X-ray Powder Diffraction

Experimental setup and standard conditions

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 0.005^o, with a minimum of 0.005^o; however, the instrument optics make values below 0.020^o 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 0.1^o, 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 0.02^o and 0.05^o. The default value is 0.00^o, 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 0.5^o and 2.0^o. The default value is 2.0^o.

- 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 1.0^o and 5.0^o. The default value is 2.0^o.

- 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 20^o 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 tablets, should be ground using mortar and pestle up to the point when a marked decrease in friction is 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 can be 'loosened' to remove any clustering, and be fixed to a silicon single crystal substrate using a minimal amount of amorphous vaseline. The powder should be spread out over the surface as evenly as possible. To avoid preferred orientation in the sample no unnecessary force should be applied to fix the powder to the vaseline.
 

Measuring procedure

All X-ray powder diffraction patterns can be measured according to a standard procedure which can be 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 can be used for a standard measuring procedure:
Start angle (2q): 3.0^o
End angle (2q): 90.0^o
Scan step width: 0.02^o
Scan type: continuous
Scan step time: 2.50 seconds
Spinner: on
 

Contact persons

  R. de Gelder    Phone 52842    Room 03.009

  J.M.M. Smits    Phone 52596    Room 03.408