$\zeta$–AgZn ($B_{b}$) Structure: A2B_hP9_147_g_ad

Picture of Structure; Click for Big Picture
Prototype : $\zeta$–AgZn
AFLOW prototype label : A2B_hP9_147_g_ad
Strukturbericht designation : $B_{b}$
Pearson symbol : hP9
Space group number : 147
Space group symbol : $\mbox{P}\bar{3}$
AFLOW prototype command : aflow --proto=A2B_hP9_147_g_ad
--params=
$a$,$c/a$,$z_2$,$x_3$,$y_3$,$z_3$


Other compounds with this structure

  • Ag10CdZn9, Ag50MgZn49

  • When $z_{2} = 0$, $x_{3} = 1/3$, $y_{3} = 0$, and $z_{3} = 1/2$, this structure becomes the hexagonal omega (C32) structure. This is an alloy phase. The (1a) and (2d) sites are pure Zn, but the (6g) site is a mixture of Ag and Zn, so we designate it as M. If the system is stoichiometric then M = (Ag4.5,Zn1.5).

Trigonal Hexagonal primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac{\sqrt{3}}{2} \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2} \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \, \mathbf{\hat{z}}\\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B_1} & = & 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(1a\right) & \mbox{Zn} \\ \mathbf{B_2} & =& \frac13 \, \mathbf{a}_{1} + \frac23 \, \mathbf{a}_{2} + z_2 \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} + \frac1{2\sqrt{3}} \, a \, \mathbf{\hat{y}} +z_2 \, c \, \mathbf{\hat{z}}& \left(2d\right) & \mbox{Zn} \\ \mathbf{B_3} & =& \frac23 \, \mathbf{a}_{1} + \frac13 \, \mathbf{a}_{2} - z_2 \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} - \frac1{2\sqrt{3}} \, a \, \mathbf{\hat{y}} -z_2 \, c \, \mathbf{\hat{z}}& \left(2d\right) & \mbox{Zn} \\ \mathbf{B_4} & =& x_3 \, \mathbf{a}_{1} + y_3 \, \mathbf{a}_{2} + z_3 \, \mathbf{a}_{3}& =& \frac12 \, \left(x_3 + y_3\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}2 \, \left(y_3 - x_3\right) \, a \, \mathbf{\hat{y}}+ z_3 \, c \, \mathbf{\hat{z}}& \left(6g\right) & \mbox{M} \\ \mathbf{B_5} & =& -y_3 \, \mathbf{a}_{1} + \left(x_3 - y_3\right) \, \mathbf{a}_{2} + z_3 \, \mathbf{a}_{3}& =& \frac12 \, \left(x_3 -2 y_3\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}2 \, x_3 \, a \, \mathbf{\hat{y}}+ z_3 \, c \, \mathbf{\hat{z}}& \left(6g\right) & \mbox{M} \\ \mathbf{B_6} & =& \left(y_3 - x_3\right) \, \mathbf{a}_{1} - x_3 \, \mathbf{a}_{2} + z_3 \, \mathbf{a}_{3}& =& \frac12 \, \left(y_3 -2 x_3\right) \, a \, \mathbf{\hat{x}}- \frac{\sqrt3}2 \, y_3 \, a \, \mathbf{\hat{y}}+ z_3 \, c \, \mathbf{\hat{z}}& \left(6g\right) & \mbox{M} \\ \mathbf{B_7} & =& - x_3 \, \mathbf{a}_{1} - y_3 \, \mathbf{a}_{2} - z_3 \, \mathbf{a}_{3}& =& - \frac12 \, \left(x_3 + y_3\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}2 \, \left(x_3 - y_3\right) \, a \, \mathbf{\hat{y}}- z_3 \, c \, \mathbf{\hat{z}}& \left(6g\right) & \mbox{M} \\ \mathbf{B_8} & =& y_3 \, \mathbf{a}_{1} + \left(y_3 - x_3\right) \, \mathbf{a}_{2} - z_3 \, \mathbf{a}_{3}& =& \frac12 \, \left(2 y_3 - x_3\right) \, a \, \mathbf{\hat{x}}- \frac{\sqrt3}2 \, x_3 \, a \, \mathbf{\hat{y}}- z_3 \, c \, \mathbf{\hat{z}}& \left(6g\right) & \mbox{M} \\ \mathbf{B_9} & =& \left(x_3 - y_3\right) \, \mathbf{a}_{1} + x_3 \, \mathbf{a}_{2} - z_3 \, \mathbf{a}_{3}& =& \frac12 \, \left(2x_3 - y_3\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}2 \, y_3 \, a \, \mathbf{\hat{y}}- z_3 \, c \, \mathbf{\hat{z}}& \left(6g\right) & \mbox{M} \\ \end{array} \]

References

  • G. Bergman and R. W. Jaross, On the Crystal Structure of the zeta Phase in the Silver–Zinc System and the Mechanism of the beta–zeta Transformation, Acta Cryst. 8, 232–235 (1955), doi:10.1107/S0365110X55000765.

Geometry files


Prototype Generator

aflow --proto=A2B_hP9_147_g_ad --params=

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