Bragg diffraction form an “inclined” crystal plane

crick · Nov 6, 2018

Homework Statement

In picture, first-order reflection from the reflection planes shown occurs when an x-ray beam of wavelength ##0.260 nm## makes an angle ##\theta=63.8°## with the top face of the crystal. What is the unit cell size ##a_0##?

Diagram of X rays hitting a crystal lattice of green dots at angle theta to the top face, with diagonal reflection planes and lattice spacing a0 marked along both axes.

Homework Equations

Bragg law
$$d=\frac{ n \lambda} {2 \sin \Theta}$$

The Attempt at a Solution

I thought I must consider an angle ##\alpha =\theta -45°=18.8°## in bragg law and then $$a_0=\sqrt{2} \frac{ \lambda} {2 \sin \alpha}$$

That's because I was sure that the angle of diffraction ##\theta## in bragg's law must always be measured with respect to the plane as in the following picture

Diagram of X-ray beams striking a crystal lattice of green atoms arranged in inclined planes, with spacing d between planes and incident and reflected rays each marked at angle theta to the crystal surface.

Nevertheless I cheked on solution manual found online here : http://omega.altervista.org/extra/key%20to%20Physics.pdf

And I found the following solution:

Worked solution: d = mλ/(2 sin θ) = (1)(0.261 × 10^-9 m)/(2 sin 63.8°) = 1.45 × 10^-10 m, then (2d)^2 = a0^2 + a0^2 and a0 = √2 d = 0.205 nm.

So the angle used in Bragg law is still ##\theta =63.8°## ! How can it be correct?

Charles Link · Nov 6, 2018

I think you got it right and the book's solution is incorrect, but I would need to double-check my result to be sure.

Bragg diffraction form an “inclined” crystal plane

Homework Statement

Homework Equations

The Attempt at a Solution

Discussion

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