MnGa$_{2}$Sb$_{2}$ Structure: A2BC2_oI20_45_c_a_c-001
| Prototype | Ga$_{2}$MnSb$_{2}$ |
| AFLOW prototype label | A2BC2_oI20_45_c_a_c-001 |
| ICSD | none |
| Pearson symbol | oI20 |
| Space group number | 45 |
| Space group symbol | $Iba2$ |
| AFLOW prototype command |
aflow --proto=A2BC2_oI20_45_c_a_c-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak x_{2}, \allowbreak y_{2}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}$ |
- The Mn site has an occupation of 0.9365.
- We shifted the origin so that the Mn atom is at the (4a) site rather than the (4b) site.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $z_{1} \, \mathbf{a}_{1}+z_{1} \, \mathbf{a}_{2}$ | = | $c z_{1} \,\mathbf{\hat{z}}$ | (4a) | Mn I |
| $\mathbf{B_{2}}$ | = | $\left(z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{2}$ | = | $c \left(z_{1} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | Mn I |
| $\mathbf{B_{3}}$ | = | $\left(y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + y_{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+b y_{2} \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (8c) | Ga I |
| $\mathbf{B_{4}}$ | = | $- \left(y_{2} - z_{2}\right) \, \mathbf{a}_{1}- \left(x_{2} - z_{2}\right) \, \mathbf{a}_{2}- \left(x_{2} + y_{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- b y_{2} \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (8c) | Ga I |
| $\mathbf{B_{5}}$ | = | $\left(- y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{2} - y_{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}- b y_{2} \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8c) | Ga I |
| $\mathbf{B_{6}}$ | = | $\left(y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{2} - y_{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+b y_{2} \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8c) | Ga I |
| $\mathbf{B_{7}}$ | = | $\left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (8c) | Sb I |
| $\mathbf{B_{8}}$ | = | $- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (8c) | Sb I |
| $\mathbf{B_{9}}$ | = | $\left(- y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8c) | Sb I |
| $\mathbf{B_{10}}$ | = | $\left(y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{3} - y_{3}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8c) | Sb I |
References
- W. Sakakibara, Y. Hayashi, and H. Takizawa, MnGa$_{2}$Sb$_{2}$, a new ferromagnetic compound synthesized under high pressure, J. Ceram. Soc. Jpn. 117, 72–75 (2009), doi:10.2109/jcersj2.117.72.
Found in
- P. Villars and K. Cenzual, Pearson's Crystal Data – Crystal Structure Database for Inorganic Compounds (2013). ASM International.
Prototype Generator
aflow --proto=A2BC2_oI20_45_c_a_c --params=$a,b/a,c/a,z_{1},x_{2},y_{2},z_{2},x_{3},y_{3},z_{3}$