Chemistry Reference
In-Depth Information
DR
Y
,andDR
Z
respectively. The shift tolerance can be as large as several pixels since
the errors can be corrected by detector calibration. The errors DX, DY and DZ can be
corrected by the calibration of the detector distance and beam center, so the tolerance
can be relatively large. The errors DR
X
, DR
Y
, and DR
Z
can only be partially
compensated by correction and calibration so the tolerance should be more critical.
Various detector distances are used for different applications. The shift caused by the
errors DX, DR
X
, DR
Y
, and DR
Z
increase with increasing r and decreasing D,sothe
tolerance must be given for the largest pixel-to-center distance (r
max
) and shortest
detector distance (D
min
). The detector correction and calibration files at several
detector distances are normally collected and saved. The files are reloaded when
the corresponding detector distance is used. Therefore, the pixel shift caused by the
reproducibility errors cannot be further corrected, so they must be kept to the
minimum. The tolerance and reproducibility should be decided based on the detector
type and the application requirements. Table 6.2 gives the equations for calculating the
pixel shift caused by each error and examples of the tolerance and reproducibility for a
11 cm round detector. The tolerance is given based on a pixel shift of approximately
three pixels and the reproducibility is based on a pixel shift of one pixel.
6.4.2 Detector Position Calibration
The detector position calibration determines the detector distance (D), swing angle
(a), and beam center (x
c
, y
c
). The appropriate calibration permits accurate calculation
of 2u and g values of pixels and diffraction features. The precise detector distance,
swing angle, and beam center are determined by taking diffraction frames of a known
standard and comparing the measured diffraction rings with the calculated rings from
the known peak 2u positions and detector position. Any polycrystalline or powder
exhibiting high stability and sharp diffraction lines can be used as calibration
standard—for instance, corundum, quartz, or silicon. The calibration can be done
manually by overlapping the calculated rings over the measured diffraction frame. By
adjusting the values of detector distance, swing angles, and beam center, the
calibrated values are found when the best overlapping occurs. Figure 6.7 shows the
diffraction frame collected from a corundum (NIST SRM 676 a-Al
2
O
3
) powder
sample with a two-dimensional diffraction system-Bruker GADDS (General Area
Detector Diffraction System). The software displays the diffraction frame and the
calculated diffraction rings (white lines) based on the standard d/I file (PDF card 46-
1212). The detector distance, swing angle, and beam center can be adjusted inter-
actively by mouse or arrow keys until all the calculated rings precisely center over the
collected diffraction rings in the data frame. In a short 2u range, the positions of the
same sets of calculated rings may be moved by either changing the swing angle or
beam center (particularly x
c
) to generate almost the same effect. In this case, the error
in swing angle may be compensated by an error in beam center. This is referred to as
the coupling effect between the detector position parameters. To get a precise
calibration and overcome the coupling effect, it is desirable to collect several frames
at different swing angles. The sensitivity of the calibration to each parameter varies
with the swing angle. For example, the diffraction frames collected at a low swing
