Rachinger correction

The Rachinger correction is one of William Albert Rachinger proposed (1927 *) recursive procedure to the disturbing - peak of a diffraction pattern in the X-ray diffraction herauszurechnen. ${\ displaystyle K _ {\ alpha _ {2}}}$

Cause of the double peak

For diffraction experiments with X-rays , radiation with the wavelength of the anode material is usually used . However, this is a doublet , i.e. 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 one another, the distance between them being dependent on the diffraction angle . For larger angles, the distance between the intensity maxima is larger. ${\ displaystyle K _ {\ alpha}}$ ${\ displaystyle 2 \ theta}$

Action

Basics

The wavelengths of - and - radiation are known, and so are their energies via the relationship ${\ displaystyle K _ {\ alpha _ {1}}}$ ${\ displaystyle K _ {\ alpha _ {2}}}$

{\ displaystyle E = h {\ frac {c_ {0}} {\ lambda}}.}

From this, the angular distance between the two Kα peaks can be determined for each diffraction angle . ${\ displaystyle \ Delta \ theta}$

It is also known how the intensities of and in the diffraction image behave. This ratio is determined by quantum mechanics and is for all anode materials: ${\ displaystyle K _ {\ alpha _ {1}}}$ ${\ displaystyle K _ {\ alpha _ {2}}}$

${\ displaystyle r = {\ frac {I _ {\ alpha _ {2}}} {I _ {\ alpha _ {1}}}} = 0 {,} 5.}$

invoice

For the calculation, it is now assumed that the -peak is only a variant of the -peak that is scaled with the factor and shifted to larger angles . ${\ displaystyle K _ {\ alpha _ {2}}}$ ${\ displaystyle r}$ ${\ displaystyle \ Delta \ theta}$ ${\ displaystyle K _ {\ alpha _ {1}}}$

The following applies to the overall intensity

{\ displaystyle I (\ theta) = I_ {1} (\ theta) + I_ {2} (\ theta)}

,

where is the intensity of the pure peak and the intensity of the pure K peak. With the above, however, applies to the intensity of the peak ${\ displaystyle I_ {1} (\ theta)}$ ${\ displaystyle K _ {\ alpha _ {1}}}$ ${\ displaystyle I_ {2} (\ theta)}$ ${\ displaystyle \ alpha _ {2}}$ ${\ displaystyle K _ {\ alpha _ {2}}}$

{\ displaystyle I_ {2} (\ theta) = r \ cdot I_ {1} (\ theta - \ Delta \ theta)}

,

so making up for the overall intensity

{\ displaystyle I (\ theta) = I_ {1} (\ theta) + r \ cdot I_ {1} (\ theta - \ Delta \ theta)}

results.

Practical implementation

Diffraction pattern before and after Rachinger correction

In order to carry out the Rachinger correction practically, one begins with a rising edge of a peak. For a certain angle the intensity of the diffraction image is taken and scaled to , at the same time the angle difference is calculated. At this point the true intensity (which would exist if there were no -peak) can be calculated by ${\ displaystyle \ theta}$ ${\ displaystyle I (\ theta)}$ ${\ displaystyle r}$ ${\ displaystyle I '(\ theta) = r \ cdot I (\ theta)}$ ${\ displaystyle \ Delta \ theta}$ ${\ displaystyle \ theta + \ Delta \ theta}$ ${\ displaystyle I_ {1}}$ ${\ displaystyle K _ {\ alpha _ {2}}}$

{\ displaystyle I_ {1} (\ theta + \ Delta \ theta) = I (\ theta + \ Delta \ theta) -I '(\ theta)}

.

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 image has been scanned.

Today this method is rarely used. Due to the performance of the computer, the peak is simply always fitted. ${\ displaystyle K _ {\ alpha _ {2}}}$

restrictions

The way in which the corrected diffraction image is calculated shows that no correction is made for the small diffraction angles. Furthermore, Rachinger's assumption that the -Peak is just a scaled variant of the -peak is incorrect, since the lines generally have different widths . Therefore, in reality there is a deviation in shape and intensity. The correction also loses its validity with a not negligibly small background, since this itself causes an unwanted correction. ${\ displaystyle K _ {\ alpha _ {2}}}$ ${\ displaystyle K _ {\ alpha _ {1}}}$

literature

William Albert Rachinger: A Correction for the α1 α2 Doublet in the Measurement of Widths of X-ray Diffraction Lines . In: Journal of Scientific Instruments . tape 25 , no. 7 , 1948, pp. 254-255 .
BE Warren, X-ray Diffraction. Dover Publications, 1969/1990, ISBN 0-486-66317-5

Individual evidence

^ MO Krause, JH Oliver: Natural widths of atomic K and L levels, Kα X-ray lines and several KLL Auger lines . In: Journal of Physical and Chemical Reference Data . tape 8 , 1979, pp. 329-338 .

[1] MO Krause, JH Oliver: Natural widths of atomic K and L levels, Kα X-ray lines and several KLL Auger lines . In: Journal of Physical and Chemical Reference Data . tape 8 , 1979, pp. 329-338 .