Hexagonal (hP)

Atom arrangement

Figure 1: Hexagonal lattice structure. X, Y, and Z crystal frame axes are colored red, green, and blue, respectively.

Slip systems

\(\textnormal{index}\)
\(\textnormal{slip direction}\)
\(\textnormal{plane normal}\)
\(1\)\([2 \bar 1 \bar 1 0]\)\((0 0 0 1)\)
\(2\)\([\bar 1 2 \bar 1 0]\)\((0 0 0 1)\)
\(3\)\([\bar 1 \bar 1 2 0]\)\((0 0 0 1)\)
basal slip system

Figure 2: \(⟨1 1 \bar 2 0⟩\{0 0 0 1\}\) basal slip system

\(\textnormal{index}\)
\(\textnormal{slip direction}\)
\(\textnormal{plane normal}\)
\(4\)\([2 \bar 1 \bar 1 0]\)\((0 \bar 1 \bar 1 0)\)
\(5\)\([\bar 1 2 \bar 1 0]\)\((\bar 1 0 0 1)\)
\(6\)\([\bar 1 \bar 1 2 0]\)\((1 \bar 1 0 0)\)
Prismatic slip system

Figure 3: \(⟨1 1 \bar 2 0⟩\{1 \bar 1 0 0\}\) prismatic slip system

\(\textnormal{index}\)
\(\textnormal{slip direction}\)
\(\textnormal{plane normal}\)
\(7\)\([0 1 \bar 1 0]\)\((2 \bar 1 \bar 1 0)\)
\(8\)\([\bar 1 0 1 0]\)\((\bar 1 2 \bar 1 0)\)
\(9\)\([1 \bar 1 0 0]\)\((\bar 1 \bar 1 2 0)\)
2nd order prismatic compound slip system

Figure 4: \(⟨\bar 1 1 0 0⟩\{1 1 \bar 2 0\}\) 2nd order prismatic compound slip system

\(\textnormal{index}\)
\(\textnormal{slip direction}\)
\(\textnormal{plane normal}\)
\(10\)\([2 \bar 1 \bar 1 0]\)\((0 1 \bar 1 1)\)
\(11\)\([\bar 1 2 \bar 1 0]\)\((\bar 1 0 1 1)\)
\(12\)\([\bar 1 \bar 1 2 0]\)\((1 \bar 1 0 1)\)
\(13\)\([1 1 \bar 2 0]\)\((\bar 1 1 0 1)\)
\(14\)\([\bar 2 1 1 0]\)\((0 \bar 1 1 1)\)
\(15\)\([1 \bar 2 1 0]\)\((1 0 \bar 1 1)\)
1st order pyramidal slip system

Figure 5: \(⟨1 1 \bar 2 0⟩\{1 0 \bar 1 1\}\) 1st order pyramidal slip system

\(\textnormal{index}\)
\(\textnormal{slip direction}\)
\(\textnormal{plane normal}\)
\(16\)\([2 \bar 1 \bar 1 3]\)\((\bar 1 1 0 1)\)
\(17\)\([\bar 1 2 \bar 1 3]\)\((\bar 1 1 0 1)\)
\(18\)\([\bar 1 \bar 1 2 3]\)\((1 0 \bar 1 1)\)
\(19\)\([\bar 2 1 1 3]\)\((1 0 \bar 1 1)\)
\(20\)\([\bar 1 2 \bar 1 3]\)\((0 1 \bar 1 1)\)
\(21\)\([1 1 \bar 2 3]\)\((0 \bar 1 1 1)\)
\(22\)\([2 \bar 1 \bar 1 3]\)\((1 \bar 1 0 1)\)
\(23\)\([\bar 1 2 \bar 1 3]\)\((1 \bar 1 0 1)\)
\(24\)\([1 1 \bar 2 3]\)\((\bar 1 0 1 1)\)
\(25\)\([2 \bar 1 \bar 1 3]\)\((\bar 1 0 1 1)\)
\(26\)\([1 \bar 2 1 3]\)\((0 1 \bar 1 1)\)
\(27\)\([\bar 1 \bar 1 2 3]\)\((0 1 \bar 1 1)\)
1st order pyramidal <c+a> slip system

Figure 6: \(⟨1 1 \bar 2 3⟩\{1 0 \bar 1 1\}\) 1st order pyramidal <c+a> slip system

\(\textnormal{index}\)
\(\textnormal{slip direction}\)
\(\textnormal{plane normal}\)
\(28\)\([2 \bar 1 \bar 1 3]\)\((\bar 2 1 1 2)\)
\(29\)\([\bar 1 2 \bar 1 3]\)\((1 \bar 2 1 2)\)
\(30\)\([\bar 1 \bar 1 2 3]\)\((1 1 \bar 2 2)\)
\(31\)\([\bar 2 1 1 3]\)\((2 \bar 1 \bar 1 2)\)
\(32\)\([1 \bar 2 1 3]\)\((\bar 1 2 \bar 1 2)\)
\(33\)\([1 1 \bar 2 3]\)\((\bar 1 \bar 1 2 2)\)
2nd order pyramidal <c+a> slip system

Figure 7: \(⟨1 1 \bar 2 3⟩\{1 1 \bar 2 2\}\) 2nd order pyramidal <c+a> slip system

Twin systems

\(η_1\)
\(K_1\)
\(η_2\)
\(K_2\)
\(⟨\bar 1 0 1 1⟩\)\(\{1 0 \bar 1 2\}\)\(⟨1 0 \bar 1 1⟩\)\(\{1 0 \bar 1 \bar 2\}\)
\(\textnormal{index}\)
\(\textnormal{slip direction}\)
\(\textnormal{plane normal}\)
\(1\)\([1 \bar 1 0 1]\)\((\bar 1 1 0 2)\)
\(2\)\([\bar 1 0 1 1]\)\((1 0 \bar 1 2)\)
\(3\)\([0 1 \bar 1 1]\)\((0 \bar 1 1 2)\)
\(4\)\([\bar 1 1 0 1]\)\((1 \bar 1 0 2)\)
\(5\)\([1 0 \bar 1 1]\)\((\bar 1 0 1 2)\)
\(6\)\([0 \bar 1 1 1]\)\((0 1 \bar 1 2)\)
twin system

Figure 8: \(⟨\bar 1 0 1 1⟩ \{1 0 \bar 1 2\}\) T1 tensile twinning in Co, Mg, Zr, Ti, and Be; compressive twinning in Cd and Zn.

\(η_1\)
\(K_1\)
\(η_2\)
\(K_2\)
\(⟨\bar 1 \bar 1 2 6⟩\)\(\{1 1 \bar 2 1\}\)\(⟨1 1 2 0⟩\)\(\{0 0 0 2\}\)
\(\textnormal{index}\)
\(\textnormal{slip direction}\)
\(\textnormal{plane normal}\)
\(7\)\([2 \bar 1 \bar 1 6]\)\((\bar 2 1 1 1)\)
\(8\)\([\bar 1 2 \bar 1 6]\)\((1 1 \bar 2 1)\)
\(9\)\([\bar 1 \bar 1 2 6]\)\((2 \bar 1 \bar 1 1)\)
\(10\)\([\bar 2 1 1 6]\)\((\bar 1 2 \bar 1 1)\)
\(11\)\([1 \bar 2 1 6]\)\((\bar 1 0 1 2)\)
\(12\)\([1 1 \bar 2 6]\)\((\bar 1 \bar 1 2 1)\)
twin system

Figure 9: \(⟨\bar 1 \bar 1 2 6⟩ \{1 1 \bar 2 1\}\) T2 tensile twinning in Co, Re, and Zr.

\(η_1\)
\(K_1\)
\(η_2\)
\(K_2\)
\(⟨1 0 \bar 1 \bar 2⟩\)\(\{1 0 \bar 1 1\}\)\(⟨3 0 \bar 3 2⟩\)\(\{1 0 \bar 1 \bar 3\}\)
\(\textnormal{index}\)
\(\textnormal{slip direction}\)
\(\textnormal{plane normal}\)
\(13\)\([\bar 1 1 0 \bar 2]\)\((\bar 1 1 0 1)\)
\(14\)\([1 0 \bar 1 \bar 2]\)\((1 0 \bar 1 1)\)
\(15\)\([0 \bar 1 1 \bar 2]\)\((0 \bar 1 1 1)\)
\(16\)\([1 \bar 1 0 \bar 2]\)\((1 \bar 1 0 1)\)
\(17\)\([\bar 1 0 1 \bar 2]\)\((\bar 1 0 1 1)\)
\(18\)\([0 1 \bar 1 \bar 2]\)\((0 1 \bar 1 1)\)
twin system

Figure 10: \(⟨1 0 \bar 1 \bar 2⟩ \{1 0 \bar 1 1\}\) C1 compressive twinning in Mg.

\(η_1\)
\(K_1\)
\(η_2\)
\(K_2\)
\(⟨1 1 \bar 2 \bar 3⟩\)\(\{1 1 \bar 2 2\}\)\(⟨2 2 \bar 4 3⟩\)\(\{1 1 \bar 2 \bar 4\}\)
\(\textnormal{index}\)
\(\textnormal{slip direction}\)
\(\textnormal{plane normal}\)
\(19\)\([2 \bar 1 \bar 1 \bar 3]\)\((2 \bar 1 \bar 1 2)\)
\(20\)\([\bar 1 2 \bar 1 \bar 3]\)\((\bar 1 2 \bar 1 2)\)
\(21\)\([\bar 1 \bar 1 2 \bar 3]\)\((\bar 1 \bar 1 2 2)\)
\(22\)\([\bar 2 1 1 \bar 3]\)\((\bar 2 1 1 2)\)
\(23\)\([1 \bar 2 1 \bar 3]\)\((1 \bar 2 1 2)\)
\(24\)\([1 1 \bar 2 \bar 3]\)\((1 1 \bar 2 2)\)
twin system

Figure 11: \(⟨1 1 \bar 2 \bar 3⟩ \{1 1 \bar 2 2\}\) C2 compressive twinning in Ti and Zr.