LaTi$_{3}$Bi$_{4}$ Structure: A4BC3_oF64_69_gho_g_gl-001
| Prototype | Bi$_{4}$LaTi$_{3}$ |
| AFLOW prototype label | A4BC3_oF64_69_gho_g_gl-001 |
| ICSD | 119550 |
| CCDC | 2335975 |
| Pearson symbol | oF64 |
| Space group number | 69 |
| Space group symbol | $Fmmm$ |
| AFLOW prototype command |
aflow --proto=A4BC3_oF64_69_gho_g_gl-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak y_{4}, \allowbreak x_{5}, \allowbreak x_{6}, \allowbreak y_{6}$ |
Other compounds with this structure
CaTi$_{3}$Bi$_{4}$, CaV$_{3}$Sb$_{4}$, CeTi$_{3}$Bi$_{4}$, DyTi$_{3}$Bi$_{4}$, ErTi$_{3}$Bi$_{4}$, EuTi$_{3}$Bi$_{4}$, GdTi$_{3}$Bi$_{4}$, HoTi$_{3}$Bi$_{4}$, LuTi$_{3}$Bi$_{4}$, NdTi$_{3}$Bi$_{4}$, PmTi$_{3}$Bi$_{4}$, PrTi$_{3}$Bi$_{4}$, SmTi$_{3}$Bi$_{4}$, TbTi$_{3}$Bi$_{4}$, TmTi$_{3}$Bi$_{4}$, YbTi$_{3}$Bi$_{4}$, Nd(Sb, Sn)$_{3}$Bi$_{4}$
- In orthorhombic systems the AFLOW prototype label standard favors orientations of where most of the free atomic parameters are along the x-axis. Thus we have rotated the published structure so that coordinates (x,y,z) $\rightarrow$ (z,y,-x), with a similar change for the lattice parameters.
- The ICSD lists Nd(Sb,Sn)$_{3}$Bi$_{4}$ as the prototype for this structure, but we prefer to use a fully ordered structure.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $- x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ | = | $a x_{1} \,\mathbf{\hat{x}}$ | (8g) | Bi I |
| $\mathbf{B_{2}}$ | = | $x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}- x_{1} \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{x}}$ | (8g) | Bi I |
| $\mathbf{B_{3}}$ | = | $- x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}$ | (8g) | La I |
| $\mathbf{B_{4}}$ | = | $x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}$ | (8g) | La I |
| $\mathbf{B_{5}}$ | = | $- x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}$ | (8g) | Ti I |
| $\mathbf{B_{6}}$ | = | $x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}$ | (8g) | Ti I |
| $\mathbf{B_{7}}$ | = | $y_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+y_{4} \, \mathbf{a}_{3}$ | = | $b y_{4} \,\mathbf{\hat{y}}$ | (8h) | Bi II |
| $\mathbf{B_{8}}$ | = | $- y_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}- y_{4} \, \mathbf{a}_{3}$ | = | $- b y_{4} \,\mathbf{\hat{y}}$ | (8h) | Bi II |
| $\mathbf{B_{9}}$ | = | $- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (16l) | Ti II |
| $\mathbf{B_{10}}$ | = | $x_{5} \, \mathbf{a}_{1}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (16l) | Ti II |
| $\mathbf{B_{11}}$ | = | $\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (16l) | Ti II |
| $\mathbf{B_{12}}$ | = | $- x_{5} \, \mathbf{a}_{1}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (16l) | Ti II |
| $\mathbf{B_{13}}$ | = | $- \left(x_{6} - y_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} - y_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} + y_{6}\right) \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+b y_{6} \,\mathbf{\hat{y}}$ | (16o) | Bi III |
| $\mathbf{B_{14}}$ | = | $\left(x_{6} - y_{6}\right) \, \mathbf{a}_{1}- \left(x_{6} - y_{6}\right) \, \mathbf{a}_{2}- \left(x_{6} + y_{6}\right) \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}- b y_{6} \,\mathbf{\hat{y}}$ | (16o) | Bi III |
| $\mathbf{B_{15}}$ | = | $\left(x_{6} + y_{6}\right) \, \mathbf{a}_{1}- \left(x_{6} + y_{6}\right) \, \mathbf{a}_{2}- \left(x_{6} - y_{6}\right) \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}+b y_{6} \,\mathbf{\hat{y}}$ | (16o) | Bi III |
| $\mathbf{B_{16}}$ | = | $- \left(x_{6} + y_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} + y_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} - y_{6}\right) \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}- b y_{6} \,\mathbf{\hat{y}}$ | (16o) | Bi III |
References
- B. R. Ortiz, H. Miao, D. S. Parker, F. Yang, G. D. Samolyuk, E. M. Clements, A. Rajapitamahuni, T. Yilmaz, E. Vescovo, J. Yan, A. F. May, and M. A. McGuire, Evolution of Highly Anisotropic Magnetism in the Titanium-Based Kagome Metals LnTi$_{3}$Bi$_{4}$ (Ln: La···Gd$^{3+}$, Eu$^{2+}$, Yb$^{2+}$), Chem. of Mater. 35, 9756–9773 (2023), doi:10.1021/acs.chemmater.3c02289.
Found in
- B. R. Ortiz, H. Zhang, K. Górnicka, D. S. Parker, G. D. Samolyuk, F. Yang, H. Miao, Q. Lu, R. G. Moore, A. F. May, and M. A. McGuire, Intricate Magnetic Landscape in Antiferromagnetic Kagome Metal TbTi$_{3}$Bi$_{4}$ and Interplay with Ln$_{2-x}$Ti$_{6+x}$Bi$_{9}$ (Ln: Tb–Lu) Shurikagome Metals, Chem. Mater. 36, 8002–8014 (2024).
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=A4BC3_oF64_69_gho_g_gl --params=$a,b/a,c/a,x_{1},x_{2},x_{3},y_{4},x_{5},x_{6},y_{6}$