Hexagonal high-temperature tridymite AlPO$_{4}$: AB4C_hP12_186_b_bc_b-001
| Prototype | AlO$_{4}$P |
| AFLOW prototype label | AB4C_hP12_186_b_bc_b-001 |
| ICSD | 279582 |
| CCDC | 1720706 |
| Pearson symbol | hP12 |
| Space group number | 186 |
| Space group symbol | $P6_3mc$ |
| AFLOW prototype command |
aflow --proto=AB4C_hP12_186_b_bc_b-001
--params=$a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak z_{2}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak z_{4}$ |
- The tridymite form of AlPO$_{4}$ is related to the tridymite forms of SiO$_{2}$. Like SiO$_{2}$ it undergoes a series of temperature driven phase transitions (Graetsch, 2002):
- The high temperature form is hexagonal, space group $P6_3mc$ #186 at temperatures above ≈ 590K (this structure)
- The first intermediate form is monoclinic, space group $P2_{1}$ #4 at temperatures above ≈ 460K
- The second intermediate form, $P2_{1}(\alpha\beta0)$ (ICSD 279583), is incommensurate but averages to a structure similar to the previous one
- This is followed by an orthorhombic form, space group $P2_{1}2_{1}2_{1}$ #19, for which we have no data.
- Near room temperature we find another monoclinic structure, space group $Pc$ #7
- The low temperature structure is triclinic, space group $P1$ #1, also measured at room temperature.
- The astute reader will recognize that we are very vague about these phase transitions, as we have found no definitive phase diagram.
- For more information on realted structures see our silica and aluminum phosphate page.
- (Graetsch, 2001) gives two forms for this structure: one with the O II atoms on the (6c) site, and the second with those atoms partially occupying four (12d) sites near that (6c) site. Since the distance of those atoms is less that 0.5Å from the
averaged
(6c) site we use the first form. - The ICSD lists LiBH$_{4}$ as the structure type, but even though both this structure and LiBH$_{4}$ share the same AFLOW prototype label, AB4C_hP12_186_b_bc_b, the structures are very different and we define them as two independent prototypes.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{1} \,\mathbf{\hat{z}}$ | (2b) | Al I |
| $\mathbf{B_{2}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\left(z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2b) | Al I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (2b) | O I |
| $\mathbf{B_{4}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2b) | O I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (2b) | P I |
| $\mathbf{B_{6}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2b) | P I |
| $\mathbf{B_{7}}$ | = | $x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $- \sqrt{3}a x_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (6c) | O II |
| $\mathbf{B_{8}}$ | = | $x_{4} \, \mathbf{a}_{1}+2 x_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{4} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (6c) | O II |
| $\mathbf{B_{9}}$ | = | $- 2 x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{4} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (6c) | O II |
| $\mathbf{B_{10}}$ | = | $- x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\sqrt{3}a x_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6c) | O II |
| $\mathbf{B_{11}}$ | = | $- x_{4} \, \mathbf{a}_{1}- 2 x_{4} \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{4} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6c) | O II |
| $\mathbf{B_{12}}$ | = | $2 x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{4} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6c) | O II |
References
- H. A. Graetsch, Hexagonal high-temperature form of aluminium phosphate tridymite from X-ray powder data, Acta Crystallogr. Sect. C 57, 665–667 (2001), doi:10.1107/S0108270101005133.
- H. A. Graetsch, Monoclinic AlPO$_{4}$ tridymite at 473 and 463 K from X-ray powder data, Acta Crystallographica C 58, i18–i20 (2002), doi:10.1107/S0108270101015773.
First cited in
- N. Anderson, M. J. Mehl, H. Eckert, S. Divilov, X. Campilongo, S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 5. Submitted to Computational Materials Science (2026).
Geometry files
Prototype Generator
aflow --proto=AB4C_hP12_186_b_bc_b --params=$a,c/a,z_{1},z_{2},z_{3},x_{4},z_{4}$