# Encyclopedia of Crystallographic Prototypes

M. J. Mehl, D. Hicks, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 1, Comp. Mat. Sci. 136, S1-S828 (2017). (doi=10.1016/j.commatsci.2017.01.017)
D. Hicks, M. J. Mehl, E. Gossett, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 2, Comp. Mat. Sci. 161, S1-S1011 (2019). (doi=10.1016/j.commatsci.2018.10.043)

## NH4NO3 II ($G0_{9}$) Structure : ABC3_tP10_100_b_a_bc

 Prototype : N(NH4)O3 AFLOW prototype label : ABC3_tP10_100_b_a_bc Strukturbericht designation : $G0_{9}$ Pearson symbol : tP10 Space group number : 100 Space group symbol : $P4bm$ AFLOW prototype command : aflow --proto=ABC3_tP10_100_b_a_bc --params=$a$,$c/a$,$z_{1}$,$z_{2}$,$z_{3}$,$x_{4}$,$z_{4}$

• Ammonium Nitrate exists in a variety of forms, (Hermann, 1937) depending on the temperature: $\begin{array}{ccccc} \text{ Phase } & \text{ Temperature ^{\circ}C } & \text{ Strukturbericht } & \text{ Page } \\ \text{ I } &\text{ 125 -- 170 } &\text{ G0_{8} } &\href{\WEBSITEPREFIX/AB_cP2_221_a_b.NH4.NO3.html}{\text{AB_cP2_221_a_b.NH4.NO3}} &\text{ } \\ \text{ II } &\text{ 84 -- 125 } &\text{ G0_{9} } &\href{\WEBSITEPREFIX/ABC3_tP10_100_b_a_bc.html}{\text{ABC3_tP10_100_b_a_bc}} &\text{ (this structure) } \\ \text{ III } &\text{ 32 -- 84 } &\text{ G0_{10} } &\href{\WEBSITEPREFIX/ABC3_oP20_62_c_c_cd.N.NH4.O.html}{\text{ABC3_oP20_62_c_c_cd.N.NH4.O}} &\text{ } \\ \text{ IV } &\text{ -17 -- 32 } &\text{ G0_{11} } &\href{\WEBSITEPREFIX/A4B2C3_oP18_59_ef_ab_af.html}{\text{A4B2C3_oP18_59_ef_ab_af}} &\text{ } \\ \text{ V } &\text{ < -17 } &\text{ Gwihabaite } &\href{\WEBSITEPREFIX/A4B2C3_tP72_77_8d_ab2c2d_6d.html}{\text{A4B2C3_tP72_77_8d_ab2c2d_6d2}} &\text{ }\end{array}$
• Data for this structure was taken at 60°C.
• The positions of the hydrogen atoms were not determined. The isolated nitrogen atoms in this structure's visualization are surrounded by four hydrogen atoms in an approximately tetrahedral arrangement. It is likely that the NH4 ions are free to rotate (Kracek, 1937).
• Both (Shinnaka, 1956) and (Hermann, 1937) state that the available X–ray diffraction data supports a space group of either $P4bm$ (#100) or $P\overline{4}2_{1}m$ (#113). The atomic positions found by Shinnaka agree with space group $P4bm$.
• (Shinnaka, 1956) states that the NO3 nitrate groups are rotating, but this rotation is almost bound in two orientations (in opposite directions). He then gives two possible orientations for the nitrate. We present the first orientation here. The second orientation is obtained by taking $z_{3} \rightarrow – z_{3}$ and $z_{4} \rightarrow – z_{4}$.
• Another way of presenting this information would be to add a second nitrate group to the primitive cell, and set the occupation of all the atoms in the nitrates at 50%. This would give a structure in space group $P4/mbm$ (#127), which might be useful as a pictorial representation but does not correctly represent the physics of the crystal, as the nitrogen and oxygen atoms in an individual nitrate ion must remain together.
• The N–O distances in this structure are about 10% smaller than the distances found in the other phases of NH4NO3. This suggests that the structure should be reevaluated.
• The positions of the hydrogen atoms in the NH4 ion were not determined, so we only provide the positions of the nitrogen atoms (labeled as NH4).

### Simple Tetragonal primitive vectors:

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

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(2a\right) & \mbox{NH_{4}} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + z_{1} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + z_{1}c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{NH_{4}} \\ \mathbf{B}_{3} & = & \frac{1}{2} \, \mathbf{a}_{1} + z_{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + z_{2}c \, \mathbf{\hat{z}} & \left(2b\right) & \mbox{N} \\ \mathbf{B}_{4} & = & \frac{1}{2} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(2b\right) & \mbox{N} \\ \mathbf{B}_{5} & = & \frac{1}{2} \, \mathbf{a}_{1} + z_{3} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + z_{3}c \, \mathbf{\hat{z}} & \left(2b\right) & \mbox{O I} \\ \mathbf{B}_{6} & = & \frac{1}{2} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(2b\right) & \mbox{O I} \\ \mathbf{B}_{7} & = & x_{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{4}\right) \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{4}\right)a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{O II} \\ \mathbf{B}_{8} & = & -x_{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{4}\right) \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{4}\right)a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{O II} \\ \mathbf{B}_{9} & = & \left(\frac{1}{2} - x_{4}\right) \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{4}\right)a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{O II} \\ \mathbf{B}_{10} & = & \left(\frac{1}{2} +x_{4}\right) \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{4}\right)a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{O II} \\ \end{array}$

### References

• Y. Shinnaka, On the Metastable Transition and the Crystal Structure of Ammonium Nitrate (Tetragonal Modification), J. Phys. Soc. Jpn. 11, 393–396 (1956), doi:10.1143/JPSJ.11.393.
• C. Hermann, O. Lohrmann, and H. Philipp, eds., Strukturbericht Band II 1928–1932 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1937).
• F. C. Kracek, S. B. Hendricks, and E. Posnjak, Group Rotation in Solid Ammonium and Calcium Nitrates, Nature 128, 410–411 (1931), doi:10.1038/128410b0.

### Found in

• 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.

### Prototype Generator

aflow --proto=ABC3_tP10_100_b_a_bc --params=