EXPERIMENTS ON HYDROGEN TRAPPING WITH ION BEAM ANALYSIS

Ikuji Takagi
Department of Nuclear Engineering
Kyoto University
Sakyo-ku, Kyoto 606-8501, Japan+81 (75) 753-5838

ABSTRACT
Depth profiles of deuterium in nickel, continuously
exposed to deuterium plasma, were observed by use of thenuclear reaction analysis. Trapping energy for deuterium innickel bombarded with energetic ions was 0.24eV, which
was determined under equilibrium between trapping andsolution sites. From the shape of the depth profile and thetrapping energy in cases of hydrogen and helium
bombardment, the traps were considered to be associatedwith radiation damages. Experiments on kinetics ofdeuterium on metal surface were also conducted.

degree to normal to observe a depth profile of deuterium
by use of the nuclear reaction analysis (NRA) with areaction of D(3He,p)4He.4 In order to produce traps, themembrane is bombarded with energetic ions such as
helium and hydrogen between the observation of NRA.
Van de Graaff
Accelerator

Temperature (ex. 523K)
Permeation Flux
D Plasma

Upstream
Chamber

Ion Bombardment
Depth Profiling (NRA)I. INTRODUCTIONp

D2 GasSampleQMA
Thermocouple TMP

RF

1.5
m )

3

-3

0.8-MeV He

27

D CONCENTRATION (×10

NICKEL, 523K
20

1.0

-2

DOSE (× 10 m )
16
4.2
0

0.5

0.0

II. EXPERIMENTAL

0.0

After the permeation reaches at the steady state, an ion
beam of helium-3 irradiates the plasma-exposed side at 45

D PlasmaFig.1 Schematic illustration for the experimental
setup and its typical procedure

We have developed an in-situ observation technique by
use of ion beam analysis,3 which is a kind of an
equilibrium
method.
Experimental
resultson
characteristics of the trapping site in nickel will be shown.
Application of the technique to study on some rate
constants of thermally activated processes for deuterium on
metal surface will also be mentioned.

Fig.1 shows schematic illustration of the experimental
setup and its typical procedure. A sample membrane is set
between two vacuum chambers of upstream anddownstream. A lamp heats up the sample while theupstream side of the sample is exposed to deuterium
rf-plasma. Permeation flux to the downstream ismonitored.

SSD
Discharge Tube

Heater

TMP
Permeation
Flux

Deuterium
Depth Profile

Al foil

3He

Downstream Chamber

Plasma-facing walls in fusion devices will bebombarded with energetic particles such as fast neutrons
and helium ions, which would produce hydrogen trappingand increase tritium inventory in the walls. There havebeen many experimental works on trapping of hydrogenisotopes, in which transient methods such as thermal
desorption1 and isothermal annealing2 are generally used.

Slit
Slit

0.5
1.0
DEPTH (µm)

1.5

Fig.2 Depth profiles of deuterium in nickel before andafter 0.8MeV-3He bombardment.5
III.

RESULTS

Depth profiles of deuterium in nickel bombarded withhelium-3 are shown in Fig.2.5 Before bombardment,
deuterium exists only on the surface and little deuterium isobserved in the bulk. After the bombardment, a broad peakappears in the bulk and its height increases withbombarding dose because traps are produced by thebombarding ions.

TRAPPED DEUTERIUM (× 10

27

-3

m )

As deuterium is absorbed on the surface, dissolved ortrapped in the bulk, the depth profile of trapped deuterium
can be estimated by substituting the profile before
bombardment from that after bombardment, which isshown in Fig.3.5
1.6
3

1.4
1.2
1.0
0.8

21

0.8-MeV He, 1.6× 10 m

-2

NICKEL
523 K

EXPERIMENTTRAPPED D
TRIM CODEDISPLACEMENT
ION

0.4
0.2
0.0

0.5
1.0
DEPTH (µ m)

1.5

Fig.3 The depth profile of trapped deuterium obtained
from the data shown in Fig.2.5 Distribution of
bombarding ions and atomic displacements are also
shown.

22

0.9MeV-H3, 3.5×10

26 -3

TRAPPED DEUTERIUM (×10 m )

8

6

o
2 45

H/m

EXPERIMENTTRAPPED D, 423 K20.5

Equilibrium Method

As the sample is continuously charged with deuterium
from the plasma in the experiment, there would be
equilibrium between the trapping and the solution sites.
The equilibrium constant f can be expressed as

Cs
C0 − CthN − C s C t(1)

where Cs and Ct are concentrations of deuterium in thesolution sites and the trapping sites, respectively, hN the
density of the solution sites and C0 the density of thetrapping sites. h is number of solution sites per host atom
and N atomic density of host metal.
Analogy to chemical reactions, f is equal to exp(-Δ
G/kT), where ΔG is the difference in free energy between
the trapping site and the solution site. When the differencein potential energy is defined as the trapping energy Et, f isexpressed as(2)

where f0 = exp(ΔS/kT) and ΔS is the entropy difference.
Under our experimental conditions, the permeation islimited by the diffusion process. It has been confirmed
from observation of transient behavior of permeation whenincident flux from the plasma is quickly changed. In the
diffusion-limited permeation, the permeation flux at thesteady state, J, and Cs is directly related by the equation,

4

0

A.

f = f 0 exp(− Et / kT )NICKEL, 453 K

TRIM (ARB.UNIT)DISPLACEMENT
H ION

0

IV. DISCUSSIONS

f =

0.6

0.0

nickel bombarded with 0.9MeV H3 (equivalent to three
0.3MeV H) ions.7 Also in this case, the profile is similar tothe distribution of the displacement. These results indicatethat the traps are associated with radiation damages, notwith presence of the bombarding helium or hydrogen ions.

1

1.5

D E P T H (µ m )Fig.4 The depth profile of trapped deuterium in nickel
bombarded with hydrogen ions.7 Distribution of
bombarding ions and atomic displacements are also
shown.
Distributions of bombarding helium-3 ions and atomic
displacements estimated by the TRIM code6 are also
shown in Fig.3. The depth profile is very similar to the
distribution of the displacement rather than that of the ions.
Fig.4 shows a depth profile of trapped deuterium in

J = DC s / L(3)where D and L are the diffusion coefficient and the sample
thickness, respectively.
As a region from the surface to the depth to which the traps
extend is much smaller than L, Cs can be regarded as
uniform. Cs is much smaller than hN. Integration of Eq.(1)over the region yields,f =Cs S0 − St
hN S t(4)

where St and S0 are areal densities of trapped deuteriumand the trapping sites, respectively.
B. Trapping Energy
Fig.5 shows temperature dependence of (a) theconcentration of dissolved deuterium, Cs, and (b) the areal
density of trapped deuterium, St, respectively. 3 St increases
with decreasing the sample temperature until it tends to besaturated. The saturated value is taken as the areal densityof the trapping sites, S0.
TEMPERATURE (K)
600
500

10

10

10

19

10

18

23

-3

22

f = 0.034exp(-0.24eV/kT)

10-4

f = 0.016exp(-0.22eV/kT)

4

0.8MeV He BOMBARDMENT
0.3MeV H BOMBARDMENT

1.4
1.6
1.8
2.0
2.2
2.4
2.6
-3
-1
RECIPROCAL TEMPERATURE ( x10 K )700

TEMPERATURE (K)
600
500
4

0.8MeV He

45

400

21

10

20

10

19

10

-5

1.5
2
2.5
-3 -1
RECIPROCAL TEMPERATURE (× 10 K )Fig.6 Arrhenius diagram of the equilibrium constantin nickel in cases of 4He and H bombardment.7

o

NICKEL

S0

10

TEMPERATURE (K)
600
500
400

700

22

-2

AREAL DENSITY OF TRAPPED D (m )

10

20

24

(b)
10

21

Cs

25

J
10

10

-2 -1

10

10

400

EQUILIBRIUM CONSTANT, f

700

-3

DEUTERIUM CONCENTRAION (m )10

26

PERMEATION FLUX (m s )(a)

It is, however, difficult because the models used foranalysis of the experimental data are different from eachother.8 The most important issue in the models would be
the pre-exponential factor f0 in Eq.(2). In some works, f0
has been assumed to be unity, that is, the difference in freeenergy is taken as the trapping energy. On the contrary, f0
in the present work is much larger than unity. The entropy
term is considered to be important for evaluation of thetritium inventory.

St

1.4
1.6
1.8
2.0
2.2
2.4
2.6
-3
-1
RECIPROCAL TEMPERATURE ( x10 K )C. Trap Density
Fig.7 shows evolution of the areal density of the traps asa function of atomic displacement.9 The trap density was
nearly proportional to the displacement in cases ofhelium-3 and hydrogen bombardment. The rate of the traps
to the displacement in helium-3 case was about three times
larger than that in hydrogen case. This is probably because
helium ions produce larger collision cascades in which
many defects survive a short-time annealing process.
3

Values of f, estimated from Eq.(4) with the above
experimental data and plotted in an Arrhenius diagram in
Fig. 67, come on straight lines, which indicates that one
kind of the traps is observed in the experiment. The
trapping energies Et are 0.24 eV for helium bombardment
and 0.22 eV for hydrogen bombardment. The traps in boththe cases would be the same.
The trapping energy obtained in the present work
should be compared with those in other researchers' works.

21

He DOSE ( × 10 m
1
2
3

-2

)
4

)

0

22

-2
21

AREAL TRAP DENSITY ( × 10 m

Fig.5 Temperature dependence of (a) theconcentration of dissolved deuterium and (b) theareal density of trapped deuterium in nickel
bombarded with 4He.3

5

0

1

H DOSE ( × 10 m
2
3

-2

)
4

5

NICKEL, 453K
4

3

0.8MeV- He
BOMBARDMENT
3
0.9MeV-H 3
BOMBARDMENT

2
1
0

0

1
2
3
23 -2
DISPLACEMENTS ( × 10 m )Fig.7 Evolution of the trap density with atomic
displacement in nickel.9

B.

Results and Discussions

V. KINETICS OF HYDROGEN ON SURFACE

E3 E4

A. Experimental

（E2）

26

Cu
0.1mm
357K

2

-0.2

0

0.2
0.4
DEPTH (µ m)vacuumf1 = F（1−θ）
f2 = k2θ2

surfacebulk

f3 = k3θ
f4 = k4c（1−θ）
f5 = DhNc/L

Fig.10 shows temperature dependence of 1/S2 for nickel
and copper membranes.11 Data come on straight lines inboth the cases. These suggests thatθis much smaller thanunity in each case and Eq.(5) can be rewritten by k2 = FSs2
/S2. The activation energies E2 for the rate constant k2 arefound to be 0.40 eV for nickel and 0.30 eV for copper.

4

0

Es

Fig.9 Schematic showings of potential energy diagram
and rate processes of hydrogen near metal surface.

8-3

CONCENTRATION (× 10 m )There is a peak at the 0-depth in the observed depth
profile as shown in Figs. 2 and 8.10 The peak would
represent absorbed deuterium on surface. The peak area istaken as the surface density of deuterium, S, here. S is
directly related to the deuterium surface coverageθbyθ= S/Ss, where Ss is the saturated deuterium density. The
concentration of deuterium just beneath the surface, C, is
known from the permeation flux J as described before andthe relative concentration, c, is defined here by c = C/hN.

6

Ed

0.6

0.8

Fig.8 A typical depth profile of deuterium in a copper
membrane exposed to deuterium plasma.10
From both the values ofθand c, some rate constants forthermally activated processes of hydrogen on metal surface
would be estimated. These constants are required forevaluation of surface recombination coefficients.
B. ModelA model used here is based on particle balance as
schematically shown in Fig.9. f1 is the incident flux to thesurface, f2, the desorption rate from the surface, f3, thejumping rate from the surface to the bulk, f4, the jumping
rate from the bulk to the surface and f5, the diffusion flux.
Particle balance between on the surface and the bulk
just beneath the surface yields f1 + f4 = f2 + f3 and f3 = f4 +
f5 , respectively. In the diffusion-limited permeation, there
would be quasi-equilibrium near the surface and f5 should
be much smaller than f3 and f4. Then,

F (1 − θ ) = k2θ 2(5)k3θ = k4c(1 − θ )(6)

Fig.10 Temperature dependence of 1/S2 on nickel andcopper membranes.11
When θ <<1, Eq.(6) is rewritten by k3 θ = k4c.
Assuming that the activation energy E4 for the rate
constant k4 is the same as that Ed for the diffusion
coefficient, k3 is expressed as (k40LSs/D0hN)(J/S), where k40
and D0 are the pre-exponential factors of k4 and D,
respectively. Fig.11 shows temperature dependence of
J/S,11 from which the values of E3 are found to be 0.57 eV
for nickel and 0.68 eV for copper.

are obtained, where c << 1 is taken into account.
The recombination coefficient Kr is a phenomenologicalconstant and would be expressed as k2k42/(hNk3)2,
according to the above model, where θ<<1 and hence k4c<< k3 are assumed. The energy term Er for Kr in theexpression form of Kr0exp(-Er/kT) can be estimated fromthe above experimental results and the activation energy
for diffusion in other works.8,12 They are 0.08 eV for nickel
and -0.29 eV for copper. It should be noted that E2 is notproper to materials but strongly depends on the surface
conditions. So the important result is that the activationenergy of E3 is experimentally determined in the present
work.

10

1

10

0

10

-1

10

-2

10

-3

10

-4

10

-5

10

-6

-1

J/S (s )700 600

TEMPERATURE (K)
500
400

300

Ni

Cu

1.5

2.0
2.5
-3
-1
1/T (× 10 K )3.0

Fig.11 Temperature dependence of J/S in nickel andcopper membranes.11
For better understandings of the recombination
phenomenon, the pre-exponential factors of k2, k3 and k4
are necessary to be known from experiments although they
have been estimated from theoretical consideration.13 The
values, however, cannot be obtained in the experimentbecause the incident flux F and the saturated density Ss are
uncertain. Determination of F and Ss remains as the issueof the present work.
VI. SUMMARY
The in-situ observation technique has been shown to be
useful for studying thermal behavior of hydrogen inmaterials. As samples are continuously charged withhydrogen from plasma, there would be equilibrium ofhydrogen between surface and bulk, the solution sites andthe trapping sites. The samples would not suffer fromdamages or sputtering because particles from plasma haveno sufficient energy and the energy of the analyzing beam
is so high that the damage production and sputtering do notoccur effectively. Both the studies on hydrogen trapping in
the bulk and hydrogen kinetics near the surface are in
progress and further results would be expected in future
works.

REFERENCES
1.

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Eichenauer
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