# How will the X ray diffraction pattern change if the crystal changes its lattice structure

(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.

• So $a,b,c$ are different in orthorhombic vs an fcc cell, right? Jul 2, 2020 at 16:50
• I believe that's correct. Jul 2, 2020 at 16:52
• please check your second equation and rewrite it as it is not consistent with the first. Jul 2, 2020 at 17:00
• See, there are 311, 131, and 113. In FCC, they are all the same. In orthorhombic, no longer so. That's the splitting. Jul 2, 2020 at 17:41
• 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)? Jul 4, 2020 at 11:37