Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: AB14C_oP64_62_c_4c5d_c-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.

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https://aflow.org/p/LZG8
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CdSnP$_{14}$ (HgPbP$_{14}$) Structure: AB14C_oP64_62_c_4c5d_c-001

Picture of Structure; Click for Big Picture
Prototype CdP$_{14}$Sn
AFLOW prototype label AB14C_oP64_62_c_4c5d_c-001
ICSD 42976
Pearson symbol oP64
Space group number 62
Space group symbol $Pnma$
AFLOW prototype command aflow --proto=AB14C_oP64_62_c_4c5d_c-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak z_{1}, \allowbreak x_{2}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak y_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak y_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak y_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak y_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak y_{11}, \allowbreak z_{11}$

Other compounds with this structure

CdPbP$_{14}$,  HgPbP$_{14}$,  HgSnP$_{14}$,  ZnPbP$_{14}$,  ZnSnP$_{14}$


  • Although (Krebs, 1958) first described this structure for HgPbP$_{14}$, but their data is very approximate, so we use the refinement made by (Scholz, 1987). They give the Wyckoff positions for CdSnP$_{14}$, so we use that as our prototype.

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

Basis vectors

Lattice coordinates Cartesian coordinates Wyckoff position Atom type
$\mathbf{B_{1}}$ = $x_{1} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ = $a x_{1} \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{1} \,\mathbf{\hat{z}}$ (4c) Cd I
$\mathbf{B_{2}}$ = $- \left(x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\left(z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{1} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4c) Cd I
$\mathbf{B_{3}}$ = $- x_{1} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{1} \, \mathbf{a}_{3}$ = $- a x_{1} \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}- c z_{1} \,\mathbf{\hat{z}}$ (4c) Cd I
$\mathbf{B_{4}}$ = $\left(x_{1} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}- \left(z_{1} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(x_{1} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}- c \left(z_{1} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4c) Cd I
$\mathbf{B_{5}}$ = $x_{2} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ = $a x_{2} \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ (4c) P I
$\mathbf{B_{6}}$ = $- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4c) P I
$\mathbf{B_{7}}$ = $- x_{2} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}$ = $- a x_{2} \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}- c z_{2} \,\mathbf{\hat{z}}$ (4c) P I
$\mathbf{B_{8}}$ = $\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}- \left(z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}- c \left(z_{2} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4c) P I
$\mathbf{B_{9}}$ = $x_{3} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ = $a x_{3} \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ (4c) P II
$\mathbf{B_{10}}$ = $- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4c) P II
$\mathbf{B_{11}}$ = $- x_{3} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ = $- a x_{3} \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ (4c) P II
$\mathbf{B_{12}}$ = $\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}- \left(z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}- c \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4c) P II
$\mathbf{B_{13}}$ = $x_{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ = $a x_{4} \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ (4c) P III
$\mathbf{B_{14}}$ = $- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4c) P III
$\mathbf{B_{15}}$ = $- x_{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ = $- a x_{4} \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ (4c) P III
$\mathbf{B_{16}}$ = $\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}- c \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4c) P III
$\mathbf{B_{17}}$ = $x_{5} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ = $a x_{5} \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ (4c) P IV
$\mathbf{B_{18}}$ = $- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4c) P IV
$\mathbf{B_{19}}$ = $- x_{5} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ = $- a x_{5} \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ (4c) P IV
$\mathbf{B_{20}}$ = $\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}- c \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4c) P IV
$\mathbf{B_{21}}$ = $x_{6} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ = $a x_{6} \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ (4c) Sn I
$\mathbf{B_{22}}$ = $- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4c) Sn I
$\mathbf{B_{23}}$ = $- x_{6} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ = $- a x_{6} \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ (4c) Sn I
$\mathbf{B_{24}}$ = $\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}- c \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4c) Sn I
$\mathbf{B_{25}}$ = $x_{7} \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ = $a x_{7} \,\mathbf{\hat{x}}+b y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ (8d) P V
$\mathbf{B_{26}}$ = $- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8d) P V
$\mathbf{B_{27}}$ = $- x_{7} \, \mathbf{a}_{1}+\left(y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ = $- a x_{7} \,\mathbf{\hat{x}}+b \left(y_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ (8d) P V
$\mathbf{B_{28}}$ = $\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b \left(y_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8d) P V
$\mathbf{B_{29}}$ = $- x_{7} \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ = $- a x_{7} \,\mathbf{\hat{x}}- b y_{7} \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ (8d) P V
$\mathbf{B_{30}}$ = $\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{7} \,\mathbf{\hat{y}}- c \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8d) P V
$\mathbf{B_{31}}$ = $x_{7} \, \mathbf{a}_{1}- \left(y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ = $a x_{7} \,\mathbf{\hat{x}}- b \left(y_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ (8d) P V
$\mathbf{B_{32}}$ = $- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b \left(y_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8d) P V
$\mathbf{B_{33}}$ = $x_{8} \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ = $a x_{8} \,\mathbf{\hat{x}}+b y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ (8d) P VI
$\mathbf{B_{34}}$ = $- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{8} \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8d) P VI
$\mathbf{B_{35}}$ = $- x_{8} \, \mathbf{a}_{1}+\left(y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ = $- a x_{8} \,\mathbf{\hat{x}}+b \left(y_{8} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ (8d) P VI
$\mathbf{B_{36}}$ = $\left(x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b \left(y_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8d) P VI
$\mathbf{B_{37}}$ = $- x_{8} \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ = $- a x_{8} \,\mathbf{\hat{x}}- b y_{8} \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ (8d) P VI
$\mathbf{B_{38}}$ = $\left(x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{8} \,\mathbf{\hat{y}}- c \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8d) P VI
$\mathbf{B_{39}}$ = $x_{8} \, \mathbf{a}_{1}- \left(y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ = $a x_{8} \,\mathbf{\hat{x}}- b \left(y_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ (8d) P VI
$\mathbf{B_{40}}$ = $- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b \left(y_{8} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8d) P VI
$\mathbf{B_{41}}$ = $x_{9} \, \mathbf{a}_{1}+y_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ = $a x_{9} \,\mathbf{\hat{x}}+b y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ (8d) P VII
$\mathbf{B_{42}}$ = $- \left(x_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{9} \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{9} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{9} \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8d) P VII
$\mathbf{B_{43}}$ = $- x_{9} \, \mathbf{a}_{1}+\left(y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ = $- a x_{9} \,\mathbf{\hat{x}}+b \left(y_{9} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ (8d) P VII
$\mathbf{B_{44}}$ = $\left(x_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(x_{9} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b \left(y_{9} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8d) P VII
$\mathbf{B_{45}}$ = $- x_{9} \, \mathbf{a}_{1}- y_{9} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ = $- a x_{9} \,\mathbf{\hat{x}}- b y_{9} \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ (8d) P VII
$\mathbf{B_{46}}$ = $\left(x_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{9} \, \mathbf{a}_{2}- \left(z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(x_{9} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{9} \,\mathbf{\hat{y}}- c \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8d) P VII
$\mathbf{B_{47}}$ = $x_{9} \, \mathbf{a}_{1}- \left(y_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ = $a x_{9} \,\mathbf{\hat{x}}- b \left(y_{9} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ (8d) P VII
$\mathbf{B_{48}}$ = $- \left(x_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{9} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b \left(y_{9} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8d) P VII
$\mathbf{B_{49}}$ = $x_{10} \, \mathbf{a}_{1}+y_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ = $a x_{10} \,\mathbf{\hat{x}}+b y_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ (8d) P VIII
$\mathbf{B_{50}}$ = $- \left(x_{10} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{10} \, \mathbf{a}_{2}+\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{10} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{10} \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8d) P VIII
$\mathbf{B_{51}}$ = $- x_{10} \, \mathbf{a}_{1}+\left(y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ = $- a x_{10} \,\mathbf{\hat{x}}+b \left(y_{10} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ (8d) P VIII
$\mathbf{B_{52}}$ = $\left(x_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{10} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(x_{10} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b \left(y_{10} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{10} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8d) P VIII
$\mathbf{B_{53}}$ = $- x_{10} \, \mathbf{a}_{1}- y_{10} \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ = $- a x_{10} \,\mathbf{\hat{x}}- b y_{10} \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ (8d) P VIII
$\mathbf{B_{54}}$ = $\left(x_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{10} \, \mathbf{a}_{2}- \left(z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(x_{10} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{10} \,\mathbf{\hat{y}}- c \left(z_{10} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8d) P VIII
$\mathbf{B_{55}}$ = $x_{10} \, \mathbf{a}_{1}- \left(y_{10} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ = $a x_{10} \,\mathbf{\hat{x}}- b \left(y_{10} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ (8d) P VIII
$\mathbf{B_{56}}$ = $- \left(x_{10} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{10} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b \left(y_{10} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8d) P VIII
$\mathbf{B_{57}}$ = $x_{11} \, \mathbf{a}_{1}+y_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ = $a x_{11} \,\mathbf{\hat{x}}+b y_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ (8d) P IX
$\mathbf{B_{58}}$ = $- \left(x_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{11} \, \mathbf{a}_{2}+\left(z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{11} \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8d) P IX
$\mathbf{B_{59}}$ = $- x_{11} \, \mathbf{a}_{1}+\left(y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ = $- a x_{11} \,\mathbf{\hat{x}}+b \left(y_{11} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ (8d) P IX
$\mathbf{B_{60}}$ = $\left(x_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(x_{11} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b \left(y_{11} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{11} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8d) P IX
$\mathbf{B_{61}}$ = $- x_{11} \, \mathbf{a}_{1}- y_{11} \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ = $- a x_{11} \,\mathbf{\hat{x}}- b y_{11} \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ (8d) P IX
$\mathbf{B_{62}}$ = $\left(x_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{11} \, \mathbf{a}_{2}- \left(z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(x_{11} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{11} \,\mathbf{\hat{y}}- c \left(z_{11} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8d) P IX
$\mathbf{B_{63}}$ = $x_{11} \, \mathbf{a}_{1}- \left(y_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ = $a x_{11} \,\mathbf{\hat{x}}- b \left(y_{11} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ (8d) P IX
$\mathbf{B_{64}}$ = $- \left(x_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b \left(y_{11} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8d) P IX

References

  • U. D. Scholz and W. Jeitschko, Preparation, crystal structure, and properties of HgSnP$_{14}$ and other polyphosphides with HgPbP$_{14}$-type structure, J. Solid State Chem. 67, 271–277 (1987), doi:10.1016/0022-4596(87)90363-X.
  • H. Krebs and T. Ludwig, Über kristallisierte Metallpolyphosphide. III. Die Struktur der Metallpolyphosphide des Typs HgPbP$_{14}$, Z. Anorganische und Allgemeine Chemie 294, 257–268 (1958), doi:10.1002/zaac.19582940502.

Prototype Generator

aflow --proto=AB14C_oP64_62_c_4c5d_c --params=$a,b/a,c/a,x_{1},z_{1},x_{2},z_{2},x_{3},z_{3},x_{4},z_{4},x_{5},z_{5},x_{6},z_{6},x_{7},y_{7},z_{7},x_{8},y_{8},z_{8},x_{9},y_{9},z_{9},x_{10},y_{10},z_{10},x_{11},y_{11},z_{11}$

Species:

Running:

Output: