Chemistry Reference
In-Depth Information
FIGURE 8.2 Diffraction cone distortion due to stress and intensity variation along g due
to texture.
backward diffraction. The regular diffraction cones are from the ideal powder sample
with no stress, so that the 2u angles and diffraction intensities are constant at all g
angles. The thick rings are distorted diffraction cones due to stresses. For a stressed
sample, 2u becomes a function of g and the sample orientation (v, c, f), that is,
2u¼2u(g, v, c, f). This function is uniquely determined by the stress tensor. The
relationship between diffraction cone distortion and the stress tensor is discussed in
Chapter 9 on stress analysis. For a textured sample, the diffraction intensity varies
along g due to an anisotropic pole density distribution. The intensity is a function of g
and the sample orientation (v, c, f), that is, I ¼ I(g, v, c, f), which is uniquely
determined by the orientation distribution function (ODF).
Texture is a measure of the orientation distribution of all grains in a sample with
respect to the sample direction (e.g., the rolling direction in a sheet metal or the
substrate normal in a thin film). Texture characterization byX-ray diffraction involves
the measurement of the peak intensity of a particular crystallographic plane at all tilt
angles with respect to a sample direction. Typically, one to four independent
crystallographic planes (different hkl values) are measured to quantify the major
orientation distribution of a material.
Plotting the intensity of each (hkl) line with respect to the sample coordinates in a
stereographic projection gives a qualitative view of the orientation of the crystallites
with respect to a sample direction. These stereographic projection plots are called
pole figures. As shown in Figure 8.3(a), the rolling direction (RD) is aligned to the
sample coordinate S
2
, the transverse direction (TD) to S
1
, and the plate normal
direction (ND) to S
3
. Let us consider a sphere with unit radius and the origin at O. A
unit vector representing an arbitrary pole direction (also the unit vector of the
diffraction) starts from the origin O and ends at the point P on the sphere. The
pole direction is defined by a set of the radial angle a and azimuthal angle b.In
