Quaternary Heusler (LiMgAuSn) Structure: ABCD_cF16_216_c_d_b_a

Picture of Structure; Click for Big Picture
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=
$a$


Other compounds with this structure

  • AuLiMgSn, CuMg2Ti, AuBiLi2, AgLi2Sn, AuLi2Sn, CuHfHg2, MnPd2Sn, and many more. See (Eberz, 1980).

  • This quaternary Heusler structure 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: \[ \begin{array}{ccccccc} \mbox{Structure} & \mbox{Struktubericht} & \mbox{AFLOW label} & \mbox{(4a)} & \mbox{(4b)} & \mbox{(4c)} & \mbox{(4d)} \\ \href{./A_cP1_221_a.html}{\mbox{simple cubic}} & A_{h} & \mbox{A_cP1_221_a} & \mbox{A} & \mbox{A} & \mbox{-} & \mbox{-} \\ \href{./A_cF4_225_a.html}{\mbox{fcc}} & A1 & \mbox{A_cF4_225_a} & \mbox{A} & \mbox{-} & \mbox{-} & \mbox{-} \\ \href{./A_cI2_229_a.html}{\mbox{bcc}} & A2 & \mbox{A_cI2_229_a} & \mbox{A} & \mbox{A} & \mbox{-} & \mbox{-} \\ \href{./A_cI2_229_a.html}{\mbox{bcc}} & A2 & \mbox{A_cI2_229_a} & \mbox{A} & \mbox{A} & \mbox{A} & \mbox{A} \\ \href{./A_cF8_227_a.html}{\mbox{diamond}} & A4 & \mbox{A_cF8_227_a} & \mbox{A} & \mbox{-} & \mbox{A} & \mbox{-} \\ \href{./AB_cF8_225_a_b.html}{\mbox{NaCl}} & B1 & \mbox{AB_cF8_225_a_b} & \mbox{A} & \mbox{B} & \mbox{-} & \mbox{-} \\ \href{./AB_cP2_221_b_a.html}{\mbox{CsCl}} & B2 & \mbox{AB_cP2_221_b_a} & \mbox{A} & \mbox{A} & \mbox{B} & \mbox{B} \\ \href{./AB_cF8_216_c_a.html}{\mbox{ZnS (zincblende)}} & B3 & \mbox{AB_cF8_216_c_a} & \mbox{A} & \mbox{-} & \mbox{B} & \mbox{-} \\ \href{./AB3_cF16_225_a_bc.html}{\mbox{BiF$_{3}$}} & D0_{3} & \mbox{AB3_cF16_225_a_bc} & \mbox{A} & \mbox{B} & \mbox{B} & \mbox{B} \\ \href{./AB3_cF16_227_a_c.html}{\mbox{NaTl}} & B32 & \mbox{AB_cF16_227_a_c} & \mbox{A} & \mbox{A} & \mbox{B} & \mbox{B} \\ \href{./ABC_cF12_216_b_c_a.html}{\mbox{half-Heusler}} & C1_{b} & \mbox{ABC_cF12_216_b_c_a} & \mbox{A} & \mbox{B} & \mbox{C} & \mbox{-} \\ \href{./AB2C_cF16_225_a_c_b.html}{\mbox{Heusler}} & L2_{1} & \mbox{AB2C_cF16_225_a_c_b} & \mbox{A} & \mbox{B} & \mbox{C} & \mbox{C} \\ \href{./AB2C_cF16_225_b_ad_c.html}{\mbox{inverse-Heusler}} & & \mbox{AB2C_cF16_225_b_ad_c} & \mbox{B} & \mbox{A} & \mbox{C} & \mbox{B} \\ \end{array} \] 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.

Face-centered Cubic primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{y}} + \frac12 \, a \, \mathbf{\hat{z}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{z}} \\ \mathbf{a}_3 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{y}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \, \mathbf{\hat{x}} + 0 \, \mathbf{\hat{y}} + 0 \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{Sn} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Mg} \\ \mathbf{B}_{3} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Au} \\ \mathbf{B}_{4} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{y}} + \frac{3}{4}a \, \mathbf{\hat{z}} & \left(4d\right) & \mbox{Li} \\ \end{array} \]

References

  • U. Eberz, W. Seelentag, and H.–U. Schuster, Zur Kenntnis farbiger ternärer und quaternärer Zintl–Phasen [Coloured Ternary and Quaternary Zintl–Phases], Z. Naturforsch. B 35, 1341–1343 (1980), doi:10.1515/znb-1980-1103.

Found in

  • {P. Villars (Chief Editor)}, ed., PAULING FILE in: Inorganic Solid Phases, SpringerMaterials (online database) (Springer Materials, Heigelberg, 2016), chap. LiMgPdSn Crystal Structure.

Geometry files


Prototype Generator

aflow --proto=ABCD_cF16_216_c_d_b_a --params=

Species:

Running:

Output: