Zircon (ZrSiO4, $S1_{1}$) Structure: A4BC_tI24_141_h_b_a

Picture of Structure; Click for Big Picture
Prototype : ZrSiO4
AFLOW prototype label : A4BC_tI24_141_h_b_a
Strukturbericht designation : $S1_{1}$
Pearson symbol : tI24
Space group number : 141
Space group symbol : $\mbox{I4}_{1}\mbox{/amd}$
AFLOW prototype command : aflow --proto=A4BC_tI24_141_h_b_a
--params=
$a$,$c/a$,$y_{3}$,$z_{3}$


Other compounds with this structure

  • BiVO4, CeSiO4, CeVO4, DyPO4, ErPO4, ErVO4, HfSO4, HoPO4, HoVO4, LuPO4, LuVO4, NdVO4, PrVO4, ScPO4, ScVO4, TbPO4, TbVO4, ThSiO4, TmPO4, TmVO4, YPO4, YVO4, YbAsO4, YbPO4, YbVO4

  • We have filed this under quartz and related structures since the Si atoms have the same type of Si–O bonding.

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} & =&\frac78 \, \mathbf{a}_{1}+ \frac18 \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& =&\frac34 \, a \, \mathbf{\hat{y}}+ \frac18 \, c \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Zr} \\ \mathbf{B}_{2} & =&\frac18 \, \mathbf{a}_{1}+ \frac78 \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{x}}+ \frac34 \, a \, \mathbf{\hat{y}}+ \frac38 \, c \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Zr} \\ \mathbf{B}_{3} & =&\frac58 \, \mathbf{a}_{1}+ \frac38 \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& =&\frac14 \, a \, \mathbf{\hat{y}}+ \frac38 \, c \, \mathbf{\hat{z}}& \left(4b\right) & \mbox{Si} \\ \mathbf{B}_{4} & =&\frac38 \, \mathbf{a}_{1}+ \frac58 \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}+ \frac18 \, c \, \mathbf{\hat{z}}& \left(4b\right) & \mbox{Si} \\ \mathbf{B}_{5} & =&\left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}+ z_{3} \, \mathbf{a}_{2}+ y_{3} \, \mathbf{a}_{3}& =&y_{3} \, a \, \mathbf{\hat{y}}+ z_{3} \, c \, \mathbf{\hat{z}}& \left(16h\right) & \mbox{O} \\ \mathbf{B}_{6} & =&\left(\frac12 - y_{3} + z_{3}\right)\, \mathbf{a}_{1}+ z_{3} \, \mathbf{a}_{2}+ \left(\frac12 - y_{3}\right) \, \mathbf{a}_{3}& =&\left(\frac12 - y_{3}\right) \, a \, \mathbf{\hat{y}}+ z_{3} \, c \, \mathbf{\hat{z}}& \left(16h\right) & \mbox{O} \\ \mathbf{B}_{7} & =&z_{3}\, \mathbf{a}_{1}+ \left(\frac12 - y_{3} + z_{3}\right) \, \mathbf{a}_{2}- y_{3} \, \mathbf{a}_{3}& =&\left(\frac14 - y_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac34 \, a \, \mathbf{\hat{y}}+ \left(\frac14 + z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(16h\right) & \mbox{O} \\ \mathbf{B}_{8} & =&z_{3}\, \mathbf{a}_{1}+ \left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}+ \left(\frac12 + y_{3}\right) \, \mathbf{a}_{3}& =&\left(\frac14 + y_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}+ \left(\frac34 + z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(16h\right) & \mbox{O} \\ \mathbf{B}_{9} & =&\left(\frac12 + y_{3} - z_{3}\right)\, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}+ \left(\frac12 + y_{3}\right) \, \mathbf{a}_{3}& =&\left(\frac12 + y_{3}\right) \, a \, \mathbf{\hat{y}}- z_{3} \, c \, \mathbf{\hat{z}}& \left(16h\right) & \mbox{O} \\ \mathbf{B}_{10} & =&- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}- y_{3} \, \mathbf{a}_{3}& =&- y_{3} \, a \, \mathbf{\hat{y}}- z_{3} \, c \, \mathbf{\hat{z}}& \left(16h\right) & \mbox{O} \\ \mathbf{B}_{11} & =&- z_{3}\, \mathbf{a}_{1}+ \left(\frac12 + y_{3} - z_{3}\right) \, \mathbf{a}_{2}+ y_{3} \, \mathbf{a}_{3}& =&\left(\frac14 + y_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac34 \, a \, \mathbf{\hat{y}}+ \left(\frac14 - z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(16h\right) & \mbox{O} \\ \mathbf{B}_{12} & =&- z_{3}\, \mathbf{a}_{1}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}+ \left(\frac12 - y_{3}\right) \, \mathbf{a}_{3}& =&\left(\frac14 - y_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}+ \left(\frac34 - z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(16h\right) & \mbox{O} \\ \end{array} \]

References

  • R. M. Hazen and L. W. Finger, Crystal structure and compressibility of zircon at high pressure, Am. Mineral. 64, 196–201 (1979).

Found in

  • R. T. Downs and M. Hall–Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).

Geometry files


Prototype Generator

aflow --proto=A4BC_tI24_141_h_b_a --params=

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