QUANTITATIVE ANALYSIS - Two-Dimensional X-Ray Diffraction - page 388

Where I g and I a are the measured integrated intensities of the g and a phase,
respectively and R g and R a are the reflection factors of the g and a phase, respectively.
The reflection factor for phase i is proportional to the theoretic relative intensity and is
given by

p hkl
v 2

R hkl
i

ðLPÞF hkl expð 2MÞ

25Þ
where p hkl is themultiplicity factor of the crystal plane (hkl), v is the volume of the unit
cell, (LP) are the Lorentz-polarization factors, F hkl is the structure factor of the crystal
plane (hkl ), and exp(2M) is the Debye-Waller factor or temperature factor. The
reflection factor R can be calculated from the above equation or found in
literature [45].
If a carbide phase is present, the volume percentage of retained austenite is
calculated from

¼ ð12 :

I g = R g

% RA ¼ 100 ð12 : 26Þ

I g = R g þ I a = R a þ I c = R c

Where I c is the measured integrated intensities of the carbide and R c is the reflection
factor (theoretic relative intensities) of the carbide. The equation may be modified for
multiple g and a peaks and multiple carbides by averaging the intensity ratio of the
same phases.

n X

n
j¼1 ðI i =

1

hI i = R i i¼ R i Þ j ð12 : 27Þ

where n is the number of peaks measured for the phase i and ðI i = R i Þ j is the intensity

ratio of the jth peak of the phase i. A two-dimensional detector can measure retained
austenite with fast data collection, good sampling statistics, and a lower measurement
limit [46]. The preferred orientation effect can also be reduced by virtual oscillation.
Figure 12.12(a) shows a 2D frame collected from a steel roller with an APEX II
CCD detector and Mo-K a radiation. Figure 12.12(b) is a profile integrated from the
2D frame in the range of 2u from 21.1 to 39.7 and g from 80 to 100 . The
background has been subtracted from the integrated profile. The profile shows three
peaks, (200), (220), and (311), from the retained austenite and two peaks, (200) and
(211), from the martensite. The above five peaks are chosen for the retained austenite
measurement because of good separations between each adjacent peak [47]. The other
peaks may be too close to be resolved. For instance, the 2u values for martensite (110)
and austenite (111) are 20.20 and 19.68 , respectively, and for martensite (310) and
austenite (400) are 46.16 and 46.52 , respectively. These peaks should be avoided
because of the difficulty of separating the peaks and determining the integrated
intensities from scrambled peaks. The diffraction profile from g-integration has been
normalized by the g-integration range, so the intensity is independent of the g-range.
In this case, the reflection factors used for conventional diffraction can be used to
calculate the retained austenite. Table 12.2 lists peak position (2u), reflection factors
from Ref. [45], measured integrated intensities and the ratio of the intensity to the
reflection factor. The retained austenite in the steel roller is measured as 21.3 percent.
This example shows the basic concept of the measurement. Since the published
reflection factors are based on the Bragg-Brentano geometry, for improved accuracy,