Amorphous Ice: Stepwise Formation of Very-High-Density Amorphous Ice from Low-Density Amorphous Ice at 125 K

On compressing low-density amorphous ice (LDA) at 125 K up to 1.6 GPa, two distinct density steps accompanied by heat evolution are observable in pressure-density curves. Samples recovered to 77 K and 1 bar after the first and second steps show the x-ray diffraction pattern of high-density amorphous ice (HDA) and very HDA (VHDA), respectively. The compression of the once formed HDA takes place linearly in density up to 0.95 GPa, where nonlinear densification and $\mathrm{HDA}\to \mathrm{VHDA}$ conversion is initiated. This implies a stepwise formation process $\mathrm{LDA}\to \mathrm{HDA}\to \mathrm{VHDA}$ at 125 K, which is to the best of our knowledge the first observation of a stepwise amorphous-amorphous-amorphous transformation sequence. We infer that the relation of HDA and VHDA is very similar to the relation between LDA and HDA except for a higher activation barrier between the former. We discuss the two options of thermodynamic versus kinetic origin of the phenomenon.

Figure 1

Pressure-density curves for isothermal compression of LDA at a rate of $20\mathrm{MPa}/\min$ at 125 K, subsequent quenching to 77 K, and decompression at $20\mathrm{MPa}/\min$. Density $\rho$ is calculated from the raw data, i.e., uniaxial displacement $\Delta x$, from equating $\rho =0.92\times 6.49/(6.49-\Delta x)$ by employing an initial density of $0.92\mathrm{g}{\mathrm{cm}}^{-3}$ for LDA at 125 K (the density of LDA at 77 K is $0.94\pm 0.02\mathrm{g}{\mathrm{cm}}^{-3}$ and decreases on increasing the temperature [28]) and an initial LDA sample height of 6.49 mm (corresponding to 0.2995 g sample in a cylinder of 8 mm diameter). The signal due to the piston-cylinder apparatus lined with 0.351 g of indium (and no ice sample) was subtracted as a baseline from the raw pressure-displacement data. We assumed a constant diameter of the piston-cylinder apparatus on changing the temperature from 125 to 77 K. All the experiments were done in a computerized (software TestXpert V7.1) “universal testing machine” (Zwick, model BZ100/TL3S) with a positional reproducibility of $\pm 5\mu \mathrm{m}$ and a spatial resolution of $0.01\mu \mathrm{m}$. All samples were kept in a container carefully designed of 0.351 g indium and of the same shape in order to exclude artifacts produced by different amounts and shapes of indium. Indium is required to prevent sudden pressure drops accompanied by shock-wave heating causing crystallization of HDA to ice XII [29].

Figure 2

Powder x-ray diffractograms for the samples $A$, $B$, and $C$ recovered at 77 K in Fig. 1. X-ray diffractograms were recorded on a diffractometer in $\theta \mathrm{\text{−}}\theta$ geometry (Siemens, model D 5000, $\mathrm{Cu}\mathrm{\text{−}}K\alpha$), equipped with a low-temperature camera from Paar at 88 K. The sample plate was in horizontal position during the whole measurement. Installation of a “Goebel” mirror allowed one to record small amounts of sample without distortion of Bragg peaks. Curves are shown on the same scale, smoothed and offset for clarity. Dashed lines are intended to guide the eye to the location of the maximum of the first broad diffraction peak. The dotted lines indicate positions of reflexes caused by traces of $I_h$, which had formed by condensation of water vapor during transfer of the sample onto the precooled x-ray sample holder (cf. Ref. 30). The sample itself is fully amorphous.

Figure 3

Top: Effect of compression rate on pressure-density curves for isothermal compression of LDA at 125 K. The protocol is analogous to the procedure described for Fig. 1 using compression rates of $6$, $20$, $600$, and $6000\mathrm{MPa}/\min$. The rate $600\mathrm{MPa}/\min$ matches the rate employed in [3]. Bottom: Change of density with increasing pressure (first derivative of curves in top panel). Areas of inelastic compression where the change exceeds ca. $0.20\mathrm{g}{\mathrm{cm}}^{-3}{\mathrm{GPa}}^{-1}$ are shaded in gray.