science

Three-dimensional X-ray diffraction

Three-dimensional X-ray diffraction is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Three-dimensional X-ray diffraction rather than just read about it. In short: Three-dimensional X-ray diffraction (3DXRD) is a microscopy technique using hard X-rays (with energy in the 30-100 keV range) to investigate the internal structure of polycrystalline materials in three dimensions. For a given sample, 3DXRD returns the shape, juxtaposition, and orientation of the crystallites ("grains") it is made of. 3DXRD allows investigating micrometer- to millimetre-sized samples with resolution…

Key takeaways

Three-dimensional X-ray diffraction belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Three-dimensional X-ray diffraction to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Three-dimensional X-ray diffraction from memory before moving on to harder problems.

Reference excerpt

Three-dimensional X-ray diffraction (3DXRD) is a microscopy technique using hard X-rays (with energy in the 30-100 keV range) to investigate the internal structure of polycrystalline materials in three dimensions. For a given sample, 3DXRD returns the shape, juxtaposition, and orientation of the crystallites ("grains") it is made of. 3DXRD allows investigating micrometer- to millimetre-sized samples with resolution ranging from hundreds of nanometers to micrometers. Other techniques employing X-rays to investigate the internal structure of polycrystalline materials include X-ray diffraction contrast tomography (DCT) and high energy X-ray diffraction (HEDM). Compared with destructive techniques, e.g. three-dimensional electron backscatter diffraction (3D EBSD), with which the sample is serially sectioned and imaged, 3DXRD and similar X-ray nondestructive techniques have the following advantages:

They require less sample preparation, thus limiting the introduction of new structures in the sample. They can be used to investigate larger samples and to employ more complicated sample environments. They enable to study how 3D grain structures evolve with time. Since measurements do not alter the sample, different types of analysis can be made in sequence.

Experimental setup 3DXRD measurements are performed using various experimental geometries. The classical 3DXRD setup is similar to the conventional tomography setting used at synchrotrons: the sample, mounted on a rotation stage, is illuminated using quasi-parallel monochromatic X-ray beam. Each time a certain grain within the sample satisfies the Bragg condition, a diffracted beam is generated. This signal is transmitted through the sample and collected by two-dimensional detectors. Since different grains satisfy the Bragg condition at different angles, the sample is rotated to probe the complete sample structure. Crucial for 3DXRD is the idea to mimic a three-dimensional detector by positioning a number of two-dimensional detectors at different distances from the centre of rotation of the sample, and exposing these either simultaneously (many detectors are semi-transparent to hard X-rays) or at different times. A 3DXRD microscope is installed at the Materials Science beamline of the ESRF.

Software To determine the crystallographic orientation of the grains in the considered sample, the following software packages are in use: Fable and GrainSpotter. Reconstructing the 3D shape of the grains is nontrivial and three approaches are available to do so, respectively based on simple back-projection, forward projection, algebraic reconstruction technique and Monte Carlo method-based reconstruction.

Applications With 3DXRD, it is possible to study in situ the time evolution of materials under different conditions. Among others, the technique has been used to map the elastic strains and stresses in a pre-strained nickel-titanium wire.

Related techniques The scientists involved in developing 3DXRD contributed to the development of three other three-dimensional non-destructive techniques for the material sciences, respectively using electrons and neutrons as a probe: three-dimensional orientation mapping in the transmission electron microscope (3D-OMiTEM), time-of-flight 3D neutron diffraction for multigrain crystallography (ToF 3DND) and laue 3D neutron diffraction (Laue3DND). Using a system of lenses, the synchrotron technique dark-field X-ray microscopy (DFXRM) extends the capabilities of 3DXRD, allowing to focus on a deeply embedded single grain and to reconstruct its 3D structure and its crystalline properties. DFXRM is under development at the European Synchrotron Research Facility (ESRF), beamline ID06. In a laboratory setting, 3D grain maps using X-rays as a probe can be obtained using laboratory diffraction contrast tomography (LabDCT), a technique derived from 3DXRD.

See also Diffraction X-ray diffraction computed tomography (XRD-CT) Synchrotron

References

Worked examples

Example 1 — a first encounter with Three-dimensional X-ray diffraction

Start with the simplest possible case. Write down what Three-dimensional X-ray diffraction claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Three-dimensional X-ray diffraction before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Three-dimensional X-ray diffraction ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Three-dimensional X-ray diffraction

In research: Three-dimensional X-ray diffraction appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Three-dimensional X-ray diffraction in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Three-dimensional X-ray diffraction is common in secondary-school and first-year university syllabi. It links to neighbouring topics Microscopy, X-ray instrumentation, so understanding it makes those chapters shorter.
In everyday life: Look for Three-dimensional X-ray diffraction outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Three-dimensional X-ray diffraction in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Three-dimensional X-ray diffraction means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Three-dimensional X-ray diffraction out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Three-dimensional X-ray diffraction in simple terms?

Why does Three-dimensional X-ray diffraction matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Three-dimensional X-ray diffraction?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Three-dimensional X-ray diffraction.