 | Acta Crystallographica Section A Acta Crystallographica Section A FOUNDATIONS AND ADVANCES |
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![[Figure 4]](lu5021fig4mag.jpg)
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Figure 4
The definition of tilt within a perovskite, based upon the geometric connectivity of the atoms. In (a) we define the cube made by the B-site ions. In (b) we define two edges of the cube (B1bB1a, B2bB2a), their midpoints (M1, M2), and then vectors between these midpoints and both the B sites (M1B1b, M1B1a, M2B2b, M2B2a) and the X (M1X1, M2X2). In (c) the midpoints are connected by a vector (M1M2), which allows us to define the `torsional' angles (X1M1M2X2, X1M1M2B2a, X1M1M2B2b, B1aM1M2X2, B1bM1M2X2). We define the `torsional' angle X1M1M2X2 as follows. Looking in the direction M1M2, the `torsional' angle is the clockwise angle through which it is necessary to rotate the line X1M1 such that the planes X1M1M2 and M1M2X2 are superimposed. The other `torsional' angles are defined analogously. The system shows in-phase tilt if X2M2M1X1 < min(X1M1M2B2a, X1M1M2B2b, B1aM1M2X2, B1bM1M2X2) as noted in (d). |
![[Figure 4]](lu5021fig4.jpg)
| FOUNDATIONS ADVANCES |
ISSN: 2053-2733
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