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Crystallography and Radiation Phenomena
Research Guide
What is Crystallography and Radiation Phenomena?
Crystallography and Radiation Phenomena is the study of how radiation (such as X-rays and relativistic particle beams) interacts with crystalline matter to determine atomic structure and to exploit crystal fields for scattering, absorption, and beam-control effects.
This literature cluster comprises 262,291 works focused on diffraction, scattering, absorption, and beam–crystal interactions, including methods such as nuclear resonant spectroscopy, synchrotron radiation, crystal collimation, and X-ray holography. Many core results are operationalized through structure-solution/refinement software and correction models, exemplified by “SIR97: a new tool for crystal structure determination and refinement” (1999) and “An empirical method for correcting diffractometer data for absorption effects” (1983). Widely used measurement relationships and radiation sources in this area include “The Scherrer Formula for X-Ray Particle Size Determination” (1939) and “First lasing and operation of an ångstrom-wavelength free-electron laser” (2010).
Topic Hierarchy
Research Sub-Topics
Crystal Channeling of Particles
This sub-topic studies steering of relativistic particles by atomic planes or axes in crystals. Researchers investigate dechanneling rates, critical angles, and applications in beam optics.
Synchrotron Radiation in Crystallography
This sub-topic explores high-brilliance X-rays from synchrotrons for atomic-resolution structure determination. Researchers optimize beamlines, develop phasing methods, and study radiation damage.
Mössbauer Spectroscopy
This sub-topic covers recoilless nuclear gamma resonance for hyperfine interaction analysis. Researchers apply it to magnetic structures, phase transitions, and thin films using synchrotron sources.
Volume Reflection in Crystals
This sub-topic examines deflection of particle beams at crystal boundaries without channeling. Researchers model angular distributions, multiple scattering, and compare with axial channeling.
X-ray Holography
This sub-topic develops coherent X-ray methods for 3D atomic imaging using reference waves. Researchers advance Gabor, Fourier, and atomic-resolution holography with synchrotron beams.
Why It Matters
Crystallography underpins practical decisions in materials characterization, chemical identification, and structural biology by turning radiation–crystal interactions into quantitative structure factors, particle-size estimates, and refined atomic models. For example, Patterson’s “The Scherrer Formula for X-Ray Particle Size Determination” (1939) provides an exact derivation of the Scherrer equation for spherical particles and compares approximation methods, enabling routine particle-size estimation from X-ray peak broadening in laboratory and synchrotron diffraction workflows. Systematic errors from radiation attenuation can dominate single-crystal measurements; Walker and Stuart’s “An empirical method for correcting diffractometer data for absorption effects” (1983) directly targets absorption as “the most serious source of systematic error” in structure-factor determination and proposes a correction method when crystals are not shaped into ideal geometries. At the instrumentation level, Emma et al.’s “First lasing and operation of an ångstrom-wavelength free-electron laser” (2010) documents operation of an ångstrom-wavelength free-electron laser, a source class that supports experiments requiring extremely bright, short-wavelength X-rays for diffraction and related radiation–matter studies. On the computation side, Troullier and Martins’ “Efficient pseudopotentials for plane-wave calculations” (1991) introduces smooth norm-conserving pseudopotentials that reduce plane-wave computational cost, supporting first-principles modeling used alongside diffraction-derived structures when interpreting radiation responses in crystals.
Reading Guide
Where to Start
Start with Patterson’s “The Scherrer Formula for X-Ray Particle Size Determination” (1939) because it provides an exact, self-contained derivation linking measurable diffraction peak widths to particle size and clarifies the approximations commonly used in practice.
Key Papers Explained
Measurement-to-structure workflows begin with how radiation encodes size/structure in patterns: Patterson’s “The Scherrer Formula for X-Ray Particle Size Determination” (1939) treats peak broadening and particle size, while Hart and Deutsch’s “Small Angle X-ray Scattering” (1983) and Guinier et al.’s “Small-Angle Scattering of X-Rays” (1956) establish small-angle scattering as a complementary regime. Converting measured intensities into reliable structure factors requires controlling systematic errors; Walker and Stuart’s “An empirical method for correcting diffractometer data for absorption effects” (1983) addresses absorption corrections central to quantitative crystallography. Structure solution and refinement are operationalized in widely used software: Altomare et al.’s “SIR97: a new tool for crystal structure determination and refinement” (1999) integrates direct-methods solution with least-squares–Fourier refinement, and Petřı́ček et al.’s “Crystallographic Computing System JANA2006: General features” (2014) extends refinement to modulated and magnetic structures across X-ray/neutron/electron diffraction. On the source and modeling side, Emma et al.’s “First lasing and operation of an ångstrom-wavelength free-electron laser” (2010) exemplifies high-brightness X-ray generation relevant to radiation–crystal experiments, while Troullier and Martins’ “Efficient pseudopotentials for plane-wave calculations” (1991) supports first-principles calculations often paired with crystallographic models to interpret radiation phenomena in solids.
Paper Timeline
Most-cited paper highlighted in red. Papers ordered chronologically.
Advanced Directions
For advanced study, connect high-brightness X-ray sources to quantitative modeling and refinement: use “First lasing and operation of an ångstrom-wavelength free-electron laser” (2010) to frame what source properties enable, then evaluate how absorption correction (“An empirical method for correcting diffractometer data for absorption effects” (1983)) and complex-structure refinement (“Crystallographic Computing System JANA2006: General features” (2014)) constrain what can be inferred from radiation data. In parallel, use “Efficient pseudopotentials for plane-wave calculations” (1991) to scrutinize how computational approximations propagate into predicted observables that should remain consistent with diffraction-validated structures.
Papers at a Glance
| # | Paper | Year | Venue | Citations | Open Access |
|---|---|---|---|---|---|
| 1 | Efficient pseudopotentials for plane-wave calculations | 1991 | Physical review. B, Co... | 15.9K | ✕ |
| 2 | <i>SIR</i>97: a new tool for crystal structure determination a... | 1999 | Journal of Applied Cry... | 9.1K | ✕ |
| 3 | The Scherrer Formula for X-Ray Particle Size Determination | 1939 | Physical Review | 8.6K | ✕ |
| 4 | An empirical method for correcting diffractometer data for abs... | 1983 | Acta Crystallographica... | 5.9K | ✕ |
| 5 | Resonance Absorption by Nuclear Magnetic Moments in a Solid | 1946 | Physical Review | 5.8K | ✓ |
| 6 | Quantum theory of many-particle systems | 1971 | — | 5.0K | ✕ |
| 7 | Small Angle X-ray Scattering | 1983 | Physics Bulletin | 4.6K | ✕ |
| 8 | Crystallographic Computing System JANA2006: General features | 2014 | Zeitschrift für Krista... | 4.6K | ✕ |
| 9 | <i>Small-Angle Scattering of X-Rays</i> | 1956 | Physics Today | 4.3K | ✕ |
| 10 | First lasing and operation of an ångstrom-wavelength free-elec... | 2010 | Nature Photonics | 3.0K | ✕ |
In the News
Science Highlights | Stanford Synchrotron Radiation Lightsource
#### Crystallography Confirms De Novo Protein Binding Modes and Hotspots ###### March 31, 2023
BNL | National Synchrotron Light Source II | News Archive
Brookhaven Lab celebrates a year of scientific successes, from creating the biggest bits of antimatter to improving qubits, catalysts, batteries, and more! ] * [ Charge density waves
Commission on Small-Angle Scattering
# Commission on Small-Angle Scattering The Commission represent the interests of the worldwide Small-Angle Scattering community, and collaborates closely with national small-angle scattering inter...
Room-temperature X-ray fragment screening with serial crystallography
Structural insights into protein-ligand interactions are essential for advancing drug development, with macromolecular X-ray crystallography being a cornerstone technique. Commonly X-ray data colle...
XDXD: End-to-end crystal structure determination with low resolution X-ray diffraction.
Determining crystal structures from X-ray diffraction data is fundamental across diverse scientific fields, yet remains a significant challenge when data is limited to low resolution. While recent ...
Code & Tools
GSAS-II is used to analyze all types of x-ray and neutron diffraction data, including single-crystal, powder, constant-wavelength, pink-beam and ti...
`crystals`is a library of data structure and algorithms to manipulate abstract crystals in a Pythonic way.`crystals`helps with reading crystallogra...
The HEXRD project is developing a cross-platform, open-source library for the general analysis of X-ray diffraction data. This includes powder diff...
The package defines objects and functions for the analysis of orientations represented as quaternions and 3D rotation vectors, accounting for cryst...
A Python and Machine Learning methods implementation for Crystal Structure Prediction and Diffraction Study ### Topics
Recent Preprints
Chapter 6. The principles of X-ray diffraction
The consideration of the secondary maxima and of the finite resolving power of the crystal is essentially what H. A. Lorentz introduced into the theory, although using Laue's diffraction, not Bragg...
X-ray Diffraction Studies of Single-Crystal Materials for Broad ...
Single-crystal materials have attracted growing interest in battery research due to their well-defined crystallographic orientation, absence of grain boundaries, and enhanced mechanical and electro...
50 Years of X-ray Diffraction
Fifty Years of Edited by P. P. Ewald Reprinted in pdf format for the IUCr XVIII Congress, Glasgow, Scotland Copyright © 1962, 1999 International Union of Crystallography
Chapter 3. Crystallography
# Crystallography ## 3.1. Descriptive Crystallography
X-ray crystallography - PROTEIN STRUCTURal Biology
X-ray crystallography is the primary protein structure determination method for the study of molecular structures at the atomic level. The technique is based on measuring the diffraction of X-rays ...
Latest Developments
Recent developments in crystallography and radiation phenomena research include advances in synchrotron- and XFEL-based macromolecular crystallography, cryo-EM, and cryo-ET, as well as the use of deep learning for end-to-end structure determination from X-ray diffraction data, as reported in 2026 (iucr.org; npj Computational Materials). Additionally, research has shown that crystals can be bent and twisted naturally during formation, and studies continue to deepen understanding of radiation damage to biological macromolecules (iucr.org, as of January 2026; MDPI).
Sources
Frequently Asked Questions
What is the practical difference between structure solution and structure refinement in crystallography?
Structure solution proposes an initial atomic model consistent with diffraction intensities, while refinement adjusts that model to best fit the measured data and constraints. “SIR97: a new tool for crystal structure determination and refinement” (1999) explicitly integrates a program devoted to solution by direct methods with a program devoted to refinement via least-squares–Fourier procedures.
How do absorption effects bias single-crystal X-ray diffraction results, and how are they corrected?
Absorption changes measured intensities in a way that can systematically distort derived structure factors, especially when the crystal is not ground to a sphere or cylinder. Walker and Stuart’s “An empirical method for correcting diffractometer data for absorption effects” (1983) proposes a correction approach aimed at reducing this dominant systematic error source in single-crystal measurements.
How is particle size estimated from X-ray diffraction peak broadening?
Particle size can be inferred from the angular breadth of diffraction peaks using the Scherrer relationship under stated assumptions. Patterson’s “The Scherrer Formula for X-Ray Particle Size Determination” (1939) gives an exact derivation for spherical particles and reports constants for half-value breadth and integral breadth, while comparing common approximations against the exact calculation.
Which tools are widely used for complex (including modulated or magnetic) crystallographic refinements?
JANA2006 is designed for structure determination and refinement of standard, modulated, and magnetic samples using X-ray, neutron, or electron diffraction data. Petřı́ček, Dušek, and Palatinus describe these capabilities in “Crystallographic Computing System JANA2006: General features” (2014).
How does small-angle X-ray scattering (SAXS) fit into crystallography and radiation–matter studies?
SAXS characterizes structure at larger real-space length scales than conventional Bragg diffraction by analyzing scattering at small angles. Hart and Deutsch’s “Small Angle X-ray Scattering” (1983) and Guinier et al.’s “Small-Angle Scattering of X-Rays” (1956) are core references that formalize SAXS as a radiation-based structural probe complementary to crystallographic diffraction.
Which computational ingredients connect first-principles electronic-structure modeling to crystallographic interpretations of radiation phenomena?
Plane-wave electronic-structure calculations often rely on pseudopotentials to represent core electrons efficiently when modeling crystalline materials. Troullier and Martins’ “Efficient pseudopotentials for plane-wave calculations” (1991) presents a procedure for smooth norm-conserving pseudopotentials designed to save computational resources in plane-wave bases, supporting practical simulations used alongside diffraction-informed structures.
Open Research Questions
- ? How can absorption-correction strategies like those in “An empirical method for correcting diffractometer data for absorption effects” (1983) be generalized to heterogeneous, irregular, or strongly absorbing crystals without introducing model-dependent bias in refined structure factors?
- ? What are the limits of validity and uncertainty quantification for particle-size inference based on the exact/approximate relationships compared in “The Scherrer Formula for X-Ray Particle Size Determination” (1939) when applied to non-spherical particles or strain-broadened peaks?
- ? How can refinement frameworks described in “Crystallographic Computing System JANA2006: General features” (2014) be extended or stress-tested for highly complex ordering (e.g., coupled modulation and magnetism) while maintaining parameter identifiability from available diffraction data?
- ? How should experimental designs using ångstrom-wavelength FEL sources described in “First lasing and operation of an ångstrom-wavelength free-electron laser” (2010) balance wavelength, intensity, and sample damage constraints to preserve crystallographic interpretability of radiation–matter signals?
- ? How can plane-wave pseudopotential choices from “Efficient pseudopotentials for plane-wave calculations” (1991) be validated against diffraction-derived observables so that simulated radiation responses in crystals remain consistent with experimentally refined structures?
Recent Trends
Within this cluster of 262,291 works, widely cited foundations continue to anchor modern workflows: peak-broadening size inference from “The Scherrer Formula for X-Ray Particle Size Determination” , absorption correction from “An empirical method for correcting diffractometer data for absorption effects” (1983), and integrated solution/refinement in “SIR97: a new tool for crystal structure determination and refinement” (1999).
1939Software capability has expanded toward complex crystallography, as summarized by Petřı́ček et al. in “Crystallographic Computing System JANA2006: General features” , which explicitly targets modulated and magnetic structures and multiple diffraction modalities.
2014Source development enabling shorter-wavelength, high-intensity experiments is exemplified by “First lasing and operation of an ångstrom-wavelength free-electron laser” , which provides a concrete reference point for ångstrom-wavelength FEL operation relevant to radiation–crystal interaction studies.
2010Across interpretation and prediction, the computational efficiency emphasis in “Efficient pseudopotentials for plane-wave calculations” remains a recurring theme because smooth norm-conserving pseudopotentials reduce plane-wave cost and thereby support routine simulation alongside diffraction and scattering analyses.
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