Correction to microscopically determined particle size according to diffraction theory

Some aspects of measuring the size and rate of dispersion of milk powder agglomerates using the Malvern Particle Sizer 2600c

Journal of Dairy Research ◽

10.1017/s0022029900028211 ◽

1994 ◽

Vol 61 (2) ◽

pp. 201-208 ◽

Cited By ~ 11

Author(s):

X. Dong Chen ◽

Richard J. Lloyd

Keyword(s):

Particle Size ◽

Size Distribution ◽

Laser Light ◽

Mechanical Stability ◽

Milk Powder ◽

Diffraction Theory ◽

Size Distributions ◽

Particle Size Distributions ◽

Powder Dispersion ◽

Particle Sizer

SummaryThe Malvern Particle Sizer, which applies Fraunhofer light diffraction theory, has recently become popular for measuring particle size distributions in dried milk and other powders. The size distribution is obtained by dispersing the powder in air or a suitable liquid in the laser light beam of the instrument. The suitability of the dry powder dispersion system (DPD system) of the Malvern Particle Sizer 2600c for characterizing agglomerated milk powders was examined. It was found that, although the instrument gave reproducible and reliable results for non-agglomerated powders (standard milk powders), milk powder agglomerates could be broken in the standard DPD system and erroneous size distributions might be obtained. However, the DPD system had potential for providing an objective test of the mechanical stability of milk powder agglomerates. In addition, the transient size distribution during dispersion of an instantized agglomerated milk powder in water was measured at intervals of about 20 s.

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A Combined Reverse Fourier Set-Up for Laser Particle Size Measurement

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.389.529 ◽

2013 ◽

Vol 389 ◽

pp. 529-532

Author(s):

Wei Sheng Liu ◽

Cui Cui Liu ◽

Chun Yu Li ◽

Yong Jie Wei

Keyword(s):

Particle Size ◽

Size Range ◽

Diffraction Theory ◽

Detector Array ◽

Particle Size Measurement ◽

Set Up ◽

Focus Plane ◽

Measure Particle Size ◽

Relative Errors ◽

Particle Sample

A combined reverse Fourier set-up was presented on Fresnel diffraction theory. The set-up was used to measure particle size distribution with laser. A particle sample is set back of a lens. A first detector array is set in the focus plane of the lens. A second lens and a second detector array are set behind the first detector and the combined focus plane of the two lenses in turn. Thus the measurable size range at on sampling is enlarged. Experimental results on some latex samples by the prototype show that the relative errors are less than 6%.

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Relative Intensities in ED Patterns From Thin Gold Films

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100096436 ◽

1972 ◽

Vol 30 ◽

pp. 636-637

Author(s):

R. H. Morriss ◽

J. D. C. Peng ◽

C. D. Melvin

Keyword(s):

Theoretical Calculations ◽

Diffraction Theory ◽

Gold Films ◽

Reasonable Accuracy ◽

Experimental Conditions ◽

Crystal Perfection ◽

Heavy Atoms ◽

Fine Focus ◽

Convergent Beam ◽

Beam Diffraction

Although dynamical diffraction theory was modified for electrons by Bethe in 1928, relatively few calculations have been carried out because of computational difficulties. Even fewer attempts have been made to correlate experimental data with theoretical calculations. The experimental conditions are indeed stringent - not only is a knowledge of crystal perfection, morphology, and orientation necessary, but other factors such as specimen contamination are important and must be carefully controlled. The experimental method of fine-focus convergent-beam electron diffraction has been successfully applied by Goodman and Lehmpfuhl to single crystals of MgO containing light atoms and more recently by Lynch to single crystalline (111) gold films which contain heavy atoms. In both experiments intensity distributions were calculated using the multislice method of n-beam diffraction theory. In order to obtain reasonable accuracy Lynch found it necessary to include 139 beams in the calculations for gold with all but 43 corresponding to beams out of the [111] zone.

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“Preparation of Single Crystalline Gold Films for ED Studies”

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100096424 ◽

1972 ◽

Vol 30 ◽

pp. 634-635

Author(s):

Joseph D. C. Peng

Keyword(s):

Crystal Morphology ◽

Diffraction Theory ◽

Scattering Matrix ◽

Vacuum Evaporation ◽

Gold Films ◽

Matrix Formulation ◽

Silver Films ◽

Single Crystalline ◽

Grating Pattern ◽

Stacking Disorder

The relative intensities of the ED spots in a cross-grating pattern can be calculated using N-beam electron diffraction theory. The scattering matrix formulation of N-beam ED theory has been previously applied to imperfect microcrystals of gold containing stacking disorder (coherent twinning) in the (111) crystal plane. In the present experiment an effort has been made to grow single-crystalline, defect-free (111) gold films of a uniform and accurately know thickness using vacuum evaporation techniques. These represent stringent conditions to be met experimentally; however, if a meaningful comparison is to be made between theory and experiment, these factors must be carefully controlled. It is well-known that crystal morphology, perfection, and orientation each have pronounced effects on relative intensities in single crystals.The double evaporation method first suggested by Pashley was employed with some modifications. Oriented silver films of a thickness of about 1500Å were first grown by vacuum evaporation on freshly cleaved mica, with the substrate temperature at 285° C during evaporation with the deposition rate at 500-800Å/sec.

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The Interpretation of Crystal Lattice Images

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s042482010009600x ◽

1972 ◽

Vol 30 ◽

pp. 550-551

Author(s):

J. M. Cowley ◽

Sumio Iijima

Keyword(s):

Crystal Orientation ◽

Diffraction Theory ◽

Phase Changes ◽

Electron Wave ◽

Crystal Lattices ◽

Heavy Atoms ◽

Lattice Images ◽

The Right ◽

Intuitive Interpretation ◽

Suitable Approximation

The imaging of detailed structures of crystal lattices with 3 to 4Å resolution, given the correct conditions of microscope defocus and crystal orientation and thickness, has been used by Iijima (this conference) for the study of new types of crystal structures and the defects in known structures associated with fluctuations of stoichiometry. The image intensities may be computed using n-beam dynamical diffraction theory involving several hundred beams (Fejes, this conference). However it is still important to have a suitable approximation to provide an immediate rough estimate of contrast and an evaluation of the intuitive interpretation in terms of an amplitude object.For crystals 100 to 150Å thick containing moderately heavy atoms the phase changes of the electron wave vary by about 10 radians suggesting that the “optimum defocus” theory of amplitude contrast for thin phase objects due to Scherzer and others can not apply, although it does predict the right defocus for optimum imaging.

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Microstructural characterization of laser-melted/roller-quenched dicalcium silicate

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100104972 ◽

1988 ◽

Vol 46 ◽

pp. 582-583

Author(s):

C. J. Chan ◽

K. R. Venkatachari ◽

W. M. Kriven ◽

J. F. Young

Keyword(s):

Particle Size ◽

Raw Materials ◽

Shape Change ◽

Microstructural Characterization ◽

Particle Size Effect ◽

Dicalcium Silicate ◽

Laser Melting ◽

Uniform Size ◽

Cell Shape Change ◽

Wide Range

Dicalcium silicate (Ca2SiO4) is a major component of Portland cement. It has also been investigated as a potential transformation toughener alternative to zirconia. It has five polymorphs: α, α'H, α'L, β and γ. Of interest is the β-to-γ transformation on cooling at about 490°C. This transformation, accompanied by a 12% volume increase and a 4.6° unit cell shape change, is analogous to the tetragonal-to-monoclinic transformation in zirconia. Due to the processing methods used, previous studies into the particle size effect were limited by a wide range of particle size distribution. In an attempt to obtain a more uniform size, a fast quench rate involving a laser-melting/roller-quenching technique was investigated.The laser-melting/roller-quenching experiment used precompacted bars of stoichiometric γ-Ca2SiO4 powder, which were synthesized from AR grade CaCO3 and SiO2xH2O. The raw materials were mixed by conventional ceramic processing techniques, and sintered at 1450°C. The dusted γ-Ca2SiO4 powder was uniaxially pressed into 0.4 cm x 0.4 cm x 4 cm bars under 34 MPa and cold isostatically pressed under 172 MPa. The γ-Ca2SiO4 bars were melted by a 10 KW-CO2 laser.

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X-ray diffraction properties of curved crystal diffractors

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100133308 ◽

1992 ◽

Vol 50 (2) ◽

pp. 1734-1735

Author(s):

W. Z. Chang ◽

D. B. Wittry

Keyword(s):

Diffraction Theory ◽

X Rays ◽

Diffraction Image ◽

X Ray Diffraction ◽

Rocking Curve ◽

X Ray ◽

Bent Crystal ◽

Diffraction Geometry ◽

Crystal Parameter ◽

Quantitative Procedure

Since Du Mond and Kirkpatrick first discussed the principle of a bent crystal spectrograph in 1930, curved single crystals have been widely utilized as spectrometric monochromators as well as diffractors for focusing x rays diverging from a point. Curved crystal diffraction theory predicts that the diffraction parameters - the rocking curve width w, and the peak reflection coefficient r of curved crystals will certainly deviate from those of their flat form. Due to a lack of curved crystal parameter data in current literature and the need for optimizing the choice of diffraction geometry and crystal materials for various applications, we have continued the investigation of our technique presented at the last conference. In the present abstract, we describe a more rigorous and quantitative procedure for measuring the parameters of curved crystals.The diffraction image of a singly bent crystal under study can be obtained by using the Johann geometry with an x-ray point source.

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Analytical Electron Microscopy study of two vehicle-aged automotive exhaust catalysts having dissimilar activities

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100153336 ◽

1989 ◽

Vol 47 ◽

pp. 272-273

Author(s):

Sooho Kim ◽

M. J. D’Aniello

Keyword(s):

Electron Microscopy ◽

Particle Size ◽

Noble Metal ◽

Catalyst Deactivation ◽

Analytical Electron Microscopy ◽

Microscopy Study ◽

Metal Particles ◽

Automotive Exhaust ◽

Exhaust Catalysts ◽

Analytical Electron

Automotive catalysts generally lose-agtivity during vehicle operation due to several well-known deactivation mechanisms. To gain a more fundamental understanding of catalyst deactivation, the microscopic details of fresh and vehicle-aged commercial pelleted automotive exhaust catalysts containing Pt, Pd and Rh were studied by employing Analytical Electron Microscopy (AEM). Two different vehicle-aged samples containing similar poison levels but having different catalytic activities (denoted better and poorer) were selected for this study.The general microstructure of the supports and the noble metal particles of the two catalysts looks similar; the noble metal particles were generally found to be spherical and often faceted. However, the average noble metal particle size on the poorer catalyst (21 nm) was larger than that on the better catalyst (16 nm). These sizes represent a significant increase over that found on the fresh catalyst (8 nm). The activity of these catalysts decreases as the observed particle size increases.

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