$\alpha$–AgI ($B23$) Structure : A21B_cI44_229_bdh_a

Picture of Structure; Click for Big Picture
Prototype : AgI
AFLOW prototype label : A21B_cI44_229_bdh_a
Strukturbericht designation : $B23$
Pearson symbol : cI44
Space group number : 229
Space group symbol : $Im\bar{3}m$
AFLOW prototype command : aflow --proto=A21B_cI44_229_bdh_a
--params=
$a$,$y_{4}$


  • Under ambient conditions, silver iodide exists as a mixture of $\beta$–AgI, which has the wurtzite ($B4$) structure, and $\gamma$–AgI, which has the zincblende ($B3$) structure (Hull, 2004). Above 420 K, AgI transforms to this superionic $\alpha$ phase. The iodine atom sits at the ($2a$) site of the bcc lattice of space group #229, while the silver atom is randomly distributed on one of the ($6b$), ($12d$), and ($24h$) Wyckoff sites in each unit cell. On average, then, each of the 21 Ag sites listed above is occupied only 4.762% of the time in any given primitive cell. This easy transport between sites drives the superionic behavior of $\alpha$–AgI.

Body-centered Cubic primitive vectors:

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

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(2a\right) & \mbox{I} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} & \left(6b\right) & \mbox{Ag I} \\ \mathbf{B}_{3} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{y}} & \left(6b\right) & \mbox{Ag I} \\ \mathbf{B}_{4} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{2}a \, \mathbf{\hat{z}} & \left(6b\right) & \mbox{Ag I} \\ \mathbf{B}_{5} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(12d\right) & \mbox{Ag II} \\ \mathbf{B}_{6} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} & \left(12d\right) & \mbox{Ag II} \\ \mathbf{B}_{7} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} & \left(12d\right) & \mbox{Ag II} \\ \mathbf{B}_{8} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(12d\right) & \mbox{Ag II} \\ \mathbf{B}_{9} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(12d\right) & \mbox{Ag II} \\ \mathbf{B}_{10} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(12d\right) & \mbox{Ag II} \\ \mathbf{B}_{11} & = & 2y_{4} \, \mathbf{a}_{1} + y_{4} \, \mathbf{a}_{2} + y_{4} \, \mathbf{a}_{3} & = & y_{4}a \, \mathbf{\hat{y}} + y_{4}a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{Ag III} \\ \mathbf{B}_{12} & = & y_{4} \, \mathbf{a}_{2}-y_{4} \, \mathbf{a}_{3} & = & -y_{4}a \, \mathbf{\hat{y}} + y_{4}a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{Ag III} \\ \mathbf{B}_{13} & = & -y_{4} \, \mathbf{a}_{2} + y_{4} \, \mathbf{a}_{3} & = & y_{4}a \, \mathbf{\hat{y}}-y_{4}a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{Ag III} \\ \mathbf{B}_{14} & = & -2y_{4} \, \mathbf{a}_{1}-y_{4} \, \mathbf{a}_{2}-y_{4} \, \mathbf{a}_{3} & = & -y_{4}a \, \mathbf{\hat{y}}-y_{4}a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{Ag III} \\ \mathbf{B}_{15} & = & y_{4} \, \mathbf{a}_{1} + 2y_{4} \, \mathbf{a}_{2} + y_{4} \, \mathbf{a}_{3} & = & y_{4}a \, \mathbf{\hat{x}} + y_{4}a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{Ag III} \\ \mathbf{B}_{16} & = & -y_{4} \, \mathbf{a}_{1} + y_{4} \, \mathbf{a}_{3} & = & y_{4}a \, \mathbf{\hat{x}}-y_{4}a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{Ag III} \\ \mathbf{B}_{17} & = & y_{4} \, \mathbf{a}_{1}-y_{4} \, \mathbf{a}_{3} & = & -y_{4}a \, \mathbf{\hat{x}} + y_{4}a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{Ag III} \\ \mathbf{B}_{18} & = & -y_{4} \, \mathbf{a}_{1}-2y_{4} \, \mathbf{a}_{2}-y_{4} \, \mathbf{a}_{3} & = & -y_{4}a \, \mathbf{\hat{x}}-y_{4}a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{Ag III} \\ \mathbf{B}_{19} & = & y_{4} \, \mathbf{a}_{1} + y_{4} \, \mathbf{a}_{2} + 2y_{4} \, \mathbf{a}_{3} & = & y_{4}a \, \mathbf{\hat{x}} + y_{4}a \, \mathbf{\hat{y}} & \left(24h\right) & \mbox{Ag III} \\ \mathbf{B}_{20} & = & y_{4} \, \mathbf{a}_{1}-y_{4} \, \mathbf{a}_{2} & = & -y_{4}a \, \mathbf{\hat{x}} + y_{4}a \, \mathbf{\hat{y}} & \left(24h\right) & \mbox{Ag III} \\ \mathbf{B}_{21} & = & -y_{4} \, \mathbf{a}_{1} + y_{4} \, \mathbf{a}_{2} & = & y_{4}a \, \mathbf{\hat{x}}-y_{4}a \, \mathbf{\hat{y}} & \left(24h\right) & \mbox{Ag III} \\ \mathbf{B}_{22} & = & -y_{4} \, \mathbf{a}_{1}-y_{4} \, \mathbf{a}_{2}-2y_{4} \, \mathbf{a}_{3} & = & -y_{4}a \, \mathbf{\hat{x}}-y_{4}a \, \mathbf{\hat{y}} & \left(24h\right) & \mbox{Ag III} \\ \end{array} \]

References

  • L. W. Strock, Kristallstruktur des Hochtemperatur–Jodsilbers $\alpha$–AgJ, Z. Physik. Chem. B 25, 441–459 (1934), doi:10.1515/zpch-1934-2535.

Found in

  • S. Hoshino, Crystal Structure and Phase Transition of Some Metallic Halides IV On the Anomalous Structure of $\alpha$–AgI, J. Phys. Soc. Jpn. 12, 315–326 (1957), doi:10.1143/JPSJ.12.315.

Geometry files


Prototype Generator

aflow --proto=A21B_cI44_229_bdh_a --params=

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