Table 3095a. P-3m1 (164) space group.

Table 3095b. Examples of materials with P-3m1 (164) space group.

	Parameters
Angles	α = 90.0°; β = 90.0°; γ = 120.0°
Material	Ba3NiNb2O9 [3]
Lattice parameters	a = b = 5.7550(5) Å; c = 7.0656(2) Å
XRD pattern	The (112) and (103) peaks in the inset indicates 1:2 ordering of B site ions (-Ni-Nb-Nb-)
HAADF Z-contrast	The intensities of the Nb and Ni atom columns in [010] direction shows the -Ni-Nb-Nb- ordering. Brightest contrast: Ba (Z=88); brighter contrast: Nb (Z = 73); weak contrast: Ni (Z=46).
Material	CaAl2Si2 [1]
Structure with AlSi4 trigonal pyramids and CaSi6 trigonal antiprisms (refer to MgAl2Ge2 below)
Material	K3Na(CrO4)2
Lattice parameters	a = b = 5.858 Å; c = 7.523 Å
Material	Mg(OH)2
Lattice parameters	a = b = 3.1420 Å; c = 4.7660 Å
Material	(K,Na)3Na(SO4)2 (aphthitalite)
Lattice parameters	a = b = 5.68 Å; c = 7.31 Å
Material	MgAl2Ge2 [1]
Lattice parameters	a = b = 4.11693(5) Å; c = 6.7873(1) Å
Cell volume V	99.627(3) Å3
Atomic coordinates	Mg: Wyckoff position = 1a, x = 0, y = 0, z = 0; Al: Wyckoff position = 2d, x = ⅓, y = ⅔, z = 0.6353(3); Ge: Wyckoff position = 2d, x = ⅓, y = ⅔, z = 0.2419(2)
Interatomic distances and coordination polyhedra	Atoms   δ (Å) Polyhedron Mg -6 Ge 2.8888(8) Al -3 Ge -1 Ge 2.5188(8) 2.6701(24) Ge -3 Al -1 Al -3 Mg 2.5188(8) 2.6701(24) 2.8888(8)
Material	α-Zr2N2S [2]
Lattice parameters	a = b = 3.605(2) Å; c = 6.412(3) Å
HRTEM	Inset: 0 0 1 zone axis electron diffraction pattern in hexagonal symmetry without superstructure reflections

For hcp crystals, the (0 0 0 l) reflections, e.g. for the case with 164 (P-3m1) space group, are forbidden when l is odd. However, those reflection positions often show diffraction intensity, which is probably caused by chemical order on the basal planes, or by double or multiple diffraction (scattering).

For [0 1 -1 0] Sb₃Te₂ in Figure 3095a, the ratio of AB/CD is the layer number (N) in a unit cell. We can know the Sb₃Te₂ crystal belongs to the P-3m1 space group as N is 9, a multiple of 3. 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 P-3m1 space group.

[0001] η-phase Cu3Si [7] (a = 4.06Å and c = 7.33Å)
[0 1 -1 0] Ge2Bi2Te5. [4]	[0 1 -1 0] Sb3Te2. [4]
[-1 2 -1 0] Ge2Bi2Te5. [4]	[2 -1 -1 0] Ge2Bi2Te5 (space group p-3m1) [4]	[2 -1 -1 0] Ge2Bi2Te5. [4]
[1 1 -2 0] Ge1Sb2Te4. [5]	[1 1 -2 0] Ge1Sb2Te4. [6] (a' = 0.425 nm and c' = 4.10 nm)	[1 1 -2 0] Ge3Sb2Te6. [6] (a' = 0.425 nm and c' = 6.26 nm)
[1 1 -2 0] Ge2Sb2Te5. [6] (a' = 0.425 nm and c' = 1.827 nm)
[3 -3 0 1] η-phase Cu3Si [7] (a = 4.06Å and c = 7.33Å)
[1 4 -11 1] Ge2Bi2Te5. [4]	[1 0 -10 -1] Ge2Bi2Te5. [4]

Figure 3095a. Examples of indexed electron diffraction (or FFT) patterns of 164 (P-3m1) HCP crystals.

[1] Svitlana Pukas, Liliya Pylypchak, Oksana Matselko, Pavlo Demchenko, Roman Gladyshevskii, MgAl2Ge2 – a new representative of the structure type CaAl2Si2, Chem. Met. Alloys 5 (2012) 59-65.
[2] Chad Alan Stoltz, Synthesis of Layered Group IV Nitride Materials by Soft Chemical Anion Metathesis, thesis, 2005.
[3] Jungmin Hwang, Magnetoelectric and Multiferroic Properties in Layered 3d Transition Metal Oxides, thesis, 2012.
[4] Chang Woo Sun, A Transmission Electron Microscopy Study on the Microstructural Properties of Te-based Chalcogenide Thin Films, Doctoral Thesis, 2010.
[5] Enzo Rotunno, Advanced analytical transmission electron microscopy methodologies for the study of the chemical and physical properties of semiconducting nanostructures, Doctoral Thesis, 2014.
[6] B. J. Kooi and J. Th. M. De Hosson, Electron diffraction and high-resolution transmission electron microscopy of the high temperature crystal structures of GexSb2Te3+x („x = 1, 2, 3…) phase change material, J. Appl. Phys.92 (7), 3584 (2002). 
[7] Cheng-Yen Wen & Frans Spaepen, In-situ electron microscopy of the phases of Cu3Si, Philosophical Magazine, 87(35), 5581-5599, 2007.