Discover Aries and Sagittarius compatibility in love, friendship, and beyond. Learn how these two fire signs create a dynamic, passionate bond full of excitement and adventure.

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Mineral resource security and flows  British Geological Survey

Equality, diversity and inclusion at BGS  British Geological Survey

Trailblazing seismologist named new editor-in-chief of GJI  The Royal Astronomical Society

Washington DC among US cities most vulnerable to space weather, scientists say  The Royal Astronomical Society

Small earthquake recorded under Powys town  Powys County Times

BGS collaborates with Icelandic colleagues to assess windfarm suitability  British Geological Survey

Forty years and counting: new topsoil data provides most extensive snapshot of environmental pollution effects  British Geological Survey

New community launched to support effective management of the subsurface  British Geological Survey

A recently discovered β polymorph of 1,3-diacetylpyrene has turned out to be a prominent negative thermal expansion material. Its unique properties can be linked to anharmonic oscillations in the crystal structure. The onset and development of anharmonic behavior have been successfully tracked over a wide temperature range by single-crystal X-ray diffraction experiments. Sufficient diffraction data quality combined with modern quantum crystallography tools allowed a thorough analysis of the elusive anharmonic effects for a moderate-scattering purely organic compound.

This study explores the high-pressure behavior of benzo[a]pyrene, revealing two previously unknown polymorphs at 4.8 and 7.1 GPa. These findings enhance our understanding of the structural dynamics and stability of polycyclic aromatic hydro­carbons under extreme conditions.

In-situ diffraction measurements reveal that magnesium chloride forms a unique high-pressure phase, a heptahydrate, above 2 GPa. The hydrogen-bonding structure appears to contain orientational disorder.

A unique phase transition, twinning and ferroelastic domain structure in [NH3(CH2)2NH3]2[ZnBr4]Br2 is found. The new additional domain structure is observed at the phase transition on heating, which is preserved after cooling to room temperature.

The hydro­thermal synthesis and structural characterization of four novel 3D pillared-layer metal–organic frameworks are studied, revealing how the malleability of copper coordination geometries drives diverse supramolecular isomerism. The findings provide new insights into designing advanced hybrid materials with tailored properties, emphasizing the significant role of reaction conditions and metal ion flexibility in determining network topologies.

Five multicomponent solid forms of an antifungal drug flucytosine are reported with a hygroscopic stability study. A detailed CSD search on the cocrystal/salts of flucytosine is evaluated and correlated the structures based on bond angles and bond distances.

This study presents the first theoretical predictions of the phase transitions, elastic properties, and thermal behavior of AuMTe2 (M = Ga, In) chalcopyrite compounds. Using density functional theory and the quasi-harmonic Debye model, key mechanical and thermodynamic properties are analyzed, offering insights valuable for future experimental validation.

Single-crystal growth, differential thermal analysis (DTA), derivative thermogravimetry (DTG), differential scanning calorimetry (DSC), X-ray structural studies and polarized microscopy observations of bis(ethylenediammonium) tetrabromozincate(II) bromide [NH3(CH2)2NH3]2[ZnBr4]Br2 are presented. A reversible phase transition is described. At room temperature, the complex crystallizes in the monoclinic system. In some cases, the single crystals are twinned into two or more large domains of ferroelastic type with domain walls in the (100) crystallographic plane. DTA and DTG measurements show chemical stability of the crystal up to ∼538 K. In the DSC studies, a reversible isostructural phase transition was revealed at ∼526/522 K on heating/cooling run, respectively. Optical observation on the heating run reveals that at the phase transition the plane of twinning (domain wall) does not disappear and additionally the appearance of a new domain structure of ferroelastic type with domain walls in the planes (101), (101), (100) and (001) is observed. The domain structure pattern is preserved after cooling to the room-temperature phase and the symmetry of this phase is unchanged.

The odd hydration number has so far been missing in the water-rich magnesium chloride hydrate series (MgCl2·nH2O). In this study, magnesium chloride heptahydrate, MgCl2·7H2O (or MgCl2·7D2O), which forms at high pressures above 2 GPa and high temperatures above 300 K, has been identified. Its structure has been determined by a combination of in-situ single-crystal X-ray diffraction at 2.5 GPa and 298 K and powder neutron diffraction at 3.1 GPa and 300 K. The single-crystal specimen was grown by mixing alcohols to prevent nucleation of undesired crystalline phases. The results show orientational disorder of water molecules, which was also examined using density functional theory calculations. The disorder involves the reconnection of hydrogen bonds, which differs from those in water ice phases and known disordered salt hydrates. Shrinkage by compression occurs mainly in one direction. In the plane perpendicular to this most compressible direction, oxygen and chlorine atoms are in a hexagonal-like arrangement.

Recent advances in quantum crystallography have shown that, beyond conventional charge density refinement, a one-electron reduced density matrix (1-RDM) satisfying N-representability conditions can be reconstructed using jointly experimental X-ray structure factors and directional Compton profiles (DCP) through semidefinite programming. So far, such reconstruction methods for 1-RDM, not constrained to idempotency, have been tested only on a toy model system (CO2). In this work, a new method is assessed on crystalline urea [CO(NH2)2] using static (0 K) and dynamic (50 K) artificial experimental data. An improved model, including symmetry constraints and frozen core-electron contribution, is introduced to better handle the increasing system complexity. Reconstructed 1-RDMs, deformation densities and DCP anisotropy are analysed, and it is demonstrated that the changes in the model significantly improve the reconstruction quality, even when there is insufficient information and data corruption. The robustness of the model and the strategy are thus shown to be well adapted to address the reconstruction problem from actual experimental scattering data.

Brucella ovis is an etiologic agent of ovine epididymitis and brucellosis that causes global devastation in sheep, rams, goats, small ruminants and deer. There are no cost-effective methods for the worldwide eradication of ovine brucellosis. B. ovis and other protein targets from various Brucella species are currently in the pipeline for high-throughput structural analysis at the Seattle Structural Genomics Center for Infectious Disease (SSGCID), with the aim of identifying new therapeutic targets. Furthermore, the wealth of structures generated are effective tools for teaching scientific communication, structural science and biochemistry. One of these structures, B. ovis leucine-, isoleucine-, valine-, threonine- and alanine-binding protein (BoLBP), is a putative periplasmic amino acid-binding protein. BoLBP shares less than 29% sequence identity with any other structure in the Protein Data Bank. The production, crystallization and high-resolution structures of BoLBP are reported. BoLBP is a prototypical bacterial periplasmic amino acid-binding protein with the characteristic Venus flytrap topology of two globular domains encapsulating a large central cavity containing the peptide-binding region. The central cavity contains small molecules usurped from the crystallization milieu. The reported structures reveal the conformational flexibility of the central cavity in the absence of bound peptides. The structural similarity to other LBPs can be exploited to accelerate drug repurposing.

The crystal structure of the intracellular domain of transforming growth factor β type I receptor (TβR1) in complex with the competitive inhibitor SB505124 is presented. The study provides insights into the structure and function of TβR1 in complex with SB505124, and as such offers molecular-level understanding of the inhibition of this critical signalling pathway. The potential of SB505124 as an avenue for therapy in cancer treatment is discussed on basis of the results.

The reciprocal of a non-primitive unit cell is not a unit cell and the basis vectors do not correspond to cell lengths.

The growth quality of AlN single crystals was improved by optimizing the crucible structure for Al vapor transport with the help of finite element simulation.

We present a demonstration of high-pressure grazing-incidence small-angle neutron scattering for soft matter thin films. The results suggest changes in water reorganization at different pressures.

Rotations of small- and wide-angle X-ray scattering samples during acquisition are shown to give a drastic improvement in the reliability of the characterization of anisotropic precipitates in metallic alloys.

This paper describes real-time statistical analysis of liquid jet images for SFX experiments at the European XFEL. This analysis forms one part of the automated jet re-alignment system for SFX experiments at the SPB/SFX instrument of European XFEL.

This study proposes an operation optimization framework for impurity-free recycling of spent lithium-ion batteries. Using a hybrid population balance equation integrated with a data-driven condition classifier, the study firstly identifies the optimal batch and semi-batch operation conditions that significantly reduce the operation time with 100% purity of product; detailed guidelines are given for industrial applications.

Here we describe TOMOMAN (TOMOgram MANager), an extensible open-sourced software package for handling cryo-electron tomography data preprocessing. TOMOMAN streamlines interoperability between a wide range of external packages and provides tools for project sharing and archival.

For the first time, a multimodal reconstruction of a magnetic thin-film structure has been found using polarised neutron reflectivity. This has been achieved by implementing the Bayesian approach in combination with error correction based on the maximum likelihood method and instrument function optimization.

The title compound is a non-liquid crystal mol­ecule. The mol­ecular crystal is consolidated by C—Br⋯O&z-dbnd;C type contacts running continuously along the [001] direction.

Grazing-incidence small-angle neutron scattering (GISANS) under pressure (HP-GISANS) at the solid (Si)–liquid (D2O) interface is demonstrated for the pressure-induced lateral morphological characterization of the nanostructure in thin (<100 nm) soft matter films. We demonstrate feasibility by investigating a hydrophobic {poly[(2,2,3,3,4,4,5,5-octafluoro)pentyl methacrylate]} (POFPMA)–hydrophilic {poly[2-(dimethylamino)ethyl methacrylate]} (PDMAEMA) brush mixture of strong incompatibility between the homopolymers, anchored on Si, at T = 45°C for two pressures, P = 1 bar and P = 800 bar. Our GISANS results reveal nanostructural rearrangements with increasing P, underlining P-induced effects in tethered polymer brush layers swollen with bulk solvent.

Nanometric precipitates in metallic alloys often have highly anisotropic shapes. Given the large grain size and non-random texture typical of these alloys, performing small- and wide-angle X-ray scattering (SAXS/WAXS) measurements on such samples for determining their characteristics (typically size and volume fraction) results in highly anisotropic and irreproducible data. Rotations of flat samples during SAXS/WAXS acquisitions are presented here as a solution to these anisotropy issues. Two aluminium alloys containing anisotropic precipitates are used as examples to validate the approach with a −45°/45° angular range. Clear improvements can be seen on the SAXS I(q) fitting and the consistency between the different SAXS/WAXS measurements. This methodology results in more reliable measurements of the precipitate's characteristics, and thus allows for time- and space-resolved measurements with higher accuracy.

In the conventional crucible structure for AlN crystal growth by physical vapor transport, owing to the long molecular transport path of Al vapor and the disruption of the gas flow by the presence of a deflector, the Al vapor easily forms polycrystals in the growth domain. The result is increased internal stress in the crystals and increased difficulty in growing large-sized crystals. On this basis, with the help of finite element simulations, a novel crucible structure is designed. This crucible not only optimizes the gas transport but also increases the radial gradient of the AlN crystal surface, making the enhanced growth rate in the central region more obvious. The thermal stresses between the deflector and the crystal are also reduced. High-quality AlN crystals with an FWHM of 79 arcsec were successfully grown with this structure, verifying the accuracy of finite element simulation of the growth of AlN crystals. Our work has important guiding significance for the growth of high-quality AlN crystals.

The dualism between direct and reciprocal space is at the origin of well known relations between basis vectors in the two spaces. It is shown that when a coordinate system corresponding to a non-primitive unit cell is adopted, this dualism has to be handled with care. In particular, the reciprocal of a non-primitive unit cell is not a unit cell but a region in reciprocal space that does not represent a unit of repetition by translation. The basis vectors do not correspond to reciprocal-space cell lengths, contrary to what is stated even in the core CIF dictionary. The corresponding unit cell is a multiple of this region. The broken correspondence between basis vectors and unit cell is at the origin of the integral reflection conditions.

In electron microscopy the principle of reciprocity is often used to imply time reversal symmetry. While this is true for elastic scattering, its applicability to inelastic scattering is less well established. From the second law of thermodynamics, the entropy for a thermally isolated system must be constant for any reversible process. Using entropy and statistical fluctuation arguments, it is shown that, while reversibility is possible at the microscopic level, it becomes statistically less likely for higher energy transfers. The implications for reciprocal imaging modes, including energy loss and energy gain measurements, as well as Kainuma's reciprocal wave model are also discussed.

The crystal structure uniformity is numerically estimated as the standard deviation of the crystal space quantizer 〈G3〉. This criterion has been applied to explore the uniformity of ionic sublattices in 21465 crystal structures of inorganic ionic compounds. In most cases, at least one kind of sublattice (whole ionic lattice, cationic or anionic sublattice) was found to be highly uniform with a small 〈G3〉 value. Non-uniform structures appeared to be either erroneous or essentially non-ionic. As a result, a set of uniformity criteria is proposed for the estimation of the stability of ionic crystal structures.

Algebraic expressions for averaging linear and nonlinear stiffness tensors from general anisotropy to different effective symmetries (11 Laue classes elastically representing all 32 crystal classes, and two non-crystalline symmetries: isotropic and cylindrical) have been derived by automatic symbolic computations of the arithmetic mean over the set of rotational transforms determining a given symmetry. This approach generalizes the Voigt average to nonlinear constants and desired approximate symmetries other than isotropic, which can be useful for a description of textured polycrystals and rocks preserving some symmetry aspects. Low-symmetry averages have been used to derive averages of higher symmetry to speed up computations. Relationships between the elastic constants of each symmetry have been deduced from their corresponding averages by resolving the rank-deficient system of linear equations. Isotropy has also been considered in terms of generalized Lamé constants. The results are published in the form of appendices in the supporting information for this article and have been deposited in the Mendeley database.

In the realm of X-ray ptychography experiments, a considerable amount of ptychography scans are typically performed within a field of view encompassing the target sample. While it is crucial to obtain overlapping scans in small increments over the region of interest for achieving high-resolution sample reconstruction, a significant number of these scans often redundantly measure the empty background within the wide field of view. To address this inefficiency, an innovative algorithm is proposed that introduces automatic guidance for data acquisition. The algorithm first directs the scan point to actively search for the object of interest within the field of view. Subsequently, it intelligently scans along the perimeter of the sample, strategically acquiring measurements exclusively within the boundary of the region of interest. By employing this approach, a reduction in the number of measurements required to obtain high-resolution reconstruction images is demonstrated, as compared with conventional raster scanning methods. Furthermore, the automatic guidance provided by the algorithm offers the added advantage of saving valuable time during the reconstruction process. Through practical implementation on real experiments, these findings showcase the efficacy of the proposed algorithm in enhancing the efficiency and accuracy of X-ray ptychography experiments. This novel approach holds immense potential for advancing sample analysis and imaging techniques in various scientific disciplines.

X-ray diffraction imaging (XDI) is utilized for visualizing the structures of non-crystalline particles in material sciences and biology. In the structural analysis, phase-retrieval (PR) algorithms are applied to the diffraction amplitude data alone to reconstruct the electron density map of a specimen particle projected along the direction of the incident X-rays. However, PR calculations may not lead to good convergence because of a lack of diffraction patterns in small-angle regions and Poisson noise in X-ray detection. Therefore, the PR calculation is still a bottleneck for the efficient application of XDI in the structural analyses of non-crystalline particles. For screening maps from hundreds of trial PR calculations, we have been using a score and measuring the similarity between a pair of retrieved maps. Empirically, probable maps approximating the particle structures gave a score smaller than a threshold value, but the reasons for the effectiveness of the score are still unclear. In this study, the score is characterized in terms of the phase differences between the structure factors of the retrieved maps, the usefulness of the score in screening the maps retrieved from experimental diffraction patterns is demonstrated, and the effective resolution of similarity-score-selected maps is discussed.

In X-ray diffraction imaging (XDI), electron density maps of a targeted particle are reconstructed computationally from the diffraction pattern alone using phase-retrieval (PR) algorithms. However, the PR calculations sometimes fail to yield realistic electron density maps that approximate the structure of the particle. This occurs due to the absence of structure amplitudes at and near the zero-scattering angle and the presence of Poisson noise in weak diffraction patterns. Consequently, the PR calculation becomes a bottleneck for XDI structure analyses. Here, a protocol to efficiently yield realistic maps is proposed. The protocol is based on the empirical observation that realistic maps tend to yield low similarity scores, as suggested in our prior study [Sekiguchi et al. (2017), J. Synchrotron Rad. 24, 1024–1038]. Among independently and concurrently executed PR calculations, the protocol modifies all maps using the electron-density maps exhibiting low similarity scores. This approach, along with a new protocol for estimating particle shape, improved the probability of obtaining realistic maps for diffraction patterns from various aggregates of colloidal gold particles, as compared with PR calculations performed without the protocol. Consequently, the protocol has the potential to reduce computational costs in PR calculations and enable efficient XDI structure analysis of non-crystalline particles using synchrotron X-rays and X-ray free-electron laser pulses.

Bone material contains a hierarchical network of micro- and nano-cavities and channels, known as the lacuna-canalicular network (LCN), that is thought to play an important role in mechanobiology and turnover. The LCN comprises micrometer-sized lacunae, voids that house osteocytes, and submicrometer-sized canaliculi that connect bone cells. Characterization of this network in three dimensions is crucial for many bone studies. To quantify X-ray Zernike phase-contrast nanotomography data, deep learning is used to isolate and assess porosity in artifact-laden tomographies of zebrafish bones. A technical solution is proposed to overcome the halo and shade-off domains in order to reliably obtain the distribution and morphology of the LCN in the tomographic data. Convolutional neural network (CNN) models are utilized with increasing numbers of images, repeatedly validated by `error loss' and `accuracy' metrics. U-Net and Sensor3D CNN models were trained on data obtained from two different synchrotron Zernike phase-contrast transmission X-ray microscopes, the ANATOMIX beamline at SOLEIL (Paris, France) and the P05 beamline at PETRA III (Hamburg, Germany). The Sensor3D CNN model with a smaller batch size of 32 and a training data size of 70 images showed the best performance (accuracy 0.983 and error loss 0.032). The analysis procedures, validated by comparison with human-identified ground-truth images, correctly identified the voids within the bone matrix. This proposed approach may have further application to classify structures in volumetric images that contain non-linear artifacts that degrade image quality and hinder feature identification.

The X-ray emission spectrometer at SPring-8 BL07LSU has recently been upgraded with advanced modifications that enable the rotation of the spectrometer with respect to the scattering angle. This major upgrade allows the scattering angle to be flexibly changed within the range of 45–135°, which considerably simplifies the measurement of angle-resolved X-ray emission spectroscopy. To accomplish the rotation system, a sophisticated sample chamber and a highly precise spectrometer rotation mechanism have been developed. The sample chamber has a specially designed combination of three rotary stages that can smoothly move the connection flange along the wide scattering angle without breaking the vacuum. In addition, the spectrometer is rotated by sliding on a flat metal surface, ensuring exceptionally high accuracy in rotation and eliminating the need for any further adjustments during rotation. A control system that integrates the sample chamber and rotation mechanism to automate the measurement of angle-resolved X-ray emission spectroscopy has also been developed. This automation substantially streamlines the process of measuring angle-resolved spectra, making it far easier than ever before. Furthermore, the upgraded X-ray emission spectrometer can now also be utilized in diffraction experiments, providing even greater versatility to our research capabilities.

X-ray ptychography is a coherent diffraction imaging technique based on acquiring multiple diffraction patterns obtained through the illumination of the sample at different partially overlapping probe positions. The diffraction patterns collected are used to retrieve the complex transmittivity function of the sample and the probe using a phase retrieval algorithm. Absorption or phase contrast images of the sample as well as the real and imaginary parts of the probe function can be obtained. Furthermore, X-ray ptychography can also provide spectral information of the sample from absorption or phase shift images by capturing multiple ptychographic projections at varying energies around the resonant energy of the element of interest. However, post-processing of the images is required to extract the spectra. To facilitate this, ProSPyX, a Python package that offers the analysis tools and a graphical user interface required to process spectral ptychography datasets, is presented. Using the PyQt5 Python open-source module for development and design, the software facilitates extraction of absorption and phase spectral information from spectral ptychographic datasets. It also saves the spectra in file formats compatible with other X-ray absorption spectroscopy data analysis software tools, streamlining integration into existing spectroscopic data analysis pipelines. To illustrate its capabilities, ProSPyX was applied to process the spectral ptychography dataset recently acquired on a nickel wire at the SWING beamline of the SOLEIL synchrotron.

Calculations and measurements of polarization-dependent soft X-ray scattering intensity are presented during a magnetic hysteresis cycle. It is confirmed that the dependence of the intensity on the magnetic moment can be linear, quadratic or a combination of both, depending on the polarization of the incident X-ray beam and the direction of the magnetic moment. With a linearly polarized beam, the scattered intensity will have a purely quadratic dependence on the magnetic moment when the magnetic moment is parallel to the scattering plane. However, with the magnetic moment perpendicular to the scattering plane, there is also a linear component. This means that, when measuring the hysteresis with linear polarization during a hysteresis cycle, the intensity will be an even function of the applied field when the change in the magnetic moment (and field) is confined within the scattering plane but becomes more complicated when the magnetic moment is out of the scattering plane. Furthermore, with circular polarization, the dependence of the scattered intensity on the moment is a combination of linear and quadratic. With the moment parallel to the scattering plane, the linear component changes with the helicity of the incident beam. Surprisingly, in stark contrast to absorption studies, even when the magnetic moment is perpendicular to the scattering plane there is still a dependence on the moment with a linear component. This linear component is completely independent of the helicity of the beam, meaning that the hysteresis loops will not be inverted with helicity.

The Materials Imaging and Dynamics (MID) instrument at the European X-ray Free-Electron Laser Facility (EuXFEL) is equipped with a multipurpose diagnostic end-station (DES) at the end of the instrument. The imager unit in DES is a key tool for aligning the beam to a standard trajectory and for adjusting optical elements such as focusing lenses or the split-and-delay line. Furthermore, the DES features a bent-diamond-crystal spectrometer to disperse the spectrum of the direct beam to a line detector. This enables pulse-resolved characterization of the EuXFEL spectrum to provide X-ray energy calibration, and the spectrometer is particularly useful in commissioning special modes of the accelerator. Together with diamond-based intensity monitors, the imager and spectrometer form the DES unit which also contains a heavy-duty beamstop at the end of the MID instrument. Here, we describe the setup in detail and provide exemplary beam diagnostic results.

Hard X-ray absorption spectroscopy is a valuable in situ probe for non-destructive diagnostics of metal sites. The low-energy interval of a spectrum (XANES) contains information about the metal oxidation state, ligand type, symmetry and distances in the first coordination shell but shows almost no dependency on the bridged metal–metal bond length. The higher-energy interval (EXAFS), on the contrary, is more sensitive to the coordination numbers and can decouple the contribution from distances in different coordination shells. Supervised machine-learning methods can combine information from different intervals of a spectrum; however, computational approaches for the near-edge region of the spectrum and higher energies are different. This work aims to keep all benefits of XANES and extend its sensitivity towards the interatomic distances in the first and second coordination shells. Using a binuclear bridged copper complex as a case study and cross-validation analysis as a quantitative tool it is shown that the first 170 eV above the edge are already sufficient to balance the contributions of Cu–O/N scattering and Cu–Cu scattering. As a more general outcome this work highlights the trivial but often overlooked importance of using `longer' energy intervals of XANES for structural refinement and machine-learning predictions. The first 200 eV above the absorption edge still do not require parametrization of Debye–Waller damping and can be calculated within full multiple scattering or finite difference approximations with only moderately increased computational costs.

This study introduces a novel iterative Bragg peak removal with automatic intensity correction (IBR-AIC) methodology for X-ray absorption spectroscopy (XAS), specifically addressing the challenge of Bragg peak interference in the analysis of crystalline materials. The approach integrates experimental adjustments and sophisticated post-processing, including an iterative algorithm for robust calculation of the scaling factor of the absorption coefficients and efficient elimination of the Bragg peaks, a common obstacle in accurately interpreting XAS data, particularly in crystalline samples. The method was thoroughly evaluated on dilute catalysts and thin films, with fluorescence mode and large-angle rotation. The results underscore the technique's effectiveness, adaptability and substantial potential in improving the precision of XAS data analysis. While demonstrating significant promise, the method does have limitations related to signal-to-noise ratio sensitivity and the necessity for meticulous angle selection during experimentation. Overall, IBR-AIC represents a significant advancement in XAS, offering a pragmatic solution to Bragg peak contamination challenges, thereby expanding the applications of XAS in understanding complex materials under diverse experimental conditions.

Synchrotron light sources can provide the required spatial coherence, stability and control to support the development of advanced lithography at the extreme ultraviolet and soft X-ray wavelengths that are relevant to current and future fabricating technologies. Here an evaluation of the optical performance of the soft X-ray (SXR) beamline of the Australian Synchrotron (AS) and its suitability for developing interference lithography using radiation in the 91.8 eV (13.5 nm) to 300 eV (4.13 nm) range are presented. A comprehensive physical optics model of the APPLE-II undulator source and SXR beamline was constructed to simulate the properties of the illumination at the proposed location of a photomask, as a function of photon energy, collimation and monochromator parameters. The model is validated using a combination of experimental measurements of the photon intensity distribution of the undulator harmonics. It is shown that the undulator harmonics intensity ratio can be accurately measured using an imaging detector and controlled using beamline optics. Finally, the photomask geometric constraints and achievable performance for the limiting case of fully spatially coherent illumination are evaluated.