P2(1)/m, P112(1)/m (11) space group

P2₁/m (11) Space Group
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Table 1669a. P2₁/m (11) space group.

Name in the International Tables for Crystallography	P2₁/m (Primitive base-centered <z-axis unique> monoclinic Bravais-lattice symmetry group)	Lattice type	P
Patterson space group	10	Point group	2/m
Crystal system	Monoclinic	Laue class	2/m
Asymm	0 ≤ x ≤ 1 and 0 ≤ y ≤ 1/4 and 0 ≤ z ≤ 1
Number of symmetry operators	4	Absence of reflections
Translation
Symmetry (atomic coordinates)	X, Y, Z; -X, 1/2+Y, -Z; -X, -Y, -Z; X, 1/2-Y, Z
Crystal examples

Table 1669b. P112₁/m (11) space group.

Name in the International Tables for Crystallography	P112₁/m	Lattice type	P
Patterson space group		Point group
Crystal system	Monoclinic	Laue class
Asymm
Number of symmetry operators		Absence of reflections	0 0 l: l ≠ 2n.
Indication by absence of reflections	A 2₁-screw axis along the c-axis
Translation
Symmetry (atomic coordinates)
Crystal examples	La₄Cu₃MoO₁₂: a ≈ 8 Å, b ≈ 7 Å, c ≈ 11 Å, γ ≈ 90° (see Figure 1669)

For La₄Cu₃MoO₁₂ crystals, both the absent reflections in the SAED [100] pattern in Figure 1669 (a) and the G-M lines in the 00l discs for odd l in the ZOLZ-CBED pattern taken along the [010] zone axis in Figure 1669 (b) indicate the presences of a 2₁ screw axis parallel to the c-axis and the forbidden reflection (00l: l≠2n). Moreover, the [010] WP (whole-pattern) in Figure 1669 (c) presents a mirror plane perpendicular to the c-axis. Therefore, according to the tables above, the La₄Cu₃MoO₁₂ crystals belong to the P112₁/m (11) space group.


(a)	(b)	(c)

Figure 1669. La₄Cu₃MoO₁₂ (a ≈ 8 Å, b ≈ 7 Å, c ≈ 11 Å, γ ≈ 90°) crystals: (a) SAED pattern along [100] zone axis; (b) ZOLZ-CBED pattern along [010] zone axis. The black arrows indicate G-M lines visible in the 00l discs for odd l, and (c) Whole pattern presenting a mirror plane perpendicular to the c-axis. Adapted from [1]

[1] Sylvie Malo, Douglas A. Vander Griend, Kenneth R. Poeppelmeier, Yanguo Wang, Vinayak P. Dravid, Crystal symmetry of La3Cu2VO9 and La4Cu3MoO12 derived from the YAlO3 hexagonal structure by transmission electron microscopy, Solid State Sciences 3 (2001) 17–23.

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