Showing papers on "Diffraction published in 2004"
TL;DR: In this article, the DICVOL04 algorithm was extended to include a tolerance to the presence of impurity (or inaccurately measured) diffraction lines, a refinement of the zero-point position, a reviewing of all input lines from the solution found from, generally, the first 20 lines, and a cell analysis, based on the concept of the reduced cell, to identify equivalent monoclinic and triclinic solutions.
Abstract: The efficiency of the successive dichotomy method for powder diffraction pattern indexing [Louer & Louer (1972). J. Appl. Cryst. 5, 271–275] has been proved over more than 30 years of usage. Features implemented in the new version of the computer program DICVOL04 include (i) a tolerance to the presence of impurity (or inaccurately measured) diffraction lines, (ii) a refinement of the `zero-point' position, (iii) a reviewing of all input lines from the solution found from, generally, the first 20 lines, (iv) a cell analysis, based on the concept of the reduced cell, to identify equivalent monoclinic and triclinic solutions, and (v) an optional analysis of input powder data to detect the presence of a significant `zero-point' offset. New search strategies have also been introduced, e.g. each crystal system is scanned separately, within the input volume limits, to limit the risk of missing a solution characterized by a metric lattice singularity. The default values in the input file have been extended to 25 A for the linear parameters and 2500 A3 for the cell volume. The search is carried out exhaustively within the input parameter limits and the absolute error on peak position measurements. Many tests with data from the literature and from powder data of pharmaceutical materials, collected with the capillary technique and laboratory monochromatic X-rays, have been performed with a high success rate, covering all crystal symmetries from cubic to triclinic. Some examples reported as `difficult' cases are also discussed. Additionally, a few recommendations for the correct practice of powder pattern indexing are reported.
1,284 citations
TL;DR: Theoretical size and strain profile functions are given by the minimum number of parameters required by physics and are compared with TEM results as mentioned in this paper, which provides crystallite size, size distribution and dislocation structure.
752 citations
TL;DR: In this paper, a method of iterative phase retrieval that uses measured intensities in the diffraction plane to solve the phase problem in a way that bypasses the problem of lens aberration was proposed.
Abstract: We propose a method of iterative phase retrieval that uses measured intensities in the diffraction plane to solve the phase problem in a way that bypasses the problem of lens aberration, leading to greatly improved spatial resolution. This method is stable, easy to implement experimentally, and can be used to view a large area of the specimen when that is desired.
750 citations
TL;DR: Not involving evanescent fields and not requiring mechanical scanning, photonic nanojets may provide a new means to detect and image nanoparticles of size well below the diffraction limit and yield a potential novel ultramicroscopy technique using visible light for detecting proteins, viral particles, and even single molecules.
Abstract: We report what we believe to be the first evidence of localized nanoscale photonic jets generated at the shadow-side surfaces of micronscale, circular dielectric cylinders illuminated by a plane wave These photonic nanojets have waists smaller than the diffraction limit and propagate over several optical wavelengths without significant diffraction We have found that such nanojets can enhance the backscattering of visible light by nanometer-scale dielectric particles located within the nanojets by several orders of magnitude Not involving evanescent fields and not requiring mechanical scanning, photonic nanojets may provide a new means to detect and image nanoparticles of size well below the diffraction limit This could yield a potential novel ultramicroscopy technique using visible light for detecting proteins, viral particles, and even single molecules; and monitoring molecular synthesis and aggregation processes of importance in many areas of biology, chemistry, material sciences, and tissue engineering
733 citations
TL;DR: Experimental results at 1.057 GHz that demonstrate the ability of a planar left-handed lens, with a relative refractive index of -1, to form images that overcome the diffraction limit are reported.
Abstract: We report experimental results at 1.057 GHz that demonstrate the ability of a planar left-handed lens, with a relative refractive index of $\ensuremath{-}1$, to form images that overcome the diffraction limit. The left-handed lens is a planar slab consisting of a grid of printed metallic strips over a ground plane, loaded with series capacitors ($C$) and shunt inductors ($L$). The measured half-power beamwidth of the point-source image formed by the left-handed lens is 0.21 effective wavelengths, which is significantly narrower than that of the diffraction-limited image corresponding to 0.36 wavelengths.
728 citations
TL;DR: An iterative phase retrieval method that uses a series of diffraction patterns, measured only in intensity, to solve for both amplitude and phase of the image wave function over a wide field of view and at wavelength-limited resolution is proposed.
Abstract: We propose an iterative phase retrieval method that uses a series of diffraction patterns, measured only in intensity, to solve for both amplitude and phase of the image wave function over a wide field of view and at wavelength-limited resolution. The new technique requires an aperture that is scanned to two or more positions over the object wave function. A simple implementation of the method is modeled and demonstrated, showing how the algorithm uses overlapping data in real space to resolve ambiguities in the solution. The technique opens up the possibility of practical transmission lensless microscopy at subatomic resolution using electrons, x rays, or nuclear particles.
707 citations
Journal Article•
TL;DR: In this article, a planar left-handed lens with a relative refractive index of 1.1 was used to overcome the diffraction limit at 1.057 GHz and achieved a half-power beamwidth of 0.21 effective wavelengths.
Abstract: We report experimental results at 1.057 GHz that demonstrate the ability of a planar left-handed lens, with a relative refractive index of $\ensuremath{-}1$, to form images that overcome the diffraction limit. The left-handed lens is a planar slab consisting of a grid of printed metallic strips over a ground plane, loaded with series capacitors ($C$) and shunt inductors ($L$). The measured half-power beamwidth of the point-source image formed by the left-handed lens is 0.21 effective wavelengths, which is significantly narrower than that of the diffraction-limited image corresponding to 0.36 wavelengths.
670 citations
TL;DR: This work demonstrates a versatile technique for imaging nanostructures, based on the use of resonantly tuned soft X-rays for scattering contrast and the direct Fourier inversion of a holographically formed interference pattern, which is a form of Fourier transform holography and appears scalable to diffraction-limited resolution.
Abstract: Our knowledge of the structure of matter is largely based on X-ray diffraction studies of periodic structures and the successful transformation (inversion) of the diffraction patterns into real-space atomic maps. But the determination of non-periodic nanoscale structures by X-rays is much more difficult. Inversion of the measured diffuse X-ray intensity patterns suffers from the intrinsic loss of phase information, and direct imaging methods are limited in resolution by the available X-ray optics. Here we demonstrate a versatile technique for imaging nanostructures, based on the use of resonantly tuned soft X-rays for scattering contrast and the direct Fourier inversion of a holographically formed interference pattern. Our implementation places the sample behind a lithographically manufactured mask with a micrometre-sized sample aperture and a nanometre-sized hole that defines a reference beam. As an example, we have used the resonant X-ray magnetic circular dichroism effect to image the random magnetic domain structure in a Co/Pt multilayer film with a spatial resolution of 50 nm. Our technique, which is a form of Fourier transform holography, is transferable to a wide variety of specimens, appears scalable to diffraction-limited resolution, and is well suited for ultrafast single-shot imaging with coherent X-ray free-electron laser sources.
626 citations
TL;DR: In this article, the isothermal tetragonal-to-monoclinic transformation of a 3Y-TZP ceramic was investigated from 70° to 130°C in water and in steam by X-ray diffraction and optical interferometer techniques.
Abstract: The isothermal tetragonal-to-monoclinic transformation of a 3Y-TZP ceramic is investigated from 70° to 130°C in water and in steam by X-ray diffraction and optical interferometer techniques. Aging kinetics followed by X-ray diffraction are fitted by the Mehl-Avrami-Johnson law, suggesting nucleation and growth to be the key mechanisms for transformation. Optical interferometer observations of highly polished samples effectively reveal a nucleation and growth micromechanism for tetragonal-to-monoclinic transformation. A model based on surface change analysis is developed that fits closely to the X-ray diffraction results.
610 citations
15 Apr 2004-Philosophical transactions - Royal Society. Mathematical, physical and engineering sciences
TL;DR: Ultraresolution microscopy far beyond the classical Abbe diffraction limit of one half wavelength (λ/2), and also beyond the practical limit (ca. λ/10) of aperture–based scanning near–field optical microscopy (SNOM), and theoretical modelling that explains and predicts s–SNOM contrast on the basis of the local dielectric function is described.
Abstract: We describe ultraresolution microscopy far beyond the classical Abbe diffraction limit of one half wavelength (lambda/2), and also beyond the practical limit (ca. lambda/10) of aperture-based scanning near-field optical microscopy (SNOM). The 'apertureless' SNOM discussed here uses light scattering from a sharp tip (hence scattering-type or s-SNOM) and has no lambda-related resolution limit. Rather, its resolution is approximately equal to the radius a of the probing tip (for commercial tips, a < 20 nm) so that 10 nm is obtained in the visible (lambda/60). A resolution of lambda/500 has been obtained in the mid-infrared at lambda = 10 microm. The advantage of infrared, terahertz and even microwave illumination is that specific excitations can be exploited to yield specific contrast, e.g. the molecular vibration offering a spectroscopic fingerprint to identify chemical composition. S-SNOM can routinely acquire simultaneous amplitude and phase images to obtain information on refractive and absorptive properties. Plasmon- or phonon-resonant materials can be highlighted by their particularly high near-field signal level. Furthermore, s-SNOM can map the characteristic optical eigenfields of small, optically resonant particles. Lastly, we describe theoretical modelling that explains and predicts s-SNOM contrast on the basis of the local dielectric function.
581 citations
Journal Article•
TL;DR: The theory of image formation is formulated in terms of the coherence function in the object plane, the diffraction distribution function of the image-forming system and a function describing the structure of the object.
Abstract: The theory of image formation is formulated in terms of the coherence function in the object plane, the diffraction distribution function of the image-forming system and a function describing the structure of the object. There results a four-fold integral involving these functions, and the complex conjugate functions of the latter two. This integral is evaluated in terms of the Fourier transforms of the coherence function, the diffraction distribution function and its complex conjugate. In fact, these transforms are respectively the distribution of intensity in an 'effective source', and the complex transmission of the optical system-they are the data initially known and are generally of simple form. A generalized 'transmission factor' is found which reduces to the known results in the simple cases of perfect coherence and complete incoherence. The procedure may be varied in a manner more suited to non-periodic objects. The theory is applied to study inter alia the influence of the method of illumination on the images of simple periodic structures and of an isolated line.
TL;DR: In this paper, a single X-ray diffraction scan was used for identifying and evaluating deformation-induced transformation in 304 austenitic stainless steel and the initial stage of transformation in this steel was most likely dominated by e−martensite formation.
TL;DR: In this article, spherical PbSe semiconductor nanocrystals with near-infrared absorption of 1100−2520 nm were synthesized in a noncoordinating solvent (1-octadecene).
Abstract: Spherical PbSe semiconductor nanocrystals with near-infrared absorption of 1100−2520 nm (corresponding to diameters of 3−13 nm) were synthesized in a noncoordinating solvent (1-octadecene). The as-prepared PbSe semiconductor nanocrystals have very narrow size distributions (σ ≅ 5−7%) without any postsynthetic size selection. High-resolution transmission electron microscopy (TEM), electron diffraction, and X-ray diffraction show that the nanocrystalline particles are single domains of rock-salt PbSe. A water-soluble form of these materials was generated through simple surface treatments.
TL;DR: In this paper, a set of well-aligned ZnO nanorods were synthesized on a Si substrate at 600 °C by 193 nm pulsed laser ablation of a target in low pressures of oxygen using electron microscopy and X-ray diffraction.
01 Jan 2004
TL;DR: In this paper, a line profile analysis of X-ray diffraction patterns for investigation of nanocrystalline systems is presented, and a Bayesian/maximum entropy method for the certification of a Nanocrystallite-size NIST standard reference material is presented.
Abstract: 1 Line Profile Analysis: A Historical Overview- 2 Convolution Based Profile Fitting- 3 Whole Powder Pattern Modelling: Theory and Applications- 4 Full Profile Analysis of X-ray Diffraction Patterns for Investigation of Nanocrystalline Systems- 5 Crystallite Size and Residual Strain/Stress Modeling in Rietveld Refinement- 6 The Quantitative Determination of the Crystalline and the Amorphous Content by the Rietveld Method: Application to Glass Ceramics with Different Absorption Coefficients- 7 Quantitative Analysis of Amorphous Fraction in the Study of the Microstructure of Semi-crystalline Materials- 8 A Bayesian/Maximum Entropy Method for the Certification of a Nanocrystallite-Size NIST Standard Reference Material- 9 Study of Submicrocrystalline Materials by Diffuse Scattering in Transmitted Wave- 10 Determining the Dislocation Contrast Factor for X-ray Line Profile Analysis- 11 X-ray Peak Broadening Due to Inhomogeneous Dislocation Distributions- 12 Determination of Non-uniform Dislocation Distributions in Polycrystalline Materials- 13 Line Profile Fitting: The Case of fcc Crystals Containing Stacking Faults- 14 Diffraction Elastic Constants and Stress Factors Grain Interaction and Stress in Macroscopically Elastically Anisotropic Solids The Case of Thin Films- 15 Interaction between Phases in Co-deforming Two-Phase Materials: The Role of Dislocation Arrangements- 16 Grain Surface Relaxation Effects in Powder Diffraction- 17 Interface Stress in Polycrystalline Materials- 18 Problems Related to X-Ray Stress Analysis in Thin Films in the Presence of Gradients and Texture- 19 Two-Dimensional XRD Profile Modelling in Imperfect Epitaxial Layers- 20 Three-Dimensional Reciprocal Space Mapping: Application to Polycrystalline CVD Diamond
15 Dec 2004-Materials Science and Engineering A-structural Materials Properties Microstructure and Processing
TL;DR: In this article, the authors measured powder diffraction pattern is fitted by the sum of a polynomial background and physically well-established theoretical profile functions, providing the size distribution function of crystallites and the characteristic parameters of the dislocation structure.
Abstract: The microstructure of ball-milled Al base Al–Mg alloys is determined by the “Convolutional Multiple Whole Profile” fitting procedure proposed for the evaluation of X-ray diffraction peak profiles. The whole measured powder diffraction pattern is fitted by the sum of a polynomial background and physically well-established theoretical profile functions. The procedure provides the size distribution function of crystallites and the characteristic parameters of the dislocation structure. The mechanical strength of the specimens is correlated to the parameters of the microstructure by the Hall–Petch and the Taylor models. Both models show that the critical resolved shear stress saturates at a Mg-solute concentration of about 2 wt.% probably due to the clustering of the Mg-solute atoms.
TL;DR: A proposal to realize lensless Fourier-transform imaging is given, and its applicability in x-ray diffraction is discussed, and a particular aspect of coincidence imaging with incoherent sources is studied.
Abstract: Entangled-photon coincidence imaging is a method to nonlocally image an object by transmitting a pair of entangled photons through the object and a reference optical system, respectively. The image of the object can be extracted from the coincidence rate of these two photons. From a classical perspective, the image is proportional to the fourth-order correlation function of the wave field. Using classical statistical optics, we study a particular aspect of coincidence imaging with incoherent sources. As an application, we give a proposal to realize lensless Fourier-transform imaging, and discuss its applicability in x-ray diffraction.
TL;DR: The effect of activation temperature on the textural and chemical properties of activated carbons prepared from pistachio-nut shells by potassium hydroxide activation was studied.
TL;DR: It is demonstrated that the localization of the predicted plasmons in acute grooves may be substantially stronger than what is allowed by the diffraction limit.
Abstract: One-dimensional localized plasmons (channel polaritons) guided by a triangular groove on a metal substrate are investigated numerically by means of a finite-difference time-domain algorithm. Dispersion, existence conditions, and dissipation of these waves are analyzed. In particular, it is demonstrated that the localization of the predicted plasmons in acute grooves may be substantially stronger than what is allowed by the diffraction limit. As a result, the predicted waves may be significant for the development of new subwavelength waveguides and interconnectors for nano-optics and photonics.
TL;DR: In this article, the buckling instability was investigated by both small angle light scattering and atomic force microscopy, demonstrating that a tunable phase grating can be created with a mechanical instability.
Abstract: We investigate a buckling instability by both small angle light scattering and atomic force microscopy, demonstrating that a tunable phase grating can be created with a mechanical instability. The instability is realized in a prestressed silicone sheet coated with a glassy polymer film. Compression of the sample results in a sinusoidally wrinkled surface where the amplitude is controlled by the degree of compression and the wavelength by film thickness. We model the system with Fourier optics, explaining the positions and relative intensities of the diffraction orders.
TL;DR: In this article, a diffraction-based data-oriented approach is proposed to enhance image resolution. But it cannot be used for super-resolution and the recovery of details smaller than the seismic wavelength, since the seismic response from these structural elements is encoded in diffractions, and diffractions are essentially lost during the conventional processing/migration sequence.
Abstract: Diffractions always need more advertising. It is true that conventional seismic processing and migration are usually successful in using specular reflections to estimate subsurface velocities and reconstruct the geometry and strength of continuous and pronounced reflectors. However, correct identification of geological discontinuities, such as faults, pinch-outs, and small-size scattering objects, is one of the main objectives of seismic interpretation. The seismic response from these structural elements is encoded in diffractions, and diffractions are essentially lost during the conventional processing/migration sequence. Hence, we advocate a diffraction-based, data-oriented approach to enhance image resolution—as opposed to the traditional image-oriented techniques, which operate on the image after processing and migration. Even more: it can be shown that, at least in principle, processing of diffractions can lead to superresolution and the recovery of details smaller than the seismic wavelength. The so-called reflection stack is capable of effectively separating diffracted and reflected energy on a prestack shot gather by focusing the reflection to a point while the diffraction remains unfocused over a large area. Muting the reflection focus and defocusing the residual wavefield result in a shot gather that contains mostly diffractions. Diffraction imaging applies the classical (isotropic) diffraction stack to these diffraction shot gathers. This focusingmuting-defocusing approach can successfully image faults, small-size scattering objects, and diffracting edges. It can be implemented both in model-independent and modeldependent contexts. The resulting diffraction images can greatly assist the interpreter when used as a standard supplement to full-wave images.
TL;DR: The fabrication and characterization of a high-quality spiral phase plate is described as a device to generate optical vortices of low (3-5) specified charge at visible wavelengths and the reproducibility of the manufacturing process is excellent.
Abstract: We describe the fabrication and characterization of a high-quality spiral phase plate as a device to generate optical vortices of low (3-5) specified charge at visible wavelengths. The manufacturing process is based on a molding technique and allows for the production of high-precision, smooth spiral phase plates as well as for their replication. An attractive feature of this process is that it permits the fabrication of nominally identical spiral phase plates made from different materials and thus yielding different vortex charges. When such a plate is inserted in the waist of a fundamental Gaussian beam, the resultant far-field intensity profile shows a rich vortex structure, in excellent agreement with diffraction calculations based on ideal spiral phase plates. Using a simple optical test, we show that the reproducibility of the manufacturing process is excellent.
TL;DR: The diffraction resolution barrier fundamentally is overcome on the basis of reversible saturable optical transitions, which might eventually allow us to investigate hitherto inaccessible details within live cells.
Book•
01 Jan 2004TL;DR: In this paper, the authors present a survey of the history of dynamical analysis of crystal surfaces and their applications in physics, including the integration of the R-matrix method and the integral method.
Abstract: Preface 1. Introduction 2. Historical survey 3. Instrumentation 4. Wave properties of electrons 5. The diffraction conditions 6. Geometrical features of the patterns 7. Kikuchi and resonance patterns 8. Real diffraction patterns 9. Electron scattering by atoms 10. Kinematic electron diffraction 11. Fourier components of the crystal potential 12. Dynamical theory: transfer matrix method 13. Dynamical theory: embedded R-matrix method 14. Dynamical theory: integral method 15. Structural analysis of crystal surfaces 16. Inelastic scattering in a crystal 17. Weakly disordered surfaces 18. Strongly disordered surfaces 19. RHEED intensity oscillations Appendix A. Fourier representations Appendix B. Green's function Appendix C. Kirchhoff's diffraction theory Appendix D. A simpler Eigenvalue problem Appendix E. Waller and Hartree equation Appendix F. Optimization of dynamical calculation Appendix G. Scattering factor References Index
TL;DR: The phase and amplitude of the oscillatory XRD signal around a new equilibrium demonstrate that displacive excitation of the zone-folded acoustic phonons is the dominant mechanism for strong excitation.
Abstract: Reversible structural changes of a nanostructure were measured nondestructively with subpicometer spatial and subpicosecond temporal resolution via x-ray diffraction (XRD). The spatially periodic femtosecond excitation of a gallium arsenide/aluminum gallium arsenide superlattice results in coherent lattice motions with a 3.5-picosecond period, which was directly monitored by femtosecond x-ray pulses at a 1-kilohertz repetition rate. Small changes (DeltaR/R = 0.01) of weak Bragg reflexes (R = 0.005) were detected. The phase and amplitude of the oscillatory XRD signal around a new equilibrium demonstrate that displacive excitation of the zone-folded acoustic phonons is the dominant mechanism for strong excitation.
TL;DR: An explicit derivation of the Green's function in a viscous and elastic medium taking into account shear, bulk, and coupling waves is reported and it is shown that transient shear waves generated with SSI are modeled very precisely by the Green’s function formalism.
Abstract: Several ultrasound-based techniques for the estimation of soft tissue elasticity are currently being investigated. Most of them study the medium response to dynamic excitations. Such responses are usually modeled in a purely elastic medium using a Green's function solution of the motion equation. However, elasticity by itself is not necessarily a discriminant parameter for malignancy diagnosis. Modeling viscous properties of tissues could also be of great interest for tumor characterization. We report in this paper an explicit derivation of the Green's function in a viscous and elastic medium taking into account shear, bulk, and coupling waves. From this theoretical calculation, 3D simulations of mechanical waves in viscoelastic soft tissues are presented. The relevance of the viscoelastic Green's function is validated by comparing simulations with experimental data. The experiments were conducted using the supersonic shear imaging (SSI) technique which dynamically and remotely excites tissues using acoustic radiation force. We show that transient shear waves generated with SSI are modeled very precisely by the Green's function formalism. The combined influences of out-of-plane diffraction, beam shape, and shear viscosity on the shape of transient waves are carefully studied as they represent a major issue in ultrasound-based viscoelasticity imaging techniques.
TL;DR: The systematic exploitation of anisotropic thermal expansion will help reduce the effects of peak overlap in the analysis of powder diffraction data.
Abstract: The optical design and performance of the high-resolution powder diffraction beam line BM16 at ESRF are discussed and illustrated. Some recent studies carried out on BM16 are described, including crystal structure solution and refinement, anomalous scattering, in situ measurements, residual strain in engineering components, investigation of microstructure, and grazing-incidence diffraction from surface layers. The beam line is built on a bending magnet, and operates in the energy range from 5 keV to 40 keV. After the move to an undulator source in 2002, it will benefit from an extented energy range up to 60 keV and increased flux and resolution. It is anticipated that enhancements to the data quality will be achieved, leading to the solution of larger crystal structures, and improvements in the accuracy of refined structures. The systematic exploitation of anisotropic thermal expansion will help reduce the effects of peak overlap in the analysis of powder diffraction data.
TL;DR: It is found that even on the scale of a few lattice vectors, the dislocation behavior is well described by the continuum approach commonly used to describe dislocations in atomic crystals.
Abstract: The dominant mechanism for creating large irreversible strain in atomic crystals is the motion of dislocations, a class of line defects in the crystalline lattice. Here we show that the motion of dislocations can also be observed in strained colloidal crystals, allowing detailed investigation of their topology and propagation. We describe a laser diffraction microscopy setup used to study the growth and structure of misfit dislocations in colloidal crystalline films. Complementary microscopic information at the single-particle level is obtained with a laser scanning confocal microscope. The combination of these two techniques enables us to study dislocations over a range of length scales, allowing us to determine important parameters of misfit dislocations such as critical film thickness, dislocation density, Burgers vector, and lattice resistance to dislocation motion. We identify the observed dislocations as Shockley partials that bound stacking faults of vanishing energy. Remarkably, we find that even on the scale of a few lattice vectors, the dislocation behavior is well described by the continuum approach commonly used to describe dislocations in atomic crystals.
TL;DR: In this article, high-resolution X-ray diffraction peak profile analysis of pure magnesium is investigated by high resolution diffraction profile functions where the strain profile is scaled for strain anisotropy by the dislocation contrast factors.
TL;DR: In this paper, a computer program, RADDOSE, is presented which is designed for use by crystallographers in optimizing the amount of data that can be obtained from a particular cryo-cooled crystal at synchrotron beamlines.
Abstract: Radiation damage restricts the useful lifetime for macromolecular crystals in the X-ray beam, even at cryotemperatures. With the development of structural genomics pipelines, it will be essential to incorporate projected crystal lifetime information into the automated data collection software routines. As a first step towards this goal, a computer program, RADDOSE, is presented which is designed for use by crystallographers in optimizing the amount of data that can be obtained from a particular cryo-cooled crystal at synchrotron beamlines. The program uses the composition of the crystal and buffer constituents, as well as the beam energy, flux and dimensions, to compute the absorption coefficients and hence the theoretical time taken to reach an absorbed dose of 2 × 10^7 Gy, the so-called `Henderson limit'. At this dose, the intensity of the diffraction pattern is predicted to be halved. A `diffraction–dose efficiency' quantity is introduced, for the convenient comparison of absorbed dose per diffracted photon for different crystals. Four example cases are considered, and the implications for anomalous data collection are discussed in the light of the results from RADDOSE.