# 1.1.3. Hexagonal (hex)



## Atom arrangement

 Figure 1: Hexagonal lattice structure.

## 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 $[\bar 1 \bar 1 2 0]$ $(0 0 0 1)$

 Figure 3: Prismatic slip system in hexagonal lattice: $\langle 1 1 \bar 2 0\rangle \{1 0 \bar 1 0\}$

 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 $[\bar 1 \bar 1 2 0]$ $(1 \bar 1 0 0)$

 Figure 4: 2nd order prismatic compound slip system in hexagonal lattice: $\langle \bar 1 1 0 0\rangle \{1 1 \bar 2 0\}$

 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 $[1 \bar 1 0 0]$ $(\bar 1 \bar 1 2 0)$

 Figure 5: 1st order pyramidal slip system in hexagonal lattice: $\langle 1 1 \bar 2 0\rangle \{1 0 \bar 1 1\}$

 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 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 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 $[1 1 \bar 2 3]$ $(\bar 1 \bar 1 2 2)$

## 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
svg 0_Indexation_topview.svg manage 456 bytes 23 May 2013 - 09:34 DavidMercier Indexation of the hexagonal unit cell
png HCP_crystal_structure.png manage 168 K 17 Oct 2012 - 17:21 PhilipEisenlohr Hexagonal lattice structure
svg HCP_crystal_structure.svg manage 2 K 17 Oct 2012 - 17:20 PhilipEisenlohr Hexagonal lattice structure (vector-based)
png HCP_slip_system_basal.png manage 175 K 17 Oct 2012 - 17:29 PhilipEisenlohr Hexagonal slip system basal
svg HCP_slip_system_basal.svg manage 3 K 17 Oct 2012 - 17:29 PhilipEisenlohr Hexagonal slip system basal (vector-based)
png HCP_slip_system_prism2nd_a.png manage 194 K 25 Jun 2013 - 10:33 DavidMercier Hexagonal slip system 2nd prismatic [a]
svg HCP_slip_system_prism2nd_a.svg manage 3 K 25 Jun 2013 - 10:33 DavidMercier Hexagonal slip system 2nd prismatic [a] (vector based)
png HCP_slip_system_prism_a.png manage 189 K 17 Oct 2012 - 17:40 PhilipEisenlohr Hexagonal slip system prismatic [a]
svg HCP_slip_system_prism_a.svg manage 3 K 17 Oct 2012 - 17:39 PhilipEisenlohr Hexagonal slip system prismatic [a] (vector-based)
png HCP_slip_system_pyramidal1st_a.png manage 199 K 17 Oct 2012 - 20:28 PhilipEisenlohr Hexagonal slip system 1st pyramidal [a]
svg HCP_slip_system_pyramidal1st_a.svg manage 3 K 17 Oct 2012 - 20:27 PhilipEisenlohr Hexagonal slip system 1st pyramidal [a] (vector-based)
png HCP_slip_system_pyramidal1st_c+a.png manage 203 K 17 Oct 2012 - 20:19 PhilipEisenlohr Hexagonal slip system 1st pyramidal [c+a]
svg 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)
png HCP_slip_system_pyramidal2nd_c+a.png manage 196 K 17 Oct 2012 - 20:46 PhilipEisenlohr Hexagonal slip system 2nd pyramidal [c+a]
svg 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)
png HCP_twin_system_compressive_K1(10-11).png manage 197 K 23 May 2013 - 09:59 DavidMercier Hexagonal twin system compressive K1(10-11)
svg HCP_twin_system_compressive_K1(10-11).svg manage 3 K 23 May 2013 - 10:00 DavidMercier Hexagonal twin system compressive K1(10-11) (vector based)
png HCP_twin_system_compressive_K1(11-22).png manage 196 K 23 May 2013 - 10:02 DavidMercier Hexagonal twin system compressive K1(11-22)
svg HCP_twin_system_compressive_K1(11-22).svg manage 3 K 23 May 2013 - 10:03 DavidMercier Hexagonal twin system compressive K1(11-22) (vector based)
png HCP_twin_system_tensile_K1(-1012).png manage 193 K 23 May 2013 - 12:16 DavidMercier Hexagonal twin system tensile K1(-1012)
svg HCP_twin_system_tensile_K1(-1012).svg manage 3 K 23 May 2013 - 12:16 DavidMercier Hexagonal twin system tensile K1(-1012) (vector-based)
png HCP_twin_system_tensile_K1(11-21).png manage 226 K 23 May 2013 - 11:53 DavidMercier Hexagonal twin system tensile K1(11-21)
svg 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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