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

on the other hand, provide an ensemble measurement of the entire sample.Because the scattering profiles are very sensitive to particle size, even smallamounts of impurities of large particles or breadth in the size distributionshows up strongly (generally in a deteriorative way) in the scatteringprofiles of the materials. Therefore, these two characterization techniques,when used in concert, provide a very effective means of characterizing thesample.A. Small-Angle X-ray Scattering Background and TheorySmall-angle x-ray scattering (SAXS) is a valuable experimental technique,which along with complementary characterization methods such as HR-TEMcan provide a detailed description of a collection of nanocrystals. SAXS measurementscan be conducted on dispersions and thin films to obtain informationabout the shape of the core, size distribution, interparticle interactions,and the symmety and range of order in a superlattice [10,13,28].Small-angle x-ray scattering experiments may be carried out usinglaboratory-scale rotating copper-anode x-ray sources or high-power synchrotronbeamlines. Laboratory-scale systems typically operate by bombarding arotating copper anode with high-energy electrons; the valence electrons in thecopper are excited to higher-energy states and decay to give off radiation withwavelengths in the x-ray regime. The radiation is typically filtered andcollimated to produce a coherent, monochromatic beam of radiation. Synchrotronsources, in contrast, operate by accelerating electrons around a ringnear the speed of light, a process that produces radiation over a wide range ofwavelengths with intensities orders of magnitude greater than that of laboratory-scaleequipment. For most applications, lab-scale equipment suffices,except in cases where high x-ray flux is required, as in cases where the scatteringdensity of the sample is low or in the case of time-dependent measurementsof dynamic phenomena [11,29].Scattering techniques, in general, measure the angular dependence of(time averaged) scattered radiation from a sample. The scattering of an incidentbeam of electromagnetic radiation or neutrons from a sample resultsfrom density and/or concentration fluctuations; x-ray scattering, for example,arises due to fluctuations between the electron density in the scattering object(e.g., nanoparticles) and the background media (e.g., solvent). Typically, theelectron density of the capping ligand does not differ significantly from thebackground solvent and the scattering may be assumed due only to the nanocrystalcore.The angle between an incident x-ray beam and the scattered beam isdenoted as 2u. In many cases, it is more illustrative to relate the scatteringangle to the scattering wave vector, q; the relationship between the two isCopyright 2004 by Marcel Dekker, Inc. All Rights Reserved.