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1.
ChemSusChem ; : e202400303, 2024 Mar 20.
Article in English | MEDLINE | ID: mdl-38507245

ABSTRACT

Advanced in situ analyses are indispensable for comprehending the catalyst aging mechanisms of Pt-based PEM fuel cell cathode materials, particularly during accelerated stress tests (ASTs). In this study, a combination of in situ small-angle and wide-angle X-ray scattering (SAXS & WAXS) techniques were employed to establish correlations between structural parameters (crystal phase, quantity, and size) of a highly active skeleton-PtCo (sk-PtCo) catalyst and their degradation cycles within the potential range of the start-up/shut-down (SUSD) conditions. Despite the complex case of the sk-PtCo catalyst comprising two distinct fcc alloy phases, our complementary techniques enabled in situ monitoring of structural changes in each crystal phase in detail. Remarkably, the in situ WAXS measurements uncover two primary catalyst aging processes, namely the cobalt depletion (regime I) followed by the crystallite growth via Ostwald ripening and/or particle coalescence (regime II). Additionally, in situ SAXS data reveal a continuous size growth over the AST. The Pt-enriched shell thickening based on the Co depletion within the first 100 SUSD cycles and particle growth induced by additional potential cycles were also collaborated by ex situ STEM-EELS. Overall, our work shows a comprehensive aging model for the sk-PtCo catalyst probed by complementary in situ WAXS and SAXS techniques.

2.
Chem Rev ; 124(3): 629-721, 2024 Feb 14.
Article in English | MEDLINE | ID: mdl-38253355

ABSTRACT

Electrochemical and electrocatalytic processes are of key importance for the transition to a sustainable energy supply as well as for a wide variety of other technologically relevant fields. Further development of these processes requires in-depth understanding of the atomic, nano, and micro scale structure of the materials and interfaces in electrochemical devices under reaction conditions. We here provide a comprehensive review of in situ and operando studies by X-ray scattering methods, which are powerful and highly versatile tools to provide such understanding. We discuss the application of X-ray scattering to a wide variety of electrochemical systems, ranging from metal and oxide single crystals to nanoparticles and even full devices. We show how structural data on bulk phases, electrode-electrolyte interfaces, and nanoscale morphology can be obtained and describe recent developments that provide highly local information and insight into the composition and electronic structure. These X-ray scattering studies yield insights into the structure in the double layer potential range as well as into the structural evolution during electrocatalytic processes and phase formation reactions, such as nucleation and growth during electrodeposition and dissolution, the formation of passive films, corrosion processes, and the electrochemical intercalation into battery materials.

3.
ACS Appl Mater Interfaces ; 15(51): 59319-59328, 2023 Dec 27.
Article in English | MEDLINE | ID: mdl-38085792

ABSTRACT

Li-ion battery cathode active materials obtained from different sources or preparation methods often exhibit broadly divergent performance and stability despite no obvious differences in morphology, purity, and crystallinity. We show how state-of-the-art, commercial, nominally single crystalline LiNi0.6Mn0.2Co0.2O2 (NMC-622) particles possess extensive internal nanostructure even in the pristine state. Scanning X-ray diffraction microscopy reveals the presence of interlayer strain gradients, and crystal bending is attributed to oxygen vacancies. Phase contrast X-ray nano-tomography reveals two different kinds of particles, welded/aggregated, and single crystal like, and emphasizes the intra- and interparticle heterogeneities from the nano- to the microscale. It also detects within the imaging resolution (100 nm) substantial quantities of nanovoids hidden inside the bulk of two-thirds of the overall studied particles (around 3000), with an average value of 12.5%v per particle and a mean size of 148 nm. The powerful combination of both techniques helps prescreening and quantifying the defective nature of cathode material and thus anticipating their performance in electrode assembly/battery testing.

4.
Nat Commun ; 14(1): 6975, 2023 Nov 01.
Article in English | MEDLINE | ID: mdl-37914690

ABSTRACT

Lithiation dynamics and phase transition mechanisms in most battery cathode materials remain poorly understood, because of the challenge in differentiating inter- and intra-particle heterogeneity. In this work, the structural evolution inside Li1-xMn1.5Ni0.5O4 single crystals during electrochemical delithiation is directly resolved with operando X-ray nanodiffraction microscopy. Metastable domains of solid-solution intermediates do not appear associated with the reaction front between the lithiated and delithiated phases, as predicted by current phase transition theory. Instead, unusually persistent strain gradients inside the single crystals suggest that the shape and size of solid solution domains are instead templated by lattice defects, which guide the entire delithiation process. Morphology, strain distributions, and tilt boundaries reveal that the (Ni2+/Ni3+) and (Ni3+/Ni4+) phase transitions proceed through different mechanisms, offering solutions for reducing structural degradation in high voltage spinel active materials towards commercially useful durability. Dynamic lattice domain reorientation during cycling are found to be the cause for formation of permanent tilt boundaries with their angular deviation increasing during continuous cycling.

5.
J Phys Chem Lett ; 14(38): 8493-8499, 2023 Sep 28.
Article in English | MEDLINE | ID: mdl-37721973

ABSTRACT

The catalytic oxidation of CO and CH4 can be strongly influenced by the structures of oxide phases that form on metallic catalysts during reaction. Here, we show that an epitaxial PdO(100) structure forms at temperatures above 600 K during the oxidation of Pd(100) by gaseous O atoms as well as exposure to O2-rich mixtures at millibar partial pressures. The oxidation of Pd(100) by gaseous O atoms preferentially generates an epitaxial, multilayer PdO(101) structure at 500 K, but initiating Pd(100) oxidation above 600 K causes an epitaxial PdO(100) structure to grow concurrently with PdO(101) and produces a thicker and rougher oxide. We present evidence that this change in the oxidation behavior is caused by a temperature-induced change in the stability of small PdO domains that initiate oxidation. Our discovery of the epitaxial PdO(100) structure may be significant for developing relationships among oxide structure, catalytic activity, and reaction conditions for applications of oxidation catalysis.

6.
Angew Chem Int Ed Engl ; 62(34): e202304293, 2023 Aug 21.
Article in English | MEDLINE | ID: mdl-37341165

ABSTRACT

The degradation of Pt-containing oxygen reduction catalysts for fuel cell applications is strongly linked to the electrochemical surface oxidation and reduction of Pt. Here, we study the surface restructuring and Pt dissolution mechanisms during oxidation/reduction for the case of Pt(100) in 0.1 M HClO4 by combining operando high-energy surface X-ray diffraction, online mass spectrometry, and density functional theory. Our atomic-scale structural studies reveal that anodic dissolution, detected during oxidation, and cathodic dissolution, observed during the subsequent reduction, are linked to two different oxide phases. Anodic dissolution occurs predominantly during nucleation and growth of the first, stripe-like oxide. Cathodic dissolution is linked to a second, amorphous Pt oxide phase that resembles bulk PtO2 and starts to grow when the coverage of the stripe-like oxide saturates. In addition, we find the amount of surface restructuring after an oxidation/reduction cycle to be potential-independent after the stripe-like oxide has reached its saturation coverage.

7.
J Phys Chem Lett ; 14(14): 3589-3593, 2023 Apr 13.
Article in English | MEDLINE | ID: mdl-37018542

ABSTRACT

The first step of electrochemical surface oxidation is extraction of a metal atom from its lattice site to a location in a growing oxide. Here we show by fast simultaneous electrochemical and in situ high-energy surface X-ray diffraction measurements that the initial extraction of Pt atoms from Pt(111) is a fast, potential-driven process, whereas charge transfer for the related formation of adsorbed oxygen-containing species occurs on a much slower time scale and is evidently uncoupled from the extraction process. It is concluded that potential plays a key independent role in electrochemical surface oxidation.

8.
Environ Sci Technol ; 56(20): 14817-14827, 2022 10 18.
Article in English | MEDLINE | ID: mdl-36184803

ABSTRACT

The mobility of 79Se, a fission product of 235U and long-lived radioisotope, is an important parameter in the safety assessment of radioactive nuclear waste disposal systems. Nonradioactive selenium is also an important contaminant of drainage waters from black shale mountains and coal mines. Highly mobile and soluble in its high oxidation states, selenate (Se(VI)O42-) and selenite (Se(IV)O32-) oxyanions can interact with magnetite, a mineral present in anoxic natural environments and in steel corrosion products, thereby being reduced and consequently immobilized by forming low-solubility solids. Here, we investigated the sorption and reduction capacity of synthetic nanomagnetite toward Se(VI) at neutral and acidic pH, under reducing, oxygen-free conditions. The additional presence of Fe(II)aq, released during magnetite dissolution at pH 5, has an effect on the reduction kinetics. X-ray absorption spectroscopy analyses revealed that, at pH 5, trigonal gray Se(0) formed and that sorbed Se(IV) complexes remained on the nanoparticle surface during longer reaction times. The Se(0) nanowires grew during the reaction, which points to a complex transport mechanism of reduced species or to active reduction sites at the tip of the Se(0) nanowires. The concomitant uptake of aqueous Fe(II) and Se(VI) ions is interpreted as a consequence of small pH oscillations that result from the Se(VI) reduction, leading to a re-adsorption of aqueous Fe(II) onto the magnetite, renewing its reducing capacity. This effect is not observed at pH 7, where we observed only the formation of Se(0) with slow kinetics due to the formation of an oxidized maghemite layer. This indicates that the presence of aqueous Fe(II) may be an important factor to be considered when examining the environmental reactivity of magnetite.


Subject(s)
Nanowires , Radioactive Waste , Selenium Compounds , Selenium , Adsorption , Coal , Ferrosoferric Oxide/chemistry , Oxidation-Reduction , Selenic Acid , Selenious Acid/chemistry , Selenium/chemistry , Steel
9.
Chem Sci ; 13(32): 9295-9304, 2022 Aug 17.
Article in English | MEDLINE | ID: mdl-36093024

ABSTRACT

Recently proposed bimetallic octahedral Pt-Ni electrocatalysts for the oxygen reduction reaction (ORR) in proton exchange membrane fuel cell (PEMFC) cathodes suffer from particle instabilities in the form of Ni corrosion and shape degradation. Advanced trimetallic Pt-based electrocatalysts have contributed to their catalytic performance and stability. In this work, we propose and analyse a novel quaternary octahedral (oh-)Pt nanoalloy concept with two distinct metals serving as stabilizing surface dopants. An efficient solvothermal one-pot strategy was developed for the preparation of shape-controlled oh-PtNi catalysts doped with Rh and Mo in its surface. The as-prepared quaternary octahedral PtNi(RhMo) catalysts showed exceptionally high ORR performance accompanied by improved activity and shape integrity after stability tests compared to previously reported bi- and tri-metallic systems. Synthesis, performance characteristics and degradation behaviour are investigated targeting deeper understanding for catalyst system improvement strategies. A number of different operando and on-line analysis techniques were employed to monitor the structural and elemental evolution, including identical location scanning transmission electron microscopy and energy dispersive X-ray analysis (IL-STEM-EDX), operando wide angle X-ray spectroscopy (WAXS), and on-line scanning flow cell inductively coupled plasma mass spectrometry (SFC-ICP-MS). Our studies show that doping PtNi octahedral catalysts with small amounts of Rh and Mo suppresses detrimental Pt diffusion and thus offers an attractive new family of shaped Pt alloy catalysts for deployment in PEMFC cathode layers.

10.
ACS Catal ; 12(6): 3256-3268, 2022 Mar 18.
Article in English | MEDLINE | ID: mdl-35359579

ABSTRACT

Co oxides and oxyhydroxides have been studied extensively in the past as promising electrocatalysts for the oxygen evolution reaction (OER) in neutral to alkaline media. Earlier studies showed the formation of an ultrathin CoO x (OH) y skin layer on Co3O4 at potentials above 1.15 V vs reversible hydrogen electrode (RHE), but the precise influence of this skin layer on the OER reactivity is still under debate. We present here a systematic study of epitaxial spinel-type Co3O4 films with defined (111) orientation, prepared on different substrates by electrodeposition or physical vapor deposition. The OER overpotential of these samples may vary up to 120 mV, corresponding to two orders of magnitude differences in current density, which cannot be accounted for by differences in the electrochemically active surface area. We demonstrate by a careful analysis of operando surface X-ray diffraction measurements that these differences are clearly correlated with the average thickness of the skin layer. The OER reactivity increases with the amount of formed skin layer, indicating that the entire three-dimensional skin layer is an OER-active interphase. Furthermore, a scaling relationship between the reaction centers in the skin layer and the OER activity is established. It suggests that two lattice sites are involved in the OER mechanism.

11.
ACS Appl Mater Interfaces ; 14(16): 18420-18430, 2022 Apr 27.
Article in English | MEDLINE | ID: mdl-35417125

ABSTRACT

Cathode catalyst layers of proton exchange membrane fuel cells (PEMFCs) typically consist of carbon-supported platinum catalysts with varying weight ratios of proton-conducting ionomers. N-Doping of carbon support materials is proposed to enhance the performance and durability of the cathode layer under operating conditions in a PEMFC. However, a detailed understanding of the contributing N-moieties is missing. Here, we report the successful synthesis and fuel cell implementation of Pt electrocatalysts supported on N-doped carbons, with a focus on the analysis of the N-induced effect on catalyst performance and durability. A customized fluidized bed reduction reactor was used to synthesize highly monodisperse Pt nanoparticles deposited on N-doped carbons (N-C), the catalytic oxygen reduction reaction activity and stability of which matched those of state-of-the-art PEMFC catalysts. Operando high-energy X-ray diffraction experiments were conducted using a fourth generation storage ring; the light of extreme brilliance and coherence allows investigating the impact of N-doping on the degradation behavior of the Pt/N-C catalysts. Tests in liquid electrolytes were compared with tests in membrane electrode assemblies in single-cell PEMFCs. Our analysis refines earlier views on the subject of N-doped carbon catalyst supports: it provides evidence that heteroatom doping and thus the incorporation of defects into the carbon backbone do not mitigate the carbon corrosion during high-potential cycling (1-1.5 V) and, however, can promote the cell performance under usual PEMFC operating conditions (0.6-0.9 V).

12.
Biomacromolecules ; 22(12): 5195-5203, 2021 12 13.
Article in English | MEDLINE | ID: mdl-34813296

ABSTRACT

Protein adsorption to surfaces is at the heart of numerous technological and bioanalytical applications, but sometimes, it is also associated with medical risks. To deepen our insights into processes involving layers of surface-adsorbed proteins, high-resolution structural information is essential. Here, we use standing-wave X-ray fluorescence (SWXF) in combination with an optimized liquid-cell setup to investigate the underwater conformation of the random-coiled phosphoprotein ß-casein adsorbed to hydrophilic and hydrophobized solid surfaces. The orientation of the protein, as determined through the distributions of sulfur and phosphorus, is found to be sensitive to the chemical nature of the substrate. While no preferred orientations are observed on hydrophobized surfaces, on hydrophilic Al oxide, ß-casein is adsorbed as a diblock copolymer with the phosphorylated domain I attached to the surface. Our results demonstrate that targeting biologically relevant chemical elements with SWXF enables a detailed investigation of biomolecular layers under near-physiological conditions.


Subject(s)
Membrane Proteins , Adsorption , Fluorescence , Protein Conformation , Surface Properties , X-Rays
13.
J Am Chem Soc ; 143(41): 17068-17078, 2021 Oct 20.
Article in English | MEDLINE | ID: mdl-34623136

ABSTRACT

The theoretical design of effective metal electrocatalysts for energy conversion and storage devices relies greatly on supposed unilateral effects of catalysts structure on electrocatalyzed reactions. Here, by using high-energy X-ray diffraction from the new Extremely Brilliant Source of the European Synchrotron Radiation Facility (ESRF-EBS) on device-relevant Pd and Pt nanocatalysts during cyclic voltammetry experiments in liquid electrolytes, we reveal the near ubiquitous feedback from various electrochemical processes on nanocatalyst strain. Beyond challenging and extending the current understanding of practical nanocatalysts behavior in electrochemical environment, the reported electrochemical strain provides experimental access to nanocatalysts absorption and adsorption trends (i.e., reactivity and stability descriptors) operando. The ease and power in monitoring such key catalyst properties at new and future beamlines is foreseen to provide a discovery platform toward the study of nanocatalysts encompassing a large variety of applications, from model environments to the device level.

14.
Chimia (Aarau) ; 75(9): 733-743, 2021 Sep 15.
Article in English | MEDLINE | ID: mdl-34526178

ABSTRACT

In this mini-review we compare two prototypical metal foam electrocatalysts applied to the transformation of CO2 into value-added products (e.g. alcohols on Cu foams and formate on Bi foams). A substantial improvement in the catalyst performance is typically achieved through thermal annealing of the as-deposited foam materials, followed by the electro-reduction of the pre-formed oxidic precursors prior or during the actual CO2 electrolysis. Utilizing highly insightful and sensitive complementary operando analytical techniques (XAS, XRD, and Raman spectroscopy) we demonstrate that this catalyst pre-activation process is entirely accomplished in case of the oxidized Cu foams prior to the formation of hydrocarbons and alcohols from the CO2. The actually active catalyst is therefore the metallic Cu derived from the precursor by means of oxide electro-reduction. Conversely, in their oxidic form, the Cu-based foam catalysts are inactive towards the CO2 reduction reaction (denoted ec-CO2 RR). Oxidized Bi foams can be regarded as an excellent counter example to the above-mentioned Cu case as both metallic and the thermally derived oxidic Bi foams are highly active towards ec-CO2 RR (formate production). Indeed, operando Raman spectroscopy reveals that CO2 electrolysis occurs upon its embedment into the oxidic Bi2O3 foam precursor, which itself undergoes partial transformation into an active sub-carbonate phase. The potential-dependent transition of sub-carbonates/oxides into the corresponding metallic Bi foam dictates the characteristic changes of the ec-CO2 RR pathway. Identical location (IL) microscopic inspection of the catalyst materials, e.g. by means of scanning electron microscopy, demonstrates substantial morphological alterations on the nm length scale on the material surface as consequence of the sub-carbonate formation and the potential-driven oxide reduction into the metallic Bi foam. The foam morphology on a mesoscopic length scale (macroporosity) remains, by contrast, fully unaffected by these phase transitions.

15.
Proc Natl Acad Sci U S A ; 118(26)2021 Jun 29.
Article in English | MEDLINE | ID: mdl-34140337

ABSTRACT

The addition of molten alkali metal salts drastically accelerates the kinetics of CO2 capture by MgO through the formation of MgCO3 However, the growth mechanism, the nature of MgCO3 formation, and the exact role of the molten alkali metal salts on the CO2 capture process remain elusive, holding back the development of more-effective MgO-based CO2 sorbents. Here, we unveil the growth mechanism of MgCO3 under practically relevant conditions using a well-defined, yet representative, model system that is a MgO(100) single crystal coated with NaNO3 The model system is interrogated by in situ X-ray reflectometry coupled with grazing incidence X-ray diffraction, scanning electron microscopy, and high-resolution transmission electron microscopy. When bare MgO(100) is exposed to a flow of CO2, a noncrystalline surface carbonate layer of ca. 7-Å thickness forms. In contrast, when MgO(100) is coated with NaNO3, MgCO3 crystals nucleate and grow. These crystals have a preferential orientation with respect to the MgO(100) substrate, and form at the interface between MgO(100) and the molten NaNO3 MgCO3 grows epitaxially with respect to MgO(100), and the lattice mismatch between MgCO3 and MgO is relaxed through lattice misfit dislocations. Pyramid-shaped pits on the surface of MgO, in proximity to and below the MgCO3 crystals, point to the etching of surface MgO, providing dissolved [Mg2+…O2-] ionic pairs for MgCO3 growth. Our studies highlight the importance of combining X-rays and electron microscopy techniques to provide atomic to micrometer scale insight into the changes occurring at complex interfaces under reactive conditions.

16.
Faraday Discuss ; 229: 176-196, 2021 May 01.
Article in English | MEDLINE | ID: mdl-33645610

ABSTRACT

In this study, we investigate the effect of thermal treatment/calcination on the stability and activity of a Na-Mn-W/SiO2 catalyst for the oxidative coupling of methane. The catalyst performance and characterisation measurements suggest that the W species are directly involved in the catalyst active site responsible for CH4 conversion. Under operating conditions, the active components, present in the form of a Na-W-O-Mn molten state, are highly mobile and volatile. By varying the parameters of the calcination protocol, it was shown that these molten components can be partially stabilised, resulting in a catalyst with lower activity (due to loss of surface area) but higher stability even for long duration OCM reaction experiments.

17.
Phys Chem Chem Phys ; 22(40): 22956-22962, 2020 Oct 21.
Article in English | MEDLINE | ID: mdl-33026372

ABSTRACT

We investigate with in situ surface X-ray diffraction (SXRD) and X-ray reflectivity (XRR) experiments the cathodic stability of an ultrathin single-crystalline IrO2(110) film with a regular array of mesoscopic rooflike structures that is supported on a RuO2(110)/Ru(0001) template. It turns out that the planarity of the single-crystalline IrO2(110) film is lost in that IrO2(110) oxide domains delaminate at a cathodic potential of -0.18 V. Obviously, the electrolyte solution is able to reach the RuO2(110) layer presumably through the surface grain boundaries of the IrO2(110) layer. Subsequently, the single-crystalline RuO2(110) structure-directing template is reduced to amorphous hydrous RuO2, with the consequence that the IrO2(110) film loses partly its adhesion to the template. From in situ XRR experiments we find that the IrO2(110) film does not swell upon cathodic polarization down to -0.18 V, while from in situ SXRD experiments, the lattice constants of IrO2(110) are shown to be not affected. The rooflike mesostructure of the IrO2(110) flakes remains intact after cathodic polarization to -0.18 V, evidencing that the crystallinity of IrO2(110) is retained.

18.
J Phys Chem Lett ; 11(21): 9057-9062, 2020 Nov 05.
Article in English | MEDLINE | ID: mdl-33045835

ABSTRACT

Down to a cathodic potentials of -1.20 V versus the reversible hydrogen electrode, the structure of IrO2(110) electrodes supported by TiO2(110) is found to be stable by in situ synchrotron-based X-ray diffraction. Such high cathodic potentials should lead to reduction to metallic Ir (Pourbaix diagram). From the IrO2 lattice parameters, determined during cathodic polarization in a H2SO4 electrolyte solution (pH 0.4), it is estimated that the unit cell volume increases by 1% due likely to proton incorporation, which is supported by the lack of significant swelling of the IrO2(110) film derived from X-ray reflectivity experiments. Ex situ X-ray photoelectron spectroscopy suggests that protons are incorporated into the IrO2(110) lattice below -1.0 V, although Ir remains exclusively in the IV+ oxidation state down to -1.20 V. Obviously, further hydrogenation of the lattice oxygen of IrO2(110) toward water is suppressed for kinetic reasons and hints at a rate-determining chemical step that cannot be controlled by the electrode potential.

19.
Phys Chem Chem Phys ; 22(39): 22260-22270, 2020 Oct 15.
Article in English | MEDLINE | ID: mdl-33001131

ABSTRACT

Identifying the structural response of nanoparticle-support ensembles to the reaction conditions is essential to determine their structure in the catalytically active state as well as to unravel the possible degradation pathways. In this work, we investigate the (electronic) structure of carbon- and oxide-supported Pt nanoparticles during electrochemical oxidation by in situ X-ray diffraction, absorption spectroscopy as well as the Pt dissolution rate by in situ mass spectrometry. We prepared ellipsoidal Pt nanoparticles by impregnation of the carbon and titanium-based oxide support as well as spherical Pt nanoparticles on an indium-based oxide support by a surfactant-assisted synthesis route. During electrochemical oxidation, we show that the oxide-supported Pt nanoparticles resist (bulk) oxide formation and Pt dissolution. The lattice of smaller Pt nanoparticles exhibits a size-induced lattice contraction in the as-prepared state with respect to bulk Pt but it expands reversibly during electrochemical oxidation. This expansion is suppressed for the Pt nanoparticles with a bulk-like relaxed lattice. We could correlate the formation of d-band vacancies in the metallic Pt with Pt lattice expansion. PtOx formation is strongest for platelet-like nanoparticles and we explain this with a higher fraction of exposed Pt(100) facets. Of all investigated nanoparticle-support ensembles, the structural response of RuO2/TiO2-supported Pt nanoparticles is the most promising with respect to their morphological and structural integrity under electrochemical reaction conditions.

20.
J Appl Crystallogr ; 53(Pt 3): 811-823, 2020 Jun 01.
Article in English | MEDLINE | ID: mdl-32684896

ABSTRACT

A family of stochastic models of disordered particles is proposed, obtained by clipping a Gaussian random field with a function that is space dependent. Depending on the shape of the clipping function, dense or hollow particles can be modelled. General expressions are derived for the form factor of the particles, for their average volume and surface area, and for their density and surface-area distributions against the distance to the particle centre. A general approximation for the form factor is also introduced, based on the density and surface-area distributions, which coincides with the Guinier and Porod expressions in the limits of low and high scattering vector magnitude q. The models are illustrated with the fitting of small-angle X-ray scattering (SAXS) data measured on Pt/Ni hollow nanoparticles. The SAXS analysis and modelling notably capture the collapse of the particles' porosity after being used as oxygen-reduction catalysts.

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