X-ray powder diffraction is a powerful technique for the identification of solid state samples. The underlying crystal structure of matter will, in principle, give rise to a unique X-ray powder diffraction pattern (which expresses the existence of lattice planes in materials) for each pure compound and for each individual component in a mixture of compounds.
Powders generally contain a very large number of randomly oriented microcrystals, each of which diffracts independently, yielding continuous cones of Bragg reflections that are recorded as lines on an X-ray powder diffractometer when these cones are crossed by the scanning counting equipment. Each line corresponds to a specific diffraction angle at which the X-ray beam is reflected by a specific set of lattice planes in the powder. Because of the random orientation of the microcrystals in the powder, all possible lattice planes will reflect sooner or later.
The combination of the unique set of angles (q)
at which a powder reflects X-rays and the corresponding intensities, yields
a fingerprint that is unique for the crystal structure (and hence its polymorph)
of each single component. The positions of the peaks in an X-ray
powder diffraction pattern are directly related to the dimensions
of the unit cell, which is defined by six so called cell parameters. The
intensities
corresponding to the peaks are related to the contents of the unit
cell (the atomic positions, or better: the electron density distribution).
Different polymorphs have different crystal structures due to a different
packing of the molecules in the lattice. This results in a different crystal
symmetry and/or unit cell parameters which directly influence the reflection
characteristics of crystals or powders. A different polymorph will in general
diffract at a different set of angles and will give other values for the
intensities. Therefore X-ray powder diffraction can be used to identify
different polymorphs or a mixture of polymorphs in a reproducible and reliable
way.
Experimental setup requires that, if a reflection is diffracted when
the incoming beam forms an angle q with a certain lattice plane, the reflected
beam is recorded at an angle 2q.
Although 2q values are part of the printed output, normally peaks are characterized by their unique 'DI-values': D stands for d-value (the distance between lattice planes), and I for intensity.
The d-values are preferred because they are independent of the type of radiation used (wavelength independent), in contrast with the 2q values. They are calculated using Bragg's Law: 2 d sinq = nl.
Because of differences in experimental conditions, normally relative
intensities are used: the strongest peak is set to 100, all other intensities
are scaled accordingly.
When interpreting X-ray powder diffraction patterns, several effects
should be taken into account. In order of importance: peak intensities
can be influenced considerably by 'preferred orientation' (i.e.
the particles are not distributed randomly) and a variety of other effects
(with lesser influence); their widths are rather dependent on particle
size (overly small particles will result in line broadening); and, as a
minor effect, their positions can be slightly influenced by the sample
thickness (i.e. changes in height adjustment), sample roughness
(i.e. smoothness of the sample surface) and sample 'transparancy'
(i.e. how deep the radiation will penetrate: an absorption-related
effect). Only some of these effects can be minimized by careful sample
preparation.
The X-ray powder diffraction pattern of a mixture of two or more components
is, to a large extent, the weighted sum of the individual patterns. However,
differences in particle sizes and absorption effects can have substantial
influence. This means that some of the effects mentioned are (or can be)
'anisotropic', depending on how large these differences are.
Experimental
Experimental setup and standard conditions
Diffractometer Type: Philips PW1820/00
Diffractometer Controller: Philips PW1710/00
Divergence Slit: Philips PW1386/55 Automatic
Irradiated Length: 12 mm
Receiving Slit: 0.2 mm
Soller Slit Collimator yes
Scatter Slit 1.0o
Monochromator: Philips PW1752/00 Curved Graphite Monochromator
Sample Holder: Philips PW1784/25
Sample Holder Substrate: Philips PW1817/32 Silicon Single Crystal
Sample Spinner: Philips PW1774/00
Rotation Speed: 2 rps
Minimum 2q: 3.0o
Maximum 2q: 150.0o
High Tension Generator: Philips PW1830/40
Radiation Type: Cu
Radiation Wavelength 1.54060Å, 1.54438Å a1, a2
Radiation Source: Philips PW2273/20 Long Fine Focus, 2200W, 60kV max
Current: 50 mA
Voltage: 40 kV
Detector: Philips PW1711/10 Proportional Detector
Lower Level PHD 35 Pulse Height Discriminator
Upper Level PHD 80
Software package: Philips PW1877 PC-APD (Automatic Powder Diffraction)
Version: 2.1A 1990
Background information for experimental parameters
The measurement of an X-ray powder diffraction pattern is controlled by a limited number of parameters, of which the start angle, the end angle and the total scan time are rather obvious. The step width must be rounded to a multiple of 0.005o, with a minimum of 0.005o; however, the instrument optics make values below 0.020o meaningless. These angular values are given in degrees 2q. Together these values determine the time per step which should at least comprise one revolution of the spinner, if used, i.e. 0.5 second per step.
The scan type can be STEP or CONTINUOUS, meaning either one fixed
angular value per step at which the counts are collected, or a continuous
scan over the angular range of the step during which the counts for that
step are collected. For smaller step widths, say below 0.1o,
the difference between these scan types is marginal.
After the measurement, data treatment may consist of removal of the
a2
component, data smoothing (but only if absolutely necessary) and peak search
including background determination.
For the stripping of the a2 component, if applied, the method
of Ladell et al. (1975) is used. A value of 1 is used for the 'Weights
and Levers' variable.
Normally data smoothing is not performed. If so, it will be stated explicitly,
and the process will then be executed in a conservative and cautious manner.
Peak searching is controlled by 4 parameters:
- minimum peak tip width: the peak width is the width of the negative second derivative region, i.e. the angular difference between the points of inflection in the corresponding data points.
(When analyzing a peak, the two halves are treated separately. For each half there is, somewhere between the base and the top, a point on the slope where the direction of a line tangent to the curve changes direction, i.e. in that point the second derivative changes sign. This procedure is a standard mathematical way of defining a peak width. Smoothing might be necessary to enable the program to identify these inflection points correctly. Cf. FWHM, the Full Width at Half Maximum, the angular distance between the two points on the two slopes halfway between the base and the top; this method depends on the ability to determine the base correctly.)
An increase of the value for the minimum peak tip width reduces the number of noice-induced peaks (very narrow peaks are discarded). If used at all, typical values are between 0.02o and 0.05o. The default value is 0.00o, i.e. no peaks are discarded.
- maximum peak tip width: a decrease of this value might also result in a reduction of the number of noice-induced peaks (very broad peaks are discarded; some noice-induced peaks and peaks resulting from amorphous components tend to be broad). If used at all, typical values are between 0.5o and 2.0o. The default value is 2.0o.
- peak base width: this parameter is used to determine the background. A higher value will give a straighter, smoother background, a lower value will result in a background that follows changes more closely.
(In theory, peaks extend to infinity in two directions. By limiting the practical base width of the peaks a more realistic estimation of the contribution of the background can be made. A value which is too small will influence net intensities considerably by subtracting too much
background contribution, a value which is too large will underestimate this contribution. A large value smoothes the background curve.)
This value becomes more important when there is a detectable fraction of an amorphous component in the sample (which especially influences the background). If used at all, typical values are between 1.0o and 5.0o. The default value is 2.0o.
- minimum significance: this parameter implies the minimum value for the statistical significance of a peak's area. This value is inversely proportional to the number of 'phantom', noice-induced peaks that will be found.
(The statistical standard deviation in any measurement at any point equals the square root from the number of counts at that point. This leads to a measure for the statistical significance for any peak area, i.e. the difference between the observed counts at the various points in the peak and the assumed background level at those points, which can be below a certain confidence level. A higher confidence level decreases the number of 'phantom' peaks, but will probably discard a (small) number of very weak peaks.)
The smaller the value, the more phantom peaks will be detected. For
this type of equipment a typical value of 0.75 should be used, which is
the default value.
We always use an automatic divergence slit system, but it is possible
to record an X-ray powder diffraction pattern using a fixed divergence
slit. This has a very significant effect on the intensities in the lower
2q region, say below 20o 2q. 'Automatic' data can be converted
to FIXED, and 'fixed' data can be converted to 'AUTOMATIC'. To enable comparison,
especially with intensity data from the Powder Diffraction Database, all
data should be FIXED. This conversion is performed on all our data by default.
Sample preparation
All samples, including the tablets, were ground using mortar and pestle up to the point when a marked decrease in friction was experienced. At this point, which is fairly reproducible, the average crystallite size is normally at its optimum for X-ray powder diffraction analysis. However, it is difficult to get similar distributions in particle size for samples differing largely in composition and crystal habit, especially when harder and softer components are mixed. A mixture or a sample in which the average crystallite size is already smaller then the optimum size as a result of the production process, which may be the case for tablets, can result in a sub-optimal average crystallite size. This will result in a broadening of the diffraction line profiles.
After grinding the powder was 'loosened' to remove any clustering, and
fixed to a silicon single crystal substrate using a minimal amount of amorphous
vaseline. The powder was spread out over the surface as evenly as possible.
To avoid preferred orientation in the sample no unnecessary force was applied
to fix the powder to the vaseline.
Measuring procedure
All X-ray powder diffraction patterns were measured according to a standard procedure which was established based on a number of trial runs to find the optimum parameters. The parameters mainly include the scan range (the angular range in which usefull information is present) and the scan time needed to collect reliable data.
The use of standard parameters facilitates the comparison of experimental
results, and the standard scan range covers the angular range reported
in the literature that is used in the discussion of the results.
The following settings were used for the standard measuring procedure:
Start angle (2q): 3.0o
End angle (2q): 90.0o
Scan step width: 0.02o
Scan type: continuous
Scan step time: 2.50 seconds
Spinner: on