Fm-3m (225) Space Group

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Fm-3m (225) Space Group

Table 3025a. Fm-3m (225) space group.

Name in the International Tables for Crystallography	Fm-3m	Lattice type	F
Patterson space group	225	Point group	m-3m
Crystal system	Cubic	Laue class	m-3m
Pearson symbol	cF12, cF8, etc.	Number of symmetry operators	192
Structure type	NaCl-type structure	d-spacing ratios of allowed Bragg reflections	1, √3, √4, √8, √11, √12, √16, √19, √20, √24, √27, ...
Symmetry (atomic coordinates)	X, Y, Z; -X, -Y, Z; -X, Y, -Z; X, -Y, -Z; Z, X, Y; Z, -X, -Y; -Z, -X, Y; -Z, X, -Y; Y, Z, X; -Y, Z, -X; Y, -Z, -X; -Y, -Z, X; Y, X, -Z; -Y, -X, -Z; Y, -X, Z; -Y, X, Z; X, Z, -Y; -X, Z, Y; -X, -Z, -Y; X, -Z, Y; Z, Y, -X; Z, -Y, X; -Z, Y, X; -Z, -Y, -X; -X, -Y, -Z; X, Y, -Z; X, -Y, Z; -X, Y, Z; -Z, -X, -Y; -Z, X, Y; Z, X, -Y; Z, -X, Y; -Y, -Z, -X; Y, -Z, X; -Y, Z, X; Y, Z, -X; -Y, -X, Z; Y, X, Z; -Y, X, -Z; Y, -X, -Z; -X, -Z, Y; X, -Z, -Y; X, Z, Y; -X, Z, -Y; -Z, -Y, X; -Z, Y, -X; Z, -Y, -X; Z, Y, X; X, 1/2+Y, 1/2+Z; -X, 1/2-Y, 1/2+Z; -X, 1/2+Y, 1/2-Z; X, 1/2-Y, 1/2-Z; Z, 1/2+X, 1/2+Y; Z, 1/2-X, 1/2-Y; -Z, 1/2-X, 1/2+Y; -Z, 1/2+X, 1/2-Y; Y, 1/2+Z, 1/2+X; -Y, 1/2+Z, 1/2-X; Y, 1/2-Z, 1/2-X; -Y, 1/2-Z, 1/2+X; Y, 1/2+X, 1/2-Z; -Y, 1/2-X, 1/2-Z; Y, 1/2-X, 1/2+Z; -Y, 1/2+X, 1/2+Z; X, 1/2+Z, 1/2-Y; -X, 1/2+Z, 1/2+Y; -X, 1/2-Z, 1/2-Y; X, 1/2-Z, 1/2+Y; Z, 1/2+Y, 1/2-X; Z, 1/2-Y, 1/2+X; -Z, 1/2+Y, 1/2+X; -Z, 1/2-Y, 1/2-X; -X, 1/2-Y, 1/2-Z
Crystal examples	CaF₂: Ca at (0, 0, 0) and F at (1/4, 1/4, 1/4). NaCl: Na at (0, 0, 0) and Cl at (1/2, 1/2, 1/2). TiN: Ti (1a) at (0, 0, 0), and N (1b) at (0, 0.5, 0) Crystals in Figure 3025b.

$Typical example of X-ray powder diffraction pattern obtained from Fm-3m structures (AgPb6SbTe8, AgPb12SbTe14, AgPb18SbTe20, Ag0.86Pb18SbTe20, AgSbTe2, and PbTe compounds)$

Figure 3025a. Typical example of X-ray powder diffraction patterns obtained from Fm-3m single-phase structures (AgPb₆SbTe₈, AgPb₁₂SbTe₁₄, AgPb₁₈SbTe₂₀, Ag_0.86Pb₁₈SbTe₂₀, AgSbTe₂, and PbTe compounds). [1] Note that we can index diffraction patterns starting from comparing experimental d-spacings and theoretical calculations obtained from known lattice parameters, for instance, use the excel file for crystals with Fm-3m space group.

	$A [001] diffraction pattern obtained from Ag0.95Pb15SbTe17 (space group: Fm-3m)$	$Electron diffraction pattern obtained from [001] Ag0.95Pb15SbTe17 (space group: Fm-3m) with splitting of electron reflections$
[0 0 1] Ag_0.95Pb₁₅SbTe₁₇. (a = 0.64 nm) [1]	[0 0 1] Ag_0.95Pb₁₅SbTe₁₇ with diffuse streaks. [1]	[001] Ag_0.95Pb₁₅SbTe₁₇ with splitting of electron reflections. [1]

[0 0 1] Ge₂Bi₂Te₅. [3]	4mm net symmetry in ZOLZ [001] zone-axis of Zr₄₁Ti₁₄Cu_12.5Ni₁₀Be_22.5 ( a = 1.185 nm) [4]
	$indexed electron diffraction patterns of FCC crystals$
[0 1 1] Ag_0.95Pb₁₅SbTe₁₇. (a = 0.64 nm) [1]	[1 1 0] Ge₂Sb₂Te₅ (GST). [2]	[1 1 0] Ge₂Bi₂Te₅. [3]
$Indexed Electron Diffraction Patterns of FCC Crystals GST$
[-1 1 1] Ge₂Sb₂Te₅ (GST). [2]	[1 1 1] Ag_0.95Pb₁₅SbTe₁₇. (a = 0.64 nm) [1]

[-1 1 2] Ag_0.95Pb₁₅SbTe₁₇. (a = 0.64 nm) [1]

Figure 3025b. Examples of indexed electron diffraction (or FFT) patterns of Fm-3m (225) cubic crystals.

[1] Eric Quarez, Kuei-Fang Hsu, Robert Pcionek, N. Frangis, E. K. Polychroniadis, and Mercouri G. Kanatzidis, Nanostructuring, Compositional Fluctuations, and Atomic Ordering in the Thermoelectric Materials AgPbmSbTe2+m. The Myth of Solid Solutions, J. AM. CHEM. SOC. 127, 9177-9190, 2005.
[2] J.J. Zhao, F.R. Liu, X.X. Han, Z. Zhu, X. Lin, F. Liu, N.X. Sun, Transmission electron microscopy study of amorphous Ge2Sb2Te5films induced by an ultraviolet single-pulse laser, Applied Surface Science 311 (2014) 83–88.
[3] Chang Woo Sun, A Transmission Electron Microscopy Study on the Microstructural Properties of Te-based Chalcogenide Thin Films, Doctoral Thesis, 2010.
[4] Q. Wei, N. Wanderka, P. Schubert-Bischoff, and M-P. Macht, S. Friedrich, Crystallization phases of the Zr41Ti14Cu12.5Ni10Be22.5 alloy after slow solidification, J. Mater. Res., 15 (8) 1729, (2000).

Practical Electron Microscopy and Database

An Online Book, Second Edition by Dr. Yougui Liao (2006)

Fm-3m (225) Space Group