Chemistry Reference
In-Depth Information
desired orientations. When used for texture measurement, two-dimensional X-ray
diffraction systems have many advantages over conventional one-dimensional
diffraction systems [1-7]. The orientation distribution of several crystallographic
planes over a range of angles can be measured simultaneously so as to get better
measurement results with less data collection time. The orientation relationship
between different phases or between different layers of thin films and substrate can
also be easily revealed by simultaneous measurement with the same sample rotation
scan. The texture can also be observed and compared directly from the 2D diffraction
frames without data processing.
8.2 POLE DENSITY AND POLE FIGURE
XRD results from ideal randomly oriented powder normally serve as a basis for
determining the relative intensity of each diffraction peak. Realistically, polycrystal-
line materials usually do not have randomly oriented grains (or crystallites). The
deviation of the statistical grain orientation distribution of a polycrystalline material
from the ideal powder ismeasured as a texture or preferred orientation. The pole figure
for a particular crystallographic plane is normally used to represent the texture of a
sample. Assuming that all grains have the same volume, each ''pole'' represents a
grain that satisfies the Bragg condition as shown in Figure 8.1(a). The pole is
conveniently represented by the unit vector of the diffraction vector (H
hkl
). If we
take the diffraction peak from an ideal powder as a reference (Figure 8.1(b)), the
diffraction peak intensity difference is due to the texture while the peak shift is due to
stress. The number of grains satisfying the Bragg condition at a particular sample
orientation can be larger or smaller than the number of grains for an ideal sample, and
likewise for the integrated intensity of that peak. The stresses in a sample can be
compressive or tensile so that the d-spacing in the corresponding direction will be
smaller or larger than the stress-free sample, and the peak position changes corre-
spondingly based on the Bragg law.
The measured 2D diffraction pattern contains two very important parameters at
each g angle: the partially integrated intensity I and the Bragg angle 2u. Figure 8.2
illustrates two diffraction cones, with one for forward diffraction and one for
Texture
Stress
Random
no stress
H
hkl
I
θ
θ
d
d
2
θ
(
a
)
(
b
)
FIGURE 8.1 (a) The definition of pole and (b) diffraction peak intensity change due to
texture and peak shift due to stress.
