NH4NO3 IV ($G0_{11}$) Structure : A4B2C3_oP18_59_ef_ab_af

Picture of Structure; Click for Big Picture
Prototype : H4N2O3
AFLOW prototype label : A4B2C3_oP18_59_ef_ab_af
Strukturbericht designation : $G0_{11}$
Pearson symbol : oP18
Space group number : 59
Space group symbol : $Pmmn$
AFLOW prototype command : aflow --proto=A4B2C3_oP18_59_ef_ab_af
--params=
$a$,$b/a$,$c/a$,$z_{1}$,$z_{2}$,$z_{3}$,$y_{4}$,$z_{4}$,$x_{5}$,$z_{5}$,$x_{6}$,$z_{6}$


  • Ammonium Nitrate exists in a variety of forms, (Hermann, 1937) depending on the temperature: \[\begin{array}{ccccc} \text{ Phase } & \text{ Temperature ${^\circ}$C } & \text{ Strukturbericht } & \text{ Page } \\ \text{ I } &\text{ 125 $--$ 170 } &\text{ $G0_{8}$ } &\href{./AB_cP2_221_a_b.NH4.NO3.html}{\text{AB_cP2_221_a_b.NH4.NO3}} &\text{ } \\ \text{ II } &\text{ 84 $--$ 125 } &\text{ $G0_{9}$ } &\href{./ABC3_tP10_100_b_a_bc.html}{\text{ABC3_tP10_100_b_a_bc}} &\text{ } \\ \text{ III } &\text{ 32 $--$ 84 } &\text{ $G0_{10}$ } &\href{./ABC3_oP20_62_c_c_cd.N.NH4.O.html}{\text{ABC3_oP20_62_c_c_cd.N.NH4.O}} &\text{ } \\ \text{ IV } &\text{ -17 $--$ 32 } &\text{ $G0_{11}$ } &\href{./A4B2C3_oP18_59_ef_ab_af.html}{\text{A4B2C3_oP18_59_ef_ab_af}} &\text{ (this structure) } \\ \text{ V } &\text{ $< -17$ } &\text{ Gwihabaite } &\href{./A4B2C3_tP72_77_8d_ab2c2d_6d.html}{\text{A4B2C3_tP72_77_8d_ab2c2d_6d2}} &\text{ }\end{array}\]
  • In the original reference (West, 1932) did not determine the positions of the hydrogen atoms. Since the hydrogen atoms are in the same space group, we continue to designate this the $G0_{11}$ structure.

Simple Orthorhombic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + z_{1} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + z_{1}c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{N I} \\ \mathbf{B}_{2} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2}-z_{1} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}}-z_{1}c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{N I} \\ \mathbf{B}_{3} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{O I} \\ \mathbf{B}_{4} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2}-z_{2} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}}-z_{2}c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{O I} \\ \mathbf{B}_{5} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(2b\right) & \mbox{N II} \\ \mathbf{B}_{6} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2}-z_{3} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}}-z_{3}c \, \mathbf{\hat{z}} & \left(2b\right) & \mbox{N II} \\ \mathbf{B}_{7} & = & \frac{1}{4} \, \mathbf{a}_{1} + y_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + y_{4}b \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{H I} \\ \mathbf{B}_{8} & = & \frac{1}{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{4}\right) \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-y_{4}\right)b \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{H I} \\ \mathbf{B}_{9} & = & \frac{3}{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{4}\right) \, \mathbf{a}_{2}-z_{4} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{4}\right)b \, \mathbf{\hat{y}}-z_{4}c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{H I} \\ \mathbf{B}_{10} & = & \frac{3}{4} \, \mathbf{a}_{1}-y_{4} \, \mathbf{a}_{2}-z_{4} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}}-y_{4}b \, \mathbf{\hat{y}}-z_{4}c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{H I} \\ \mathbf{B}_{11} & = & x_{5} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(4f\right) & \mbox{H II} \\ \mathbf{B}_{12} & = & \left(\frac{1}{2} - x_{5}\right) \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{5}\right)a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(4f\right) & \mbox{H II} \\ \mathbf{B}_{13} & = & -x_{5} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2}-z_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}}-z_{5}c \, \mathbf{\hat{z}} & \left(4f\right) & \mbox{H II} \\ \mathbf{B}_{14} & = & \left(\frac{1}{2} +x_{5}\right) \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2}-z_{5} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}}-z_{5}c \, \mathbf{\hat{z}} & \left(4f\right) & \mbox{H II} \\ \mathbf{B}_{15} & = & x_{6} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(4f\right) & \mbox{O II} \\ \mathbf{B}_{16} & = & \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{6}\right)a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(4f\right) & \mbox{O II} \\ \mathbf{B}_{17} & = & -x_{6} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2}-z_{6} \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}}-z_{6}c \, \mathbf{\hat{z}} & \left(4f\right) & \mbox{O II} \\ \mathbf{B}_{18} & = & \left(\frac{1}{2} +x_{6}\right) \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2}-z_{6} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}}-z_{6}c \, \mathbf{\hat{z}} & \left(4f\right) & \mbox{O II} \\ \end{array} \]

References

  • C. S. Choi, J. E. Mapes, and E. Prince, The structure of ammonium nitrate (IV), Acta Crystallogr. Sect. B Struct. Sci. 28, 1357–1361 (1972), doi:10.1107/S0567740872004303.
  • C. D. West, The Crystal Structure of Rhombic Ammonium Nitrate, J. Am. Chem. Soc. 54, 2256–2260 (1932), doi:10.1021/ja01345a013.
  • C. Hermann, O. Lohrmann, and H. Philipp, eds., Strukturbericht Band II 1928–1932 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1937).

Geometry files


Prototype Generator

aflow --proto=A4B2C3_oP18_59_ef_ab_af --params=

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