Plasma and Fusion Research: Regular Articles

Volume 11, 2405026 (2016)

A Study on Hydrogen Transport in Liquid Metals under SteadyState Plasma Bombardment∗)
Hailin BI1) , Yoshi HIROOKA1,2) and Juro YAGI2)
1)

The Graduate University for Advanced Studies, Toki 509-5292, Japan
2)
National Institute for Fusion Science, Toki 509-5292, Japan(Received 30 November 2015 / Accepted 3 February 2016)

Hydrogen Plasma-driven Permeation (PDP) experiments through two diﬀerent liquid metal membranes:
lithium and GaInSn have been conducted in the temperature range from 300 to 500 ◦ C. A technique employing a mesh sheet to hold a liquid metal for PDP has been utilized for the first time. It has been found that PDP issurface recombination limited for lithium and is diﬀusion limited for GaInSn. Hydrogen surface recombinationcoeﬃcients for liquid lithium and hydrogen diﬀusivity in GaInSn have been obtained respectively.
c 2016 The Japan Society of Plasma Science and Nuclear Fusion ResearchKeywords: liquid lithium, GaInSn, plasma-driven permeation, hydrogen plasma, recombination coeﬃcient, diffusivity
DOI: 10.1585/pfr.11.2405026

1. Introduction
The application of liquid metals as plasma facing
materials (PFM) draws increasing interest as a potential
means to resolve the technical issues associated with exhaust power and particle handing in magnetic fusion devices [1, 2]. Molten lithium is one of the candidates forthis application because of its low atomic number and highabsorptivity of impinging species. It has been used in fusion devices including NSTX [3] and EAST [4]. In these
confinement devices, it is considered that the interactionof hydrogen plasma with liquid lithium plays an importantrole in determining edge plasma characteristics and hencecore confinement performance.
GaInSn is a kind of liquid metal at room temperature,and has been used for modeling of various liquid metal
processes in industrial field and MHD study for flowing
liquid metal owing to the low reactivity and toxicity of its
components [5, 6]. In J×B-force convected liquid metal
experiment, flowing GaInSn has also shown ability of reducing both hydrogen and helium recycling when facing toplasma bombardment [7]. Then it is deduced that GaInSn
is also promising as a PFM in fusion reactors, though more
information is needed to evaluate the feasibility.
Fick’s laws have been successfully applied to describehydrogen diﬀusion in solid materials in the field of plasmawall interaction [8, 9]. Hydrogen diﬀusivities in the bulkof materials and hydrogen recombination coeﬃcients atthe surface of materials are essential parameters to studyhydrogen retention in materials and hydrogen transport,
including hydrogen permeation and hydrogen recycling.
However, hydrogen diﬀusivities in liquid lithium show
author’s e-mail: bi.hailin@nifs.ac.jp∗) This article is based on the presentation at the 25th International Toki
Conference (ITC25).

several orders diﬀerence in literature, and opposite opinions are existed about that if the surface reaction rate is adominant process for hydrogen transport in liquid lithium[10, 11]. For GaInSn, no information related to hydrogentransport is available in literature as we know. Due to theircritical importance to the application of liquid metals infusion reactors, these technical issues must be clearly addressed.
In the present work, experiments on hydrogen PDP
though liquid lithium and GaInSn membranes have been
conducted, holding liquid metals on a sheet mesh by surface tension. PDP through solid titanium membranes havealso been conducted as a step prior to liquid lithium inthis work, due to titanium and liquid lithium are both hydride forming metals. Hydrogen permeation breakthroughcurves have been obtained experimentally, as well as temperature eﬀects on steady state PDP flux.

2. Experimental
2.1 VEHICLE-1 facility
Shown in Fig. 1 is the PDP setup for liquid metals
in a laboratory-scale linear plasma device, VEHICLE-1.
Details of VEHICLE-1 facility and its plasma diagnostics
have been described elsewhere [12]. In this work the electron temperature is ∼ 10 eV and the plasma density is of
the order of 1010 cm−3 . The ion bombardment flux is of
the order of 1016 H/cm2 s, and the bombarding energy is
set at 100 eV by applying a negative DC bias on the sample tray. A liquid metal sample is fixed in such a waythat the upstream surface is exposed to hydrogen plasma,
while the downstream side is pumped to ultrahigh vacuum(10−6 - 10−5 Pa). And the two chambers are sealed by theliquid metal. The plasma-facing area is 6.6 cm2 , and the total area of openings is 0.66 cm2 . The thickness of lithium

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c 2016 The Japan Society of Plasma
Science and Nuclear Fusion Research

Plasma and Fusion Research: Regular Articles

Volume 11, 2405026 (2016)

(a)

(b)

Fig. 2 Temperature dependence on the hydrogen steady state
PDP flux through titanium membranes with thickness of
0.1 mm and 1 mm.
Fig. 1 (a) Schematic diagram of the experimental setup for PDP
through liquid metals. (b) Surface tension to hold a liquid
metal.

is ∼ 2 mm before melting, and the thickness of GaInSn is∼ 6 mm. A resistive heater is positioned beneath the meshto control the sample temperature, which is measured by athermocouple. The hydrogen permeation flux due to PDP
is monitored by the partial pressure of H2 measured by aquadrupole mass spectrometer (QMS).

2.2

The mesh-surface tension method

The use of a sheet mesh to hold a liquid metal sample
is based on the assumption that surface tensions of liquid
metals are relatively high [13, 14]. To avoid liquid metal
dropping down through the mesh, upward force provided
by the surface tension should be larger than the weight ofliquid metal and pressure diﬀerence caused by gases in upstream chamber. Shown in Fig. 1 (b) is the stress balanceon liquid lithium set on the mesh, which can be describedby:sin θ × 2πRσ = πR2 (P + ρgd), 0◦ < θ ≤ 90◦ . (1)Where σ is the surface tension of liquid lithium, R
is the radius the pore, d is the thickness, ρ is the density,and P is neutral gas pressure in upstream chamber, θ isthe angle between the direction of surface tension and horizontal line. In our experiments, the radius of the pores
R is 0.2 mm, and typical hydrogen pressure P in upstream
chamber for running plasma is ∼ 0.1 Pa. For liquid lithiumwith thickness of 2 mm at 500 ◦ C, surface tension σ is0.356 N/m. Then θ will be 0.17◦ calculated from equation(1), which suggests that surface tension is suﬃcient to holdliquid lithium.

3. Results and Discussion
In the steady-state PDP model, three regimes are considered [8]: (1) the DD-regime: diﬀusion limited releaseof hydrogen from both the upstream and downstream surfaces; (2) the RD-regime: recombination limited releasefrom the upstream surface and diﬀusion limited releasefrom the downstream surface; (3) the RR-regime: recombination limited release from both surfaces. The steadystate PDP flux is inversely proportional to the membranethickness for the DD-regime and the RD-regime, while it
is independent of the membrane thickness for RR-regime.

3.1 Titanium
Hydrogen steady state PDP fluxes through 0.1 mm and1 mm titanium membranes have been obtained in the temperature range from 331 to 532 ◦ C. As shown in Fig. 2,
there is no thickness eﬀect on the steady state PDP flux.
Then, it is concluded that PDP through titanium underthese conditions is surface recombination limited.
In this experimental temperature range, the hydrogen steady state PDP flux is in the range from 1.09 ×
1013 H/cm2 s to 1.65 × 1015 H/cm2 s, and the surface recombination coeﬃcient derived from [15] is in the range from
1.2 × 10−28 cm4 /s to 3.7 × 10−27 cm4 /s. Then, the hydrogenconcentration in titanium at steady state is evaluated to bein the range from 3.01 × 1020 H/cm3 to 6.68 × 1020 H/cm3 ,which shows high dynamic retention of hydrogen in titanium during PDP.

3.2 Lithium
Hydrogen PDP experiments on liquid lithium havebeen conducted in the temperature range from 313 to402 ◦ C. The Pressure-Concentration-Temperature (PCT)
diagram of the LiH-Li system has been obtained based on
the data evaluated by H. Borgstedt [16], as shown in Fig. 3.
The equilibrium pressure of LiH-Li in the temperature range from 313 to 402 ◦ C is from 4.5 × 10−4 Pa to
9.1 × 10−2 Pa. And the corresponding hydrogen solubility limit is from 1.76 × 1020 H/cm3 to 5.82 × 1020 H/cm3 ,taken from the PCT diagram. The pressure in the upstream

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Volume 11, 2405026 (2016)

Fig. 3 Pressure-Concentration-Temperature (PCT) diagram of
the LiH-Li system.

Fig. 4 Hydrogen recombination coeﬃcients for liquid lithium.

chamber (0.1 Pa) for running plasma is higher than theequilibrium pressure of LiH-Li, so there is no reemission
flux at the upstream surface of lithium. And the measuredhydrogen permeation flux at steady state is in the range
from 6.36 × 1012 H/cm2 s to 2.12 × 1015 H/cm2 s, whichis less than the implantation flux at upstream. Therefore
the dissolved hydrogen concentration in lithium will always increase until solid LiH starts to precipitate at theupstream surface, meaning the LiH-Li system will transform from αliq phase to αliq +βsol phase. Then dissolvedhydrogen concentration at upstream surface is fixed to bethe hydrogen solubility limit.
In the experiment, the steady state permeation flux isestablished within 3 hours, which shows a big diﬀerencecompared with time lag tlag based on the assumption ofdiﬀusion-limited PDP. So hydrogen PDP through liquid
lithium is not diﬀusion limited but recombination limited,which has been found in titanium as well.
For recombination limited PDP, the hydrogen concentration at downstream surface is approximate to the dissolved hydrogen concentration at upstream surface when
the steady state permeation flux is established. Then therecombination coeﬃcient Kr can be obtained by equation:

Fig. 5 Comparison of experimental data and simulation resultson hydrogen PDP breakthrough curve for liquid lithium.

Fig. 6 Comparison of Hydrogen diﬀusivities in liquid lithium.

Kr =J2.
Cs(2)Where J is the steady state PDP flux and Cs is thedissolved hydrogen concentration at downstream surface.
The temperature dependence on hydrogen recombinationcoeﬃcients has been obtained, which is close to deuterium
recombination coeﬃcients in liquid lithium [17], as shownin Fig. 4.
The simulation results of breakthrough curve with different diﬀusivity values in Fig. 5 show that diﬀusivities inthe orders of 10−5 - 10−3 cm2 /s are all close to the experimental data. As diﬀusivity plays a minor role in a recombination limited PDP, to get precise diﬀusivities from PDP isinfeasible. However, the recombination limited PDP in thiswork suggests that diﬀusivity of hydrogen in liquid lithium
is suﬃciently rapid, which supports Moriyama’s results, as
shown in Fig. 6.

3.3 GaInSnHydrogen PDP experiments through GaInSn havebeen conducted in the temperature range of from 400 to500 ◦ C. The temperature dependence on the steady state
PDP flux is shown in Fig. 7. Hydrogen permeation break-2405026-3

Plasma and Fusion Research: Regular Articles

Volume 11, 2405026 (2016)

Fig. 7 Temperature eﬀects on hydrogen PDP steady state flux
through GaInSn with thickness of 6 mm.

Fig. 9 Time evolution of hydrogen concentration profile inGaInSn during PDP for D = 2 × 10−4 cm2 /s.

4. Summary
Hydrogen PDP through liquid lithium and GaInSn has
been investigated experimentally using a plasma-wall interactions facility: VEHICLE-1. A technique employing
a mesh sheet to hold a liquid metal for PDP has been utilized for the first time. It has been found that PDP throughtitanium and liquid lithium are both surface recombination
limited and is diﬀusion limited for GaInSn. Temperatureeﬀects on hydrogen recombination coeﬃcients for liquid
lithium have been obtained. And hydrogen diﬀusivity in
GaInSn is found to be in the range of 1 - 3 × 10−4 cm2 /s at489 ◦ C.
Fig. 8 Comparison of experimental data and simulation resultson hydrogen PDP breakthrough curve for GaInSn.

through curve at 489 ◦ C is shown in Fig. 8. At steady state,
following equations are satisfied.
J = K2 × C22 ,C1 − C2,
J = D×dJ1 = J0 − J = K1 × C12 .

(3)
(4)
(5)

Where J is the permeation flux, J0 is the implantation
flux, J1 is the reemission flux, d is the thickness of the sample, C1 and C2 is the hydrogen concentration at upstream
surface and downstream surface respectively. As the diffusivity D and recombination coeﬃcient at upstream surface K1 and downstream surface K2 are all unknown, K1= K2 is assumed for simulation in this work. Diﬀusivity isset as 1 × 10−4 , 2 × 10−4 , 3 × 10−4 cm2 /s as three cases,
and the corresponding recombination coeﬃcients is 3.3 ×
10−19 , 1.3 × 10−18 , 3.0 × 10−18 cm4 /s. Hydrogen permeation breakthrough curves in the three cases are comparedwith experimental data in Fig. 8. At 489 ◦ C, the hydrogendiﬀusivity is likely to be in the range of 1 - 3 × 10−4 cm2 /s.
And time evolution of hydrogen concentration profiles areshown in Fig. 9. It is found that hydrogen dynamic retention in GaInSn during PDP is about 4 orders magnitude
lower than in titanium and liquid lithium.

Acknowledgments
The authors would like to acknowledge Dr. N.
Ashikawa and Mr. Y. Xu for their help during experimental
operation.
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