α-MgAgSb Structure: ABC_tI48_120_abe_i_i-001
| Prototype | AgMgSb |
| AFLOW prototype label | ABC_tI48_120_abe_i_i-001 |
| ICSD | 187151 |
| CCDC | 1696271 |
| Pearson symbol | tI48 |
| Space group number | 120 |
| Space group symbol | $I\overline{4}c2$ |
| AFLOW prototype command |
aflow --proto=ABC_tI48_120_abe_i_i-001
--params=$a, \allowbreak c/a, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak z_{5}$ |
- MgAgSb is found in three forms (Kirkham, 2012; Mi, 2017):
- $\alpha$–MgAgSb (this phase), the tetragonal ground state phase.
- $\beta$–MgAgSb takes on the matlockite ($E0_{1}$ structure, which can be considered as a ternary form of Cu$_{2}$Sb ($C38$).
- $\gamma$–MgAgSb is in the cubic half-Heusler ($C1_{b}$) structure.
- The range of stability of these structures is rather uncertain. The $\alpha$-phase exists below 300°C, the $\beta$-phase is observed in the range 300-395°C, and $\gamma$–MgAgSb is found at all temperatures above 27°C.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4a) | Ag I |
| $\mathbf{B_{2}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}$ | = | $\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4a) | Ag I |
| $\mathbf{B_{3}}$ | = | $0$ | = | $0$ | (4b) | Ag II |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4b) | Ag II |
| $\mathbf{B_{5}}$ | = | $\left(x_{3} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{3} + \frac{1}{4}\right) \, \mathbf{a}_{2}+2 x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (8e) | Ag III |
| $\mathbf{B_{6}}$ | = | $- \left(x_{3} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{3} - \frac{1}{4}\right) \, \mathbf{a}_{2}- 2 x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (8e) | Ag III |
| $\mathbf{B_{7}}$ | = | $- \left(x_{3} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(x_{3} + \frac{3}{4}\right) \, \mathbf{a}_{2}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (8e) | Ag III |
| $\mathbf{B_{8}}$ | = | $\left(x_{3} + \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(x_{3} - \frac{3}{4}\right) \, \mathbf{a}_{2}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (8e) | Ag III |
| $\mathbf{B_{9}}$ | = | $\left(y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (16i) | Mg I |
| $\mathbf{B_{10}}$ | = | $- \left(y_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} - z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (16i) | Mg I |
| $\mathbf{B_{11}}$ | = | $- \left(x_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(y_{4} - z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} - y_{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (16i) | Mg I |
| $\mathbf{B_{12}}$ | = | $\left(x_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (16i) | Mg I |
| $\mathbf{B_{13}}$ | = | $\left(- y_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16i) | Mg I |
| $\mathbf{B_{14}}$ | = | $\left(y_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{4} - y_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16i) | Mg I |
| $\mathbf{B_{15}}$ | = | $\left(x_{4} - z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{4} - z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- c \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16i) | Mg I |
| $\mathbf{B_{16}}$ | = | $- \left(x_{4} + z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{4} + z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- c \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16i) | Mg I |
| $\mathbf{B_{17}}$ | = | $\left(y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (16i) | Sb I |
| $\mathbf{B_{18}}$ | = | $- \left(y_{5} - z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} - z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (16i) | Sb I |
| $\mathbf{B_{19}}$ | = | $- \left(x_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(y_{5} - z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (16i) | Sb I |
| $\mathbf{B_{20}}$ | = | $\left(x_{5} - z_{5}\right) \, \mathbf{a}_{1}- \left(y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5}\right) \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (16i) | Sb I |
| $\mathbf{B_{21}}$ | = | $\left(- y_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16i) | Sb I |
| $\mathbf{B_{22}}$ | = | $\left(y_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16i) | Sb I |
| $\mathbf{B_{23}}$ | = | $\left(x_{5} - z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{5} - z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5}\right) \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- c \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16i) | Sb I |
| $\mathbf{B_{24}}$ | = | $- \left(x_{5} + z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{5} + z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5}\right) \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- c \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16i) | Sb I |
References
- M. J. Kirkham, A. M. dos Santos, C. J. Rawn, E. Lara-Curzio, J. W. Sharp, and A. J. Thompson, {\em Ab initio} determination of crystal structures of the thermoelectric material MgAgSb, Phys. Rev. B 85, 144120 (2012), doi:10.1103/PhysRevB.85.144120.
Found in
- J.-L. Mi, P.-J. Ying, M. Sist, H. Reardon, P. Zhang, T.-J. Zhu, X.-B. Zhao, and B. B. Iversen, Elaborating the Crystal Structures of MgAgSb Thermoelectric Compound: Polymorphs and Atomic Disorders, Chem. Mater. 29, 6378–6388 (2017), doi:10.1021/acs.chemmater.7b01768.
First cited in
- N. Anderson, M. J. Mehl, H. Eckert, S. Divilov, X. Campilongo, S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 5. Submitted to Computational Materials Science (2026).
Geometry files
Prototype Generator
aflow --proto=ABC_tI48_120_abe_i_i --params=$a,c/a,x_{3},x_{4},y_{4},z_{4},x_{5},y_{5},z_{5}$