SC16 (CuCl) Structure: AB_cP16_205_c_c

Picture of Structure; Click for Big Picture
Prototype : CuCl
AFLOW prototype label : AB_cP16_205_c_c
Strukturbericht designation : None
Pearson symbol : cP16
Space group number : 205
Space group symbol : $\mbox{Pa}\bar{3}$
AFLOW prototype command : aflow --proto=AB_cP16_205_c_c
--params=
$a$,$x_1$,$x_2$


  • This is a tetragonally bonded structure which packs more efficiently than diamond. This structure is related to BC8 in the same way that zincblende (B3) is related to diamond (A4): we replace half of the atoms by another species, such that the four nearest neighbors of each atom are of the other species. See (Crain, 1995) and references therein. The reference compound chosen here, found in (Hull, 1994), is stable at about 5 GPa.

Simple Cubic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B_1} & =&x_1 \, \mathbf{a}_{1}+ x_1 \, \mathbf{a}_{2}+ x_1 \, \mathbf{a}_{3}& =&x_1 \, \, a \, \mathbf{\hat{x}}+ x_1 \, \, a \, \mathbf{\hat{y}}+ x_1 \, \, a \, \mathbf{\hat{z}}& \left(8c\right) & \mbox{Cl} \\ \mathbf{B_2} & =&\left(\frac12 - x_1\right) \, \mathbf{a}_{1}- x_1 \, \mathbf{a}_{2}+ \left(\frac12 + x_1\right) \, \mathbf{a}_{3}& =&\left(\frac12 - x_1\right) \, \, a \, \mathbf{\hat{x}}- x_1 \, \, a \, \mathbf{\hat{y}}+ \left(\frac12 + x_1\right) \, \, a \, \mathbf{\hat{z}}& \left(8c\right) & \mbox{Cl} \\ \mathbf{B_3} & =&- x_1 \, \mathbf{a}_{1}+ \left(\frac12 + x_1\right) \, \mathbf{a}_{2}+ \left(\frac12 - x_1\right) \, \mathbf{a}_{3}& =&- x_1 \, \, a \, \mathbf{\hat{x}}+ \left(\frac12 + x_1\right) \, \, a \, \mathbf{\hat{y}}+ \left(\frac12 - x_1\right) \, \, a \, \mathbf{\hat{z}}& \left(8c\right) & \mbox{Cl} \\ \mathbf{B_4} & =&\left(\frac12 + x_1\right) \, \mathbf{a}_{1}+ \left(\frac12 - x_1\right) \, \mathbf{a}_{2}- x_1 \, \mathbf{a}_{3}& =&\left(\frac12 + x_1\right) \, \, a \, \mathbf{\hat{x}}+ \left(\frac12 - x_1\right) \, \, a \, \mathbf{\hat{y}}- x_1 \, \, a \, \mathbf{\hat{z}}& \left(8c\right) & \mbox{Cl} \\ \mathbf{B_5} & =&- x_1 \, \mathbf{a}_{1}- x_1 \, \mathbf{a}_{2}- x_1 \, \mathbf{a}_{3}& =&- x_1 \, \, a \, \mathbf{\hat{x}}- x_1 \, \, a \, \mathbf{\hat{y}}- x_1 \, \, a \, \mathbf{\hat{z}}& \left(8c\right) & \mbox{Cl} \\ \mathbf{B_6} & =&\left(\frac12 + x_1\right) \, \mathbf{a}_{1}+ x_1 \, \mathbf{a}_{2}+ \left(\frac12 - x_1\right) \, \mathbf{a}_{3}& =&\left(\frac12 + x_1\right) \, \, a \, \mathbf{\hat{x}}+ x_1 \, \, a \, \mathbf{\hat{y}}+ \left(\frac12 - x_1\right) \, \, a \, \mathbf{\hat{z}}& \left(8c\right) & \mbox{Cl} \\ \mathbf{B_7} & =&x_1 \, \mathbf{a}_{1}+ \left(\frac12 - x_1\right) \, \mathbf{a}_{2}+ \left(\frac12 + x_1\right) \, \mathbf{a}_{3}& =&x_1 \, \, a \, \mathbf{\hat{x}}+ \left(\frac12 - x_1\right) \, \, a \, \mathbf{\hat{y}}+ \left(\frac12 + x_1\right) \, \, a \, \mathbf{\hat{z}}& \left(8c\right) & \mbox{Cl} \\ \mathbf{B_8} & =&\left(\frac12 - x_1\right) \, \mathbf{a}_{1}+ \left(\frac12 + x_1\right) \, \mathbf{a}_{2}+ x_1 \, \mathbf{a}_{3}& =&\left(\frac12 - x_1\right) \, \, a \, \mathbf{\hat{x}}+ \left(\frac12 + x_1\right) \, \, a \, \mathbf{\hat{y}}+ x_1 \, \, a \, \mathbf{\hat{z}}& \left(8c\right) & \mbox{Cl} \\ \mathbf{B_9} & =&x_2 \, \mathbf{a}_{1}+ x_2 \, \mathbf{a}_{2}+ x_2 \, \mathbf{a}_{3}& =&x_2 \, \, a \, \mathbf{\hat{x}}+ x_2 \, \, a \, \mathbf{\hat{y}}+ x_2 \, \, a \, \mathbf{\hat{z}}& \left(8c\right) & \mbox{Cu} \\ \mathbf{B}_{10} & =&\left(\frac12 - x_2\right) \, \mathbf{a}_{1}- x_2 \, \mathbf{a}_{2}+ \left(\frac12 + x_2\right) \, \mathbf{a}_{3}& =&\left(\frac12 - x_2\right) \, \, a \, \mathbf{\hat{x}}- x_2 \, \, a \, \mathbf{\hat{y}}+ \left(\frac12 + x_2\right) \, \, a \, \mathbf{\hat{z}}& \left(8c\right) & \mbox{Cu} \\ \mathbf{B}_{11} & =&- x_2 \, \mathbf{a}_{1}+ \left(\frac12 + x_2\right) \, \mathbf{a}_{2}+ \left(\frac12 - x_2\right) \, \mathbf{a}_{3}& =&- x_2 \, \, a \, \mathbf{\hat{x}}+ \left(\frac12 + x_2\right) \, \, a \, \mathbf{\hat{y}}+ \left(\frac12 - x_2\right) \, \, a \, \mathbf{\hat{z}}& \left(8c\right) & \mbox{Cu} \\ \mathbf{B}_{12} & =&\left(\frac12 + x_2\right) \, \mathbf{a}_{1}+ \left(\frac12 - x_2\right) \, \mathbf{a}_{2}- x_2 \, \mathbf{a}_{3}& =&\left(\frac12 + x_2\right) \, \, a \, \mathbf{\hat{x}}+ \left(\frac12 - x_2\right) \, \, a \, \mathbf{\hat{y}}- x_2 \, \, a \, \mathbf{\hat{z}}& \left(8c\right) & \mbox{Cu} \\ \mathbf{B}_{13} & =&- x_2 \, \mathbf{a}_{1}- x_2 \, \mathbf{a}_{2}- x_2 \, \mathbf{a}_{3}& =&- x_2 \, \, a \, \mathbf{\hat{x}}- x_2 \, \, a \, \mathbf{\hat{y}}- x_2 \, \, a \, \mathbf{\hat{z}}& \left(8c\right) & \mbox{Cu} \\ \mathbf{B}_{14} & =&\left(\frac12 + x_2\right) \, \mathbf{a}_{1}+ x_2 \, \mathbf{a}_{2}+ \left(\frac12 - x_2\right) \, \mathbf{a}_{3}& =&\left(\frac12 + x_2\right) \, \, a \, \mathbf{\hat{x}}+ x_2 \, \, a \, \mathbf{\hat{y}}+ \left(\frac12 - x_2\right) \, \, a \, \mathbf{\hat{z}}& \left(8c\right) & \mbox{Cu} \\ \mathbf{B}_{15} & =&x_2 \, \mathbf{a}_{1}+ \left(\frac12 - x_2\right) \, \mathbf{a}_{2}+ \left(\frac12 + x_2\right) \, \mathbf{a}_{3}& =&x_2 \, \, a \, \mathbf{\hat{x}}+ \left(\frac12 - x_2\right) \, \, a \, \mathbf{\hat{y}}+ \left(\frac12 + x_2\right) \, \, a \, \mathbf{\hat{z}}& \left(8c\right) & \mbox{Cu} \\ \mathbf{B}_{16} & =&\left(\frac12 - x_2\right) \, \mathbf{a}_{1}+ \left(\frac12 + x_2\right) \, \mathbf{a}_{2}+ x_2 \, \mathbf{a}_{3}& =&\left(\frac12 - x_2\right) \, \, a \, \mathbf{\hat{x}}+ \left(\frac12 + x_2\right) \, \, a \, \mathbf{\hat{y}}+ x_2 \, \, a \, \mathbf{\hat{z}}& \left(8c\right) & \mbox{Cu} \\ \end{array} \]

References

  • S. Hull and D. A. Keen, High–pressure polymorphism of the copper(I) halides: A neutron–diffraction study to sim10 GPa, Phys. Rev. B 50, 5868–5885 (1994), doi:10.1103/PhysRevB.50.5868.
  • J. Crain, G. J. Ackland, and S. J. Clark, Exotic structures of tetrahedral semiconductors, Rep. Prog. Phys. 58, 705–754 (1995), doi:10.1088/0034-4885/58/7/001.

Geometry files


Prototype Generator

aflow --proto=AB_cP16_205_c_c --params=

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