In
X-ray
An X-ray, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation. Most X-rays have a wavelength ranging from 10 picometers to 10 nanometers, corresponding to frequencies in the range 30&nb ...
diffraction
Diffraction is defined as the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a s ...
, the Rachinger correction is a method for accounting for the effect of an undesired K-alpha 2 peak in the energy spectrum. Ideally, diffraction measurements are made with X-rays of a single wavelength. Practically, the x-rays for a measurement are usually generated in an
X-ray tube
An X-ray tube is a vacuum tube that converts electrical input power into X-rays. The availability of this controllable source of X-rays created the field of radiography, the imaging of partly opaque objects with penetrating radiation. In contrast ...
from a metal's
K-alpha line. This generation creates x-rays at a variety of wavelengths, but most of the non K-alpha X-rays can be blocked from reaching the sample by filters. However, the K-alpha line is actually two x-ray lines close together: the stronger K-alpha 1 peak, and the weaker K-alpha 2 peak. Compared to other radiation such as the
Bremsstrahlung
''Bremsstrahlung'' (), from "to brake" and "radiation"; i.e., "braking radiation" or "deceleration radiation", is electromagnetic radiation produced by the deceleration of a charged particle when deflected by another charged particle, typicall ...
, the K-alpha two peak is more difficult to filter mechanically. The Rachinger correction is a recursive method suggested by William Albert Rachinger (1927) to eliminate the disturbing
peak.
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
ASCII ( ), abbreviated from American Standard Code for Information Interchange, is a character encoding standard for electronic communication. ASCII codes represent text in computers, telecommunications equipment, and other devices. Because of ...
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 computers, the
peak can be fit simultaneously.
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
*
* {{cite book
, last= Warren
, first=B. E.
, date=1969
, title=X-ray Diffraction
, url=
, location=
, publisher=Dover Publications
, page=
, isbn=0-486-66317-5
, author-link=
References
X-ray crystallography