MgZn$_{2}$ Hexagonal Laves ($C14$) Structure: AB2_hP12_194_f_ah-001
| Prototype | MgZn$_{2}$ |
| AFLOW prototype label | AB2_hP12_194_f_ah-001 |
| Strukturbericht designation | $C14$ |
| Mineral name | Hexagonal Laves |
| ICSD | 46006 |
| Pearson symbol | hP12 |
| Space group number | 194 |
| Space group symbol | $P6_3/mmc$ |
| AFLOW prototype command |
aflow --proto=AB2_hP12_194_f_ah-001
--params=$a, \allowbreak c/a, \allowbreak z_{2}, \allowbreak x_{3}$ |
Other compounds with this structure
BaMg$_{2}$, CaCd$_{2}$, CaLi$_{2}$, CaMg$_{2}$, CdCu$_{2}$, CrBe$_{2}$, DyOs$_{2}$, DyRu$_{2}$, DyTc$_{2}$, ErMg$_{2}$, ErMn$_{2}$, ErOs$_{2}$, ErRu$_{2}$, ErTc$_{2}$, FeBe$_{2}$, GdOs$_{2}$, GdRu$_{2}$, GdTc$_{2}$, HfCr$_{2}$, HfFe$_{2}$ (HT), HfMn$_{2}$ (HT), HfRe$_{2}$, HoMg$_{2}$, HoOs$_{2}$, HoRe$_{2}$, HoRu$_{2}$, HoTc$_{2}$, KNa$_{2}$, KPb$_{2}$, LuMn$_{2}$, LuOs$_{2}$, LuRe$_{2}$, LuRh$_{2}$, LuRu$_{2}$, LuTe$_{2}$, MgZn$_{2}$, MnBe$_{2}$, MoBe$_{2}$, MoFe$_{2}$, NbCr$_{2}$ (HT), NbFe$_{2}$, NbMn$_{2}$, NdMn$_{2}$, NdOs$_{2}$, PrMn$_{2}$, PrOs$_{2}$, PuOs$_{2}$, ReBe$_{2}$, RuBe$_{2}$, ScMn$_{2}$, ScOs$_{2}$, ScRe$_{2}$, ScRu$_{2}$, ScTc$_{2}$, SmOs$_{2}$, SrMg$_{2}$, $\alpha$-TaCo$_{2}$ (LT), TaCr$_{2}$ (HT), TaFe$_{2}$, TaMn$_{2}$, TbOs$_{2}$, TbRe$_{2}$, TbRu$_{2}$, TbTc$_{2}$, ThMn$_{2}$, ThRe$_{2}$, TiCr$_{2}$ (HT), TiFe$_{2}$, TiMn$_{2}$, TiZn$_{2}$, TmMn$_{2}$, TmRu$_{2}$, TmTc$_{2}$, UNi$_{2}$, URe$_{2}$ (HT), URe$_{2}$, VBe$_{2}$, WBe$_{2}$, WFe$_{2}$, YOs$_{2}$, YRe$_{2}$, YRu$_{2}$, YTc$_{2}$, ZrCr$_{2}$, ZrMn$_{2}$, ZrOs$_{2}$, ZrRe$_{2}$, ZrRu$_{2}$ (HT), ZrTc$_{2}$, Co$_{3}$Mn$_{2}$Ge, Co$_{3}$Mo$_{2}$Si, Cr$_{3}$Ta$_{2}$Cu, Fe$_{3}$Zr$_{2}$Ga, Nb$_{3}$Co$_{2}$Si, Ni$_{3}$Nb$_{2}$Si, Ni$_{3}$Ta$_{2}$Si, Ni$_{3}$Ti$_{2}$Si
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Zn I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2a) | Zn I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (4f) | Mg I |
| $\mathbf{B_{4}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4f) | Mg I |
| $\mathbf{B_{5}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{2} \,\mathbf{\hat{z}}$ | (4f) | Mg I |
| $\mathbf{B_{6}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}- \left(z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c \left(z_{2} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4f) | Mg I |
| $\mathbf{B_{7}}$ | = | $x_{3} \, \mathbf{a}_{1}+2 x_{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{3} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | Zn II |
| $\mathbf{B_{8}}$ | = | $- 2 x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{3} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | Zn II |
| $\mathbf{B_{9}}$ | = | $x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- \sqrt{3}a x_{3} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | Zn II |
| $\mathbf{B_{10}}$ | = | $- x_{3} \, \mathbf{a}_{1}- 2 x_{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{3} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | Zn II |
| $\mathbf{B_{11}}$ | = | $2 x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{3} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | Zn II |
| $\mathbf{B_{12}}$ | = | $- x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\sqrt{3}a x_{3} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | Zn II |
References
- T. Ohba, Y. Kitano, and Y. Komura, The charge-density study of the Laves phases, MgZn$_2$ and MgCu$_2$, Acta Crystallogr. Sect. C 40, 1–5 (1984), doi:10.1107/S0108270184002791.
Prototype Generator
aflow --proto=AB2_hP12_194_f_ah --params=$a,c/a,z_{2},x_{3}$