Archerite (KH$_{2}$PO$_{4}$) Structure: A2BC4D_oF64_43_b_a_2b_a-001
| Prototype | H$_{2}$KO$_{4}$P |
| AFLOW prototype label | A2BC4D_oF64_43_b_a_2b_a-001 |
| Mineral name | archerite |
| ICSD | 31151 |
| Pearson symbol | oF64 |
| Space group number | 43 |
| Space group symbol | $Fdd2$ |
| AFLOW prototype command |
aflow --proto=A2BC4D_oF64_43_b_a_2b_a-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak z_{5}$ |
- In our original determination of this structure (Hicks, 2019) we neglected to note that (Levy, 1954) used a non-standard representation of space group $Fdd2$ #43, effectively changing the direction of the screw axis and inaccurately describing the H$_{2}$PO$_{4}$ radicals. After viewing the ICSD entry and consulting the original work we realized our error and correct it here.
- This structure is stable below 121K, and the data was taken at 113K. The high temperature structure is tetragonal with disordered hydrogen. (Levy, 1954)
- The origin of the $z$-axis is not restricted in space group $Fdd2$ #43. Here it is fixed by putting the phosphorous atom at the origin.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $z_{1} \, \mathbf{a}_{1}+z_{1} \, \mathbf{a}_{2}- z_{1} \, \mathbf{a}_{3}$ | = | $c z_{1} \,\mathbf{\hat{z}}$ | (8a) | K I |
| $\mathbf{B_{2}}$ | = | $\left(z_{1} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(z_{1} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(z_{1} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8a) | K I |
| $\mathbf{B_{3}}$ | = | $z_{2} \, \mathbf{a}_{1}+z_{2} \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}$ | = | $c z_{2} \,\mathbf{\hat{z}}$ | (8a) | P I |
| $\mathbf{B_{4}}$ | = | $\left(z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(z_{2} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8a) | P I |
| $\mathbf{B_{5}}$ | = | $\left(- x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (16b) | H I |
| $\mathbf{B_{6}}$ | = | $\left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(- x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (16b) | H I |
| $\mathbf{B_{7}}$ | = | $- \left(x_{3} + y_{3} - z_{3} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3} + z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3} - z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- b \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | H I |
| $\mathbf{B_{8}}$ | = | $\left(x_{3} + y_{3} + z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{3} + y_{3} - z_{3} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{3} - y_{3} + z_{3} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+b \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | H I |
| $\mathbf{B_{9}}$ | = | $\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (16b) | O I |
| $\mathbf{B_{10}}$ | = | $\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (16b) | O I |
| $\mathbf{B_{11}}$ | = | $- \left(x_{4} + y_{4} - z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4} + z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4} - z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- b \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | O I |
| $\mathbf{B_{12}}$ | = | $\left(x_{4} + y_{4} + z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + y_{4} - z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{4} - y_{4} + z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+b \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | O I |
| $\mathbf{B_{13}}$ | = | $\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+b y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (16b) | O II |
| $\mathbf{B_{14}}$ | = | $\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- b y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (16b) | O II |
| $\mathbf{B_{15}}$ | = | $- \left(x_{5} + y_{5} - z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5} + z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} - z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{5} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- b \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | O II |
| $\mathbf{B_{16}}$ | = | $\left(x_{5} + y_{5} + z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5} - z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{5} - y_{5} + z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+b \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | O II |
References
- H. A. Levy, S. W. Peterson, and S. H. Simonsen, Neutron Diffraction Study of the Ferroelectric Modification of Potassium Dihydrogen Phosphate, Phys. Rev. 93, 1120–1121 (1954), doi:10.1103/PhysRev.93.1120.
- D. Hicks, M. J.Mehl, M. Esters, C. Oses, O. Levy, G. L. W. Hart, C. Toher, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 3, Comput. Mater. Sci. 199, 110450 (2021), doi:10.1016/j.commatsci.2021.110450.
Found in
- R. T. Downs and M. Hall-Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).
Prototype Generator
aflow --proto=A2BC4D_oF64_43_b_a_2b_a --params=$a,b/a,c/a,z_{1},z_{2},x_{3},y_{3},z_{3},x_{4},y_{4},z_{4},x_{5},y_{5},z_{5}$