ZrFe$_{4}$Si$_{2}$ Structure: A4B2C_tP14_136_i_f_a-001
| Prototype | Fe$_{4}$Si$_{2}$Zr |
| AFLOW prototype label | A4B2C_tP14_136_i_f_a-001 |
| ICSD | 87172 |
| Pearson symbol | tP14 |
| Space group number | 136 |
| Space group symbol | $P4_2/mnm$ |
| AFLOW prototype command |
aflow --proto=A4B2C_tP14_136_i_f_a-001
--params=$a, \allowbreak c/a, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak y_{3}$ |
Other compounds with this structure
BaCd$_{4}$Pt$_{2}$, DyFe$_{4}$Ge$_{2}$, DyNi$_{4}$As$_{2}$, ErFe$_{4}$Ge$_{2}$, ErNi$_{4}$P$_{2}$, GdNi$_{4}$As$_{2}$, GdRe$_{4}$Si$_{2}$, HoFe$_{4}$Ge$_{2}$, LuFe$_{4}$Ge$_{2}$, LuNi$_{4}$As$_{2}$, LuRe$_{4}$Si$_{2}$, ScFe$_{4}$P$_{2}$, ScFe$_{4}$Si$_{2}$, ScNi$_{4}$As$_{2}$, SmRe$_{4}$Si$_{2}$, SrCd$_{4}$Pt$_{2}$, TbRe$_{4}$Si$_{2}$, TmFe$_{4}$Ge$_{2}$, TmRe$_{4}$Si$_{2}$, UMn$_{4}$P$_{2}$, YFe$_{4}$Ge$_{2}$, YNi$_{4}$As$_{2}$, YNi$_{4}$P$_{2}$, YRe$_{4}$Si$_{2}$, YbNi$_{4}$P$_{2}$, ZrFe$_{4}$P$_{2}$, ZrNi$_{4}$As$_{2}$
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Zr I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2a) | Zr I |
| $\mathbf{B_{3}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}$ | (4f) | Si I |
| $\mathbf{B_{4}}$ | = | $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}$ | (4f) | Si I |
| $\mathbf{B_{5}}$ | = | $- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4f) | Si I |
| $\mathbf{B_{6}}$ | = | $\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4f) | Si I |
| $\mathbf{B_{7}}$ | = | $x_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}$ | (8i) | Fe I |
| $\mathbf{B_{8}}$ | = | $- x_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}$ | (8i) | Fe I |
| $\mathbf{B_{9}}$ | = | $- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8i) | Fe I |
| $\mathbf{B_{10}}$ | = | $\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8i) | Fe I |
| $\mathbf{B_{11}}$ | = | $- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8i) | Fe I |
| $\mathbf{B_{12}}$ | = | $\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8i) | Fe I |
| $\mathbf{B_{13}}$ | = | $y_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}$ | = | $a y_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}$ | (8i) | Fe I |
| $\mathbf{B_{14}}$ | = | $- y_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}$ | = | $- a y_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}$ | (8i) | Fe I |
References
- Y. P. Yarmolyuk, L. A. Lysenko, and E. I. Gladyshevsky, Crystal Structure of ZrFe$_{4}$Si$_{2}$ – A New Structure Type of Ternary Silicides, Dopov. Akad. Nauk Ukr. RSR, Ser. A 37, 281–284 (1975). In Russian.
Found in
- P. Schobinger-Papamantellos, J. Rodrı́guez-Carvajal, G. André, N. P. Duong, K. H. J. Buschow, and P. Tolédano, Simultaneous structural and magnetic transitions in YFe$_{4}$Ge$_{2}$ studied by neutron diffraction and magnetic measurements, J. Magn. Magn. Mater. 236, 14–27 (2001), doi:10.1016/S0304-8853(01)00442-5.
Prototype Generator
aflow --proto=A4B2C_tP14_136_i_f_a --params=$a,c/a,x_{2},x_{3},y_{3}$