Chemistry Reference
In-Depth Information
fitting, and peak intensity and integrated intensity evaluations. Background correction
eliminates the scattered intensity not contributing to the diffraction profile. It is
performed by subtracting a linear intensity distribution based on the background
intensities at both the lower 2u side and the higher 2u side of the diffraction peak.
The background region should be distanced sufficiently from the 2u peak so that the
correction will not truncate the diffraction profile. The 2u ranges of the low back-
ground and high background should be determined based on the width of the 2u peak
and available background in the profile. Based on a normal distribution, a 2u range
of two times the FWHM covers of the 98 percent peak intensity, and three times the
FWHM covers more than 99.9 percent, so the background intensity should be
determined at more than 1-1.5 FWHM away from the peak position. In cases where
the diffraction profile contains background information only on one side of the peak,
the background should be determined from extrapolation of either the available
background or a flat background. The background correction can be neglected for
a low background profile or if the error caused by the background is tolerable for the
application.
Smoothing of the diffraction profilemay be applied to reduce the effect of counting
statistics on background determination, K
a2
corrections, and calculation of the peak
position. Smoothing is not always necessary and beneficial because it may only
provide a cosmetic effect to the diffraction profile, and may even smear or distort the
diffraction profile.
The peak position can be evaluated by various methods, such as gravity, sliding
gravity, and profile fitting by parabolic, pseudo-Voigt, or Pearson VII func-
tions [3,17,40]. In the gravity method (also called the centroid method), the center
of gravity of the diffraction profile is calculated and used as the peak position. The
intensities in the profiles used in the calculation of the gravity center are subtracted
by a background value (threshold). The threshold value is a percentage of the net peak
height. The recommended threshold is 20 percent. A lower threshold may introduce
inconsistency in peak position determination. The sliding gravity method is a
modified method that improves the final results by an iterative process. First, the
center of gravity is calculated at several user-defined threshold values, typically
between 10 and 80 percent. A list of threshold-dependent stress values and the
corresponding standard deviations are then calculated. The final peak position is then
generated from the weighted average of all gravity center values from the first step.
The weight of each gravity center value is based on the standard deviation of the
corresponding stress value. The stress value is then calculated from the final peak
position.
When the peak position is evaluated by the profile fitting method, the measured
data points on the diffraction profile are fitted to a given function with several
unknown parameters by the least squares method. The peak position is then given by
the resulting parameters. Many functions have been used, such as Gaussian, Cauchy
(or Lorentz), Voigt, pseudo-Voigt, and Pearson VII [41]. All these functions may be
fitted to the complete diffraction profile with a large number of data points for good
statistics. The quality of the fitting result depends on the consistency in shape between
the measured profile and the fitting function. Among these functions, the Pearson VII
