Rachinger correction

The Rachinger correction is a recursive method suggested by William Albert Rachinger (1927) to eliminate the disturbing  peak from X-ray diffraction.

Cause of the double peak 
For diffraction experiments with X-rays radiation is usually used with the  Wavelength of the anode material . However, this is a doublet, so in reality two slightly different wavelengths. According to the diffraction conditions of the Laue or Bragg equation, both wavelengths each generate an intensity maximum. These maxima are very close to each other, with their distance depending on the diffraction angle . For larger angles, the distance of the intensity maxima is greater.

Procedure

Basics 
The wavelengths of  and  radiation are also known to increase their energy through the relationship:

From this, the angular distance can be determined for each diffraction angle   determine the two Kα peaks.

Furthermore, it is known how the intensities of   and  behave in the diffraction pattern. This ratio is determined quantum mechanically and is for all anode materials:

Calculation 
The total intensity is:

,

where  is the intensity of the pure  peak and  the intensity of the pure  peak.

The intensity of  peak can be expressed as:

,

so the overall intensity is:

Practical Implementation 

To practically perform the Rachinger correction, one starts on a rising edge of a peak. For a certain angle  becomes the intensity of the diffraction image   take and with  scales with , at the same time the angle difference becomes te calculated . At the point  can the true intensity  (which, if there is no peak) would be calculated by:
.

Since the measured values of X-ray diffraction experiments are usually available as ASCII tables, this procedure can be repeated step by step until the entire diffraction pattern has been run through.

Today this method is hardly used anymore. Due to the power of the computer, the  peak (einfach immer mitgefittet??).

Restrictions 
From the way the corrected diffraction image is calculated, it follows that no correction is made for the small diffraction angles. Furthermore, the assumption Rachinger that it is   Peak just a scaled variant of the  peaks are not correct, as the lines generally have different widths. Therefore, in reality there is a deviation in form and intensity. Also, the correction loses its validity for a non-negligible background, since this itself causes an unwanted correction.

Literature

References 

Category:Crystallography