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I keep coming across the term pseudocubic unit cell while reading about orthorhombic perovskite structures. No clear explanation is given in papers. Can someone please tell me how these structures are generated and what exactly is meant by them?

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I personally think the introduction of the pseudo-cubic unit cell is for the purpose of better reflecting the phase transition. For example, when you have cubic to orthorhombic transition, you can say that the unit cell is still "cubic", with respect to the changing of the unit vectors length. Then if looking at the diffraction pattern, the original degenerate peaks corresponding to certain cubic reflections now split. The reason is simple since originally the repetition of atoms in each direction (e.g. along a, b and c) is identical for cubic structure. Now when we have the orthorhombic structure, still we have the repetition of atoms along the a, b and c directions but with different repetition distances (d-spacing). So now we have similar pattern of atoms repetition but with different d-spacings. Projected onto the diffraction pattern, we see the splitting of the originally degenerate peaks. Therefore the "cubic" in pseudo-cubic stresses the "similar pattern" and "pseudo" stresses the different d-spacing (which corresponds to the splitting of diffraction peaks). If the distortion of the structure is not that big, the splitting should not be that obvious as well, and that's exactly what it is meant by "pseudo" - they are nearly identical, but not yet, still some difference there.

As for the construction of the pseudo-cubic unit cell, I think the orthorhombic unit cell is just a pseudo-cobic one, if I understand it correctly. But I am not sure on that.

At last, I found a paper which does mention the construction of the pseudo-cobic cell from the monoclinic unit cell. Maybe irrelevant to the post, but I will put it here for reference: Crystals 2014, 4, 273-295; doi:10.3390/cryst4030273

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