Equation of state of ammonia dihydrate up to 112 GPa by static and dynamic compression experiments in diamond anvil cells

A. Mondal, R. J. Husband, H.-P. Liermann, and C. Sanchez-Valle

Phys. Rev. B 107, 224108 – Published 23 June 2023

Abstract

Understanding the high-pressure behavior of ammonia hydrates is relevant for modeling the interior of solar and extrasolar icy bodies. We present here the results of high-pressure x-ray diffraction studies on ammonia-dihydrate (ADH) at room temperature (298 K) up to 112 GPa, employing both static and dynamic compression experiments performed in diamond anvil cells. The derived pressure-volume (P-V) compression curves are in excellent agreement regardless of the compression technique. In contrast to early theoretical predictions, our results indicate the stability of the disordered molecular alloy (DMA) phase, a body centered cubic (bcc) structure, and the absence of self-ionization in the investigated pressure range. By combining the P-V data from seven different compression runs, we derive the first equation of state for ADH-DMA based on the third-order Birch-Murnaghan formalism with best-fit parameters: $V_{0} = 23.96 \pm 0.03$ ( $Å^{3}$ /molecule), $B_{0} = 9.95 \pm 0.14$ GPa, and $B_{0}^{'} = 6.59 \pm 0.03$ . The instantaneous bulk modulus directly derived from the quasicontinuous compression curves displays a smooth increase upon compression that further supports the absence of structural transitions.

Received 18 April 2023
Revised 7 June 2023
Accepted 8 June 2023

DOI:https://doi.org/10.1103/PhysRevB.107.224108

Physics Subject Headings (PhySH)

High-pressure studies Hydrogen bonds Phase transitions

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

A. Mondal ¹, R. J. Husband ², H.-P. Liermann ², and C. Sanchez-Valle ¹

¹Institut für Mineralogie, Universität Münster, 48149 Münster, Germany
²Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, 22607 Hamburg, Germany

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Issue

Vol. 107, Iss. 22 — 1 June 2023

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Images

Figure 1
Selected x-ray diffraction patterns of the ADH-DMA phase recorded upon compression at 298 K in (a) static compression, sDAC2 and sDAC4 samples (incident energy 42.7 keV) and (b) dynamic compression, dDAC1 run (incident energy 25.6 keV). Bragg reflections corresponding to the ADH-DMA phase are marked by black squares. The other major reflections correspond to the gold (Au) pressure marker (yellow circles). Weak Re reflections from the gaskets are also present in some spectra.
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Figure 2
Intensity plot showing the evolution of diffraction patterns collected for dDAC1 in Image number vs 2θ space. The (110) diffraction line of the ADH-DMA phase is most intense reflection and can be traced over the full compression range. The inset shows the propagation of pressure during the corresponding run. The initial, final, and highest pressure reached during the ramp compression is indicated in the graph.
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Figure 3
X-ray diffraction pattern of ADH-DMA phase at (a) 42.5 GPa and (b) 72 GPa at room temperature (run sDAC1). The black circles are experimental data and the red line is the Le Bail refinement fit. Colored sticks show the position of the Bragg reflections for the sample, the Re gasket, and the Au pressure calibrant correspondingly. The green line represents the difference between observed and calculated profile patterns. The goodness of fit parameters are as follows: (a) $R_{wp} = 0.3321, R_{p} = 0.1825, χ^{2} = 1.014$ , and (b) $R_{wp} = 0.4735, R_{p} = 0.2146, χ^{2} = 2$ .
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Figure 4
(a) Pressure-volume data for the ADH-DMA phase obtained in all static (four runs) and dynamic (three runs) compression experiments. Data from all runs are in excellent agreement and fall within the error envelop (grey shadowed area) outlined by the grey dashed line. The solid line represents a joint fit to all datasets by a third order Birch-Murnaghan EoS. (b) Pressure evolution of the instantaneous bulk modulus of the ADH-DMA phase calculated directly by numerical differentiation of the P-V curve, $B = - V \frac{d P}{d V}$ , for selected static and dynamic compression runs. The smaller volume changes ( $d V$ ) as the material densifies result in higher fluctuations in the instantaneous bulk modulus in the high-pressure range.
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Figure 5
Comparison of the compression curves of DMA/DIMA phases in the $N H_{3} - H_{2} O$ system. Grey shadowed area outlined by the grey dashed line indicates the error envelope in our ADH-DMA experimental data. Experimentally obtained ADH-DMA phase volumes do not match the calculated ADH-DMA volume assuming ideal mixing between $N H_{3}$ and $H_{2} O$ with 1:2 mixing ratio (ADH ideal).
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