42
METHODS OF MEASURING PROPERTIES
the Debye-Scherrer diffraction results for over 20,000 compounds are available to
researchers in a JCPDS powder diffraction card file. This method has been widely
used to obtain the structures of powders of nanoparticles.
X-ray crystallography is helpful for studying a series of isomorphic crystals, that
is, crystals with the same crystal structure but different lattice constants, such as the
solid solution series Ga,-,In,As or GaAs,-,Sb,, where x can take on the range of
values 0 I x 5 1. For these cubic crystals the lattice constant a will depend on x since
indium (In) is larger than gallium (Ga), and antimony (Sb) is larger than arsenic
(As), as the data in Table B.l indicate. For this case Vegard’s law, Eq. (2.8) of
Section 2.1.4, is a good approximation for estimating the value of a if x is known,
or the value of x if a is known.
3.2.3. Particle Size Determination
In the previous section we discussed determining the sizes of grains in polycrystalline materials via X-ray diffraction. These grains can range from nanoparticles with
size distributions such as that sketched in Fig. 3.3 to much larger micrometer-sized
particles, held together tightly to form the polycrystalline material. This is the bulk
or clustered grain limit. The opposite limit is that of grains or nanoparticles
dispersed in a matrix so that the distances between them are greater than their
average diameters or dimensions. It is of interest to know how to measure the sizes,
or ranges of sizes, of these dispersed particles.
The most straightforward way to determine the size of a micrometer-sized grain is
to look at it in a microscope, and for nanosized particles a transmission electron
microscope (TEM), to be discussed in Section 3.3.1, serves this purpose. Figure 3.6
shows a TEM micrograph of polyaniline particles with diameters close to l00nm
dispersed in a polymer matrix.
Another method for determining the sizes of particles is by measuring how they
scatter light. The extent of the scattering depends on the relationship between the
particle size d and the wavelength 1 of the light, and it also depends on the
polarization of the incident light beam. For example, the scattering of white light,
which contains wavelengths in the range from 400 nrn for blue to 750 nrn for red, off
the nitrogen and oxygen molecules in the atmosphere with respective sizes d = 0.11
and 0.12 nm, explains why the light reflected from the sky during the day appears
blue, and that transmitted by the atmosphere at sunrise and sunset appears red.
Particle size determinations are made using a monochromatic (single-wavelength)
laser beam scattered at a particular angle (usually 90°) for parallel and perpendicular
polarizations. The detected intensities can provide the particle size, the particle
concentration, and the index of refraction. The Rayleigh-Gans theory is used to
interpret the data for particles with sizes d less than O.lA, which corresponds to the
case for nanoparticles measured by optical wavelengths. The example of a laser
beam nanoparticle determination shown in Fig. 3.7 shows an organic solvent
dispersion with sizes ranging from 9 to 30 nrn, peaking at 12 nm. This method is
applicable for use with nanoparticles that have diameters above 2 nm, and for smaller
nanoparticles other methods must be used.
METHODS OF MEASURING PROPERTIES
the Debye-Scherrer diffraction results for over 20,000 compounds are available to
researchers in a JCPDS powder diffraction card file. This method has been widely
used to obtain the structures of powders of nanoparticles.
X-ray crystallography is helpful for studying a series of isomorphic crystals, that
is, crystals with the same crystal structure but different lattice constants, such as the
solid solution series Ga,-,In,As or GaAs,-,Sb,, where x can take on the range of
values 0 I x 5 1. For these cubic crystals the lattice constant a will depend on x since
indium (In) is larger than gallium (Ga), and antimony (Sb) is larger than arsenic
(As), as the data in Table B.l indicate. For this case Vegard’s law, Eq. (2.8) of
Section 2.1.4, is a good approximation for estimating the value of a if x is known,
or the value of x if a is known.
3.2.3. Particle Size Determination
In the previous section we discussed determining the sizes of grains in polycrystalline materials via X-ray diffraction. These grains can range from nanoparticles with
size distributions such as that sketched in Fig. 3.3 to much larger micrometer-sized
particles, held together tightly to form the polycrystalline material. This is the bulk
or clustered grain limit. The opposite limit is that of grains or nanoparticles
dispersed in a matrix so that the distances between them are greater than their
average diameters or dimensions. It is of interest to know how to measure the sizes,
or ranges of sizes, of these dispersed particles.
The most straightforward way to determine the size of a micrometer-sized grain is
to look at it in a microscope, and for nanosized particles a transmission electron
microscope (TEM), to be discussed in Section 3.3.1, serves this purpose. Figure 3.6
shows a TEM micrograph of polyaniline particles with diameters close to l00nm
dispersed in a polymer matrix.
Another method for determining the sizes of particles is by measuring how they
scatter light. The extent of the scattering depends on the relationship between the
particle size d and the wavelength 1 of the light, and it also depends on the
polarization of the incident light beam. For example, the scattering of white light,
which contains wavelengths in the range from 400 nrn for blue to 750 nrn for red, off
the nitrogen and oxygen molecules in the atmosphere with respective sizes d = 0.11
and 0.12 nm, explains why the light reflected from the sky during the day appears
blue, and that transmitted by the atmosphere at sunrise and sunset appears red.
Particle size determinations are made using a monochromatic (single-wavelength)
laser beam scattered at a particular angle (usually 90°) for parallel and perpendicular
polarizations. The detected intensities can provide the particle size, the particle
concentration, and the index of refraction. The Rayleigh-Gans theory is used to
interpret the data for particles with sizes d less than O.lA, which corresponds to the
case for nanoparticles measured by optical wavelengths. The example of a laser
beam nanoparticle determination shown in Fig. 3.7 shows an organic solvent
dispersion with sizes ranging from 9 to 30 nrn, peaking at 12 nm. This method is
applicable for use with nanoparticles that have diameters above 2 nm, and for smaller
nanoparticles other methods must be used.