Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

given by q = |q| = (4k/E) sin(u). The scattering wave vector is inverselyproportional to a characteristic distance, d, in the system: q = 2k/d.Scattered radiation is collected using solid-state or gas-filled detectorsand corrected for background scattering due to solvent, window materials,and so forth present in the experimental system. For systems with no preferredorientation (1D) or with 3D orientation, the scattering patterns areradially symmetric and the scattered intensity may be radially averaged andexpressed as a function of the scattering vector.For the general case of scattering from a homogeneous system, the scatteredx-ray intensity I( q) depends proportionally on the shape factor forindividual nanocrystals P( q), and the static structure factor S( q), which resultsfrom multiple scattering in the sample: I( q) ~ P( q)S( q). The proportionalityconstant depends on the number of scatterers, the difference in electron densitybetween the nanocrystals and the background media, and the incident x-rayflux. P( q) and S( q) result from intraparticle and interparticle scattering,respectively [30].P( q) is determined from the distribution of scattering centers within aparticle (i.e., the electron distribution within the particle for SAXS), andanalytic expressions for many geometries have been developed. For mostmetal nanocrystals, it is a generally a good assumption to treat the metal coreas a sphere of homogeneous electron density, although Murray and coworkershave found that some systems are better described as ellipsoidalparticles [31,32]. Overall, very different particle shapes give rise to qualitativelysimilar shape factors, although scattering from spherical particles issomewhat uniquely characterized by oscillations at medium values of q. S( q)contains information regarding interparticle interactions and reveals structuralorder in the system [30]. For a nanocrystal sample, P( q) can be measureddirectly from a dilute dispersion of noninteracting particles, as S( q) = 1. Forthe case of ordered nanocrystal films, S( q) exhibits sharp peaks due to Braggdiffraction between crystallographic superlattice planes in the superlatticeand I( q) deviates strongly from P( q) as seen in Figure 6.B. Nanocrystal DispersionsDilute nanocrystal dispersions allow direct measurement of P( q) to provideinformation about the particle size and size distribution. Figures 6 and 7 showdifferent representations of SAXS data that can aid the analysis, each with itsadvantages and disadvantages: standard form {log[I( q)] versus q} Guinierplots {ln[I( q)] versus q 2 }, and Porod plots [I( q)q 4 versus q].Guinier plots provide useful information at relatively low scatteringangles and must be used with care (Figure 7). At low angles, the radius ofgyration R g , can be determined from a plot of ln[I( q)] versus q 2 becauseCopyright 2004 by Marcel Dekker, Inc. All Rights Reserved.