Question about Powder X-ray diffraction experiment

[Clara Chung]

I don’t understand why do we use power in this experiment. If we use powder, the d spacings of each crystalline will be oriented randomly, why won’t the angle of reflection changes? I don’t understand the idea of using powder in the experiment.

Thank you so much

 

[Charles Link]

I believe the answer is because the Bragg peak occurs at at specific angle/direction between incident beam and scattering direction. Bragg scattering is a combination of specular reflection off of a single crystal plane (basically a zeroth order diffraction maximum) as well as constructive interference between adjacent planes. By having random orientation of the scatterers, the Bragg peaks will only occur for a very small percentage of the small crystals of the powder. (I believe I have this part correct). Most of the crystals in the powder do not have the proper incident angle to make a Bragg peak. $\\$ When you get a Bragg peak from a given crystal, the scattering will be in a ring, (i.e. for each single small crystal, it will occur somewhere in the ring), because the scattering is no longer in a single plane for all of the crystals that satisfy the Bragg condition.

 

[Clara Chung]

I believe the answer is because the Bragg peak occurs at at specific angle/direction between incident beam and scattering direction. Bragg scattering is a combination of specular reflection off of a single crystal plane (basically a zeroth order diffraction maximum) as well as constructive interference between adjacent planes. By having random orientation of the scatterers, the Bragg peaks will only occur for a very small percentage of the small crystals of the powder. (I believe I have this part correct). Most of the crystals in the powder do not have the proper incident angle to make a Bragg peak. $\\$ When you get a Bragg peak from a given crystal, the scattering will be in a ring, because the scattering is no longer in a single plane for all of the crystals that satisfy the Bragg condition.

cool!

 

[Charles Link]

One additional item=and I think I have this correct=the Bragg peak does not require the incident beam to precisely have the proper angle of incidence to get a Bragg peak. Because the process works off of diffraction, (and perhaps also because of the thermal motion of the individual atoms), the Bragg condition only needs to be met within a small $\Delta \theta$ for a given small crystal to have the proper angle of incidence to get a specular reflection that also results in a Bragg peak. Also, since the powder consists of small crystal particles, the diffraction pattern from a reflection will cover a finite $\Delta \theta$, (still small though), rather than the infinitesimal $\Delta \theta$ that would result from a larger crystal. $\\$ And this is my own deduction, but I believe I have this part correct, is smaller particles of the powder would make for a larger $\Delta \theta$. In addition, the solid angle of cone of acceptance $\Delta \Omega$ for the incident beam to be such that the crystal particle meets the $\Delta \theta$ requirement is proportional to $(\Delta \theta )^2$. Thereby, it would be advantageous to have a somewhat fine powder, in order to increase $\Delta \theta$ to have a much higher percentage of crystal particles meet the $\Delta \theta$ requirement to participate in the ring of Bragg scattering that occurs. $\\$ And here is a "link" that agrees with my statement of post 2 that only a small percentage of the particles participate in making the Bragg ring: http://prism.mit.edu/xray/oldsite/Basics of X-Ray Powder Diffraction.pdf The powder diffraction method is discussed around page 25. (The pages are not numbered).

 

[Andy Resnick]

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I don’t understand why do we use power in this experiment. If we use powder, the d spacings of each crystalline will be oriented randomly, why won’t the angle of reflection changes? I don’t understand the idea of using powder in the experiment.

Thank you so much

Powder diffraction makes it easier to analyze hard-to-crystallize samples. All crystals will have some disordering, using a powder allows 'averaging' over the disorder, leaving only the lattice contributions. Powder diffraction also does not require large crystals, so sample preparation is often cheaper and faster.

https://en.wikipedia.org/wiki/Powder_diffraction