square Planar Complexes

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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 30, 2026

$On-Chip Crystallization and Large-Scale Serial Diffraction at Room Temperature$

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Published on: March 11, 2022

Quasicrystals - a paradigm shift in crystallography?

Walter Steurer¹

¹Laboratory of Crystallography, ETH Zurich, Vladimir-Prelog-Weg 10, CH-8093 Zurich, Switzerland steurer@mat.ethz.ch.

|May 8, 2014

Summary

The discovery of quasicrystals redefined crystal structures and diffraction theory. These unique materials, found across multiple scales, challenge traditional crystallography and may represent a scientific paradigm shift.

Area of Science:

Materials Science
Crystallography
Condensed Matter Physics

Background:

Quasicrystals exhibit long-range order but lack translational symmetry.
Their discovery challenged the traditional definition of a crystal.
Quasicrystals exist at atomic, mesoscopic, and macroscopic scales.

Purpose of the Study:

To assess the impact of quasicrystal discovery on crystallography.
To determine if quasicrystals represent a scientific revolution or paradigm shift.
To provide an overview of current quasicrystal research.

Main Methods:

Literature review of quasicrystal research.
Analysis of the consequences for crystal definition and diffraction theory.
Discussion of quasicrystals' role in thermodynamic equilibrium.

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Main Results:

Quasicrystals significantly impacted the understanding of long-range order.
The definition of 'crystal' and diffraction theory were revised.
Quasicrystals have been observed in diverse systems from atomic to macro scales.

Conclusions:

The discovery of quasicrystals has profoundly influenced crystallography.
It prompted a re-evaluation of fundamental concepts in materials science.
Quasicrystals represent a significant paradigm shift in our understanding of ordered matter.