Structural phase transition in NH₄F under extreme pressure conditions

Abstract

Ammonium fluoride (NH₄F) exhibits a variety of crystalline phases depending on temperature and pressure. By employing Raman spectroscopy and synchrotron X-ray diffraction beyond megabar pressures (up to 140 GPa), we have here observed a novel dense solid phase of NH₄F, characterised by the tetragonal P4/nmm structure also observed in other ammonium halides under less extreme pressure conditions, typically a few GPa. Using detailed ab-initio calculations and reevaluating earlier theoretical models pertaining to other ammonium halides, we examine the microscopic mechanisms underlying the transition from the low-pressure cubic phase (P-43m) to the newly identified high-pressure tetragonal phase (P4/nmm). Notably, NH₄F exhibits distinctive properties compared to its counterparts, resulting in a significantly broader pressure range over which this transition unfolds, facilitating the identification of its various stages. Our analysis points to a synergistic interplay driving the transition to the P4/nmm phase, which we name phase VIII. At intermediate pressures (around 40 GPa), a displacive transition of fluorine ions initiates a tetragonal distortion of the cubic phase. Subsequently, at higher pressures (around 115 GPa), every second ammonium ion undergoes a rotational shift, adopting an anti-tetrahedral arrangement. This coupled effect orchestrates the transition process, leading to the formation of the tetragonal phase.

Fig. 1. Phase diagram of NH₄F.

Schematic phase diagram of ammonium fluoride including the phase transition from the tetragonal phase IIIt to the tetragonal phase VIII found in this work. Space groups are given in parentheses.

Fig. 2. X-ray diffraction patterns and their analysis.

a Calculated X-ray diffraction patterns for perfect powders of NH₄F-IIIt (space group P-4m2) and NH₄F-VIII (space group P4/nmm) at 115 GPa (a = 3.9 Å and c = 2.6 Å). Tick marks indicate the positions of the Bragg reflections and Miller indices are also reported. b Representative X-ray diffraction patterns of the sample at the indicated pressures (λ = 0.4101 Å). The symbols * and # indicate a Re (gasket material) and a Au (pressure standard) peak, respectively. The vertical lines indicate two peaks which do not emanate from the sample (their positions do not shift with pressure). c Best fits of the most intense diffraction signal using two Gaussians. d Unit cell volume per number of NH₄F molecules in the cell. e Cell dimensions. f √2c/a ratio. Error bars correspond to one standard deviation. Legend of (d) also applies to (e, f). Symbols represent experimental data, dashed lines represent DFT calculations. Data of ref. are also reported.

Fig. 3. Raman spectroscopy data.

Raman spectra measured upon compression at pressures from 6 to 140 GPa: (a) lattice mode; (b) ${\mathrm{NH}}_4^{+}$ bending region and (c) N-H stretching region. All measured pressure points are reported.

Fig. 4. Variation of the Raman shift as a function of the pressure.

Top panels: measured (a) lattice mode, (b) bending region and (c) stretching region. The shaded areas highlight the III to IIIt phase transition then the IIIt to VIII phase transition at higher pressure. Lower panels: theoretical (a’) lattice mode, (b’) bending region and (c’) stretching region. The size of the dots is given by the intensity of the Raman peaks.

Fig. 5. Structural differences and transition path.

a Transition pattern from the NH₄F-III (space group P-43m) to the NH₄F-VIII (space group P4/nmm) phase, including the intermediate NH₄F-IIIt (space group P-4m2) phase. The pattern shows the lattice tetragonal distortion linked to the F displacement in phase IIIt (red arrows), and the rotation of every second NH₄ cation (anti-tetrahedral order) accompanied by further displacement of F ions in phase VIII (orange arrow). b Pair distribution functions for the heavy atom lattices for NH₄F-III and NH₄F-VIII at 100 GPa. c 2D potential energy surfaces in NH₄F, linking NH₄F-III at (0,0) to NH₄F-VIII at (90,1.0), where the x coordinate is the NH₄ tetrahedron rotation in degrees and the y coordinate is the F ion displacement and tetragonal distortion relative to phase VIII. From left to right the calculations are for 50/100/150 GPa. d Relative enthalpies for nudged elastic band calculations from phase III to phase VIII, initialised along the orange paths shown in (c).