Local structural motifs and extended-range order in liquid and solid ammonia under pressure

Neutron-diffraction measurements of the local structure in deuterated ammonia have been conducted up to pressures of 2.1 GPa at ambient temperature. Total pair-distribution functions, determined by Fourier analysis of the static structure factor, are used to examine the structural changes from the first neighbors to extended ranges of $\sim$30 $\AA$ in both the liquid and solid state. In the proton-disordered crystalline phase III, the first coordination shell is almost identical to that of the higher-pressure, ordered phase IV. The H-bond correlation is observed as a distinct shoulder at 2.5 $\AA$. A similar local structure is seen in the liquid at a pressure just below freezing, and, in particular, a pronounced H-bond correlation is observed in the liquid across the pressure range studied. A substantial increase in the ordering length scale of the liquid is observed at high pressure with correlations extending to at least 25 $\AA$ compared to $\sim$12 $\AA$ at ambient. The decay of the primary oscillations in the extended range is exponential and well described by a simple-liquid model, implying that, despite persistent H bonding, packing considerations become the dominant structural driver as density increases.

Figure 1

Structural phase diagram of pure hydrogenous ammonia. The I-II transition line and the melting line of phase I are taken from Mills et al. (Ref. 42). The melt line of phases II and III and the III-IV transition temperature are from Ninet and Datchi (Ref. 6). The II-III transition temperature appears to be not well determined. The dashed line shown is taken from Gauthier et al. (Ref. 43), who cites a private communication with R. L. Mills. Each solid phase is labeled with its Hermann-Mauguin space group (in brackets) and whether the local structure is orientationally disordered (dis) or ordered (ord).

Figure 2

Visualization (Ref. 44) of ammonia phase I, where blue (large) spheres indicate N atoms, pink (small) spheres indicate H(D) atoms, and dashed lines represent H-bonds. The figure shows the first pseudo-fcc 12-fold coordination shell of molecules about the central molecule labeled A. These neighboring molecules adopt an arrangement where six are H bonded to molecule A (three donating and three accepting), while the other six are not bonded to molecule A. The pseudo-close-packed layers lie parallel to the a-b plane.

Figure 3

Atomic densities for relevant states of ammonia. Open squares indicate Kumagai and Toriumi's low-pressure densities (Ref. 20), the solid black line passing through these are the NIST Standard Reference Data. Fortes et al.'s equations of state (EOS) (Ref. 21) for phases I and IV (solid lines, marked) offset to pass through Von Dreele's room-temperature data point at 1.28 GPa (Ref. 4), shown as a star. The solid horizontal line gives our experimentally measured density for phase III, with horizontal dash-dot lines showing the standard deviation. The vertical gray band indicates the corresponding estimated range of pressure for our phase-III data point.

Figure 4

The Rietveld fit to phase III at 2.1 GPa. Circles indicate data points, the solid line passing through these is the fit and the line below these the residual. All peaks in the pattern are accounted for by the $Fm\overline{3}m$ space group. The inset shows the 67$\%$ probability contour of the deuteron thermal ellipsoids, suggesting the molecular orientations are completely disordered in the temporally and spatially averaged structure measured by the Bragg diffraction measurement.

Figure 5

The $S$($Q$) data for the room-temperature liquid at ambient pressure and just below pressure-induced freezing at room temperature at 1.0 GPa as well as the solid phase III at 2.1 GPa (red). These data were truncated where the $S$($Q$) crosses a value of 1.0 (at 12.0 $\AA$${}^{-1}$) in order to minimize truncation ripples in the Fourier transforms. The weak Bragg peak in the liquid data at 3.2 $\AA$${}^{-1}$ is due to a small amount of gold loaded with the sample with the aim of providing pressure calibration but which was found to be insensitive to the small pressure change of 1.0 GPa. Also shown by a dotted line is the expected scattering due to self-scattering of the molecule $S_{\mathrm{intra}}$($Q$), as described in the text. The inset shows the behavior in the low-$Q$ region.

Figure 6

Shows the measured $G$($r$) for phase III and calculated $G$($r$) for phases I and IV; data are shown above 2 $\AA$, reflecting the intermolecular structure. The statistical noise in the calculated $G$($r$) arises from the finite number of molecules in the simulation box. Also shown in gray in the lower half of the figure are the distinct partials (scaled according to their Faber-Ziman weights) that make up the total $G$($r$) for phase IV. The inset shows the low-$r$ part of the measured and calculated $G$($r$) spanning the first coordination shell. The shoulder on the low-$r$ side of the main peak, marked with an arrow in the inset, corresponds to the first intermolecular N-D correlation, i.e., the H-bonded contact.

Figure 7

(a) The $D$($r$) correlation functions for both liquids extending from first intermolecular contact to 30 $\AA$. The data for the 1.0-GPa liquid are offset by 1.0 on the $y$ axis for clarity. Superimposed on the 1.0-GPa liquid data as a dashed curve is a simple Ornstein-Zernike model fitted between 4.3 and 28 $\AA$. The inset shows the $G$($r$) data for both liquids and phase III at low $r$, including the two intramolecular peaks and the first coordination shell. The H-bond correlation is marked here by an arrow. (b) $r$[$G$($r$)-1] for crystalline phase III out to 120 $\AA$. The decay of the oscillations with increasing $r$ reflects the finite $dQ$ resolution of the instrument. The gray curve indicates the expected falloff in $r$ space for a diffractometer with a Gaussian resolution function of width 0.03 $\AA$${}^{-1}$.