$\alpha$–U ($A20$) Structure: A_oC4_63_c

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Prototype : $\alpha$–U
AFLOW prototype label : A_oC4_63_c
Strukturbericht designation : $A20$
Pearson symbol : oC4
Space group number : 63
Space group symbol : $\mbox{Cmcm}$
AFLOW prototype command : aflow --proto=A_oC4_63_c
--params=
$a$,$b/a$,$c/a$,$y_{1}$


Other elements and compounds with this structure

  • Tb, Dy, Ge (metastable), AgCd (random alloy), γ–Ti

  • Using data for the $\alpha$–U structure at 4.2K. (Vohra, 2001) showed that at pressures above 116 GPa titanium transforms from the hexagonal omega ($C32$) phase to this phase. This structure was studied by (Wentzcovitch, 1987) as a possible pathway for the pressure-induced transformation of magnesium from the hcp ($A3$) to the bcc ($A2$) phase. Much like the trigonal omega phase ($C6$), we can generate several high-symmetry structures from this phase by the appropriate choice of parameters. \[ \begin{array}{cp{2.0cm}p{2.0cm}p{2.0cm}p{2.0cm}} \mbox{$\textbf{Lattice parameter}$} & \mbox{$\textbf{hcp}$} & \mbox{$\textbf{bcc}$} & \mbox{$\textbf{fcc}$} & \mbox{$\textbf{simple cubic}$} \\ a & a_{hcp} & a_{bcc} & a_{fcc} & a_{sc} \\ b & \sqrt{3}a_{hcp} & \sqrt{2}a_{bcc} & a_{fcc} & a_{sc} \\ c & c_{hcp} & \sqrt{2}a_{bcc} & a_{fcc} & 2a_{sc} \\ y & \frac{1}{6} & \frac{1}{4} & \frac{1}{4} & 0 \\ \mbox{$\textit{Strukturbericht}$} & A3 & A2 & A1 & A_{h} \\ \mbox{Pearson symbol} & \mbox{hP2} & \mbox{cI2} & \mbox{cF4} & \mbox{cP1} \\ \mbox{Space group} & \mbox{P6$_{3}$/mmc} & \mbox{Im$\bar{3}$m} & \mbox{Fm$\bar{3}$m} & \mbox{Pm$\bar{3}$m} \\ \end{array} \]

Base-centered Orthorhombic primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac12 \, b \, \mathbf{\hat{y}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, b \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \, \mathbf{\hat{z}} \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\& & & & & & \\ \mathbf{B}_{1} & =& - y_{1} \, \mathbf{a}_{1} + y_{1} \, \mathbf{a}_{2} + \frac14 \, \mathbf{a}_{3}& =& y_{1} \, b \, \mathbf{\hat{y}} + \frac14 \, c \mathbf{\hat{z}}& \left(4c\right) & \mbox{U} \\ \mathbf{B}_{2} & =& y_{1} \, \mathbf{a}_{1} - y_{1} \, \mathbf{a}_{2} + \frac34 \, \mathbf{a}_{3}& =& - y_{1} \, b \, \mathbf{\hat{y}} + \frac34 \, c \mathbf{\hat{z}}& \left(4c\right) & \mbox{U} \\ \end{array} \]

References

  • C. S. Barrett, M. H. Mueller, and R. L. Hitterman, Crystal Structure Variations in Alpha Uranium at Low Temperatures, Phys. Rev. 129, 625–629 (1963), doi:10.1103/PhysRev.129.625.
  • Y. K. Vohra and P. T. Spencer, Novel gamma–Phase of Titanium Metal at Megabar Pressures, Phys. Rev. Lett. 86, 3068–3071 (2001), doi:10.1103/PhysRevLett.86.3068.
  • R. M. Wentzcovitch and M. L. Cohen, Theoretical model for the hcp–bcc transition in Mg, Phys. Rev. B 37, 5571–5576 (1988), doi:10.1103/PhysRevB.37.5571.

Geometry files


Prototype Generator

aflow --proto=A_oC4_63_c --params=

Species:

Running:

Output: