Novel strategy for space group determination in real space

doi:10.1016/j.jmst.2022.04.058

Abstract

Abstract:

Traditional space group determination methods are all in reciprocal space, which involves ambiguous identification on some space groups which have glide plane and screw axes. The novel strategy herein for space group determination in real space is based on the atom resolution high angle annular dark field (HAADF) technology. Three HAADF images in three specific crystal zone axes are needed at most. The proposed strategy for space group determination is easy and effective.

Key words: Space group, Real space, HAADF (high angle annular dark field)

Yi Yang, Rui Li, Bingbing Yin, Qibin Yang. Novel strategy for space group determination in real space[J]. J. Mater. Sci. Technol., 2023, 132: 252-259.

Figures/Tables 13

Table 1. Characteristic directions of the seven crystal systems.

Crystal system	Characteristic directions
Triclinic	[001]	[100]	[010]
Monoclinic	[001]	[100]	[010]
Orthorhombic	[001]	[100]	[010]
Tetragonal	[001]	[100]	[110]
Trigonal	[001]	[100]	[210]
Hexagonal	[001]	[100]	[210]
Cubic	[001]	[111]	[110]

Fig. 1. Schematic diagram of 17 2D space groups.

Fig. 2. HAADF images of TiSi: (a) [001], (b) [100] and (c) [010].

Table 2. Information of probable space groups.

Space group	[001]		[100]		[010]
25	p2mm	a′=a	p1m1	a′=b	p11m	a′=c
		b′=b		b′=c		b′=a
		0, 0, z		x, 0, 0		0, y, 0
27	p2mm	a′=a	p1m1	a′=b	p11m	$a′=\frac{1}{2}c$
		b′=b		$b′=\frac{1}{2}c$		b′=a
		0, 0, z		x, 0, 0		0, y, 0
39	p2mm	a′=a	p1m1	$a′=\frac{1}{2}b$	p11m	$a′=\frac{1}{2}c$
		$b′=\frac{1}{2}b$		$b′=\frac{1}{2}c$		b′=a
		0, 0, z		x, 0, 0		0, y, 0
42	p2mm	$a′=\frac{1}{2}a$	p1m1	$a′=\frac{1}{2}b$	p11m	$a′=\frac{1}{2}c$
		$b′=\frac{1}{2}b$		$b′=\frac{1}{2}c$		$b′=\frac{1}{2}a$
		0, 0, z		x, 0, 0		0, y, 0

Table 3. Parameters of the conventional unit cell.

	[001]	[100]	[010]
a'	3.621 Å	6.489 Å	4.971 Å
b'	6.496 Å	4.970 Å	3.623 Å

Fig. 3. HAADF images of Mn: (a) [110], (b) [111], (c) IFFT of (a), and (d) IFFT of (b).

Fig. 4. HAADF images of the π phase: (a) [001], (b) [110], and (c) [111].

Fig. 5. (a) Atomic projections of the space group I23 at the [001] zone axis, (b) atomic projection of the space group $I{{2}_{1}}3$ at the [001] zone axis (Wyckoff positions x = 0.1, y = 0.2, z = 0.3; x = y = z = 0).

Fig. 6. Atomic projections of space group 65 (Wyckoff positions: x = 0.1, y = 0.2, z = 0.5; x = y = z = 0).

Fig. 7. (a) and (b) Atomic projections of Fmmm and F222, respectively, at the [110] zone axis (Wyckoff positions: x = 0.1, y = 0.2, z = 0.3).

Fig. 8. Crystal structure model of OSCl4.

Fig. 9. Wyckoff positions: (a) 75, (b) 77, and (c) 81.

Fig. 10. Atomic projections of space groups 75, 77, and 81 at the [010] zone axis (Wyckoff position: x = 0, y = 0.5, z = 0.3).

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