Nb$_{6}$Sn$_{5}$ Structure: A6B5_oI44_71_egkl_fghl-001
| Prototype | Nb$_{6}$Sn$_{5}$ |
| AFLOW prototype label | A6B5_oI44_71_egkl_fghl-001 |
| ICSD | 105232 |
| Pearson symbol | oI44 |
| Space group number | 71 |
| Space group symbol | $Immm$ |
| AFLOW prototype command |
aflow --proto=A6B5_oI44_71_egkl_fghl-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak x_{2}, \allowbreak y_{3}, \allowbreak y_{4}, \allowbreak y_{5}, \allowbreak y_{7}, \allowbreak z_{7}, \allowbreak y_{8}, \allowbreak z_{8}$ |
Other compounds with this structure
Ti$_{6}$Sn$_{5}$
- (Ogren, 1965) state that what we have labeled the Sn-II (4g) site is only occupied 92% of the time.
- (Villars, 2018) and others use Ti$_{6}$Sn$_{5}$ as the prototype for this structure. We follow (Pearson, 1967) and use Nb$_{6}$Sn$_{5}$ as the prototype.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ | = | $a x_{1} \,\mathbf{\hat{x}}$ | (4e) | Nb I |
| $\mathbf{B_{2}}$ | = | $- x_{1} \, \mathbf{a}_{2}- x_{1} \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{x}}$ | (4e) | Nb I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}$ | (4f) | Sn I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}$ | (4f) | Sn I |
| $\mathbf{B_{5}}$ | = | $y_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{3}$ | = | $b y_{3} \,\mathbf{\hat{y}}$ | (4g) | Nb II |
| $\mathbf{B_{6}}$ | = | $- y_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{3}$ | = | $- b y_{3} \,\mathbf{\hat{y}}$ | (4g) | Nb II |
| $\mathbf{B_{7}}$ | = | $y_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{3}$ | = | $b y_{4} \,\mathbf{\hat{y}}$ | (4g) | Sn II |
| $\mathbf{B_{8}}$ | = | $- y_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{3}$ | = | $- b y_{4} \,\mathbf{\hat{y}}$ | (4g) | Sn II |
| $\mathbf{B_{9}}$ | = | $\left(y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+y_{5} \, \mathbf{a}_{3}$ | = | $b y_{5} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4h) | Sn III |
| $\mathbf{B_{10}}$ | = | $- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- y_{5} \, \mathbf{a}_{3}$ | = | $- b y_{5} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4h) | Sn III |
| $\mathbf{B_{11}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (8k) | Nb III |
| $\mathbf{B_{12}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}- \frac{1}{4}c \,\mathbf{\hat{z}}$ | (8k) | Nb III |
| $\mathbf{B_{13}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- \frac{1}{4}b \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (8k) | Nb III |
| $\mathbf{B_{14}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}$ | = | $- \frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (8k) | Nb III |
| $\mathbf{B_{15}}$ | = | $\left(y_{7} + z_{7}\right) \, \mathbf{a}_{1}+z_{7} \, \mathbf{a}_{2}+y_{7} \, \mathbf{a}_{3}$ | = | $b y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (8l) | Nb IV |
| $\mathbf{B_{16}}$ | = | $- \left(y_{7} - z_{7}\right) \, \mathbf{a}_{1}+z_{7} \, \mathbf{a}_{2}- y_{7} \, \mathbf{a}_{3}$ | = | $- b y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (8l) | Nb IV |
| $\mathbf{B_{17}}$ | = | $\left(y_{7} - z_{7}\right) \, \mathbf{a}_{1}- z_{7} \, \mathbf{a}_{2}+y_{7} \, \mathbf{a}_{3}$ | = | $b y_{7} \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (8l) | Nb IV |
| $\mathbf{B_{18}}$ | = | $- \left(y_{7} + z_{7}\right) \, \mathbf{a}_{1}- z_{7} \, \mathbf{a}_{2}- y_{7} \, \mathbf{a}_{3}$ | = | $- b y_{7} \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (8l) | Nb IV |
| $\mathbf{B_{19}}$ | = | $\left(y_{8} + z_{8}\right) \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{2}+y_{8} \, \mathbf{a}_{3}$ | = | $b y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (8l) | Sn IV |
| $\mathbf{B_{20}}$ | = | $- \left(y_{8} - z_{8}\right) \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{2}- y_{8} \, \mathbf{a}_{3}$ | = | $- b y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (8l) | Sn IV |
| $\mathbf{B_{21}}$ | = | $\left(y_{8} - z_{8}\right) \, \mathbf{a}_{1}- z_{8} \, \mathbf{a}_{2}+y_{8} \, \mathbf{a}_{3}$ | = | $b y_{8} \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (8l) | Sn IV |
| $\mathbf{B_{22}}$ | = | $- \left(y_{8} + z_{8}\right) \, \mathbf{a}_{1}- z_{8} \, \mathbf{a}_{2}- y_{8} \, \mathbf{a}_{3}$ | = | $- b y_{8} \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (8l) | Sn IV |
References
- J. R. Ogren, T. G. Ellis, and J. F. Smith, The structure of Nb$_{6}$Sn$_{5}$, Acta Cryst. 18, 968–973 (1965), doi:10.1107/S0365110X6500230X.
- 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).
Found in
- P. Villars, H. Okamoto, and K. Cenzual, eds., ASM Alloy Phase Diagram Database (ASM International, 2018), chap. Niobium-Tin Binary Phase Diagram (2009 Li M.). Copyright © 2006-2018 ASM International.
Prototype Generator
aflow --proto=A6B5_oI44_71_egkl_fghl --params=$a,b/a,c/a,x_{1},x_{2},y_{3},y_{4},y_{5},y_{7},z_{7},y_{8},z_{8}$