(I asked this question on another community without getting much help there,I hence post it here as it may be more of a chemistry question. I apologize if my question has an obvious answer, I'm only a beginner)

A text says: An X - ray diffraction experiment is carried out on a crystalline solid having FCC structure at room temperature. The solid undergoes a phase transformation on cooling and shows orthorhombic structure with small decrease in its unit cell lengths as compared to the FCC unit cell lengths. As a result the 311 line of the XRD pattern corresponding to the FCC system will split into a triplet

Now this is what i could think about it: We know that the interplanar distance for an orthorhombic lattice is given as $$ d=\frac{1}{\sqrt{\frac{h^{2}}{a^{2}}+\frac{k^{2}}{b^{2}}+\frac{l^{2}}{c^{2}}}} $$ and using Bragg's law we can find the angle at which constructive interference occurs as $$ \sin \theta=\frac{\lambda}{2 d}=\frac{\lambda}{2} \sqrt{\frac{k^{2}}{a^{2}}+\frac{k^{2}}{b^{2}}+\frac{l^{2}}{c^{2}}}$$ using the values of$${h k l}$$$$={3 1 1}$$ we obtain the diffraction angle which is unique as given by the above equation. Beyond this I cannot understand what to do,how does any splitting occur, what am I missing.

  • 1
    $\begingroup$ So $a,b,c$ are different in orthorhombic vs an fcc cell, right? $\endgroup$
    – Jon Custer
    Jul 2 '20 at 16:50
  • $\begingroup$ I believe that's correct. $\endgroup$
    – Kashmiri
    Jul 2 '20 at 16:52
  • 1
    $\begingroup$ please check your second equation and rewrite it as it is not consistent with the first. $\endgroup$
    – porphyrin
    Jul 2 '20 at 17:00
  • 2
    $\begingroup$ See, there are 311, 131, and 113. In FCC, they are all the same. In orthorhombic, no longer so. That's the splitting. $\endgroup$ Jul 2 '20 at 17:41
  • 1
    $\begingroup$ You'll get used to it, too. Then again, how would a beginner know the meaning of angular brackets (which is not universal, mind you)? $\endgroup$ Jul 4 '20 at 11:37

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