Ag5Pb2O6 Structure: A5B6C2_hP13_157_2ac_2c_b

Picture of Structure; Click for Big Picture
Prototype : Ag5Pb2O6
AFLOW prototype label : A5B6C2_hP13_157_2ac_2c_b
Strukturbericht designation : None
Pearson symbol : hP13
Space group number : 157
Space group symbol : $P31m$
AFLOW prototype command : aflow --proto=A5B6C2_hP13_157_2ac_2c_b
--params=
$a$,$c/a$,$z_{1}$,$z_{2}$,$z_{3}$,$x_{4}$,$z_{4}$,$x_{5}$,$z_{5}$,$x_{6}$,$z_{6}$


  • The original reference (Byström, 1950) lists this structure as Ag5Pb2O6, while (Villars, 1985) lists it as Ag2PbO3. (Byström, 1950) provides three Wyckoff positions for Ag (1a, 1a, and 3c), while (Villars, 1985) only provides two (1a and 3c), giving rise to the stoichiometry discrepancy. While both descriptions yield space group #157, the authors use the structure and coordinates provided by the original reference (Byström, 1950).

Trigonal Hexagonal primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \, \mathbf{\hat{z}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & z_{1} \, \mathbf{a}_{3} & = & z_{1}c \, \mathbf{\hat{z}} & \left(1a\right) & \mbox{Ag I} \\ \mathbf{B}_{2} & = & z_{2} \, \mathbf{a}_{3} & = & z_{2}c \, \mathbf{\hat{z}} & \left(1a\right) & \mbox{Ag II} \\ \mathbf{B}_{3} & = & \frac{1}{3} \, \mathbf{a}_{1} + \frac{2}{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(2b\right) & \mbox{Pb} \\ \mathbf{B}_{4} & = & \frac{2}{3} \, \mathbf{a}_{1} + \frac{1}{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(2b\right) & \mbox{Pb} \\ \mathbf{B}_{5} & = & x_{4} \, \mathbf{a}_{1} + z_{4} \, \mathbf{a}_{3} & = & \frac{1}{2}x_{4}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(3c\right) & \mbox{Ag III} \\ \mathbf{B}_{6} & = & x_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & \frac{1}{2}x_{4}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(3c\right) & \mbox{Ag III} \\ \mathbf{B}_{7} & = & -x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} + z_{4}c \, \mathbf{\hat{z}} & \left(3c\right) & \mbox{Ag III} \\ \mathbf{B}_{8} & = & x_{5} \, \mathbf{a}_{1} + z_{5} \, \mathbf{a}_{3} & = & \frac{1}{2}x_{5}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{5}a \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(3c\right) & \mbox{O I} \\ \mathbf{B}_{9} & = & x_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & \frac{1}{2}x_{5}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{5}a \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(3c\right) & \mbox{O I} \\ \mathbf{B}_{10} & = & -x_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}} + z_{5}c \, \mathbf{\hat{z}} & \left(3c\right) & \mbox{O I} \\ \mathbf{B}_{11} & = & x_{6} \, \mathbf{a}_{1} + z_{6} \, \mathbf{a}_{3} & = & \frac{1}{2}x_{6}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{6}a \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(3c\right) & \mbox{O II} \\ \mathbf{B}_{12} & = & x_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & \frac{1}{2}x_{6}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{6}a \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(3c\right) & \mbox{O II} \\ \mathbf{B}_{13} & = & -x_{6} \, \mathbf{a}_{1}-x_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}} + z_{6}c \, \mathbf{\hat{z}} & \left(3c\right) & \mbox{O II} \\ \end{array} \]

References

Found in

  • P. Villars and L. D. Calvert, eds., Pearson's Handbook of Crystallographic Data for Intermetallic Phases, vol. 1 (American Society of Metals, Materials Park, Ohio, 1985).

Geometry files


Prototype Generator

aflow --proto=A5B6C2_hP13_157_2ac_2c_b --params=

Species:

Running:

Output: