Why we always take 2θ in degree in the XRD pattern. why we not take into radian of XRD pattern?
Respected Sir,
2θ is used because we can see diffracted pattern from incident beam so the angle of incident and reflected are combine to become 2θ.
The conversion factor used to change degrees to radians (D2R) was 0.0174532925199433, and d is in angstroms.
Bragg equation is most important in crystallography, it is relation of T/2T angle, wavelength and interplanar distances in a crystal/material. Using the Bragg equation you can calculate interplanar distances in a crystal. The set of such distances and relative intensities of diffraction peaks in diffraction pattern is characteristic of a compound/material, so it is widely used for quantitative and qualitative PXRD analysis.
Dear Sanjeet Kumar Paswan ,
I think it is due to historical reasons.
Reading and display of angles in degree(s) is more catchy than in radians; at least for me...
Best regards
G.M.
I agree with GM.
Although if I'm doing trigonometry or calculus, I think more readily in multiples of π for arguments of trig functions. I do not like to work in decimal radians to measure angles I'm physically working with.
It's easy to think of a right angle as π/2 or 90° but 1.5708 not so much (actually I might recognize 1.57). We find it easier to work with angles that vary from 0 to 180 and where hundredths of a degree are meaningful rather than 0 - 3.1416 where 0.0001 are meaningful.
If you want to challenge the sensibility (versus just curious), challenge the practice of plotting diffractograms as intensity vs angle instead of intensity vs Q or d. (Some diffraction subfields do routinely plot diffractograms as functions of Q, when they are used to working with different radiation energies.)
2θ is used because we can see diffracted pattern from incident beam so the angle of incident and reflected are combine to become 2θ. The conversion factor used to change degrees to radians (D2R) was 0.0174532925199433, and d is in angstroms.
Agree with the above answers, however, use below conversion equation.
d=2πϴ/360
Where d radian in arcsec, Theta in degree and Pi is 3.14159265
In addition, FWHM is measured in arcsec
In direct space the Bragg's law is 2dsinθ = nλ; in the reciprocal space, all the diffracted beams represented in a diffraction pattern are generated by the intersection of the Ewald sphere with a reciprocal lattice point. In the reciprocal space, the Bragg's law is Q = 4π/λ sinθ = 2π/d.
So the best (and meaningful) way to plot a diffraction pattern is to use Q as horizontal scale, instead of an angle. Q depends only on the structural properties of your sample (is always the same, independently on the wavelength of the scattering radiation λ). Conversely, if you use an angle, the position of the diffraction peaks will change with wavelength.
Last thing; according to IUCR convention, indexed peaks must be indicated without parentheses.
For this, I would recommend the latest preprint article at link DOI: 10.13140/RG.2.2.27720.65287/3 or at link https://www.researchgate.net/publication/352830671
Sanjeet Kumar Paswan My protractor is marked in degrees and not radians... A single radian is quite large: 57.2958 degrees (360/2pi) in a radian. So, it's not so really convenient for practical measurement. I agree with historical reasons - the ancients didn't have the most accurate grasp of pi so degrees (360 in a circle related to the ancient year/rotation of the earth) was the practical measure employed to describe a circle.
- Badges
- Science topic
- Similar topics
- Mathematics