Structure of liquid ammonia at high pressures and temperatures

The structure of liquid ammonia (${\mathrm{NH}}_3$) is investigated from 1 to 6.3 GPa and up to 800 K by means of synchrotron x-ray diffraction (XRD) and ab initio molecular dynamics (AIMD) simulations. The XRD data are used to extract the molecular structure factor $S_{\mathrm{mol}}\left(Q\right)$, pair distribution function (PDF) $g_{\mathrm{mol}}\left(r\right)$, and the density of ${\mathrm{NH}}_3$. There is an excellent agreement between present $S_{\mathrm{mol}}\left(Q\right)$ and $g_{\mathrm{mol}}\left(r\right)$ at our lowest density and those reported in reference neutron experiments. Our densities agree better with the equation of state (EoS) of Tillner-Roth et al. [DKV-Tagungsbericht (Hannover, New York, 1993), Vol. 20, p. 167] than with more recent EoS models. The experimental structure factor and PDF are well reproduced by AIMD simulations using either the Becke-Lee-Yang-Parr or the Perdew-Burke-Ernzerhof exchange-correlation functional. The shapes of $S_{\mathrm{mol}}\left(Q\right)$ and $g_{\mathrm{mol}}\left(r\right)$ vary little over the investigated pressure range and suggest a compact liquid with weak orientational correlations between molecules, which is corroborated by the coordination number varying from 12.7 to $\sim 14$. The simulations are used to study the evolution of the site-site pair distribution functions, which reveals that the number of H bonds per molecule (between 1.5 and 2) do not evolve with density and that the distribution of H atoms around N atoms becomes more and more anisotropic with pressure.

Figure 1

(Top) Phase diagram of ${\mathrm{NH}}_3$ after Ninet and Datchi [7]. The red circles show the $P-T$ points where experimental data were taken, the black star is the critical point, and the dashed line is the Frenkel line. (Bottom) Representation of the structures of ${\mathrm{NH}}_3-\mathrm{I}$ and ${\mathrm{NH}}_3-\mathrm{IV}$. The colored lines show hydrogen bonds with different colors for bonds of different lengths and angles.

Figure 2

Integrated x-ray-diffraction patterns from a ${\mathrm{NH}}_3$ fluid sample at 4.3 GPa, 690 K, with and without the MCC. The red and blue solid lines, respectively, are patterns obtained with and without the MCC. The red and blue dashed lines are the respective patterns from the empty cell with and without MCC. The intensities for the patterns obtained without MCC have been divided by 20 to scale with those measured with the MCC.

Figure 3

Optimum density and scale factor for ammonia at 4.8 GPa and 800 K as a function of $Q_{\max }$. The average density is $36.3\pm 1.5{\mathrm{molecules}\mathrm{nm}}^{-3}$.

Figure 4

Evolution with pressure of the density of liquid ammonia. The red and blue colors are for $T=800$ and $T=690\mathrm{K}$, respectively. The squares are experimental data, the lozenges are from AIMD simulations with the PBE functional, and up-triangles are from AIMD simulations with the BLYP functional. The solid and dashed lines are the densities obtained with the EoS of Tillner-Roth et al. [55] and Jahangiri and Behnejad [56], respectively. Blue down-triangles are taken from the AIMD simulations of Bethkenhagen et al. [57] at 700 K.

Figure 5

Experimental results from the present x-ray-diffraction study of liquid ${\mathrm{NH}}_3$. Panels (a) and (b) show the molecular structure factor and pair distribution functions, respectively, obtained at the indicated pressures. The curves are offset by 0.5 for clarity. The temperature was 800 K except for the patterns labeled by the ${}^{*}$ symbol for which the temperature was 690 K. The dashed lines are $S_{\mathrm{mol}}\left(Q\right)$ and $g_{\mathrm{mol}}\left(r\right)$ calculated using the experimental data from Ricci et al. [10] at 273 K and 0.483 MPa. Panel (c) shows ${(Q_M/Q_{M0})}^3$ as a function of $\rho /{\rho }_0$, where $Q_M$ is the position of the main diffraction peak, $\rho$ is the liquid density, $Q_{M0}=20.65{\mathrm{nm}}^{-1}$ and ${\rho }_0=22.6{\mathrm{molecules}\mathrm{nm}}^{-3}$ correspond to the values of liquid ammonia at 273 K and 0.483 MPa reported by Ricci et al. [10]. Filled and open squares are experimental data from the present paper and Ref. [10], respectively. Blue and red are for $T=690$ and $T=800\mathrm{K}$, respectively. The solid line is a linear fit to the data. Panel (d) shows the first-neighbor distance as a function of density, determined as described in the text. The squares are present experimental data, and the lozenges are from AIMD simulations with the PBE functional.

Figure 6

Evolution with density of the coordination number in liquid ${\mathrm{NH}}_3$. The squares and lozenges represent experimental and AIMD results, respectively. Red and blue are for $T=800$ and 690 K, respectively.

Figure 7

Results from AIMD simulations. (a) Comparison among the NN, NH, and HH partial PDFs obtained using either the PBE or BLYP functional at the fixed density of $39.4{\mathrm{molecules}\mathrm{nm}}^{-3}$ and 800 K. Offsets of 1.5 and 3 are applied to NH and HH distributions, respectively. The arrows designate the three humps at $r\simeq 0.21$, 0.29, and 0.37 nm in the NH partial PDF. (b) Comparison between the experimental (red solid lines) and the theoretical (blue dashed lines) $g_{\mathrm{mol}}\left(r\right)$ at close densities. The $\rho$ values in ${\mathrm{molecules}/\mathrm{nm}}^3$ are indicated for each curve. The theoretical $g_{\mathrm{mol}}\left(r\right)$ were obtained with the PBE functional. Curves are offset by 1. (c) Evolution with density of the theoretical partial PDFs. The blue dotted, green dashed, orange dot-dashed, and red solid lines correspond to $\rho$ values of 24.5, 29, 33.8, and $39.4{\mathrm{molecules}\mathrm{nm}}^{-3}$, respectively. Offsets of 1.5 and 2.5 are applied for NH and HH distributions, respectively.

Figure 8

Partial PDFs of liquid ammonia at low density. The green solid, blue dotted, and red dashed lines are, respectively, the experimental data of Ricci et al. [10] at 273 K, 0.483 MPa, the AIMD simulations of Boese et al. [17] with the BLYP functional at the same $P,T$ conditions, and our AIMD simulations at $24.5{\mathrm{molecules}\mathrm{nm}}^{-3}$, 700 K using the PBE functional.