W$_{5}$Si$_{3}$ ($D8_{m}$) Structure: A3B5_tI32_140_ah_bk-001
| Prototype | Si$_{3}$W$_{5}$ |
| AFLOW prototype label | A3B5_tI32_140_ah_bk-001 |
| Strukturbericht designation | $D8_{m}$ |
| ICSD | 73331 |
| Pearson symbol | tI32 |
| Space group number | 140 |
| Space group symbol | $I4/mcm$ |
| AFLOW prototype command |
aflow --proto=A3B5_tI32_140_ah_bk-001
--params=$a, \allowbreak c/a, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak y_{4}$ |
Other compounds with this structure
Cr$_{5}$Ge$_{3}$, Cr$_{5}$Si$_{3}$, Mo$_{5}$Si$_{3}$, Nb$_{5}$Si$_{3}$, Ta$_{5}$Si$_{3}$, Ti$_{5}$Ga$_{3}$, V$_{5}$Si$_{3}$, Ti$_{3}$Sb, Hf$_{5}$Co$_{1-x}$Sb$_{2+x}$, Hf$_{5}$Cr$_{1-x}$Sb$_{2+x}$, Hf$_{5}$Cu$_{1-x}$Sb$_{2+x}$, Hf$_{5}$Fe$_{1-x}$Sb$_{2+x}$, Hf$_{5}$Ni$_{1-x}$Sb$_{2+x}$, Hf$_{5}$Pd$_{1-x}$Sb$_{2+x}$, Hf$_{5}$Rh$_{1-x}$Sb$_{2+x}$, Hf$_{5}$Ru$_{1-x}$Sb$_{2+x}$, Hf$_{5}$V$_{1-x}$Sb$_{2+x}$, Zr$_{5}$Co$_{0.5}$Sb$_{2.5}$, Zr$_{5}$Cr$_{1-x}$Bi$_{2+x}$, Zr$_{5}$Cr$_{1-x}$Sb$_{2+x}$, Zr$_{5}$Fe$_{0.5}$Sb$_{2.5}$, Zr$_{5}$Mn$_{1-x}$Bi$_{2+x}$, Zr$_{5}$Mn$_{1-x}$Sb$_{2+x}$, Zr$_{5}$Ni$_{0.5}$Sb$_{2.5}$, Zr$_{5}$Rh$_{0.5}$Sb$_{2.5}$, Zr$_{5}$Ru$_{0.5}$Sb$_{2.5}$
- (Pearson, 1958) refers to this as the
T1 phase.
- Removing the atoms from the (4b) site transforms this into the $D2_{c}$ U$_{6}$Mn structure or the V$_{4}$SiSb$_{2}$ structure.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4a) | Si I |
| $\mathbf{B_{2}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}$ | = | $\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4a) | Si I |
| $\mathbf{B_{3}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4b) | W I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4b) | W I |
| $\mathbf{B_{5}}$ | = | $\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+\left(2 x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}$ | (8h) | Si II |
| $\mathbf{B_{6}}$ | = | $- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- \left(2 x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}$ | (8h) | Si II |
| $\mathbf{B_{7}}$ | = | $x_{3} \, \mathbf{a}_{1}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}$ | (8h) | Si II |
| $\mathbf{B_{8}}$ | = | $- x_{3} \, \mathbf{a}_{1}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}$ | (8h) | Si II |
| $\mathbf{B_{9}}$ | = | $y_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+\left(x_{4} + y_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}$ | (16k) | W II |
| $\mathbf{B_{10}}$ | = | $- y_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- \left(x_{4} + y_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}$ | (16k) | W II |
| $\mathbf{B_{11}}$ | = | $x_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+\left(x_{4} - y_{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}$ | (16k) | W II |
| $\mathbf{B_{12}}$ | = | $- x_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}- \left(x_{4} - y_{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}$ | (16k) | W II |
| $\mathbf{B_{13}}$ | = | $\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{4} - y_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (16k) | W II |
| $\mathbf{B_{14}}$ | = | $- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (16k) | W II |
| $\mathbf{B_{15}}$ | = | $\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (16k) | W II |
| $\mathbf{B_{16}}$ | = | $- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (16k) | W II |
References
- B. Aronsson, The Crystal Structure of Mo$_{5}$Si$_{3}$ and W$_{5}$Si$_{3}$, Acta Chem. Scand. 9, 1107–1110 (1955), doi:10.3891/acta.chem.scand.09-1107.
Found in
- W. B. Pearson, A Handbook of Lattice Spacings and Structures of Metals and Alloys, International Series of Monographs on Metal Physics and Physical Metallurgy, vol. 4 (Pergamon Press, Oxford, London, Edinburgh, New York, Paris, Frankfort, 1958), 1964 reprint with corrections edn.
Prototype Generator
aflow --proto=A3B5_tI32_140_ah_bk --params=$a,c/a,x_{3},x_{4},y_{4}$