On the Retrieval of Particle Size Distributions from Small-Angle Scattering Data: the Influence of Statistical Data Dispersion

1998 ◽  
Vol 31 (2) ◽  
pp. 149-153 ◽  
Author(s):  
M. Mulato ◽  
D. Tygel ◽  
I. Chambouleyron
Keyword(s):  
Particle Size ◽  
Small Angle ◽  
Statistical Data ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Size Distributions ◽  
Particle Size Distributions ◽  
Angle Scattering

The Influence of the Available Scattering Vector Range on the Retrieval of Particle-Size Distributions from Small-Angle Scattering Intensity Data

1997 ◽  
Vol 30 (5) ◽  
pp. 808-810 ◽  
Author(s):  
M. Mulato ◽  
D. Tygel ◽  
I. Chambouleyron
Keyword(s):  
Particle Size ◽  
Small Angle ◽  
Numerical Experiments ◽  
Small Angle Scattering ◽  
Size Distributions ◽  
Intensity Data ◽  
Particle Size Distributions ◽  
Scattering Intensity ◽  
Angle Scattering

The determination of the particle-size distribution [D(r)] from small-angle scattering intensity data is discussed. The influence of the maximum available scattering vector h max on D(r) retrieval is investigated with the help of numerical experiments with previously known solutions. The numerical corrector method provides a good answer even in cases where h max is much smaller than those values necessary with other retrieval methods.

Maximum-entropy method as a routine tool for determination of particle size distributions by small-angle scattering

2004 ◽  
Vol 37 (1) ◽  
pp. 32-39 ◽  
Author(s):  
Dragomir Tatchev ◽  
Rainer Kranold
Keyword(s):  
Particle Size ◽  
Fourier Transform ◽  
Small Angle ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
Size Distributions ◽  
Particle Size Distributions ◽  
Angle Scattering ◽  
The Fourier Transform

Several aspects of the application of the maximum-entropy method (MEM) to the determination of particle size distributions by small-angle scattering (SAS) are discussed. The `historic' version of the MEM produces completely satisfying results. Limiting the data error from below (i.e.imposing a minimal relative error) is proposed as a solution of some convergence problems. The MEM is tested against the Fourier transform technique. The size distribution of Pb particles in an Al–Pb alloy is determined by the MEM and the Fourier transform technique. The size distributions obtained by transmission electron microscopy (TEM) and SAXS show partial agreement.

scholarly journals Improvements and considerations for size distribution retrieval from small-angle scattering data by Monte Carlo methods

2013 ◽  
Vol 46 (2) ◽  
pp. 365-371 ◽  
Author(s):  
Brian R. Pauw ◽  
Jan Skov Pedersen ◽  
Samuel Tardif ◽  
Masaki Takata ◽  
Bo B. Iversen
Keyword(s):  
Monte Carlo ◽  
Small Angle ◽  
Free Particle ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Convergence Criterion ◽  
Size Distributions ◽  
Trial And Error ◽  
Angle Scattering ◽  
Scattering Measurement

Monte Carlo (MC) methods, based on random updates and the trial-and-error principle, are well suited to retrieve form-free particle size distributions from small-angle scattering patterns of non-interacting low-concentration scatterers such as particles in solution or precipitates in metals. Improvements are presented to existing MC methods, such as a non-ambiguous convergence criterion, nonlinear scaling of contributions to match their observability in a scattering measurement, and a method for estimating the minimum visibility threshold and uncertainties on the resulting size distributions.

scholarly journals Small-angle scattering from polydisperse particles with a diffusive surface

2014 ◽  
Vol 47 (2) ◽  
pp. 642-653 ◽  
Author(s):  
Olexandr V. Tomchuk ◽  
Leonid A. Bulavin ◽  
Viktor L. Aksenov ◽  
Vasil M. Garamus ◽  
Oleksandr I. Ivankov ◽  
...  
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Power Law ◽  
Small Angle ◽  
Scattering Length ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Scattering Length Density ◽  
Angle Scattering

Particles with a diffusive surface, characterized by a deviation from the Porod power-law asymptotic behavior in small-angle scattering towards an exponent below −4, are considered with respect to the polydispersity problem. The case of low diffusivity is emphasized, which allows the description of the scattering length density distribution within spherically isotropic particles in terms of a continuous profile. This significantly simplifies the analysis of the particle-size distribution function, as well as the change in the scattering invariants under contrast variation. The effect of the solvent scattering contribution on the apparent exponent value in power-law-type scattering and related restrictions in the analysis of the scattering curves are discussed. The principal features and possibilities of the developed approach are illustrated in the treatment of experimental small-angle neutron scattering data from liquid dispersions of detonation nanodiamond. The obtained scattering length density profile of the particles fits well with a transition of the diamond states of carbon inside the crystallites to graphite-like states at the surface, and it is possible to combine the diffusive properties of the surface with the experimental shift of the mean scattering length density of the particles compared with that of pure diamond. The moments of the particle-size distribution are derived and analyzed in terms of the lognormal approximation.

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