Ga2Hf Structure: A2B_tI24_141_2e_e

Picture of Structure; Click for Big Picture
Prototype : Ga2Hf
AFLOW prototype label : A2B_tI24_141_2e_e
Strukturbericht designation : None
Pearson symbol : tI24
Space group number : 141
Space group symbol : $\mbox{I4}_{1}\mbox{/amd}$
AFLOW prototype command : aflow --proto=A2B_tI24_141_2e_e
--params=
$a$,$c/a$,$z_{1}$,$z_{2}$,$z_{3}$


Other compounds with this structure

  • Al2Mg, Al2Ti, Ga2Ti, In2Zr, Pb2Pr, Pb2Pu, PuSn2

  • When $z_{1}=1/4$, $z_{2}=5/12$, and $z_{3}=1/12$, the atoms are on the sites of the indium (A6) lattice. If, in this case, $c=6a$, the atoms are on the sites of a face-centered cubic lattice, and if $c=a/\sqrt{2}$, the atoms are on the site of a body-centered cubic lattice. This lattice is placed with the face-centered cubic lattices because most known structures have $c$ near $6a$.

Body-centered Tetragonal primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & =&\left(\frac14 + z_{1}\right) \, \mathbf{a}_{1}+ z_{1} \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& =&\frac14 \, a \, \mathbf{\hat{y}}+ z_{1} \, c \, \mathbf{\hat{z}}& \left(8e\right) & \mbox{Ga I} \\ \mathbf{B}_{2} & =&z_{1} \, \mathbf{a}_{1}+ \left(\frac14 + z_{1}\right) \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}+ \left(\frac34 + z_{1}\right) \, c \, \mathbf{\hat{z}}& \left(8e\right) & \mbox{Ga I} \\ \mathbf{B}_{3} & =&\left(\frac34 - z_{1}\right) \, \mathbf{a}_{1}- z_{1} \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& =&\frac34 \, a \, \mathbf{\hat{y}}- z_{1} \, c \, \mathbf{\hat{z}}& \left(8e\right) & \mbox{Ga I} \\ \mathbf{B}_{4} & =&- z_{1} \, \mathbf{a}_{1}+ \left(\frac34 - z_{1}\right) \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{x}}+ \frac34 \, a \, \mathbf{\hat{y}}+ \left(\frac14 - z_{1}\right) \, c \, \mathbf{\hat{z}}& \left(8e\right) & \mbox{Ga I} \\ \mathbf{B}_{5} & =&\left(\frac14 + z_{2}\right) \, \mathbf{a}_{1}+ z_{2} \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& =&\frac14 \, a \, \mathbf{\hat{y}}+ z_{2} \, c \, \mathbf{\hat{z}}& \left(8e\right) & \mbox{Ga II} \\ \mathbf{B}_{6} & =&z_{2} \, \mathbf{a}_{1}+ \left(\frac14 + z_{2}\right) \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}+ \left(\frac34 + z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(8e\right) & \mbox{Ga II} \\ \mathbf{B}_{7} & =&\left(\frac34 - z_{2}\right) \, \mathbf{a}_{1}- z_{2} \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& =&\frac34 \, a \, \mathbf{\hat{y}}- z_{2} \, c \, \mathbf{\hat{z}}& \left(8e\right) & \mbox{Ga II} \\ \mathbf{B}_{8} & =&- z_{2} \, \mathbf{a}_{1}+ \left(\frac34 - z_{2}\right) \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{x}}+ \frac34 \, a \, \mathbf{\hat{y}}+ \left(\frac14 - z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(8e\right) & \mbox{Ga II} \\ \mathbf{B}_{9} & =&\left(\frac14 + z_{3}\right) \, \mathbf{a}_{1}+ z_{3} \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& =&\frac14 \, a \, \mathbf{\hat{y}}+ z_{3} \, c \, \mathbf{\hat{z}}& \left(8e\right) & \mbox{Hf} \\ \mathbf{B}_{10} & =&z_{3} \, \mathbf{a}_{1}+ \left(\frac14 + z_{3}\right) \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}+ \left(\frac34 + z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(8e\right) & \mbox{Hf} \\ \mathbf{B}_{11} & =&\left(\frac34 - z_{3}\right) \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& =&\frac34 \, a \, \mathbf{\hat{y}}- z_{3} \, c \, \mathbf{\hat{z}}& \left(8e\right) & \mbox{Hf} \\ \mathbf{B}_{12} & =&- z_{3} \, \mathbf{a}_{1}+ \left(\frac34 - z_{3}\right) \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{x}}+ \frac34 \, a \, \mathbf{\hat{y}}+ \left(\frac14 - z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(8e\right) & \mbox{Hf} \\ \end{array} \]

References

  • K. Schubert, H. G. Meissner, M. Pötzschke, W. Rossteutscher, and E. Stolz, Einige Strukturdaten metallischer Phasen (7), Naturwissenschaften 49, 57 (1962).

Found in

  • P. Villars and L. Calvert, Pearson's Handbook of Crystallographic Data for Intermetallic Phases (ASM International, Materials Park, OH, 1991), 2nd edn., pp. 3436.

Geometry files


Prototype Generator

aflow --proto=A2B_tI24_141_2e_e --params=

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