Table 1 Crystallographic elements and parameters of twin systems in hcp metals

From: Atomic structures of twin boundaries in hexagonal close-packed metallic crystals with particular focus on Mg

TPa

TDb \(\overrightarrow{b}\)

\(|\frac{1}{2}\overrightarrow{b}|\)

d

\(d/|\frac{1}{2}\overrightarrow{b}|\)

\(\{10\bar{1}1\}\)

\(\frac{1}{2}\langle 10\bar{1}2\rangle\)

\(\frac{a}{2}\sqrt{\frac{3}{4}+{x}^{2}}\) (0.92\(a\))

\(a\frac{x}{2\sqrt{3}\sqrt{4{x}^{2}+3}}\) (0.13\(a\))

\(\frac{2x}{\sqrt{3}(4{x}^{2}+3)}\)

\(\{10\bar{1}2\}\)

\(\langle 10\bar{1}1\rangle\)

\(\frac{a}{2}\sqrt{3+{x}^{2}}\) (1.19\(a\))

\(a\frac{x}{2\sqrt{3{x}^{2}+9}}\) (0.20\(a\))

\(\frac{x}{\sqrt{3}({x}^{2}+3)}\)

  1. The parameter a is the lattice constant, x = c/a. Data for Mg are given in brackets
  2. a TP twinning plane
  3. b TD twinning direction
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