High-pressure properties of dense metallic zirconium hydrides studied by ab initio calculations

Kazutaka Abe

Phys. Rev. B 98, 134103 – Published 10 October 2018

Abstract

Zirconium-hydrogen compounds under pressure are investigated by using ab initio density functional calculations. In addition to the high-pressure phases so far predicted, other new metallic phases of ${ZrH}_{3}$ , ${ZrH}_{4}$ , and ${ZrH}_{6}$ are found above about 170, 110, and 150 GPa, respectively. The estimated superconducting transition temperatures of the ${ZrH}_{4}$ and ${ZrH}_{6}$ phases are as follows: 78 K in the $F d d d {ZrH}_{4}$ (140 GPa), 47 K in the $I 4 / m m m {ZrH}_{4}$ (230 GPa), 55 K in the $C m c 2_{1} {ZrH}_{6}$ (160 GPa), 153 K in the $P 2_{1} / c {ZrH}_{6}$ (295 GPa), and 114 K in the $I 4 / m m m {ZrH}_{6}$ (295 GPa). The $I 4 / m m m$ structure of ${ZrH}_{4}$ is actually the structure similarly predicted for ${MgH}_{4}$ and ${ScH}_{4}$ . Also, the $I 4 / m m m$ structure of ${ZrH}_{6}$ is a close modification of the $I m \bar{3} m$ structure proposed for ${MgH}_{6}$ and ${ScH}_{6}$ . The structural resemblances observed in these magnesium, scandium, and zirconium hydrides suggest that diagonally adjacent elements tend to have similar chemical trends, namely, diagonal relationships, which are expected to serve as a helpful guide to searching for new metallic hydrides.

Received 7 June 2018

DOI:https://doi.org/10.1103/PhysRevB.98.134103

Physics Subject Headings (PhySH)

First-principles calculations Pressure effects Superconductivity

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Kazutaka Abe

Research Institute of Electrical Communication, Tohoku University, 2-1-1 Katahira, Aoba, Sendai, Miyagi 980-8577, Japan

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Vol. 98, Iss. 13 — 1 October 2018

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Images

Figure 1
Relative enthalpy (per atom) of ${Zr}_{1 - x} H_{x}$ as a function of $x$ for $0 \leq x \leq 1$ (top two panels) and for $3 / 4 \leq x \leq 1$ (bottom two panels), where the clamped nuclei approximation and the harmonic approximation are compared. Stable phases are connected with solid lines. The structures considered in each composition are summarized below, where the transition pressures are those within the harmonic approximation: in ZrH, $C m c m$ [20] (or $I 4 / m m m$ [36]) $- (155 GPa) \to R \bar{3} m$ [20]; in ${ZrH}_{2}$ , $I 4 / m m m$ [20] $- (150 GPa) \to C 2 / m$ ; in ${ZrH}_{3}$ , $P m \bar{3} n$ [20] $- (170 GPa) \to R \bar{3} c$ ; in ${ZrH}_{4}$ , $F d d d - (210 GPa) \to I 4 / m m m$ ; in ${ZrH}_{5}$ , $C m - (135 GPa) \to C 2 / m - (410 GPa) \to C 2 / c$ [35]; in ${ZrH}_{6}$ , $C m c 2_{1}$ -HP $- (275 GPa) \to$ either $P 2_{1} / c$ or $I 4 / m m m - (320 GPa) \to I 4 / m m m$ . The enthalpy of zirconium is calculated for hcp and bcc structures [37], and hydrogen for the $C 2 / c$ [38], the $C m c a$ -12 [38], the $C m c a$ [39], and the Cs-IV ( $I 4_{1} / a m d$ ) [40] structures.
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Figure 2
Comparisons of enthalpies in ${ZrH}_{4}$ (left) and in ${ZrH}_{6}$ (right), where the ionic system is treated in the harmonic approximation. The fine dotted lines mean that the structures have imaginary-frequency phonons at the pressures, where the ZPE is calculated by neglecting the unstable phonon modes. The enthalpy of ${ZrH}_{3}$ is calculated for the $P m \bar{3} n$ [20] and the $R \bar{3} c$ structures, and hydrogen for the $C 2 / c$ [38], the $C m c a$ -12 [38], the $C m c a$ [39], and the Cs-IV ( $I 4_{1} / a m d$ ) [40] structures.
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Figure 3
New high-pressure phases of ${ZrH}_{3}$ , ${ZrH}_{4}$ , and ${ZrH}_{6}$ . The bonds between H atoms are drawn with a cutoff distance of 1.25 Å.
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Figure 4
Density of states (DOS) and partial DOS (PDOS). DOS (solid line) is given per valence electron, where the valence of Zr is chosen to be 4. Zr PDOS (dashed line) and H PDOS (dotted line) are given per formula unit; namely, $X$ PDOS ( $X = Zr$ or H) is obtained by summing the DOS projected on $X$ atoms and then dividing the sum by the number of formula units in the unit cell. (a) the $R \bar{3} c {ZrH}_{3}$ at 260 GPa; (b) the $F d d d {ZrH}_{4}$ at 140 GPa; (c) the $I 4 / m m m {ZrH}_{4}$ at 230 GPa; (d) the $C m c 2_{1}$ -HP ${ZrH}_{6}$ at 160 GPa; (e) the $P 2_{1} / c {ZrH}_{6}$ at 295 GPa; (f) the $I 4 / m m m {ZrH}_{6}$ at 295 GPa.
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Figure 5
Eliashberg function $α^{2} F$ multiplied by $2 / ω$ (i.e., $2 α^{2} F / ω$ ) of the $R \bar{3} c {ZrH}_{3}$ , the $F d d d {ZrH}_{4}$ , the $I 4 / m m m {ZrH}_{4}$ , the $C m c 2_{1}$ -HP ${ZrH}_{6}$ , the $P 2_{1} / c {ZrH}_{6}$ , and the $I 4 / m m m {ZrH}_{6}$ . The data of the $I 4 / m m m {ZrH}_{6}$ at 255 GPa is presented just for comparison; the phase is unstable at the pressure [Fig. 2].
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Figure 6
Comparisons of enthalpies in ${MgH}_{4}$ (left) and in ${MgH}_{6}$ (right), where the ionic system is treated in the harmonic approximation. The other details are the same as those explained in Fig. 2.
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