Bragg angles widths

The line width of the X-ray source is on the order of 1 eV for A1 or Mg Ka sources but can be reduced to better than about 0.3 eV with the use of a monochromator. A monochromator contains a quartz crystal which is positioned at the correct Bragg angle for A1 Ka radiation. The monochromator narrows this line significantly and focuses it onto the sample. It also cuts out all unwanted X-ray satellites and background radiation. An important advantage of using a monochromator is that heat and secondary electrons generated by the X-ray source cannot reach the sample. 

Reflection Bragg angle (degrees) Rocking curve width (arc Extinction distance (/im)... 

As the crystallite size decreases, the width of the diffraction peak increases. To either side of the Bragg angle, the diffracted beam will destructively interfere and we expect to see a sharp peak. However, the destructive interference is the resultant of the summation of all the diffracted beams, and close to the Bragg angle it takes diffraction from very many planes to produce complete destructive interference. In small crystallites not enough planes exist to produce complete destructive interference, and so we see a broadened peak. 

Table 1. Calculated electromagnetic energies and line widths of the antiprotonic transitions measured with the crystal spectrometer. The energy resolution AEexp of the Bragg spectrometer was determined from narrow transitions of antiprotonic noble gases. Ob stands for the Bragg angle...

Fig. 15. Typical peak width at half-height [W ) as a function of the Bragg angle 0. The minimum occurs for 6 close to the Bragg angle of the monochromator...

I. All possible variables (positions and shapes) are refined independently for each peak or with some constraints. For example, an asymmetry parameter is usually a variable, common for all peaks full width at half maximum or even all peak shape function parameters may be common for all peaks, especially if a relatively narrow range of Bragg angles is processed. When justified by the quality of data, an independent fit of all or most parameters produces best results. A major problem in this approach (i.e. all parameters are free and unconstrained) occurs when clusters of reflections include both strong and weak Bragg peaks. Then, peak shape parameters corresponding to weak Bragg peaks may become... 

Figure 4.17. The distribution of full widths at half maximum as a function of Bragg angle obtained using DMSNT (open circles, solid line) and WinCSD (filled triangles, dash-dotted line) algorithms. The lines represent parabolic fit of the two sets of data to illustrate the trend.

Table 5.1. Relative integrated intensities (///q), Bragg angles and full widths at half maximum (FWHM) of Bragg peaks observed in the LaNi4 85Sno,i5 powder diffraction pattern collected...

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