(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.
