Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: A3B4_oC56_63_2c2f_ac3f-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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Nb$_{4}$As$_{3}$ Structure: A3B4_oC56_63_2c2f_ac3f-001

Picture of Structure; Click for Big Picture
Prototype As$_{3}$Nb$_{4}$
AFLOW prototype label A3B4_oC56_63_2c2f_ac3f-001
ICSD 15032
Pearson symbol oC56
Space group number 63
Space group symbol $Cmcm$
AFLOW prototype command aflow --proto=A3B4_oC56_63_2c2f_ac3f-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak y_{2}, \allowbreak y_{3}, \allowbreak y_{4}, \allowbreak y_{5}, \allowbreak z_{5}, \allowbreak y_{6}, \allowbreak z_{6}, \allowbreak y_{7}, \allowbreak z_{7}, \allowbreak y_{8}, \allowbreak z_{8}, \allowbreak y_{9}, \allowbreak z_{9}$

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

Basis vectors

Lattice coordinates Cartesian coordinates Wyckoff position Atom type
$\mathbf{B_{1}}$ = $0$ = $0$ (4a) Nb I
$\mathbf{B_{2}}$ = $\frac{1}{2} \, \mathbf{a}_{3}$ = $\frac{1}{2}c \,\mathbf{\hat{z}}$ (4a) Nb I
$\mathbf{B_{3}}$ = $- y_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ = $b y_{2} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ (4c) As I
$\mathbf{B_{4}}$ = $y_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ = $- b y_{2} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ (4c) As I
$\mathbf{B_{5}}$ = $- y_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ = $b y_{3} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ (4c) As II
$\mathbf{B_{6}}$ = $y_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ = $- b y_{3} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ (4c) As II
$\mathbf{B_{7}}$ = $- y_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ = $b y_{4} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ (4c) Nb II
$\mathbf{B_{8}}$ = $y_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ = $- b y_{4} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ (4c) Nb II
$\mathbf{B_{9}}$ = $- y_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ = $b y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ (8f) As III
$\mathbf{B_{10}}$ = $y_{5} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- b y_{5} \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8f) As III
$\mathbf{B_{11}}$ = $- y_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $b y_{5} \,\mathbf{\hat{y}}- c \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8f) As III
$\mathbf{B_{12}}$ = $y_{5} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ = $- b y_{5} \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ (8f) As III
$\mathbf{B_{13}}$ = $- y_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ = $b y_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ (8f) As IV
$\mathbf{B_{14}}$ = $y_{6} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- b y_{6} \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8f) As IV
$\mathbf{B_{15}}$ = $- y_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $b y_{6} \,\mathbf{\hat{y}}- c \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8f) As IV
$\mathbf{B_{16}}$ = $y_{6} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ = $- b y_{6} \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ (8f) As IV
$\mathbf{B_{17}}$ = $- y_{7} \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ = $b y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ (8f) Nb III
$\mathbf{B_{18}}$ = $y_{7} \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- b y_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8f) Nb III
$\mathbf{B_{19}}$ = $- y_{7} \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $b y_{7} \,\mathbf{\hat{y}}- c \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8f) Nb III
$\mathbf{B_{20}}$ = $y_{7} \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ = $- b y_{7} \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ (8f) Nb III
$\mathbf{B_{21}}$ = $- y_{8} \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ = $b y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ (8f) Nb IV
$\mathbf{B_{22}}$ = $y_{8} \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- b y_{8} \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8f) Nb IV
$\mathbf{B_{23}}$ = $- y_{8} \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $b y_{8} \,\mathbf{\hat{y}}- c \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8f) Nb IV
$\mathbf{B_{24}}$ = $y_{8} \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ = $- b y_{8} \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ (8f) Nb IV
$\mathbf{B_{25}}$ = $- y_{9} \, \mathbf{a}_{1}+y_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ = $b y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ (8f) Nb V
$\mathbf{B_{26}}$ = $y_{9} \, \mathbf{a}_{1}- y_{9} \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- b y_{9} \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8f) Nb V
$\mathbf{B_{27}}$ = $- y_{9} \, \mathbf{a}_{1}+y_{9} \, \mathbf{a}_{2}- \left(z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $b y_{9} \,\mathbf{\hat{y}}- c \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8f) Nb V
$\mathbf{B_{28}}$ = $y_{9} \, \mathbf{a}_{1}- y_{9} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ = $- b y_{9} \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ (8f) Nb V

References


Prototype Generator

aflow --proto=A3B4_oC56_63_2c2f_ac3f --params=$a,b/a,c/a,y_{2},y_{3},y_{4},y_{5},z_{5},y_{6},z_{6},y_{7},z_{7},y_{8},z_{8},y_{9},z_{9}$

Species:

Running:

Output: