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The sections in this article are Definitions and Generalities Particles Particle Size Nuclearity of Particles Dispersion Relationships Between Particle Size, Surface Area and Dispersion Methods of Particle Size Measurement Particle Size Measurements by Gas Chemisorption Introduction and Principles Gas Adsorption–Desorption Methods A Static Methods B Dynamic Methods C Desorption Methods Choice of Adsorbate Gases Hydrogen Chemisorption; HydrogenOxygen Titration Conclusion and Recommendations X ‐Ray Diffraction Line Broadening Analysis Introduction Elementary Line Broadening Analysis: the Scherrer Equation Complete Line Profile Analysis: the W arren– A verbach Method Examples of Application of Classical LBA to Catalysts Whole‐Powder Pattern Fitting Methods: the Rietveld Refinement Limits of Application of Methods Conclusion Small‐Angle X ‐Ray Scattering Analysis Introduction Specific Surface Area Measurements: P orod's Law Mean Size Parameters: Guinier Radius Calculation of Size Distribution Application of SAXS to Metal Particle Size Determination in Supported Catalysts Anomalous Small‐Angle X ‐Ray Scattering ( ASAXS ) Conclusion Determination of Particle Size by Electron Microscopy Scope Fundamentals of Imaging and Contrast A Transmission Electron Microscope B Scanning Transmission Electron Microscope C Scanning Electron Microscope Preparation of Samples for TEM and STEM Examination Particle Size Measurement Selected Examples of Particle Size Distribution Selected Examples of 3D Localization of Particles in Supports by Electron Tomography Particle Size Measurements by Magnetic Methods

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Absolute ethylene/ethane separation is achieved by ethane exclusion on silver-exchanged zeolite A adsorbent. This molecular sieving type separation is attributed to the pore size of the adsorbent, which falls between ethylene and ethane kinetic diameters.

H-MFI type zeolitic materials of different Si/Al ratios have been completely or partially cesium-exchanged (cesium content ranging from 0.7 to 7.7 Cs/unit-cell (uc)). Examined with synchrotron X-ray powder diffractometry, an anhydrous sample with the Cs6.6H0.3Al6.9Si89.1O192 chemical composition revealed at ambient temperature the presence of five discrete Cs locations: Cs1 located in the channel intersection near a 10-ring window of the zigzag channel; Cs2 and Cs2', both located in the straight channel but 1.23 A apart; Cs3 and Cs3', both located in the zigzag channel and rather close to each other (2.51 A). The populations of the Cs species amounted to 2.61/0.81/1.85/0.86/0.47/uc for Cs1/2/2'/3/3', respectively. The continuous but multimodal nature of the C2 split site is well-described by a joint-probability density function. The 10-ring of the straight channel in the framework is highly elliptical (epsilon = 1.218). The populations for the same sites were also determined at higher temperatures: 131, 237, 344, and 450 degrees C. At 450 degrees C, Cs2' has migrated toward the center of the channel intersection, and the site separation between Cs2 and Cs2' has lengthened to 2.23 A. Using a temperature-controlled laboratory X-ray diffractometer, similar studies were carried out on partially or almost totally Cs-exchanged samples from various sources with differing Cs contents. They show that over the 0.7 to 4 Cs/uc range all the individual Cs populations vary linearly as a function of total Cs/uc present. At higher total Cs/uc content (4 to approximately 7 Cs/uc) solely Cs1 continues to do so. For Cs2+Cs2' and Cs3+Cs3', the variation is almost linear over the whole concentration range. Computer simulations using a 6-exp-1 Buckingham-type atom-atom van der Waals interaction model yield six possible Cs sites in the actual Cs6.6MFI framework structure. Four of them lie very close to those determined from difference Fourier maps using the room temperature data. A fifth one is close to the Cs2' species after thermal migration at 450 degrees C, and the sixth one is close to the center of the channel intersection. However, this latter site is observed experimentally only in the case of hydrated CsMFI phases. In the anhydrous Cs6.6MFI phase at room temperature, the shortest Cs-framework oxygen distance is Cs3'-O25 = 3.08 A, and the next shortest distances are Cs1-O26 = 3.37, Cs2-O11 = 3.34, Cs2'-O22 = 3.47, and Cs3-O20 = 3.34 A. The framework T(Si,Al) sites most involved in these contacts are the T9, T11, T12, T10, and T3 sites. This implies that these sites are prime candidates for Si/Al substitution.

Copper-exchanged Cu-MFI (Cu-ZSM-5) materials have been prepared by reacting H-MFI samples with 0.1 M Cu(II) acetate solutions. Interpretation (Rietveld method) of X-ray powder diffraction (XRPD) profiles corresponding to two fully dehydrated Cu-MFI phases, reveals the presence of several independent extra framework Cu centers. In H 1.04 Cu(I) 1.19 Cu(II) 0.51 MFI and H 1.99 Cu(I) 2.37 Cu(II) 0.00 MFI, four and five Cu cations are located, respectively. In these two phases, the Cu1/Cu2/Cu2′/Cu3/Cu3′ populations are 0.0/1.07/0.02/ 0.17/0.45 and 0.18/1.12/0.44/0.20/0.50 per unit cell (uc), respectively. Cu2 is the most populated one. The shortest distances between copper sites and framework oxygen atoms involve the Cu1, Cu2, and Cu2′ sites (Cu-O in the 1.99-2.32 Å range). The Cu1, Cu3, and Cu3′ sites are trapped in secondary five and six ring channel sections of the MFI framework. Cu2 and Cu2′ are very close to the 10-membered rings of the straight channel sections. One or both of these cations, which are immediately accessible to guest molecules, appear to be the prime candidates for the catalytically active sites in copper-exchanged MFI.

The evolution of the gap of a nanoscaled insulator material, namely, Gd 2 O 3 , has been observed by means of vacuum ultraviolet excitation spectra of a dopant ͑Eu 3+ ͒. The nanoparticles have been synthesized by the low energy cluster beam deposition technique and grown afterward by different annealing steps. A gap shift towards the blue is observed, similar to what is observed in semiconductor nanoparticles. Despite the strong ionic character of the material, the evolution exhibits a behavior similar to covalent materials. The evolution of the gap for Gd 2 O 3 follows the same empiric rule that has been derived for semiconductors ͑ZnO, CuBr, Si, and CdS͒. It shows that, in spite of the strong ionic character of the material ͑0.9 on the scale of Phillips͒, the amount of covalency is important enough for creating a significant delocalization of the electron with regard to its hole.

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