NaZn$_{13}$ ($D2_{3}$) Structure: AB13_cF112_226_a_bi-001
| Prototype | NaZn$_{13}$ |
| AFLOW prototype label | AB13_cF112_226_a_bi-001 |
| Strukturbericht designation | $D2_{3}$ |
| ICSD | 105173 |
| Pearson symbol | cF112 |
| Space group number | 226 |
| Space group symbol | $Fm\overline{3}c$ |
| AFLOW prototype command |
aflow --proto=AB13_cF112_226_a_bi-001
--params=$a, \allowbreak y_{3}, \allowbreak z_{3}$ |
Other compounds with this structure
AmBe$_{13}$, BaCu$_{13}$, BaZn$_{13}$, CaBe$_{13}$, CaZn$_{13}$, CdZn$_{13}$, CeBe$_{13}$, CsCd$_{13}$, DyBe$_{13}$, ErBe$_{13}$, EuBe$_{13}$, HfBe$_{13}$, KCd$_{13}$, KZn$_{13}$, LaBe$_{13}$, LuBe$_{13}$, MgBe$_{13}$, NbBe$_{13}$, NdBe$_{13}$, PtBe$_{13}$, PuBe$_{13}$, RbCd$_{13}$, ScBe$_{13}$, SmBe$_{13}$, SrBe$_{13}$, SrZn$_{13}$, TbBe$_{13}$, ThBe$_{13}$, TmBe$_{13}$, UBe$_{13}$, VBe$_{13}$, YBe$_{13}$, YbBe$_{13}$, ZrBe$_{13}$, CeNi$_{8.5}$Si$_{4.5}$, LaFe$_{13-x-y}$Co$_{y}$Al$_{x}$, LaFe$_{13-x-y}$Co$_{y}$Si$_{x}$, NdFe$_{13-x-y}$Co$_{y}$Si$_{x}$
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (8a) | Na I |
| $\mathbf{B_{2}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{3}{4}a \,\mathbf{\hat{z}}$ | (8a) | Na I |
| $\mathbf{B_{3}}$ | = | $0$ | = | $0$ | (8b) | Zn I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (8b) | Zn I |
| $\mathbf{B_{5}}$ | = | $\left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{y}}+a z_{3} \,\mathbf{\hat{z}}$ | (96i) | Zn II |
| $\mathbf{B_{6}}$ | = | $- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{y}}+a z_{3} \,\mathbf{\hat{z}}$ | (96i) | Zn II |
| $\mathbf{B_{7}}$ | = | $\left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{y}}- a z_{3} \,\mathbf{\hat{z}}$ | (96i) | Zn II |
| $\mathbf{B_{8}}$ | = | $- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{y}}- a z_{3} \,\mathbf{\hat{z}}$ | (96i) | Zn II |
| $\mathbf{B_{9}}$ | = | $\left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{z}}$ | (96i) | Zn II |
| $\mathbf{B_{10}}$ | = | $- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{z}}$ | (96i) | Zn II |
| $\mathbf{B_{11}}$ | = | $\left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a z_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{z}}$ | (96i) | Zn II |
| $\mathbf{B_{12}}$ | = | $- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a z_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{z}}$ | (96i) | Zn II |
| $\mathbf{B_{13}}$ | = | $- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}+a z_{3} \,\mathbf{\hat{y}}$ | (96i) | Zn II |
| $\mathbf{B_{14}}$ | = | $\left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}+a z_{3} \,\mathbf{\hat{y}}$ | (96i) | Zn II |
| $\mathbf{B_{15}}$ | = | $- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}- a z_{3} \,\mathbf{\hat{y}}$ | (96i) | Zn II |
| $\mathbf{B_{16}}$ | = | $\left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}- a z_{3} \,\mathbf{\hat{y}}$ | (96i) | Zn II |
| $\mathbf{B_{17}}$ | = | $- \left(y_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{3} - z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- a \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96i) | Zn II |
| $\mathbf{B_{18}}$ | = | $\left(y_{3} - z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- a \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96i) | Zn II |
| $\mathbf{B_{19}}$ | = | $\left(- y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{3} - z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+a \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96i) | Zn II |
| $\mathbf{B_{20}}$ | = | $\left(y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+a \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96i) | Zn II |
| $\mathbf{B_{21}}$ | = | $\left(- y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+a \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96i) | Zn II |
| $\mathbf{B_{22}}$ | = | $\left(y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{3} - z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+a \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96i) | Zn II |
| $\mathbf{B_{23}}$ | = | $- \left(y_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{3} - z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- a \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96i) | Zn II |
| $\mathbf{B_{24}}$ | = | $\left(y_{3} - z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- a \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96i) | Zn II |
| $\mathbf{B_{25}}$ | = | $\left(y_{3} - z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (96i) | Zn II |
| $\mathbf{B_{26}}$ | = | $- \left(y_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (96i) | Zn II |
| $\mathbf{B_{27}}$ | = | $\left(y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{3} - z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (96i) | Zn II |
| $\mathbf{B_{28}}$ | = | $\left(- y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{3} - z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (96i) | Zn II |
References
- D. P. Shoemaker, R. E. Marsh, F. J. Ewing, and L. Pauling, Interatomic distances and atomic valences in NaZn$_{13}$, Acta Cryst. 5, 637–644 (1952), doi:10.1107/S0365110X52001763.
Prototype Generator
aflow --proto=AB13_cF112_226_a_bi --params=$a,y_{3},z_{3}$