Experimental and Theoretical Revisit of Ca-H Superhydrides: Anharmonic Effects on Phase Stability and Superconductivity

TL;DR

Problem: determining stable high‑Tc hydrides in the Ca–H system under pressure is complicated by anharmonic effects and conflicting experimental observations. Approach: combine a neural‑network potential with the stochastic self‑consistent harmonic approximation (SSCHA–ACNN) to compute anharmonic free energies and map the temperature–pressure phase diagram, then validate predictions with high‑pressure synthesis experiments. Findings: Ca8H46−δ is stable at $0$ K, CaH6 becomes thermodynamically stable at high temperatures (approximately $T$ ≈ 400–500 K), and high‑Tc CaH6 is realized under appropriate synthesis conditions, while hydrogen deficiency explains Tc suppression upon decompression; experiments confirm Ca8H46−δ formation at 165–167 GPa and Tc behavior consistent with theory. Significance: demonstrates the pivotal role of lattice anharmonicity in stabilizing hydrogen‑rich superconductors and provides a practical framework to predict and engineer stable high‑Tc hydrides.

Abstract

The prediction of superconductivity above 200 K in CaH6 revolutionized research on hydrogen-rich superconductors, and subsequent experiments have verified this prediction, while unidentified peaks in XRD and the decrease in superconducting temperature upon decompression indicate that unresolved issues remain. In this work, we combine theory and experiment to construct an accurate temperature-pressure phase diagram of the Ca-H system and identify the stability ranges of the candidate superconducting phases by considering anharmonic effects. Our results demonstrate that type-I clathrate Ca8H46-delta structures become thermodynamically stable at 0 K when anharmonic effects are considered. Notably, we found that the previously predicted CaH6 phase achieves stability above 500 K, underscoring the significant role of temperature and anharmonic effects in stabilizing this intriguing high-pressure phase. Experimentally, we have successfully synthesized Ca8H46-delta phases at low temperatures, thereby validating our theoretical predictions. Our findings offer insights into the structure and superconducting mechanisms of hydrides.

Figures (4)

• Figure 1: (a) Formation enthalpy of Ca–H compounds at 130-200 GPa relative to CaH$_4$ and H$_2$, calculated at the harmonic level. Solid symbols represent thermodynamically stable phases, while open symbols denote metastable ones. (b) Gibbs free energy difference between Ca$_8$H$_{48}$ and Ca$_8$H$_{46}$ + H$_2$ as a function of temperature, calculated at the harmonic level.
• Figure 2: (a) Formation enthalpy of Ca–H compounds at 130-200 GPa relative to CaH$_4$ and H$_2$, calculated at the anharmonic level. Solid symbols represent thermodynamically stable phases, while open symbols denote metastable ones. (b) Gibbs free energy difference between Ca$_8$H$_{48}$ and Ca$_8$H$_{46}$ + H$_2$ as a function of temperature, calculated at the anharmonic level.
• Figure 3: Synchrotron XRD of Ca$_8$H$_{46}$ collected at 167 GPa. The upper panel shows the 2D diffraction image (“cake”), while the lower panel presents the integrated diffraction pattern. Red circles are the observed XRD data, the blue line is the Rietveld refinement profile of Ca$_8$H$_{46}$, and the black line represents the difference between the observed and calculated intensities. Green ticks mark the Bragg peak positions of the Pm$\bar{3}$n–Ca$_4$H$_{23}$ phase. Peaks labeled “Pt” originate from the platinum gasket.
• Figure 4: Pressure dependence of $T_\mathrm{c}$ in Ca–H Superhydrides. The figure presents calculated anharmonic $T_\mathrm{c}$ for CaH$_6$ and Ca$_8$H$_{44-46}$ in two structural types: Ca$_8$H$_{46-\delta}$ and CaH$_{6-\delta}$. For each type, multiple space group structures were considered. Hollow symbols and dashed lines represent individual calculations, while solid symbols and solid lines indicate their averages. Shaded regions denote the estimated error range. Experimental data from Ma et al.CaH6-实验2 and Li et al.CaH6-实验1 are shown as black squares and a purple triangle, respectively.