Half–Heusler ($C1_{b}$) Structure: ABC_cF12_216_b_c_a

Picture of Structure; Click for Big Picture
Prototype : AgAsMg
AFLOW prototype label : ABC_cF12_216_b_c_a
Strukturbericht designation : $C1_{b}$
Pearson symbol : cF12
Space group number : 216
Space group symbol : $\mbox{F}\bar{4}\mbox{3m}$
AFLOW prototype command : aflow --proto=ABC_cF12_216_b_c_a
--params=
$a$


Other compounds with this structure

  • MnNiSb, AuMgSn, CdLiP, BiMgNi, RhSnTi, numerous

  • All of the atoms are located on the sites of a body-centered cubic lattice. This is sometimes called the half–Heusler structure because it is identical to the L21 (Heusler) structure with half of the copper atoms missing. The Mg and Ag atoms form a rock salt (B1) structure, while the As and either the Mg or Ag atoms form a zincblende (B3) structure. If the atoms on the (4a) and (4c) sites are identical, this reduces to the fluorite (C1) 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:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \mathbf{\hat{x}} + 0 \mathbf{\hat{y}} + 0 \mathbf{\hat{z}} & \left(4a\right) & \mbox{Mg} \\ \mathbf{B}_{2} & =& \frac12 \mathbf{a}_{1} + \frac12 \mathbf{a}_{2} + \frac12\mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{y}} + \frac12 \, a \, \mathbf{\hat{z}}& \left(4b\right) & \mbox{Ag} \\ \mathbf{B}_{3} & =& \frac14 \mathbf{a}_{1} + \frac14 \mathbf{a}_{2} + \frac14\mathbf{a}_{3}& =& \frac14 \, a \, \mathbf{\hat{x}} + \frac14 \, a \, \mathbf{\hat{y}} + \frac14 \, a \, \mathbf{\hat{z}}& \left(4c\right) & \mbox{As} \\ \end{array} \]

References

  • H. Nowotny and W. Sibert, Ternäre Valenzverbindungen in den Systemen Kupfer(Silber)–Arsen(Antimon,Wismut)–Magnesium, Z. Metallkd. 33, 391–394 (1941).

Found in

  • W. B. Pearson, The Crystal Chemistry and Physics of Metals and Alloys (Wiley– Interscience, New York, London, Sydney, Toronto, 1972)., pp. 386.

Geometry files


Prototype Generator

aflow --proto=ABC_cF12_216_b_c_a --params=

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