# What can be concluded from two different values for the interplanar distance between planes of atoms in an X-Ray diffraction experiment?

I analyzed an unknown Alkali Halide crystal using x-rays from a copper source. I need to find the d-spacing for this crystal, i.e. the interplanar distance between planes of atoms.

I found my $K_\alpha$ and $K_\beta$ peaks and used Bragg's Law to calculate the d-spacing. However, these values do not match. Is this an experimental error or could the non-matching values be correct somehow?

For $K_\alpha$:

$$d_{hkl}=\frac{λ}{(2 \sin⁡(θ))}=\frac{(1.54184 Å )}{(2 \sin⁡((28.3°)/2) )}=0.771 Å$$

For $K_\beta$:

$$d_{hkl}=\frac{λ}{(2 \sin⁡(θ))}=\frac{(1.39222 Å )}{(2 \sin⁡((25.7°)/2) )}=2.488 Å$$

My attempt: in both cases, I assumed that these were first order peaks. Could it be that the $K_\beta$ peak is actually a third order peak? If so, then $n=3$ and $d_{hkl}=2.313 Å$. This is reasonably close to the other value. But then what would that tell me about the crystal?

• You analyzed it with... what? XRD? I have never seen Bragg's law applied to $K_\alpha$ and $K_\beta$ directly like that. What peaks? can you show the entire diffractogram, if indeed it was an XRD that was done? – Stian Yttervik Oct 16 '17 at 7:37
• @StianYttervik I used a TEL-X-OMETER to collect the intensity measurements. So yes, x-ray diffraction. – whatwhatwhat Oct 17 '17 at 0:59
• However, I only collected 2 peaks, not the entire range of angles. I was told that these two peaks corresponded to the $K_\alpha$ and $K_\beta$ peaks. – whatwhatwhat Oct 17 '17 at 1:00
• The item you linked to is both an XRF and an XRD. Are you sure you have recieved a diffractogram problem? I ask, because $K_\alpha$ and $K_\beta$ is notation used for emission of x-rays (for instance, in fluorescense), NOT their reflection. Which leads me to believe you have been handed an XRF problem, but I won't speculate without information... In either case, the smallest lattice spacing (a) for alkali halides is $\ce{LiF}$ at a > 4.0 Å so there is that... – Stian Yttervik Oct 17 '17 at 7:26