Small-angle X-ray scattering intensity of multiscale models of spheres

Sorbier, Loïc; Moreaud, Maxime; Humbert, Séverine

doi:10.1107/s1600576719013839

Cited by 6 publications

(13 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The porosity or void-void two-point correlation function of the union of Boolean models is the product of the porosity or void-void correlation functions of each model. The solid fraction or solid-solid two-point correlation function of the intersection of Boolean models is the product of the solid fraction or solid-solid correlation functions of each model (Gommes, 2018;Sorbier et al, 2019). A one-scale Boolean model with a size and shape distribution of grains may be viewed as a union of Boolean models of these grains having a specific size and shape.…”

Section: Union and Intersection Of Modelsmentioning

confidence: 99%

“…Provided that the P distribution allows one to evaluate its partial moments in a closed analytical form, equation ( 25) can be evaluated numerically. Partial moments can be analytically evaluated for monomodal, exponential, gamma, lognormal (Sorbier et al, 2019) and normal distribution laws, for example.…”

Section: K Hmentioning

confidence: 99%

“…They are, however, restricted to models with known analytical covariance, namely spheres, and a very simple particle-size distribution (Sonntag et al, 1981;Gille, 2011) or an arbitrary but discrete distribution (Gommes, 2018). Sorbier et al (2019) proposed to extend this approach to multiscale Boolean models of spheres with arbitrary distribution laws, giving explicit formulae for lognormal, gamma and exponential distributions. Their work is, however, restricted to spherical particles and aggregates.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Small-angle X-ray scattering intensity of multiscale models of spheroids

et al. 2023

Self Cite

View full text Add to dashboard Cite

The microstructure of heterogeneous catalysts often consists of multiscale aggregates of nanoparticles, some of which are highly anisotropic. Therefore, small-angle X-ray scattering, in classical or anomalous mode, is a valuable tool to characterize this kind of material. Yet, the classical exploitation of the scattered intensities through form and structure factors or by means of Boolean models of spheres is questionable. Here, it is proposed to interpret the scattered intensities through the use of multiscale Boolean models of spheroids. The numerical procedure to compute scattered intensities of such models is given and then validated on asymptotic diluted Boolean models, and its applicability is demonstrated for the characterization of alumina catalyst supports.

show abstract

Section: Union and Intersection Of Modelsmentioning

confidence: 99%

Section: K Hmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Small-angle X-ray scattering intensity of multiscale models of spheroids

et al. 2023

Self Cite

View full text Add to dashboard Cite

show abstract

“…Here, k 0 and k are the wave vectors of the X-rays before and after scattering. The scattering angle 2θ is related to q by q = 4π sin(θ)/λ (Sorbier et al, 2019). Since the scattering arises from the interaction between X-rays and the electron clouds of the atoms, theoretically the scattering intensity can be written as…”

Section: Simulation Of Scattering Intensitymentioning

confidence: 99%

Machine learning-accelerated small-angle X-ray scattering analysis of disordered two- and three-phase materials

Röding

Tomaszewski²,

Yu³

et al. 2022

Front. Mater.

View full text Add to dashboard Cite

Small-angle X-ray scattering (SAXS) is a useful technique for nanoscale structural characterization of materials. In SAXS, structural and spatial information is indirectly obtained from the scattering intensity in the spectral domain, known as the reciprocal space. Therefore, characterizing the structure requires solving the inverse problem of finding a plausible structure model that corresponds to the measured scattering intensity. Both the choice of structure model and the computational workload of parameter estimation are bottlenecks in this process. In this work, we develop a framework for analysis of SAXS data from disordered materials. The materials are modeled using Gaussian Random Fields (GRFs). We study the case of two phases, pore and solid, and three phases, where a third phase is added at the interface between the two other phases. Further, we develop very fast GPU-accelerated, Fourier transform-based numerical methods for both structure generation and SAXS simulation. We demonstrate that length scales and volume fractions can be predicted with good accuracy using our machine learning-based framework. The parameter prediction executes virtually instantaneously and hence the computational burden of conventional model fitting can be avoided.

show abstract

“…As explained previously, the interest of the proposed morphological model compared to DLVO simulations is to be able to simulate large systems, representative of porous materials. Once the system is generated, it is possible to calculate textural properties, nitrogen physisorption isotherm (Wang, 2015) or SAXS curves (Sorbier, 2019). However, the present state of the model enables only a sensitivity study of the packing porosity with respect to the compactness parameters α and β .…”

Section: Relationship Between the Compactness Parameters And The Packing Porositymentioning

confidence: 99%

Simulation of Large Aggregate Particles System With a New Morphological Model

et al. 2021

Self Cite

View full text Add to dashboard Cite

For the development of a new porous material such as catalytic carrier, the control of the textural properties is of fundamental importance. In order to move towards rational synthesis, it is necessary to better understand the physical phenomena that generate a defined solid structure. A contribute to this purpose can be achieved by studying the aggregation process inside colloidal suspensions, leading to porosity generation: this phenomenon can be described with a Brownian dynamics model that, for any set of chemical parameters, gives access to the mass distribution and the fractal dimension of colloidal aggregates. However, this model cannot be used for the simulation of large colloidal systems, due to its high computational time, limiting comparison with analytical methods, which probe the whole multi-scale system. This problem is solved by developing a new aggregation morphological model, wherein the fractal dimension is tuned with two compactness parameters. An efficient simulation algorithm is proposed in case of spheres, for which the fractal dimension of the generated aggregates varies between 1.2 and 3. Brownian dynamics results are used to parametrize this purely geometric model, in order to constrain the size and the morphology of the aggregates created. The large numerical solid will be representative of the textural properties of a real solid and will give more information on the porous network. It could be used, for example, to simulate diffusive transport coupled with chemical reaction and to study the impact of the geometry of the porous system on the catalytic performance.

show abstract

Small-angle X-ray scattering intensity of multiscale models of spheres

Cited by 6 publications

References 32 publications

Small-angle X-ray scattering intensity of multiscale models of spheroids

Small-angle X-ray scattering intensity of multiscale models of spheroids

Machine learning-accelerated small-angle X-ray scattering analysis of disordered two- and three-phase materials

Simulation of Large Aggregate Particles System With a New Morphological Model

Contact Info

Product

Resources

About