Evidence from x-ray diffraction of orientational ordering in phase III of solid hydrogen at pressures up to 183 GPa

X-ray powder-diffraction experiments on solid hydrogen are performed at pressures up to 183 GPa and low temperature of 100 K. A transition into phase III is confirmed by in situ Raman-scattering measurements. Two diffraction peaks corresponding to the 100 and 101 lines of the hcp structure are observed above the II-III phase-transition pressure of 160 GPa, indicating that the hydrogen molecules in phases II and III are still in the vicinity of the hcp lattice point up to 183 GPa. Assuming a hexagonal structure for these phases, the lattice parameter, $c$ decreases by 1.5% at the II-III phase transition. The behavior is consistent with a theoretically proposed feature of classical orientational ordering of rotating hydrogen molecules for phase III.

Figure 1

(Color online) (a) Representative diffraction image of phase I of solid hydrogen recorded at 82 GPa and 100 K. The image shows a texture because of the preferred orientation of the powder sample and the Debye rings are defective. The texture maintained in phase III. This indicates a nonreconstructive mechanism for the transitions to phases II and III. (b) Typical x-ray powder-diffraction pattern of high-pressure phase III at 174 GPa. Two diffraction lines from the hydrogen sample are clearly observed. Lines labeled “$Re$” correspond to those from the rhenium metal gasket. Because the background due to Compton scattering x-ray from the diamond anvils was very strong and the intensity ratios of signal to background for the 100 and 101 lines were around 1/250 and 1/300, respectively, the background was numerically subtracted in the profile. Inset shows a part of the diffraction image at 174 GPa.

Figure 2

(Color online) Pressure evolution of $d$ values of diffraction lines from hydrogen detected in six experimental runs at 100 K. Different symbols represent the different runs. The lines corresponded to the 100 and 101 reflections of the hcp structure. Those of the 002 reflection observed at 103 and 120 GPa are also plotted.

Figure 3

(Color online) Pressure dependence of Raman-active vibron frequencies at pressures up to 175 GPa at 100 K. The Raman signal from phase III clearly appears at 156 GPa and the signal from phase II disappears at 166 GPa. Phases II and III coexisted at pressures between 155 and 166 GPa, and vibron frequency decreased by about $80{\text{cm}}^{-1}$ at the II-III phase transition. The present results are consistent with those of a previous report shown by a broken line (Ref. 18).

Figure 4

(Color online) (a) Pressure dependences of lattice parameters $a$ and $c$, and $c/a$ ratio, which are determined by assuming an hcp structure for phases II and III. $a$ and $c$ were normalized with the values, $1.977\text{Å}$ and $3.133\text{Å}$, respectively, at 73 GPa. Vertical broken lines represent the region in which phases II and III coexist. The lattice parameter $c$, decreases abruptly by 1.5% at the II-III phase transition. In contrast, the decreasing rate of $a$ turns a little slower at the transition. The $c/a$ ratio also decreases to 1.55–1.56 at the transition. (b) Pressure dependence of the molar volume. The solid line corresponds to the result of a least-squares fit of the equation of state by Vinet (Ref. 19) to the data for phase I, where the bulk modulus $K_0=0.275\left(6\right)\text{GPa}$ and its pressure derivative $K_0^{\prime }=0.639\left(3\right)$ with the molar volume $V_0=23.0{\text{cm}}^3/\text{mol}$ at 0.1 MPa and low temperature. Dashed lines are guides for the eyes. The volume reduction, $\Delta V$, in the II-III transition was estimated to be around 1% or less.