Hg2TiCu Inverse Heusler Structure : AB2C_cF16_216_b_ad_c

Picture of Structure; Click for Big Picture
Prototype : CuHg2Ti
AFLOW prototype label : AB2C_cF16_216_b_ad_c
Strukturbericht designation : None
Pearson symbol : cF16
Space group number : 216
Space group symbol : $F\bar{4}3m$
AFLOW prototype command : aflow --proto=AB2C_cF16_216_b_ad_c
--params=
$a$


Other compounds with this structure

  • Mn2CoAl, Mn2CoGa, Mn2CoIn, Li2AgSb, Li2CuSn, Li2CuSb, Li2AgAl, Li2AgIn, Li2AgSb, Li2AgSn, Li2AgPb, Li2AgBi, Li2AuGa, Li2AuIn, Li2AuSb, Li2AuSn, Li2AuPb, and Li2AuTl

  • Most of the literature on Inverse Heusler compounds identifies Hg2TiCu as the prototype structure, however (Villars, 2016) and (Villars, 2016a) use the Li2AgSb structure found in (Pauly, 1968) as the prototype. Although it is tempting to use the older paper, we follow the majority and use Hg2TiCu as the prototype.
  • The inverse Heusler structure is a variation of the Quaternary Heusler structure, where the mercury atoms are on adjacent face–centered cubic sublattices, forming a diamond structure. Contrast this with the standard Heusler ($L1_{2}$) structure, where the like atoms are at second–neighbor positions in the fcc lattice.
  • This structure is also referred to as the XA or X$_{\mathrm{a}}$ 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:

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

References

  • H. Pauly, A. Weiss, and H. Witte, The Crystal Structure of the Ternary Intermetallic Phases Li2$EX$ ($E$=Cu, Ag, Au; $X$=Al, Ga, In, Tl, Si, Ge, Sn, Pb, Sb, Bi), Z. Metallkd. 59, 47–58 (1968).

Found in

Geometry files


Prototype Generator

aflow --proto=AB2C_cF16_216_b_ad_c --params=

Species:

Running:

Output: