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Determination of Crystal Structures

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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...

Lattice Centering and Coordination Number

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The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
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Updated: Jun 16, 2026

Comprehensive Characterization of Extended Defects in Semiconductor Materials by a Scanning Electron Microscope

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Published on: May 28, 2016

Determination of lattice parameters from multiple CBED patterns: a statistical approach.

G Brunetti¹, E Bouzy, J J Fundenberger

¹Laboratoire d'Etude des Textures et Application aux Matériaux (LETAM), UMR CNRS 7078, Ile du Saulcy, 57045 Metz Cedex 1, France.

Ultramicroscopy

|January 26, 2010

Summary

This study quantifies measurement uncertainties in lattice parameters using Convergent Beam Electron Diffraction (CBED). Analyzing multiple diffraction patterns significantly enhances precision and accuracy, overcoming common limitations.

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Quantitative Atomic-Site Analysis of Functional Dopants/Point Defects in Crystalline Materials by Electron-Channeling-Enhanced Microanalysis

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Published on: May 10, 2021

Area of Science:

Materials Science
Crystallography
Electron Microscopy

Background:

Convergent Beam Electron Diffraction (CBED) is a powerful technique for determining crystal structure.
Accurate measurement of lattice parameters is crucial for understanding material properties.
Kinematic approximation in CBED introduces uncertainties that need quantification.

Purpose of the Study:

To analyze and quantify the uncertainties in lattice parameter measurements using CBED under kinematic approximation.
To investigate the impact of systematic and random errors on measurement precision.
To propose and evaluate methods for enhancing the accuracy and precision of CBED measurements.

Main Methods:

Acquisition and analysis of numerous diffraction patterns from a silicon sample at 93 K using a LaB(6) Transmission Electron Microscope (TEM).
Statistical analysis of random errors, confirming adherence to normal distribution.
Evaluation of single-pattern versus multiple-pattern analysis for lattice parameter determination.

Main Results:

Random errors in single-pattern measurements follow a normal distribution, yielding a precision of 3-4 x 10(-4).
Multiple pattern analysis significantly improves both accuracy and precision.
Precision of 1.5-2 x 10(-4) for the lattice parameter 'a' using three HOLZ line patterns.
Precision of 5 x 10(-4) for the complete set of lattice parameters using six diffraction patterns.

Conclusions:

Multiple pattern analysis is essential for improving the accuracy and precision of CBED lattice parameter measurements.
This approach effectively addresses the non-uniqueness of solutions often encountered in CBED studies.
The proposed method offers a straightforward way to enhance measurement reliability in electron diffraction analysis.