Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: A7BC10_hP18_162_ceg_a_hk-001

If you are using this page, please cite:
H. Eckert, S. Divilov, M. J. Mehl, D. Hicks, A. C. Zettel, M. Esters. X. Campilongo and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 4. Submitted to Computational Materials Science.

Links to this page

https://aflow.org/p/RQ68
or https://aflow.org/p/A7BC10_hP18_162_ceg_a_hk-001
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Trigonal Au$_{7}$P$_{10}$I Structure: A7BC10_hP18_162_ceg_a_hk-001

Picture of Structure; Click for Big Picture
Prototype Au$_{7}$IP$_{10}$
AFLOW prototype label A7BC10_hP18_162_ceg_a_hk-001
ICSD 8059
Pearson symbol hP18
Space group number 162
Space group symbol $P\overline{3}1m$
AFLOW prototype command aflow --proto=A7BC10_hP18_162_ceg_a_hk-001
--params=$a, \allowbreak c/a, \allowbreak z_{3}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak z_{6}$

  • There is some controversy about the structure of Au$_{7}$P$_{10}$I. (Binnewies, 1978) put it in the hexagonal $P\overline{6}2m$ #189 space group, but (Jeitschko, 1979) place it in the trigonal $P\overline{3}1m$ #162 space group. The structures are distinct, and to our knowledge the dispute has not been resolved, so we present both structures.
  • We have shifted the origin, moving the iodine atoms from the (1b) to (1a) Wyckoff positions.

\[ \begin{array}{ccc} \mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}} \end{array}\]

Basis vectors

Lattice coordinates Cartesian coordinates Wyckoff position Atom type
$\mathbf{B_{1}}$ = $0$ = $0$ (1a) I I
$\mathbf{B_{2}}$ = $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}$ = $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}$ (2c) Au I
$\mathbf{B_{3}}$ = $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}$ = $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}$ (2c) Au I
$\mathbf{B_{4}}$ = $z_{3} \, \mathbf{a}_{3}$ = $c z_{3} \,\mathbf{\hat{z}}$ (2e) Au II
$\mathbf{B_{5}}$ = $- z_{3} \, \mathbf{a}_{3}$ = $- c z_{3} \,\mathbf{\hat{z}}$ (2e) Au II
$\mathbf{B_{6}}$ = $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ = $\frac{1}{4}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{4}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ (3g) Au III
$\mathbf{B_{7}}$ = $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ = $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{4}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ (3g) Au III
$\mathbf{B_{8}}$ = $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ (3g) Au III
$\mathbf{B_{9}}$ = $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ (4h) P I
$\mathbf{B_{10}}$ = $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ (4h) P I
$\mathbf{B_{11}}$ = $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ (4h) P I
$\mathbf{B_{12}}$ = $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ (4h) P I
$\mathbf{B_{13}}$ = $x_{6} \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{3}$ = $\frac{1}{2}a x_{6} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ (6k) P II
$\mathbf{B_{14}}$ = $x_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ = $\frac{1}{2}a x_{6} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ (6k) P II
$\mathbf{B_{15}}$ = $- x_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ = $- a x_{6} \,\mathbf{\hat{x}}+c z_{6} \,\mathbf{\hat{z}}$ (6k) P II
$\mathbf{B_{16}}$ = $- x_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ = $- \frac{1}{2}a x_{6} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ (6k) P II
$\mathbf{B_{17}}$ = $- x_{6} \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{3}$ = $- \frac{1}{2}a x_{6} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ (6k) P II
$\mathbf{B_{18}}$ = $x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ = $a x_{6} \,\mathbf{\hat{x}}- c z_{6} \,\mathbf{\hat{z}}$ (6k) P II

References

  • W. Jeitschko and M. H. Möller, The crystal structures of Au$_{2}$P$_{3}$ and Au$_{7}$P$_{10}$I, polyphosphides with weak Au-Au interactions, Acta Crystallogr. Sect. B 35, 573–579 (1979), doi:10.1107/S0567740879004180.
  • M. Binnewies, Darstellung, Kristallstruktur und Eigenschaften von Au$_{7}$P$_{10}$I, Z. Naturforsch. B 33, 570–571 (1978), doi:10.1515/znb-1978-0521.

Prototype Generator

aflow --proto=A7BC10_hP18_162_ceg_a_hk --params=$a,c/a,z_{3},z_{5},x_{6},z_{6}$

Species:

Running:

Output: