Solubility of deuterium and hydrogen in fcc iron at high pressures and temperatures

An isobar $x\left(T\right)$ of deuterium solubility in iron is constructed at $P=6.3\mathrm{GPa}$ and $100\le T\le 800{}^{\circ }\mathrm{C}$ based on the results of thermal desorption analysis of $\mathrm{Fe}{\mathrm{D}}_x$ samples produced by quenching under high ${\mathrm{D}}_2$ pressure to the temperature of liquid nitrogen. The experiment confirms the value of $x=0.64$ at $T=715{}^{\circ }\mathrm{C}$ proposed previously in a neutron diffraction work [Machida et al., Nature Commun. 5, 5063 (2014)] for γ iron deuteride under the assumption that deuterium atoms occupy both octa- and tetrahedral interstices in its fcc metal lattice. An estimate of $\mathrm{\Delta }V/x=2.2{\AA }^3/\mathrm{atom}$ D made in that work for the deuterium-induced volume expansion $\mathrm{\Delta }V\left(x\right)$ of fcc iron is also confirmed. To prove that the absorption of protium leads to a similar volume expansion, we constructed an isotherm $x\left(P\right)$ of hydrogen solubility in fcc iron at $T=600{}^{\circ }\mathrm{C}$ and ${\mathrm{H}}_2$ pressures from 4.3 to 7.4 GPa. The available $\mathrm{\Delta }V\left(P,T\right)$ data of in situ x-ray diffraction studies of iron hydrides [T. Hiroi et al., J. Alloys Compd. 404–406, 252 (2005); H. Saitoh et al., J. Alloys Compd. 706, 520 (2017)] agree with this isotherm under the assumption that $\mathrm{\Delta }V/x=2.2{\AA }^3/\mathrm{atom}$ H. The transformation between the high-temperature fcc (γ) and low-temperature dhcp (ε′) deuterides of iron is shown to occur at 260 °C, which is approximately 100 °C lower than the temperature of the γ ↔ ε′ transformation in the Fe-H system at the same pressure of 6.3 GPa.

Figure 1

T-P phase diagram of the Fe-H system [35] (black lines). α stands for dilute solid solutions of hydrogen in body centered cubic α-Fe with atomic ratios H/Fe of $x<0.01$ [36]; ε′ is the approximately stoichiometric FeH hydride with a double hcp metal lattice; γ is the hydride with an fcc metal lattice and variable hydrogen concentration. The open orange square indicates the point ($P_{\mathrm{D}2}=6.3\mathrm{GPa}$, $T=715{}^{\circ }\mathrm{C}$) chosen for the in situ ND experiment in Ref. [27]. The blue triangles show the temperatures of synthesis of Fe-D samples along the isobar at $P_{\mathrm{D}2}=6.3\mathrm{GPa}$. The open up-triangles refer to the γ deuterides; the solid down-triangles are for the ε′ ones. The red circles indicate the ${\mathrm{H}}_2$ pressures of synthesis of Fe-H samples along the isotherm at $T=600{}^{\circ }\mathrm{C}$. The solid circles refer to the samples, which retained hydrogen during their quenching to the liquid ${\mathrm{N}}_2$ temperature; the crossed circles are for the samples decomposed in the course of the quenching while crossing the α field of dilute hydrogen solutions at high temperatures.

Figure 2

Hydrogen release from the quenched $\mathrm{Fe}{\mathrm{D}}_{1.00\left(3\right)}$ and $\mathrm{Fe}{\mathrm{H}}_{0.83\left(3\right)}$ samples heated in vacuum at a rate of 10 °C/min.

Figure 3

Experimental isobar of deuterium solubility in iron at a ${\mathrm{D}}_2$ pressure of 6.3 GPa presented as triangles interpolated with dashed curves for use as a guide for the eyes. The solid triangles stand for the low-temperature stoichiometric monodeuteride ε′-FeD with a dhcp metal lattice. Open triangles are for the high-temperature γ-$\mathrm{Fe}{\mathrm{D}}_x$ with an fcc metal lattice and variable composition. The orange squares show results of Ref. [27] of modeling the neutron diffraction pattern of a γ-$\mathrm{Fe}{\mathrm{D}}_x$ sample assuming that D atoms could fill only octahedral O sites in its fcc metal lattice (solid square) or occupied both O sites and tetrahedral T sites (open square). The open magenta diamond shows the hydrogen content $x=\mathrm{H}/\mathrm{Fe}$ of a $\gamma \text{−}\mathrm{Fe}{\mathrm{H}}_x$ sample synthesized in an ${\mathrm{H}}_2$ atmosphere at the same P = 6.3 GPa and $T=715{}^{\circ }\mathrm{C}$ as the γ-$\mathrm{Fe}{\mathrm{D}}_x$ sample in Ref. [27].

Figure 4

T-P phase diagram of the Fe-H system [37] with the line of the α ↔ γ transformation (dash-dot brown curve) taken from Ref. [35]. The small solid black symbols indicate positions of the $\alpha \to {\varepsilon }^{\prime }$ and $\alpha \to \gamma$ and ${\varepsilon }^{\prime }\to \gamma$ transitions, while the small open black symbols stand for the corresponding reverse transitions. Large open orange triangles show the positions of the ${\varepsilon }^{\prime }\to \gamma$ and $e\to {\varepsilon }^{\prime }$ transitions observed in Ref. [29]. The large solid blue circle represents the point of the ε′ ↔ γ equilibrium in the Fe-D system determined in the present work. The dashed blue line crossing this circle shows a tentative position of the phase boundary ε′ ↔ γ in the Fe-D system.

Figure 5

Atomic ratios $x=\mathrm{H}/\mathrm{Fe}$ of Fe-H samples loaded with hydrogen at 600 °C and pressures indicated along the horizontal axis. The ratios shown with the red circles are determined by thermal desorption analysis (TDA) in the present paper; the synthesis conditions of the samples are indicated in Fig. 1 using the same symbols. The open magenta diamond stands for the sample hydrogenated at $P_{\mathrm{H}2}=6.3\mathrm{GPa}$ and 715 °C; a point for this sample is indicated in Fig. 3 with the same symbol. All other data are derived from the results of previous in situ synchrotron x-ray diffraction studies [28, 29] (see text).

Figure 6

Partial volume ${\beta }_{\mathrm{H}}=d{V}_a/dx$ of hydrogen at ambient pressure and room or lower temperature in the O sites of fcc hydrides $\mathrm{Mn}{\mathrm{H}}_{0.41}$, CoH, and NiH [1] (solid blue diamonds); in the O sites of hcp hydrides $\mathrm{Mn}{\mathrm{H}}_{0.65–0.96}$, and $\mathrm{Co}{\mathrm{H}}_{0–0.5}$ [1] (open blue diamonds); in the T sites of fcc dihydride $\mathrm{Co}{\mathrm{H}}_2$ [13] (solid olive circle) and in the T sites of hcp dihydride $\mathrm{Cr}{\mathrm{H}}_2$ [17] (open olive circle). The open red star shows the experimental ${\beta }_{\mathrm{H}}$ value at elevated temperatures for fcc $\mathrm{Fe}{\mathrm{D}}_{0.64}$ [27] and for fcc iron hydrides (result of the present paper).