visible. However, with decreasing annealing temperature the separation of the
two lines becomes poorer; this is caused by the increasing width of the
diffraction lines. In any case, the slight asymmetric line profile indicated
the presence of the tetragonal phase, as the (002) peak has about double
the intensity of the (200) peak. Additionally, it cannot be excluded that in the
range of the small particles, and low annealing temperature, a significant
fraction of the material remained cubic. A detailed analysis of the line profile by
the authors led to the conclusion that there should be a content of both phases;
however, a clear result was not achieved.
When comparing X-ray diffraction and electron diffraction, there is one
essential difference – X-rays applied for structural analyses usually are in wavelength range between 0.05 and 0.22 nm, although most common is the use of
CuKa radiation with a wavelength of 0.154 nm. In order to obtain optimal
conditions for analysis of the linewidth with respect to particle size, the application of a monochromator is often recommended. In the case of electron diffraction, the energy of the electrons is selected to be in a range from 100 to 200 keV.
This is equivalent to a wavelength range from 2.5 Â 10
À3 to 3.7 Â 10
À3 nm.
Additionally, electron diffraction is based on registration with photo plates or
CCDs (charge-coupled devices), whereas X-ray diffraction applies goniometer
readings, as depicted in Figures 12.9 and 12.11.
A typical electron diffraction pattern of nanoparticles, together with the
corresponding electron micrographs, is shown in Figure 12.12. These micrographs and diffraction patterns are taken from the same study as in Figures
12.9 and 12.10. In Figure 12.12a, the powder is seen in the as-produced state,
with particle sizes ranging from 2 to 3 nm. For easier observation, some of the
particles are highlighted. In contrast to the X-ray diffraction spectrum displayed
in Figure 12.9, where only one weak shoulder is visible, the electron diffraction
pattern in Figure 12.12b shows six clearly visible lines; this is a quite oftenobserved phenomenon in that, especially for small particles, electron diffraction
patterns show more detail as compared to X-ray diffraction patterns. In
connection with the electron diffraction pattern, the theoretically expected
diffraction pattern is also shown. Figure 12.12c shows the same specimen
after annealing at 873 K; this specimen now consists of a mixture of the anatase
and rutile phases. The process of grain growth during annealing led to a
relatively broad particle size distribution in the range from 5 to 20 nm, with a
majority of the particles found in the range below 10 nm. As the intensity of the
diffraction lines is weighted by the particle volume, the average particle size
determined by X-ray diffraction was 13 nm.
The electron diffraction pattern displays an additional interesting feature, namely
that small bright spots can be seen within the diffraction rings. These spots stem
from a limited number of larger particles that give diffraction patterns of that high
intensity. It should be noted that the uniform rings come from a large number of
randomly oriented particles. However, one large particle provides only one set of
diffraction points; a series of larger particles in the electron beam results in spotted
rings, as shown in Figure 12.12d.
12.3 X-Ray and Electron Diffraction j347
two lines becomes poorer; this is caused by the increasing width of the
diffraction lines. In any case, the slight asymmetric line profile indicated
the presence of the tetragonal phase, as the (002) peak has about double
the intensity of the (200) peak. Additionally, it cannot be excluded that in the
range of the small particles, and low annealing temperature, a significant
fraction of the material remained cubic. A detailed analysis of the line profile by
the authors led to the conclusion that there should be a content of both phases;
however, a clear result was not achieved.
When comparing X-ray diffraction and electron diffraction, there is one
essential difference – X-rays applied for structural analyses usually are in wavelength range between 0.05 and 0.22 nm, although most common is the use of
CuKa radiation with a wavelength of 0.154 nm. In order to obtain optimal
conditions for analysis of the linewidth with respect to particle size, the application of a monochromator is often recommended. In the case of electron diffraction, the energy of the electrons is selected to be in a range from 100 to 200 keV.
This is equivalent to a wavelength range from 2.5 Â 10
À3 to 3.7 Â 10
À3 nm.
Additionally, electron diffraction is based on registration with photo plates or
CCDs (charge-coupled devices), whereas X-ray diffraction applies goniometer
readings, as depicted in Figures 12.9 and 12.11.
A typical electron diffraction pattern of nanoparticles, together with the
corresponding electron micrographs, is shown in Figure 12.12. These micrographs and diffraction patterns are taken from the same study as in Figures
12.9 and 12.10. In Figure 12.12a, the powder is seen in the as-produced state,
with particle sizes ranging from 2 to 3 nm. For easier observation, some of the
particles are highlighted. In contrast to the X-ray diffraction spectrum displayed
in Figure 12.9, where only one weak shoulder is visible, the electron diffraction
pattern in Figure 12.12b shows six clearly visible lines; this is a quite oftenobserved phenomenon in that, especially for small particles, electron diffraction
patterns show more detail as compared to X-ray diffraction patterns. In
connection with the electron diffraction pattern, the theoretically expected
diffraction pattern is also shown. Figure 12.12c shows the same specimen
after annealing at 873 K; this specimen now consists of a mixture of the anatase
and rutile phases. The process of grain growth during annealing led to a
relatively broad particle size distribution in the range from 5 to 20 nm, with a
majority of the particles found in the range below 10 nm. As the intensity of the
diffraction lines is weighted by the particle volume, the average particle size
determined by X-ray diffraction was 13 nm.
The electron diffraction pattern displays an additional interesting feature, namely
that small bright spots can be seen within the diffraction rings. These spots stem
from a limited number of larger particles that give diffraction patterns of that high
intensity. It should be noted that the uniform rings come from a large number of
randomly oriented particles. However, one large particle provides only one set of
diffraction points; a series of larger particles in the electron beam results in spotted
rings, as shown in Figure 12.12d.
12.3 X-Ray and Electron Diffraction j347