24P092-P
Simulation of deuterium trapping and thermal desorption from W exposed tolow energy high flux plasma
Aleksandr Rusinov1, Koichiro Honda1, Mizuki Sakamoto2, Hideki Zushi3, Tetsuo Tanabe, Yuri
Gasparyan4, Alexandr Pisarev4
1

Interdisciplinary Graduate School for Engineering Sciences, Kyushu University, Japan
2
Plasma Research Center, University of Tsukuba, Japan
3
Research Institute for Applied Mechanics, Kyushu University, Japan
4
National Research Nuclear University, Russia

Deuterium trapping and thermal desorption from W are simulated by the TMAP7 code under high flux
(3×1021 at/m2sec) and low energy plasma exposure conditions where atomic source is at the very surface
node without radiation defects generation. The trapping sites are assumed to be distributed uniformly. Theresults are compared with TDS experiments and it is discussed whether the model of simple diffusion via
trapping-detrapping process can be applied or not. The influence of sample thickness, fluence and theirradiation temperature on the shape and position of thermal desorption peaks is discussed based on
retrapping effect during diffusion of atoms into and out of the bulk.

1. Introduction
Hydrogen isotopes and tungsten materialinteractions have been investigated widely. Thereare many works devoted to modeling of thethermal desorption of isotopes trapped in thedefects of tungsten material, e.g. [1,2]. Usually,
the experiments and consequently the modeling
have been performed with high energy ofbombarded particles (an order of keV). At theseenergies the trapping is determined by the defects
produced by radiation damage. The contributionof intrinsic defects inside the bulk is usually
negligible in this case. Low energy ions areunable to create defetcs via collisions. In this casethe retention and TDS peak position are mainly
determined by trapping at intrinsic defects inside
the material. In case of plasma irradiation highflux of low energy particles creates large
diffusion flux into the bulk. Thus, trapping insuch kind of experiments should be determinedby simple diffusion involving trapping-detrapping
processes. This study is devoted to clarify thepecularities of TDS spectra behavior after W
irradiation at these conditions.
2. Modeling
Modeling of plasma irradiation and TDS wasperformed using the TMAP7 code [3]. This code
allows calculating trapping inside the bulk
according to one-dimensional diffusion equation,
which takes into account trapping-detrapping
processes:∂C∂C t+ ∇J = S −∂t∂t∂C t α t Cte=− αtC t∂t
Ne0Ct = Ct − C tαt = E ; α r = ν 0 exp  − t λ RT D

2

where C is concentration of soluted deuterium, Jis diffusion flux of deuterium, S is internal sourceof deuterium, Ct is concentration of trappeddeuterium, Cte is concentration of empty trappingsites, Ct0 is total concentration of trapping sites, αtand αr are trapping and release rate, respectively.
The following parameters were varied in thecalculations: the recombination coefficient, thetrapping sites detrapping energy, trapping sites
density, trapping sites depth distribution, sample
length. The plasma irradiation process wassimulated as an internal particle source at thesecond node (0.5nm from the surface) with the rateof incoming flux. Thus, the incoming flux ofplasma particles didn’t create any radiation defects
inside the material.
Usually the calculation parameters were thefollowings: the sample length 0.1 mm, the plasma
particles flux 3×1021 D/m2, the traps density 0.01%(uniformly distributed), the diffusion coefficient
DD=2.9×10-7exp(-0.39[eV]/kT)[m2/sec],therecombination
coefficient
Kr=3.2×10-5exp(-1.16[eV]/kT)[at/m4sec],thetrapping rate αt=1013exp(-0.39[eV]/kT), the release
rate αr=1013exp(-Et[eV]/kT), (Et – trapping energy,
i.e. Et=Eb+Ed), irradiation temperature 500 K, TDS
ramping rate 1 K/sec.

3. Results and discussion
Fluence dependence (FD) of the retention at
various trapping energies is shown in Fig. 1. In [4]it is reported that square root behavior of theretention is governed by diffusion, while smaller
slope may indicate additional loss mechanisms; e.g.,surface roughness may alternate escape pathwaysfor diffusing D atoms. In a diffusion limited regime
the depth profiles have long tail extended deeply inthe bulk. From fig. 1 it is seen that in the presenceof trapping sites FD also has square root behaviour.
FD measured in W foil also showed square root
dependence. Therefore, square root behavior
undoubtedly means permeation inside the bulk evenfor trapping limited regime. But, with Et increasing
FD slope gradually decreases. This is caused byvery small probability for the detrapping process,when diffusion inside the bulk is stronglysupressed.
In the calculations it was observed that TDS peakshifts with the fluence to higher temperatures due todeeper diffusion of D atoms. This shift wasobserved in our experiments with the W foil andcannot be explained by the first or the second orderdesorption model.
Temperature dependence (TD) of the retention
has maximum (fig. 2). The maximum in TD cannot
be explained by a diffusion model. The smaller thetemperatures the smaller the diffusion coefficient,
therefore the larger the retention. In [5] the decreaseof the retention in TD was explained by larger valueof the diffusion coefficient in the implantation zonethat could be due to “ion induced desorption”. In
our calculations it is shown that in the presence of
uniformly distributed defects the retention isgoverned by trapping sites. At low temperatures thetrapping sites are slowly saturated whereas thediffusion into the bulk is supressed. As thetemperature increases D atoms can diffuse inside
the bulk and total integral results in the increase of
the retention. At even higher temperatures theretention decreases due to high probability fordetrapping. The maximum position depends on thetrapping energy (fig. 2).
The shape and positions of TDS peak depend not
only on the trapping energy but also on the otherfactors. Desorption from the trapping sites with asingle trapping energy results in asymmetric TDS
peak looking like two peaks.

Fig.1. Fluence dependence of the retention for variousEt (Tirr=500K, 2h irradiation)

Fig.2. Temperature dependence of the retention forvarious Et (2h irradiation)

The shoulder or the second peak can be causedby the desorption from the back side of the sample,
which is delayed by traps. The traps concentrationand depth distribution influence on the peak
position. The larger the defects concentration level,
the higher the peak temperature. The sample
thickness also can change TDS spectra. The larger
the thickness the longer the tail of high temperaturepart of the peak. In the regime when the retention issatutated the larger thickness of the material results
not only in the change of the shape but also insustantial retention increase.
References[1] M. Poon, A.A. Haasz, J.W. Davis, Journal of Nuclear
Materials 374 (2008) 390–402[2] O.V. Ogorodnikova, J. Roth, M. Mayer, Journal ofNuclear Materials 313–316 (2003) 469–477[3] G. R. Longhurst, TMAP7 User Manual, October
2004[4] Zhe Tian, Deuterium retention in polycrystalline
tungsten, PhD thesis[5] T. Venhaus, R. Causey, R. Doerner et al., JNM,
290-293 (2001) 505-508