AFLOW Prototype: ABCD_cF16_216_c_d_b_a
Prototype | : | LiMgAuSn |
AFLOW prototype label | : | ABCD_cF16_216_c_d_b_a |
Strukturbericht designation | : | None |
Pearson symbol | : | cF16 |
Space group number | : | 216 |
Space group symbol | : | $F\bar{4}3m$ |
AFLOW prototype command | : | aflow --proto=ABCD_cF16_216_c_d_b_a --params=$a$ |
quaternary Heuslerstructure can be considered as the parent of a wide variety of structures, depending on the occupancy of the (4a), (4b), (4c), and (4d) Wyckoff positions. Consider atoms of type A, B, C, D, distributed in this structure. By placing these atoms on the appropriate Wyckoff positions we find the following structures: \[ \begin{array}{ccccccc} \text{Structure} & \text{Struktubericht} & \text{AFLOW label} & \text{(4a)} & \text{(4b)} & \text{(4c)} & \text{(4d)} \\ \href{./A_cP1_221_a.html}{\text{simple cubic}} & A_{h} & \text{A_cP1_221_a} & \text{A} & \text{A} & \text{-} & \text{-} \\ \href{./A_cF4_225_a.html}{\text{fcc}} & A1 & \text{A_cF4_225_a} & \text{A} & \text{-} & \text{-} & \text{-} \\ \href{./A_cI2_229_a.html}{\text{bcc}} & A2 & \text{A_cI2_229_a} & \text{A} & \text{A} & \text{-} & \text{-} \\ \href{./A_cI2_229_a.html}{\text{bcc}} & A2 & \text{A_cI2_229_a} & \text{A} & \text{A} & \text{A} & \text{A} \\ \href{./A_cF8_227_a.html}{\text{diamond}} & A4 & \text{A_cF8_227_a} & \text{A} & \text{-} & \text{A} & \text{-} \\ \href{./AB_cF8_225_a_b.html}{\text{NaCl}} & B1 & \text{AB_cF8_225_a_b} & \text{A} & \text{B} & \text{-} & \text{-} \\ \href{./AB_cP2_221_b_a.html}{\text{CsCl}} & B2 & \text{AB_cP2_221_b_a} & \text{A} & \text{A} & \text{B} & \text{B} \\ \href{./AB_cF8_216_c_a.html}{\text{ZnS (zincblende)}} & B3 & \text{AB_cF8_216_c_a} & \text{A} & \text{-} & \text{B} & \text{-} \\ \href{./AB3_cF16_225_a_bc.html}{\text{BiF$_{3}$}} & D0_{3} & \text{AB3_cF16_225_a_bc} & \text{A} & \text{B} & \text{B} & \text{B} \\ \href{./AB3_cF16_227_a_c.html}{\text{NaTl}} & B32 & \text{AB_cF16_227_a_c} & \text{A} & \text{A} & \text{B} & \text{B} \\ \href{./ABC_cF12_216_b_c_a.html}{\text{half-Heusler}} & C1_{b} & \text{ABC_cF12_216_b_c_a} & \text{A} & \text{B} & \text{C} & \text{-} \\ \href{./AB2C_cF16_225_a_c_b.html}{\text{Heusler}} & L2_{1} & \text{AB2C_cF16_225_a_c_b} & \text{A} & \text{B} & \text{C} & \text{C} \\ \href{./AB2C_cF16_225_b_ad_c.html}{\text{inverse-Heusler}} & & \text{AB2C_cF16_225_b_ad_c} & \text{B} & \text{A} & \text{C} & \text{B} \\ \end{array} \] The ordering of this structure is somewhat arbitary. So long as Sn and Mg are on either the (4a)/(4b) or (4c)/(4d) sites, with Au and Li on the opposite sites, we will get the same structure.
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \, \mathbf{\hat{x}} + 0 \, \mathbf{\hat{y}} + 0 \, \mathbf{\hat{z}} & \left(4a\right) & \text{Sn} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(4b\right) & \text{Mg} \\ \mathbf{B}_{3} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(4c\right) & \text{Au} \\ \mathbf{B}_{4} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{y}} + \frac{3}{4}a \, \mathbf{\hat{z}} & \left(4d\right) & \text{Li} \\ \end{array} \]