dictate that a ¯at-plate sample be used, spray drying the
sample to minimize preferred orientation should be
considered. Rotation of a ¯at-plate sample in its own
plane will not correct preferred-orientation effects.
An ideal particle size within a powder sample is circa
1±5 mm. If large crystallites are used, there are fewer
crystallites in the sample and nonrandomness (i.e. not all
crystallite orientations are equally represented) may
become a problem. This can cause nonsystematic inac-
curacies in the relative intensities that, unlike preferred-
orientation effects, cannot be corrected at the re®ne-
ment stage. Sample rotation will improve the particle
statistics and is strongly recommended. If smaller
particles are used, line-broadening effects due to crys-
tallite size begin to become apparent. If there are one or
more large crystallites within a sample of smaller ones
(`rocks in the dust'), the relative intensities of the
re¯ections originating from the larger crystallites will be
too high in comparison with the other re¯ections and as
with nonrandomness, no correction can be applied at the
re®nement stage. For more information on sample
preparation, see Bish & Reynolds (1989) or Buhrke et al.
(1998).
The 2 values should be carefully calibrated using
several peaks from a standard material (e.g. NIST Si
standard SRM 640b and/or ¯uorophlogopite mica SRM
675 for low angles). Almost any diffractometer can be
adjusted so that the deviations of the measured peak
positions from the correct ones are less than 0.01
(2).
Furthermore, the diffractometer should be set-up to give
a low background and maximum peak resolution (small
peak widths) if a complex pattern with signi®cant
re¯ection overlap is to be measured [e.g. small receiving
slits, pre-detector Soller slits if available, receiving slit on
the focusing circle, 0.3 mm capillary or smaller for
transmission geometry, monochromatic radiation (e.g.
Cu K
1
rather than Cu K
1,2
, if possible)]. Although
longer data-acquisition times are required with mono-
chromatic radiation, its use is particularly advantageous:
the number of lines in the pattern is halved (so the
severe overlap of re¯ections begins at higher angles) and
the background is lower. If both
1
and
2
components
are used in the data collection, the spectral distribution
(intensity ratios) and dispersion (pro®le changes as a
function of 2) must also be calibrated.
Any temptation to smooth the diffraction data before
doing a Rietveld re®nement must be resisted.
Smoothing introduces point-to-point correlations (off-
diagonal weight matrix elements) which will give falsely
lowered e.s.d.'s in the re®nement. For more information
on data-collection aspects, the reader is referred to the
results of the second round robin (Hill & Cranswick,
1994), to the review on powder diffraction by Langford
& Loue
È
r (1996) and to the monograph edited by Bish &
Post (1989) mentioned earlier. For information
regarding the effect of systematic errors on powder
diffraction data see Wilson (1963).
Synchrotron. There are a number of options for data
collection at a synchrotron facility, which may not be
familiar to users of conventional laboratory equipment
and which should be discussed in detail with the
beamline scientist prior to starting an experiment. These
options involve a compromise between resolution,
intensity and peak-to-background discrimination, and
among the many factors to be considered are (i) the
diffraction geometry (e.g. monochromator, crystal
analyzer, single slits, Soller slits), (ii) detectors [e.g.
scintillator, semiconductor, linear or curved position-
sensitive detector (PSD), imaging plate (IP), charge-
coupled detector (CCD)], (iii) sample geometry (e.g.
¯at-plate in symmetric or grazing incidence re¯ection,
¯at-plate in symmetric or normal transmission, capil-
lary) and (iv) wavelength (typically 0.3±2.5 A
Ê
for a
bending-magnet beamline, depending on the energy of
the synchrotron source).
The best instrumental resolution [circa 0.01±
0.02
(2)] and peak-to-background discrimination are
obtained with a crystal analyzer (CA) mounted in the
diffraction path between the sample and the detector,
but only at the expense of considerably reduced
counting statistics. However, the relatively low counting
rates in this case can be compensated for if a multi-
analyzer detector (Toraya et al., 1996; Hodeau et al.,
1996) is available. The best counting statistics are
obtained with area detectors such as an IP, a PSD or a
CCD.
The wavelength and zero offset should be calibrated
with a reference material. The Si SRM 640b standard
gives signi®cantly broadened peaks, whereas the NIST
LaB
6
standard SRM 660 gives close to instrumental
resolution and is probably a better choice. Commonly
used wavelengths at second-generation sources range
between 0.7 and 1.2 A
Ê
(1.54 A
Ê
is unlikely to be an
optimal choice because of excessive attenuation). At
a third-generation or high-energy source, even shorter
wavelengths down to circa 0.3 A
Ê
are available.
Problems with highly crystalline samples, in which
there is insuf®cient sampling of grains suitably oriented
for diffraction, may be exacerbated at a synchrotron
source because of the highly collimated nature of the
incident monochromatic beam; it is thus essential to
rotate or rock the sample during data collection. For
capillary samples, the diameter of the capillary and the
wavelength should be chosen so that R (where is the
linear absorption coef®cient and R is the diameter of the
cylinder) is not too large (see International Tables for
Crystallography, 1995; Sabine et al., 1998). If R is larger
than 1, the simple form of the absorption correction is
no longer valid and a more sophisticated correction is
needed. Corrections of this type are not currently
implemented in most Rietveld programs, so they need to
be applied to the raw data prior to re®nement. In
practice, it is dif®cult to load capillaries less than 0.2 mm
in diameter and thus short wavelengths (or samples
38 RIETVELD REFINEMENT GUIDELINES
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