α-U ($A20$) Structure: A_oC4_63_c-001
Other compounds with this structure
Bk, Ce, Cf, Cm, Dy, Ge (metastable), Tb, γ-Ti, AgCd (random alloy)
- Uranium has two temperature-driven structural phase transitions (Donohue, 1974):
- Below 662$^\circ$C it is in the ground state $\alpha$–U structure ($A20$). (this structure)
- In the range 662-772$^\circ$C it is in the $\beta$–U structure ($A_{b}$).
- Above 772$^\circ$C to the melting point at 1135$^\circ$C it is in the body-centered cubic structure ($A2$).
- We show 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 with the appropriate choice of parameters:
Lattice Parameter hcp bcc fcc Simple Cubic $a$ $a_{hcp}$ $a_{bcc}$ $a_{fcc}$ $\sqrt{2}a_{sc}$ $b$ $\sqrt{3}a_{hcp}$ $\sqrt{2}a_{bcc}$ $a_{fcc}$ $\sqrt{2}a_{sc}$ $c$ $c_{hcp}$ $\sqrt{2}a_{bcc}$ $a$ $2 a_{sc}$ $y$ $\frac16$ $\frac14$ $\frac14$ 0 Strukturbericht $A3$ $A2$ $A1$ $A_{h}$ Pearson Symbol hP2 cI2 cF4 cP1 Space group $P6_{3}/mmc$ $Im\overline{3}m$ $Fm\overline{3}m$ $Pm\overline{3}m$ Number 194 229 225 221
(This corrects the values of $a$ and $b$ for the simple cubic structure published in (Mehl, 2017).)
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $- y_{1} \, \mathbf{a}_{1}+y_{1} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $b y_{1} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4c) | U I |
| $\mathbf{B_{2}}$ | = | $y_{1} \, \mathbf{a}_{1}- y_{1} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- b y_{1} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4c) | U I |
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.
- J. Donohue, The Structures of the Elements (Robert E. Krieger Publishing Company, New York, 1974).
- Y. K. Vohra and P. T. Spencer, Novel γ-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.
- M. J. Mehl, D. Hicks, C. Toher, O. Levy, R. M. Hanson, G. Hart, and S. Curtarolo, The AFLOW library of crystallographic prototypes: part 1, Comput. Mater. Sci. 136, S1–S828 (2017), doi:10.1016/j.commatsci.2017.01.017.
First cited in
- M. J. Mehl, D. Hicks, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 1, Comp. Mat. Sci. 136, S1-S828 (2017). (doi=10.1016/j.commatsci.2017.01.017)
Geometry files
Prototype Generator
aflow --proto=A_oC4_63_c --params=$a,b/a,c/a,y_{1}$