1.1.3. Hexagonal (hex)

Atom arrangement

Figure 1: Hexagonal lattice structure.

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Slip systems

Figure 2: Basal slip system in hexagonal lattice: $\langle 1 1 \bar 2 0\rangle \{0 0 0 1\}$

index slip direction plane normal
1 $[2 \bar 1 \bar 1 0]$ $(0 0 0 1)$
2 $[\bar 1 2 \bar 1 0]$ $(0 0 0 1)$
3 $[\bar 1 \bar 1 2 0]$ $(0 0 0 1)$

index slip direction plane normal
4 $[2 \bar 1 \bar 1 0]$ $(0 1 \bar 1 0)$
5 $[\bar 1 2 \bar 1 0]$ $(\bar 1 0 1 0)$
6 $[\bar 1 \bar 1 2 0]$ $(1 \bar 1 0 0)$

index slip direction plane normal
7 $[0 1 \bar 1 0]$ $(2 \bar 1 \bar 1 0)$
8 $[\bar 1 0 1 0]$ $(\bar 1 2 \bar 1 0)$
9 $[1 \bar 1 0 0]$ $(\bar 1 \bar 1 2 0)$

index slip direction plane normal
10 $[2 \bar 1 \bar 1 0]$ $(0 1 \bar 1 1)$
11 $[\bar 1 2 \bar 1 0]$ $(\bar 1 0 1 1)$
12 $[\bar 1 \bar 1 2 0]$ $(1 \bar 1 0 1)$
13 $[1 1 \bar 2 0]$ $(\bar 1 1 0 1)$
14 $[\bar 2 1 1 0]$ $(0 \bar 1 1 1)$
15 $[1 \bar 2 1 0]$ $(1 0 \bar 1 1)$

Figure 6: 1st order pyramidal <c+a> slip system in hexagonal lattice: $\langle 1 1 \bar 2 3\rangle \{1 0 \bar 1 1\}$

index slip direction plane normal
16 $[2 \bar 1 \bar 1 3]$ $(\bar 1 1 0 1)$
17 $[1 \bar 2 1 3]$ $(\bar 1 1 0 1)$
18 $[\bar 1 \bar 1 2 3]$ $(1 0 \bar 1 1)$
19 $[\bar 2 1 1 3]$ $(1 0 \bar 1 1)$
20 $[\bar 1 2 \bar 1 3]$ $(0 \bar 1 1 1)$
21 $[1 1 \bar 2 3]$ $(0 \bar 1 1 1)$
22 $[\bar 2 1 1 3]$ $(1 \bar 1 0 1)$
23 $[\bar 1 2 \bar 1 3]$ $(1 \bar 1 0 1)$
24 $[1 1 \bar 2 3]$ $(\bar 1 0 1 1)$
25 $[2 \bar 1 \bar 1 3]$ $(\bar 1 0 1 1)$
26 $[1 \bar 2 1 3]$ $(0 1 \bar 1 1)$
27 $[\bar 1 \bar 1 2 3]$ $(0 1 \bar 1 1)$

Figure 7: 2nd order pyramidal <c+a> slip system in hexagonal lattice: $\langle 1 1 \bar 2 3\rangle \{1 1 \bar 2 2\}$

index slip direction plane normal
28 $[2 \bar 1 \bar 1 3]$ $(\bar 2 1 1 2)$
29 $[\bar 1 2 \bar 1 3]$ $(1 \bar 2 1 2)$
30 $[\bar 1 \bar 1 2 3]$ $(1 1 \bar 2 2)$
31 $[\bar 2 1 1 3]$ $(2 \bar 1 \bar 1 2)$
32 $[1 \bar 2 1 3]$ $(\bar 1 2 \bar 1 2)$
33 $[1 1 \bar 2 3]$ $(\bar 1 \bar 1 2 2)$

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Twin systems

Figure 8: $K_1$ $\langle 1 0 \bar 1 \bar 1\rangle$ - $n_1$ $\{1 0 \bar 1 2\}$ T1 - Tensile twinning in Co, Mg, Zr, Ti, and Be; compressive twinning in Cd and Zn.

$\eta_1$ $K_1$ $\eta_2$ $K_2$
$\langle \bar 1 0 1 1\rangle$ $\{1 0 \bar 1 2\}$ $\langle 1 0 \bar 1 1\rangle$ $\{1 0 \bar 1 \bar 2\}$

index slip direction plane normal
1 $[1 \bar 1 0 1]$ $(\bar 1 1 0 2)$
2 $[\bar 1 0 1 1]$ $(1 0 \bar 1 2)$
3 $[0 1 \bar 1 1]$ $(0 \bar 1 1 2)$
4 $[\bar 1 1 0 1]$ $(1 \bar 1 0 2)$
5 $[1 0 \bar 1 1]$ $(\bar 1 0 1 2)$
6 $[0 \bar 1 1 1]$ $(0 1 \bar 1 2)$

Figure 9: $K_1$ $\langle \bar 1 \bar 1 2 6\rangle$ - $n_1$ $\{1 1 \bar 2 1\}$ T2 - Tensile twinning in Co, Re, and Zr.

$\eta_1$ $K_1$ $\eta_2$ $K_2$
$\langle \bar 1 \bar 1 2 6\rangle$ $\{1 1 \bar 2 1\}$ $\langle 1 1 2 0\rangle$ $\{0 0 0 2\}$

index slip direction plane normal
7 $[2 \bar 1 \bar 1 6]$ $(\bar 2 1 1 1)$
8 $[\bar 1 2 \bar 1 6]$ $(1 \bar 2 1 1)$
9 $[\bar 1 \bar 1 2 6]$ $(1 1 \bar 2 1)$
10 $[\bar 2 1 1 6]$ $(2 \bar 1 \bar 1 1)$
11 $[1 \bar 2 1 6]$ $(\bar 1 2 \bar 1 1)$
12 $[1 1 \bar 2 6]$ $(\bar 1 \bar 1 2 1)$

Figure 10: $K_1$ $\langle 1 0 \bar 1 \bar 2\rangle$ - $n_1$ $\{1 0 \bar 1 1\}$ C1 - Compressive twinning in Mg.

$\eta_1$ $K_1$ $\eta_2$ $K_2$
$\langle 1 0 \bar 1 \bar 2\rangle$ $\{1 0 \bar 1 1\}$ $\langle 3 0 \bar 3 2\rangle$ $\{1 0 \bar 1 \bar 3\}$

index slip direction plane normal
13 $[\bar 1 1 0 \bar 2]$ $(\bar 1 1 0 1)$
14 $[1 0 \bar 1 \bar 2]$ $(1 0 \bar 1 1)$
15 $[0 \bar 1 1 \bar 2]$ $(0 \bar 1 1 1)$
16 $[1 \bar 1 0 \bar 2]$ $(1 \bar 1 0 1)$
17 $[\bar 1 0 1 \bar 2]$ $(\bar 1 0 1 1)$
18 $[0 1 \bar 1 \bar 2]$ $(0 1 \bar 1 1)$

Figure 11: $K_1$ $\langle 1 1 \bar 2 \bar 3\rangle$ - $n_1$ $\{1 1 \bar 2 2\}$ C2 - Compressive twinning in Ti and Zr.

$\eta_1$ $K_1$ $\eta_2$ $K_2$
$\langle 1 1 \bar 2 \bar 3\rangle$ $\{1 1 \bar 2 2\}$ $\langle 2 2 \bar 4 3\rangle$ $\{1 1 \bar 2 \bar 4\}$

index slip direction plane normal
19 $[2 \bar 1 \bar 1 \bar 3]$ $(2 \bar 1 \bar 1 2)$
20 $[\bar 1 2 \bar 1 \bar 3]$ $(\bar 1 2 \bar 1 2)$
21 $[\bar 1 \bar 1 2 \bar 3]$ $(\bar 1 \bar 1 2 2)$
22 $[\bar 2 1 1 \bar 3]$ $(\bar 2 1 1 2)$
23 $[1 \bar 2 1 \bar 3]$ $(1 \bar 2 1 2)$
24 $[1 1 \bar 2 \bar 3]$ $(1 1 \bar 2 2)$

Topic attachments
I Attachment Action Size Date Who Comment
0_Indexation_topview.svgsvg 0_Indexation_topview.svg manage 456 bytes 23 May 2013 - 09:34 DavidMercier Indexation of the hexagonal unit cell
HCP_crystal_structure.pngpng HCP_crystal_structure.png manage 168 K 17 Oct 2012 - 17:21 PhilipEisenlohr Hexagonal lattice structure
HCP_crystal_structure.svgsvg HCP_crystal_structure.svg manage 2 K 17 Oct 2012 - 17:20 PhilipEisenlohr Hexagonal lattice structure (vector-based)
HCP_slip_system_basal.pngpng HCP_slip_system_basal.png manage 175 K 17 Oct 2012 - 17:29 PhilipEisenlohr Hexagonal slip system basal
HCP_slip_system_basal.svgsvg HCP_slip_system_basal.svg manage 3 K 17 Oct 2012 - 17:29 PhilipEisenlohr Hexagonal slip system basal (vector-based)
HCP_slip_system_prism2nd_a.pngpng HCP_slip_system_prism2nd_a.png manage 194 K 25 Jun 2013 - 10:33 DavidMercier Hexagonal slip system 2nd prismatic [a]
HCP_slip_system_prism2nd_a.svgsvg HCP_slip_system_prism2nd_a.svg manage 3 K 25 Jun 2013 - 10:33 DavidMercier Hexagonal slip system 2nd prismatic [a] (vector based)
HCP_slip_system_prism_a.pngpng HCP_slip_system_prism_a.png manage 189 K 17 Oct 2012 - 17:40 PhilipEisenlohr Hexagonal slip system prismatic [a]
HCP_slip_system_prism_a.svgsvg HCP_slip_system_prism_a.svg manage 3 K 17 Oct 2012 - 17:39 PhilipEisenlohr Hexagonal slip system prismatic [a] (vector-based)
HCP_slip_system_pyramidal1st_a.pngpng HCP_slip_system_pyramidal1st_a.png manage 199 K 17 Oct 2012 - 20:28 PhilipEisenlohr Hexagonal slip system 1st pyramidal [a]
HCP_slip_system_pyramidal1st_a.svgsvg HCP_slip_system_pyramidal1st_a.svg manage 3 K 17 Oct 2012 - 20:27 PhilipEisenlohr Hexagonal slip system 1st pyramidal [a] (vector-based)
HCP_slip_system_pyramidal1st_c+a.pngpng HCP_slip_system_pyramidal1st_c+a.png manage 203 K 17 Oct 2012 - 20:19 PhilipEisenlohr Hexagonal slip system 1st pyramidal [c+a]
HCP_slip_system_pyramidal1st_c+a.svgsvg HCP_slip_system_pyramidal1st_c+a.svg manage 3 K 17 Oct 2012 - 20:19 PhilipEisenlohr Hexagonal slip system 1st pyramidal [c+a] (vector-based)
HCP_slip_system_pyramidal2nd_c+a.pngpng HCP_slip_system_pyramidal2nd_c+a.png manage 196 K 17 Oct 2012 - 20:46 PhilipEisenlohr Hexagonal slip system 2nd pyramidal [c+a]
HCP_slip_system_pyramidal2nd_c+a.svgsvg HCP_slip_system_pyramidal2nd_c+a.svg manage 3 K 17 Oct 2012 - 20:46 PhilipEisenlohr Hexagonal slip system 2nd pyramidal [c+a] (vector-based)
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HCP_twin_system_compressive_K1(11-22).pngpng HCP_twin_system_compressive_K1(11-22).png manage 196 K 23 May 2013 - 10:02 DavidMercier Hexagonal twin system compressive K1(11-22)
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HCP_twin_system_tensile_K1(-1012).pngpng HCP_twin_system_tensile_K1(-1012).png manage 193 K 23 May 2013 - 12:16 DavidMercier Hexagonal twin system tensile K1(-1012)
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HCP_twin_system_tensile_K1(11-21).pngpng HCP_twin_system_tensile_K1(11-21).png manage 226 K 23 May 2013 - 11:53 DavidMercier Hexagonal twin system tensile K1(11-21)
HCP_twin_system_tensile_K1(11-21).svgsvg HCP_twin_system_tensile_K1(11-21).svg manage 3 K 23 May 2013 - 11:53 DavidMercier Hexagonal twin system tensile K1(11-21) (vector-based)
This topic: Documentation > Background > CrystalLattice > Hex
Topic revision: 12 Feb 2019, PhilipEisenlohr
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