this can be understood as a variation of the exit angle when it is determined with respect to the extended incoming beam and this angle is 2θ for all points
This is all due to Bragg's equation. The incident ray and reflected ray all making the angle theta with a crystal plane.Reflections from planes set at theta angle with respect to the incident beam generates a reflected beam at an angle 2-theta from the incident beam.
Bragg’s law is always having the angle calculation with respect to incident x-ray beam; therefore, the measurement needs always to be taken with respect to incident x-ray beam rather than the sample. For that it says the sample will make Ө angle with incident x-ray beam, where diffracted x-ray will make 2Ө angle with incident x-ray beam.
This is due to Bragg’s equation. Here theta is the angle between incident beam of x ray and crystallographic reflecting plane, which is also equal to the angle between reflected beam and crystallographic plane. On the other hand, 2- theta is the angle between transmitted x-ray beam and reflected beam. Here we observe the transmitted and reflected beam.
In case of bragg law theta is the angle between incident x ray and reflected x ray . For satisfaction bragg diffraction incident angle should be equal reflected angle with the sample crystallograpic plane. So sin theta is consider not sin2theta.
But to draw intensity verse theta graph 2theta is uses because here 2theta is angle between diffracted x-ray with incident x-ray beam. Here diffracted ray gives intensity only.
XRD instrument works such a way that angle of incident(theta) = angle of reflection to maintain a constant focusing distance by changing relative positions of incident x ray, sample surface and reflected x ray. So the angle between incident and reflected x ray will be 2 theta.(please refer to the picture attached)
There is no physical reason for using 2 theta more frequently than theta. The answer to your question is TRADITION. The first succesful and meaningful experiments with diffraction of x-rays were performed in the Debye-Scherrer camera. It was the cylindrical black box with the photographic film inside, mounted circumferentially. The not reflected beam hit the film opposite the entry window. If it was reflected by lattice planes which met the Bragg's law (at the incidence angle of theta), the beam was inclined by the angle of 2 theta (incidence angle plus reflection angle) - see the image uploaded by Najathulla B C , and THIS 2 THETA angle was observed after the film was developed and fixed. The distance between the not reflected beam (2 theta = 0) and the reflected beam was measured by a simple ruler. The number read from the ruler was directly related to 2 theta, and not single theta. And that's it!
BTW, the unreflected beam was very strong, so it overexposed the film and finding the spot was practically impossible, so a simple trick was used: since left and right sides of the pattern on the film were symmetrical (mirror symmetry), the distance between the corresponding L and R beams were measured, yielding 4 theta. But the 2 theta remained as the basic measure in diffraction analysis.
θ is the angle between incident beam and the crystallographic reflecting plane. It is also equal to the angle between reflected beam and the crystallographic plane.
2 θ is the angle between transmitted beam and reflected beam.
In any experiment the transmitted and reflected beam can be observed, so 2 θ is an experimentally measurable quantity. But the crystallographic plane cannot be observed. So θ cannot be determined directly. This is the reason behind using intensity vs. 2 θ plots for x-ray diffraction.
Can θ be called as a diffraction angle too OR we should multiply it by 2 to be called as a diffraction angle? especially when needed to solve a problem (question).
Here theta is the angle between incident beam of x ray and crystallographic reflecting plane, which is also equal to the angle between reflected beam and crystallographic plane. ... But to draw intensity verse theta graph 2theta is uses because here 2theta is angle between diffracted x-ray with incident x-ray beam.
Only those crystallites whose bragg planes are at an angle θ with respect to the incident angle will diffract at an angle 2θ with respect to the incident beam (or at an angle θ with respect to the diffracting planes). So that is the reason, you always use 2θ instead of θ.
2 theta is the angle of detector position from the incident X-ray beam. The incident angle is always half of the detector angle.
θ is the angle between the incident beam and the crystallographic reflecting plane. It is also equal to the angle between the reflected beam and the crystallographic plane.
In powder x-ray diffractometry the powder sample is loaded in a small disc-like container and its surface is carefully flattened. The disc is put on one axis of the diffractometer and tilted by an angle θ while a detector, a scintillation counter, rotate around it on an arm at twice this angle. This configuration is known under the name Bragg–Brentano θ-2θ. Another configuration is the Bragg–Brentano θ-θ configuration in which the sample is stationary while the X-ray tube and the detector are rotated around it.
The angle formed between the x-ray source and the detector is 2θ. This configuration is most convenient for loose powders. Thus the 2 θ is the angle between transmitted beam and reflected beam. In an experiment, the transmitted and the reflected beam can be observed, but the crystallographic plane cannot be observed, so 2 θ is an experimentally measurable quantity. That's why in the x-ray powder diffractometry analysis, we use intensity vs. 2 θ plots.
Acknowledgment:
- M. Birkholz (2005). Thin Film Analysis by X-Ray Scattering. Wiley-VCH. ISBN 978-3-527-31052-4.
- Kaspar Kallip (Photo: X-ray diffractometer reproduce under CC BY-SA 4.0, 30 November 2015)
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the angle between incident ray and reflected ray is 2* theta, X ray diffractometer
measures detector position in this way ( intensity in leiu to this 2*theta). that's why it is easier to directly have a plot to intensity vs 2*theta.
thanks & regards,
g.sudhakar
phd(materials engineering)
hcu
To get a sustainable solution to your problem, please refer to the preprint article given at link DOI: 10.13140/RG.2.2.27720.65287/3 or at link https://www.researchgate.net/publication/352830671.
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