STRESS MEASUREMENT - Two-Dimensional X-Ray Diffraction - page 305

TABLE 9.7 The Measured Stress with the Conventional sin 2 c Method and
the 2D Method

sin 2 c

Method 2D Method with Various Numbers of Data Points

Data points per frame 1 points 3 points 5 points 7 points 9 points

Total data points 7 points 21 points 35 points 49 points 63 points

Stress (MPa) 77662 769 38 77533 77726 76923

The data points at g ¼90 from seven frames, a typical data set for an
v-diffractometer, were used to calculate stress with the conventional sin 2 c method.
To compare the gain from having increased data points with the 2D method, the
stress was calculated from 3, 5, 7, and 9 data points on each frame. The results from
the conventional sin 2 c method and the 2D method are summarized in Table 9.7 and
compared in Figure 9.21(b). The measured residual stress is compressive and the
stress values from different methods agree very well. With the data taken from
the same measurement (seven frames), the 2D method gives lower statistical error,
and the error decreases with increasing number of data points from the diffraction
ring.

9.5.2 Virtual Oscillation for Stress Measurement

In the case of materials with large grain size or microdiffraction with a small X-ray
beam size, the diffraction profiles are distorted due to poor counting statistics. To
solve this problem with conventional detectors, some kinds of sample oscillations,
either translational oscillations or angular oscillations, are used to bring more
crystallites into the diffraction condition. In another words, the purpose of oscillations
is to bring more crystallites into the condition so that the normal of the diffracting
crystal plane coincides with the instrument diffraction vector. For 2D detectors, when
g-integration is used to generate the diffraction profile, we actually integrate the data
collected in a range of various diffraction vectors. Since the effect of g-integration on
sampling statistics is equivalent to angular oscillation on the c axis in a conventional
diffractometer, the effect is referred to as virtual oscillation, and Dc is the virtual
oscillation angle. Given in Chapter 7, the virtual oscillation angle Dc can be
calculated from the integration range Dg by

103Þ
In conventional oscillation, mechanical movement may result in some sample
position error. Since there is no actual physical movement of the sample stage during
data collection, virtual oscillation can avoid this error.
For example, Figure 9.22 is a frame taken from a SS304 stainless steel plate with
Cr-K a radiation. The large grain size results in a spotty diffraction ring. A diffraction
profile collected with a point detector may have a rough profile. g-integration
from 80 to 100 results in a smooth diffraction profile so that the 2u value can be
accurately determined. In this case, Dg ¼20 and u64 , so the virtual oscillation

Dc ¼ 2arcsin½cos u sinðDg= 2Þ ð9 :