Hydrogen-induced volume expansion in hexagonal close-packed iron: Effects of pressure and temperature

Hydrogen is a promising candidate for the light element in terrestrial planetary cores. Its incorporation into iron causes significant volume expansion, leading to a substantial density deficit. Although extensive studies have been conducted on iron hydride (FeH$_{x}$) with the fcc structure, the thermoelastic properties on FeHx with hcp structure (hcp-FeH$_{x}$) remain unconstrained because of the experimental difficulties to control hydrogen content. Here, we synthesized hcp-FeH$_{x}$ with controlled hydrogen contents under high-pressure and high-temperature conditions. We carried out \textit{in situ} X-ray diffraction measurements on hcp-FeH$_{x}$ at 10--25~GPa and 300--900~K using a Kawai-type mutilanvil apparatus and constructed their equations of state. By combining our results with previously reported equations of state for hcp-Fe and experimental determinations of hydrogen content in hcp-FeH$_{x}$, we demonstrated that the discrepancies in the hydrogen-induced volume expansion coefficient can be clearly explained by its pressure and temperature dependence. Our results revealed that the hydrogen-induced volume expansion of hcp-Fe exhibits a strong temperature dependence at low pressures, but its temperature effect significantly weakens with increasing pressure. We also showed that the density reduction of Fe by hydrogenation depends on its crystal structure. These findings demonstrate that estimates of hydrogen content in iron at planetary interior conditions based on hydrogen-induced volume expansion need to be revised by properly accounting for its $PT$-dependence and crystal structure.