GdSi$_{2}$ Structure: AB2_oI12_74_e_2e-001
| Prototype | GdSi$_{2}$ |
| AFLOW prototype label | AB2_oI12_74_e_2e-001 |
| ICSD | 291182 |
| Pearson symbol | oI12 |
| Space group number | 74 |
| Space group symbol | $Imma$ |
| AFLOW prototype command |
aflow --proto=AB2_oI12_74_e_2e-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak z_{2}, \allowbreak z_{3}$ |
Other compounds with this structure
GeSi$_{2}$, HoSi$_{2}$, LaGe$_{2}$, TbSi$_{2}$, DySi$_{1.4}$, GdSi$_{1.4}$, NdSi$_{1.4}$, PrSi$_{1.4}$, SmSi$_{1.4}$, YSi$_{1.4}$
- (Zou, 2015) find that the Si-I site has 96.8% occupancy and the Si-II site has 81.2% occupancy, so the actual stoichiometry of their sample is GdSi$_{1.78}$.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\left(z_{1} + \frac{1}{4}\right) \, \mathbf{a}_{1}+z_{1} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{1} \,\mathbf{\hat{z}}$ | (4e) | Gd I |
| $\mathbf{B_{2}}$ | = | $- \left(z_{1} - \frac{3}{4}\right) \, \mathbf{a}_{1}- z_{1} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}b \,\mathbf{\hat{y}}- c z_{1} \,\mathbf{\hat{z}}$ | (4e) | Gd I |
| $\mathbf{B_{3}}$ | = | $\left(z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{1}+z_{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (4e) | Si I |
| $\mathbf{B_{4}}$ | = | $- \left(z_{2} - \frac{3}{4}\right) \, \mathbf{a}_{1}- z_{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}b \,\mathbf{\hat{y}}- c z_{2} \,\mathbf{\hat{z}}$ | (4e) | Si I |
| $\mathbf{B_{5}}$ | = | $\left(z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (4e) | Si II |
| $\mathbf{B_{6}}$ | = | $- \left(z_{3} - \frac{3}{4}\right) \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}b \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (4e) | Si II |
References
- J. D. Zou, J. Liu, and M. Yan, Crystal structure and magnetic properties of GdSi$_{1.78}$, Gd(Si$_{0.684}$Ge$_{0.316}$)$_{1.78}$, GdGe$_{1.57}$, and GdSn$_{2}$ compounds, J. Magn. Magn. Mater. 385, 77–82 (2015), doi:10.1016/j.jmmm.2015.02.057.
- W. B. Pearson, A Handbook of Lattice Spacings and Structures of Metals and Alloys, Volume 2, International Series of Monographs on Metal Physics and Physical Metallurgy, vol. 8 (Pergamon Press, Oxford, London, Edinburgh, New York, Toronto, Sydney, Paris, Braunschweig, 1967).
Prototype Generator
aflow --proto=AB2_oI12_74_e_2e --params=$a,b/a,c/a,z_{1},z_{2},z_{3}$