XRD Academy | Thermo Fisher Scientific

Bragg's law

XRD Basics

X-ray diffraction (XRD) is among the most effective non-destructive tools for identifying and characterizing polycrystalline materials with respect to their crystallography, polymorphic structures, phases and crystallinity changes. By measuring the diffraction angle of a primary X-ray beam according to Bragg’s Law (λ = 2d sinθ, with λ: wavelength, d: d spacing, θ: diffraction angle), it is possible to characterize and identify various polycrystalline materials in many research and industrial applications.

Many XRD solutions are routinely used in sectors as varied as applied materials, geological samples, pharmaceuticals, nanomaterials, and more. Sometimes for some characterizations in routine quality assurance and control of raw materials (cement, metals, etc.), it’s preferable to use integrated instrumentation like X-ray diffraction and fluorescence (XRF-XRD).

If you would like to learn more about using XRD, or XRF-XRD instruments for your application, speak with a member of our team.

XRD Fundamentals

What is XRD?

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X-ray diffraction (XRD) is a foundational technology in solid-state science, providing unique insights into the composition and structural arrangement of crystallized samples. The relevant data are obtained by measuring the diffracted intensity of a primary X-ray beam against the diffraction angle, as per Bragg’s Law. In compliance with this law, different geometries in transmission or reflection mode can be arranged to analyze the samples.

X-Ray diffraction is a phenomenon in which the atoms of a crystal, by virtue of their uniform spacing, cause an interference pattern of the waves in an incident beam of X-rays. The crystal's atomic planes act on the X-rays in the same way a uniformly ruled grating acts on a beam of light (see polarization). The interference pattern is specific to each substance and gives information on the structure of the atoms or molecules in the crystal.

In an XRD measurement, a sample is placed within a chamber and is bombarded with a beam of primary X-rays at an angle defined by the relevant diffraction geometry. The Bragg-Brentano geometry is among the most common methods used in powder XRD, otherwise known as XRPD. It relies on multiple moving parts to detect the secondary scattered X-rays from a sample and obtain a full diffraction pattern.

Provided Bragg’s Law has been satisfied, when the primary X-ray beam interacts with the sample it will diffract and produce a secondary beam that can be acquired by a detector. This yields a diffraction pattern that is characteristic of the unique crystallographic structure of the sample.

Asymmetric mode with a PSD real time detector

In contrast to this Bragg-Brentano geometry that requires a goniometer with mobile parts, it is possible to obtain a real-time full pattern without this motor constraint by using a Thermo Scientific PSD (Position Sensitive Detector). Schematic of this geometry is shown here.

XRD patterns allow to perform a variety of structural investigations, such as fingerprinting of phase content, which requires a comparison of the relative intensities and positions of reflections against existing data in available databases. This is one of the most widely accepted methods for phase control (including the polymorphism considerations) and quantification in many research and industrial processes.

Applications

Understanding the structure of your materials can help you adapt to new challenges unique to your research or industrial domains. We offer the products, services and technologies to help you understand your materials, regardless of the application. See our listing of resources for XRD in these areas:

Various attachments are used with our ARL EQUINOX powder X-ray diffractometers for making acquisitions in real time thanks to fast detectors and for measuring the sample under different forms and environments, to study high or low temperature phase transitions, to define thin film characteristics and other properties.

XRD Products

XRD Product Guide

Thermo Fisher Scientific powder X-ray diffractometers are delivered under the trusted ARL EQUINOX product line, featuring both compact benchtop and full-scale XRD solutions.

According to your needs, various attachments are used with our ARL EQUINOX powder X-ray diffractometers for making acquisitions in real time thanks to fast detectors.

Analysis of structures and phases on polycrystalline materials
Qualitative and quantitative phase analysis
Polymorphic identification and amorphous versus crystalline phases
Crystallite size and preferred orientations
Thin films analysis: Grazing incidence XRD (GIXRD), X-ray reflectometry (XRR)
In-situ studies: phase transitions and structural investigations (low and high temperatures, non-ambient atmosphere, under humidity, …)

ARL X’TRA Companion X-ray Diffractometer

ARL X'TRA Companion diffractometer is perfectly designed to be a cost-effective solution for routine QC/QA in industrial laboratories. Thanks to its state-of-the art solid-state 2D detector, high resolution data is collected within minutes. This robust and accurate benchtop X-ray diffractometer comes with one-click Rietveld quantification capabilities and automated result transmission to a LIMS, and it complies with international X-ray safety regulations.

ARL EQUINOX 100

The ARL EQUINOX 100 is the perfect instrument for fast acquisitions when space becomes a priority, thanks to its fully integrated water-cooling system and its plugging into a standard electrical power outlet. With its excellent performance, it is perfectly designed for a cost-effective solution for routine QC/QA in industrial labs or structural and phase analysis in R&D laboratory or teaching.