J. Guterl1, R.D. Smirnov1, S.I. Krasheninnikov1, B. Uberuaga2, A.F. Voter2, D. Perez2

1. University of California San Diego, La Jolla, CA 92093, USA

2. Los Alamos National Laboratory, Los Alamos, NM 8754, USA

2014 Joint ICTP-IAEA Conference on Models and Data for Plasma-Material Interaction in Fusion Devices

Contact: jguterl@ucsd.edu

Modeling of hydrogen desorption from

tungsten surface

This work is performed under the auspices of USDOE Grant No. DE-FG02-04ER54739

and the PSI Science Center Grant DE-SC0001999 at UCSD 1

Hydrogen retention and recycling on metallic plasma-facing components are among key-issues

for future fusion devices due to safety and operational reasons. For tungsten, which has been

chosen as divertor material in ITER, desorption parameters experimentally measured for

fusion-related conditions show a large discrepancy. In this paper, we investigate hydrogen

recombination and desorption on tungsten surfaces by performing molecular dynamics

simulations and accelerated molecular dynamics simulations to analyze adsorption states,

diffusion, hydrogen recombination into molecules and desorption from tungsten surfaces,

and clustering of hydrogen on tungsten surfaces. The validity of tungsten hydrogen

interatomic potential is discussed in the light of MD simulations results, and hydrogen surface

diffusion properties and effects of clustering on hydrogen desorption are analyzed. A kinetic

model is introduced to describe the competition between surface diffusion, clustering and

recombination, and different desorption regimes are identified. Characteristics of these regimes

are compared to thermodesorption experiments data.

Topics: H retention in W, H desorption from W surface, H clustering & diffusion on W

surface, Temperature Accelerated molecular Dynamics, Molecular Dynamics

2

Abstract

3

In future fusion devices, retention and recycling of hydrogen isotopes in PFCs

material induced by exposure of plasma facing components (PFCs) to continuous

large plasma flux (~1020 − 1024𝑚−2𝑠−1 ) during long periods ( ~400𝑠) are among key-issues due to:

safety issues (total quantity of 𝐻3 < 700𝑔 in ITER)

synergetic effects between plasma and PFCs

impurities release in plasma

Divertor in ITER + PFCs in DEMO are planned to be in tungsten

Retention in PFCs modeled with reaction-diffusion equations (R-D) due to large

time and space scales relevant for fusion reactor conditions

Boundary conditions of R-D equations determined by surface processes:

H desorption flux Γ𝑑𝑒𝑠 from W surface usually described as desorption of 𝐻2 formed by recombination of adsorbed H atoms on surface (second-order kinetic

process):

Γ𝑑𝑒𝑠 = 𝐾0𝑒−𝐸𝑑𝑒𝑠𝑇

𝐾𝑟

𝑐𝑠2 (1)

Introduction 1/3

Understanding mechanisms involved in hydrogen retention and outgassing in

W is essential

4

Experimental data show:

Large discrepancies for 𝐾0 and 𝐸𝑑𝑒𝑠 and contradictory temperature dependencies of 𝐾𝑟 (a)

Several binding states for adsorbed hydrogen on tungsten

surfaces observed in thermodesorption experiments

[Tamm1971,Markelj2013]

Desorption kinetic order may be different from 2 [Tamm1971]

Desorption parameters ( 𝐸𝑑𝑒𝑠, 𝐾0) vary significantly when hydrogen surface coverage exceeds 0.5 (b,c) [Alnot1989]

Introduction 2/3

From [Roth2011]

𝐾𝑟

(a)

(b) From [Alnot1989]

𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑐𝑜𝑣𝑒𝑟𝑎𝑔𝑒 𝜃 (x10)

(c)

From [Alnot1989]

𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑐𝑜𝑣𝑒𝑟𝑎𝑔𝑒 𝜃 (x10)

surface processes are complex and may be not well described by (1)

+ desorption regime depends on surface coverage

However, surface processes may not affect retention if recombination rate

coefficient is large enough (𝐾𝑟 > 10−24𝑚4𝑠−1) [Roth2011, Causey2002]:

True at high temperature but surface desorption regimes may be different for

thermodesorption experiments (TDE) and for divertor in ITER conditions:

In high-recycling regime: Γ𝑖𝑛 ≈ Γ𝑑𝑒𝑠 and Γ𝑑𝑒𝑠 < Γ𝑚𝑎𝑥 = 𝐾0 𝑒−𝐸𝑑𝑒𝑠𝑇 (𝑐𝑠

𝑠𝑎𝑡)2, 𝑐𝑠𝑠𝑎𝑡 ≈ 1019𝑚−2

Better description of hydrogen desorption mechanisms from W surface is needed

We propose to investigate atomic processes governing H surface

desorption from W using molecular dynamics simulations (MD) 5

Introduction 3/3

Surface saturation by hydrogen?!?

W W

𝐸𝑏 [𝑒𝑉]

6

Frozen W surface not relevant for H adsorption

W-H adsorption energy 𝐸𝑎𝑑𝑠 = 𝐸𝑊𝐻 − 𝐸𝐻 − 𝐸𝑊 mapped by slowly approaching H along z-direction toward W

surface maintained at T~0K by viscous force

Hydrogen adsorption and diffusion on W surface 1/3

(T)

MD simulations setup: W-H Tersoff type potential Δ𝑡~0.1𝑓𝑠 Box ≈ 8x8 lattice cells and surfaces Frozen W bottom layers

: initial position of W atoms on relaxed surface

𝐸𝑎𝑑𝑠 >𝐸𝐻22

in agreement with 𝐻2 dissociation on W surface [Hickmott1960]

Single H desorption at T>1600K with 𝐸𝑑𝑒𝑠 = 2.91𝑒𝑉 [Hickmott1960] surface: tight-binding potential shows 𝐸𝑎𝑑𝑠 = −2.4𝑒𝑉 for (B) site [Forni1992] W-H Juslin’s potential gives reasonable description of adsorption sites

(B)

(O)

(D) (T)

(B)

(O)

𝐸𝑎𝑑𝑠 = 2.4𝑒𝑉 𝐵 , 2.3𝑒𝑉 𝑇 , 2.1𝑒𝑉 𝑂 , 2𝑒𝑉 (𝐷) 𝐸𝑎𝑑𝑠 = 1.6𝑒𝑉 𝐵 , 2.35𝑒𝑉 𝑇 , 2.4𝑒𝑉 𝑂

x

y

z

Activation energies 𝐸(𝑖)→(𝑗) of hydrogen transition between adsorption sites needed

to characterize diffusion of hydrogen on W surface

𝐸𝑎𝑑𝑠 map not relevant for diffusion paths because H motion in x and y directions necessary to characterize transition

Analysis of diffusion process on surface with Temperature accelerated MD

(TAD, low T=500K, high T=1300K) used to calculated 𝐸(𝑖)→(𝑗)

show (fig.2):

Hydrogen adsorption and diffusion on W surface 2/3

(T) (T2)

additional ads. site (T2) with 𝐸𝑎𝑑𝑠 = 2.15𝑒𝑉 (fig.1)

transition 𝑇 → 𝐵 : 𝐸 𝑇 →(𝐵) ≈ 0.55𝑒𝑉

transition 𝐵 → 𝑇 : 𝐸 𝐵 →(𝑇) ≈ 0.35𝑒𝑉

𝐸(𝑖)→(𝑗) < 0.35𝑒𝑉 for other transitions

transitions between adjacent ads. sites

H migration between lattice cells

through (B) sites.

Transition analysis suggests that H diffusion on

surface limited by transition 𝑇 → 𝐵 and thus activation energy for diffusion 𝐸𝐷 ≈ 𝐸(𝑇)→(𝐵) ≈

0.55𝑒𝑉. BUT… (see next slide)

7

Act.energy for transitions btw adsorption sites

W surface 𝐸𝑏 [𝑒𝑉]

Figure 2

Figure 1

8

BUT… 𝐸 𝑖 → 𝑗 ,𝑗≠(𝐵) < 𝐸(𝑖)→(𝐵) ⇒ H explores (T,T2,O,D) before exploring (B)

H easily migrates from (T) to (D) 𝐸 𝑇 → 𝐷 < 0.1eV , which tends to modify effective

potential structure in lattice cells and affect migration to other lattice cells:

During TAD run, H resides in (T,T2,D,0) much longer

than in (B) 𝑡𝑟𝑒𝑠(𝑇,𝑇2,𝐷,0)

~10−7𝑠>> 𝑡𝑟𝑒𝑠(𝐵)~10−9𝑠

H diffusion on W surface might be complex:

pre-exponential factor and 𝐸𝐷 in H diffusion coefficient

may depend on temperature

Experimental measurements of H diffusion coefficient on W surface for

T>220K [Daniels1995] show 𝐸𝐷 ≈ 0.30𝑒𝑉:

in reasonable agreement with 𝐸𝑠𝑖𝑡𝑒→(𝑇) ≈ 0.35𝑒𝑉 𝑎𝑛𝑑 𝐸(𝑇)→ 𝐵 ≈ 0.55𝑒𝑉

𝐸𝐷 < 𝐸(𝑇)→ 𝐵 in agreement with assumption of complex H diffusion

Conclusions:

W-H interatomic potential may well describe main features of adsorption sites on W

surfaces

Existence of many ads. sites may induce complex H diffusion on W surfaces

Better assessment of W-H interatomic potential required (DFT?) for further

quantitative analysis of adsorption and diffusion of H on W surfaces. For instance,

existence of (D) sites is questionable regarding their narrowness.

Hydrogen adsorption and diffusion on W surface 3/3

H molecular desorption = H recombination into 𝐻2 + desorption of 𝐻2 from surface

𝐻2 dissociation experimentally observed on tungsten surface [Hickmott1960]

⇒ H recombination into 𝐻2 governs hydrogen molecular desorption

MD simulations of H molecular desorption on W surface:

Characteristic time of desorption process: 𝜏𝑑𝑒𝑠~ 1013𝑒−𝐸𝑑𝑒𝑠𝑇

−1

𝑠

Experimental H molecular desorption activation energy 𝐸𝑑𝑒𝑠 ≈ 1.6𝑒𝑉 [Tamm1971]

High simulation temperatures required: for T 1𝑛𝑠

TAD simulations cannot be used because dramatic decrease of TAD efficiency with more

than one H

At T>2000K, H diffuse from W surface into W bulk

⟹ dramatic decrease of H surface coverage 𝜃 and of recombination rate of H into 𝐻2

Injection of H at constant rate into bottom layers of W samples (fig. 3) to balance H

desorption + maintain 𝜃 > 0.1 + steady desorption to estimate desorption rates

9

Hydrogen molecular desorption from W surface 1/3

H

𝐻2

tungsten

𝐻

Figure 3

Time [10xps]

# d

eso

rbe

d a

tom

s

Figure 4

At T=2500K (fig. 4):

Desorption of H as single atom

NO 𝐻2 desorption for 𝑡𝑠𝑖𝑚 ≈ 5𝑛𝑠 ≫ 𝜏𝑑𝑒𝑠

MD results contradict experimental

observations!

10

To determine why no H molecular desorption at T=2500K:

Calculation of potential energy 𝐸𝑝 of 2 H atoms on frozen W

surface moving toward each other along the same axis in the

plan of W surface layer (z=0) to force H recombination (fig.

5+6)

Large and sharp H recombination barrier (~ 7eV)

when H-H distance is about 1.6Å (red curve on fig 6)

Hydrogen molecular desorption from W surface 2/3

Figure 5

When all three-body interactions (TBI) involving H in

Tersoff potential turned off (TBI amplitude 𝛾 = 0): no more large H recombination barrier (brown curve

on fig. 6)

In [Juslin2005], amplitude of H-W-H interactions

𝛾𝐻−𝑊−𝐻 = 12.33 much larger than other TBI involving 2H (𝛾 < 0.1)

γ=0

𝑈𝑖𝑛𝑡 = 𝑓𝑐 𝑟𝑖𝑗 𝑓𝑅 𝑟𝑖𝑗 +1

1 + 𝑓𝑐 𝑟𝑖𝑘 𝛾𝑖𝑗𝑘𝑔 𝜃𝑖𝑗𝑘 𝑒𝜆3 𝑟𝑖𝑗−𝑟𝑖𝑘

𝑘≠𝑖,𝑗

𝑓𝐴 𝑟𝑖𝑗𝑖≠𝑗𝑖

Magnitude of TBI Tersoff potential

Sharp recombination barrier ↘ when 𝛾𝐻−𝑊−𝐻 ↘ (fig.6)

activation energy 𝑬𝒓 for H recombination into 𝑯𝟐 on W surface may strongly depends on 𝜸𝑯−𝑾−𝑯

Figure 6

11

activation energy 𝐸𝑟 for H recombination into 𝐻2 may strongly depend on 𝛾𝐻−𝑊−𝐻 => validation with MD simulations at 2500K (fig. 7+8):

𝐻2 desorption rate increases when 𝛾𝐻−𝑊−𝐻 ↘

when γHWH > 1, desorption rate very low due to high value of 𝐸𝑟 > 2𝑒𝑉

when γHWH = 0, 𝐻2 sticked to W surface, which may contradict 𝐻2 dissociation on W surface experimentally observed [Hickmott1960]

0 < 𝛾𝐻−𝑊−𝐻 < 1 to qualitatively reproduce H molecular desorption from W

MD simulations for 𝛾𝐻−𝑊−𝐻= 0.55 and different temperatures: Arrhenius plot(fig. 9) gives 𝐸des ≈ 𝐸𝑟 ≈ 1.5𝑒𝑉 in agreement with exp. values 𝐸des ≈ 1.6𝑒𝑉[Tamm1971]

Conclusions:

W-H potential in [Juslin2005] dot not qualitatively describe H recombination into 𝐻2 because TBI parameters

𝜸𝑯−𝑾−𝑯 ~𝟎. 𝟓 needed when H molecular recombination expected in MD

Hydrogen molecular desorption from W surface 3/3

Figure 9

𝛄𝐇𝐖𝐇 = 𝟏. 𝟑𝟓 𝛄𝐇𝐖𝐇 = 𝟎. 𝟓𝟓

Figure 7 Figure 8

Time [ps]

# d

eso

rbe

d a

tom

s

Time [ps]

# d

eso

rbe

d a

tom

s

12

Investigations on effects of high hydrogen surface concentration on hydrogen

recombination process suggested by experimental data (fig. (b,c) [Alnot1989])

MD simulations performed for H coverage 𝜃~0.1 on tungsten and surfaces at T=1500K (H atoms do not diffuse from W surface to W bulk)

After ~10ps, stable elongated hydrogen clusters on W surfaces (fig. 10)

Due to H-H distance >1.3Å in clusters, weak H-H interactions in clusters ( 3)

𝐸𝑏𝑘𝐻 < 0.1𝑒𝑉 for small clusters (𝑘 ≤ 3)

Previously, 𝐸𝑎𝑑𝑠 ≈ 2.4𝑒𝑉 (slide 6) so increase of binding energy of H to W surface

in large clusters: ΔE𝑏 =𝐸𝑏𝑘𝐻 − 𝐸𝑎𝑑𝑠≈ 0.7𝑒𝑉. ΔE𝑏 weakly varies with cluster size

Hydrogen clustering on tungsten surface 1/4

t=1ns t=10ps t=0ps

Figure 10

13

ΔE𝑏 due to sub-surface trapping sites (fig. 11), which can be reached by H atoms surrounded by other H

Sub-surface trapping sites induce stronger binding of H atoms to W surface due to

the presence of rows of W atoms above H atoms (fig. 11)

T=1500K ⇒ 𝜈𝑑𝑒𝑠 ≈ 107𝑠−1: Effects of H clustering on

H desorption cannot be observed in MD simulations

H clustering may affect hydrogen desorption by:

increasing the residency time of H in the vicinity of other H atoms

reducing qqty of isolated H which can recombine in small clusters(𝑘 ≤ 3)

affecting recombination path for two adjacent H atoms in clusters

Formation and dissolution of k-atoms clusters at concentration 𝑐𝑘 can be modeled as trapping & detrapping processes defined by:

the trapping rate 𝜈𝑡𝑟 𝑘 = 𝜈𝑡𝑟,0𝑓 𝑘 𝑒−𝐸𝑡𝑟(𝑘)

𝑇 , the detrapping rate 𝜈𝑑𝑡 𝑘 = 𝜈𝑑𝑡,0𝑓 𝑘 𝑒−𝐸𝑑𝑡 𝑘

𝑇

the desorption rate 𝜈𝑑𝑒𝑠 𝑘 = 𝜈𝑑𝑒𝑠,0𝑓 𝑘 𝑒−𝐸𝑑𝑒𝑠(𝑘)

𝑇 where 𝑓 𝑘 ~𝑘 (elongated cluster)

Since Δ𝐸𝑏 weakly varies with the size of large clusters:

𝐸𝑑𝑒𝑠 𝑘 ≈ 𝐸𝑑𝑒𝑠 + Δ𝐸𝑑𝑒𝑠 where 𝐸𝑑𝑒𝑠=activation energy for recomb. of two isolated H

𝐸𝑑𝑡 𝑘 ≈ 𝐸𝐷 + Δ𝐸𝑑𝑡 where Δ𝐸𝑑𝑡 = binding energy of hydrogen atom to cluster

By definition, Δ𝐸𝑑𝑒𝑠=0 for small clusters and for large clusters: Δ𝐸𝑑𝑒𝑠 > 0 or Δ𝐸𝑑𝑒𝑠 < 0

Hydrogen clustering on tungsten surface 2/4

Figure 11

14

NEB: Δ𝐸𝑑𝑡 ≲ Δ𝐸𝑏 = 0.7𝑒𝑉 for large clusters and Δ𝐸𝑑𝑡 < 0.1𝑒𝑉 for small clusters

Exp. values of 𝐸𝑑𝑒𝑠 :𝐸𝑑𝑒𝑠 ≈ 1.6𝑒𝑉 [Tamm1971] ⇒ 𝜈𝑑𝑒𝑠 ≪ 𝜈𝑑𝑡 (fast detrapping)

When :

total H surface concentration 𝑐𝑡𝑜𝑡 small enough to avoid cluster percolation: 𝐿𝑐 𝑘 𝑐𝑡𝑜𝑡 ≪ 1 where 𝐿𝑐(𝑘) = typical length of k-atoms clusters

fast diffusion compared to cluster dissolution (𝑐𝑡𝑜𝑡𝐷𝐻 ≫ 𝜈𝑑𝑡)

No significant activation energy for trapping of H in clusters (𝐸𝑡𝑟 < 𝐸𝑑𝑡)

Then cluster formation limited by diffusion of H atoms (𝐸𝑡𝑟(𝑘) ≈ 𝐸𝐷)

H clusters not diffusing on surface

Within previous assumptions:

equilibrium of cluster surface concentrations 𝒄𝒌 is determined by the balance between formation and dissolution of clusters

coexistence of large and small clusters is only possible in a very narrow range of

temperature and hydrogen concentration

Surface coverage regime determined by the nucleation process of small clusters:

if fast nucleation 𝑃𝑐𝑙𝑢𝑠𝑡𝑒𝑟 =𝜈𝑡𝑟 2,3 𝜃

𝜈𝑑𝑡 2,3> 1 , large clusters dominate (large cluster regime LCR)

if slow nucleation (𝑃𝑐𝑙𝑢𝑠𝑡𝑒𝑟 < 1), small clusters dominate (small cluster regime SCR)

Δ𝐸𝑑𝑡 < 0.1𝑒𝑉 for small clusters, 𝑃𝑐𝑙𝑢𝑠𝑡𝑒𝑟 ≈ 𝐶0𝜃 with 𝐶0~𝑂 1 (LCR when 𝜃 > 0.1)

Hydrogen clustering on tungsten surface 3/4

15

Effects of H clustering on H desorption estimated with ratio R:

𝑅 = 𝜈𝑡𝑟 𝑘−1 𝜃𝑘−1 𝑐1𝜈𝑑𝑒𝑠 𝑘 𝜃𝑘𝜈𝑑𝑡 𝑘 𝜃𝑘

desorption from k−atom cluster

/𝜈𝑡𝑟 2 𝜃1

2𝜈𝑑𝑒𝑠 2 𝜃2

𝜈𝑑𝑡 2 𝜃2

desorption from 2−atoms clusters

⇒ 𝑅 ≈ 𝐶𝑅𝑘𝜃𝑘−1

𝜃1 𝑒−

Δ𝐸𝑑𝑒𝑠−Δ𝐸𝑑𝑡𝑇 , 𝐶𝑅~𝑂(1) (2)

Time evolution of 𝜃𝑡𝑜𝑡 is then described by (3) where Γ𝑑𝑒𝑠 is the desorption flux

𝑑𝜃𝑡𝑜𝑡𝑑𝑡= Γ𝑑𝑒𝑠 ≈ 2𝜈𝑑𝑒𝑠,0𝑒

−𝐸𝑑𝑒𝑠𝑇 𝜃12 1 + 𝐶𝑅𝑘𝑚𝑎𝑥

𝜃𝑘𝑚𝑎𝑥𝜃1𝑒−Δ𝐸𝑑𝑒𝑠−Δ𝐸𝑑𝑡𝑇

𝑅

, 𝐶𝑅~𝑂(1) (3)

In LCR (𝑃𝑐𝑙𝑢𝑠𝑡𝑒𝑟 > 1), 𝜃𝑡𝑜𝑡 ≈ 𝑘𝑚𝑎𝑥𝜃𝑘𝑚𝑎𝑥 with 𝜃𝑘𝑚𝑎𝑥 ≫ 𝜃𝑘 and 𝜃𝑘𝑚𝑎𝑥 ~𝜃1𝑚 with 𝑚~𝑘𝑚𝑎𝑥:

if 𝑅 ≫ 1, cluster-controlled desorption regime: H desorption dominated by recombination in large clusters and 𝜞𝒅𝒆𝒔 ∝ 𝜽𝒕𝒐𝒕. Effective desorption energy 𝑬𝒅𝒆𝒔 = 𝑬𝒅𝒆𝒔 + 𝚫𝑬𝒅𝒆𝒔 − 𝚫𝑬𝒅𝒕 and effective pre-exp. factor 𝝂𝒅𝒆𝒔,𝟎~𝝂𝒅𝒆𝒔,𝟎𝜽𝟏/𝜽𝒕𝒐𝒕

If 𝑅 ≪ 1, hydrogen desorption is dominated by recombination in small clusters and in SCR: 𝜞𝒅𝒆𝒔∝ 𝜽𝒕𝒐𝒕

𝟐

Experiments show 𝐸𝑑𝑒𝑠 ↘ from 1.6𝑒𝑉 𝑡𝑜 1𝑒𝑉 and 𝜈𝑑𝑒𝑠,0 ↘ by 8 orders when

𝜃𝑡𝑜𝑡 > 0.5 [Alnot1989], which may be described with cluster model:

transition from SCR to LCR is sudden, at 𝜃 > 0.1 and in LCR 𝜃𝑘𝑚𝑎𝑥𝜃1≫ 1 ⇒ 𝑅 >> 1

If in LCR : Δ𝐸𝑑𝑒𝑠 − Δ𝐸𝑑𝑡 ≈ −0.6𝑒𝑉 ⇒ Δ𝐸𝑑𝑒𝑠 ≈ 0.1eV (weak effects of clustering on desorption)

If in LCR : 𝜈𝑑𝑒𝑠~𝜈𝑑𝑒𝑠,0𝜃1

𝜃𝑡𝑜𝑡≪ 𝜈𝑑𝑒𝑠,0 ⇒ qualitative description of 𝜈𝑑𝑒𝑠,0 drop when 𝜃𝑡𝑜𝑡 > 0.5

Hydrogen clustering on tungsten surface 4/4

𝜃𝑘 =𝑐𝑘

𝑐𝑠𝑎𝑡𝑢𝑟𝑎𝑡𝑖𝑜𝑛 = surface coverage of k-atoms clusters

16

MD simulations performed with W-H Tersoff interatomic potential from [Juslin2005]

H adsorption and diffusion on W surface:

Many H ads. sites on W surfaces and main features of bridge sites and H migration

between ads. sites are in qualitative agreement with experimental observations.

Many adsorption sites may lead to complex H diffusion on W surface. But

quantitative analysis strongly depends on interatomic potential.

Hydrogen molecular desorption from W surface

H molecular desorption not well described by W-H Tersoff interatomic potential

Three-body interactions parameters of this potential should be adjusted to

qualitatively reproduce main features of H recombination into 𝐻2.

Hydrogen clustering on tungsten surface

When H surface coverage is high, H clustering is observed on W surface

Kinetic model to qualitatively describe effects of clustering on molecular desorption:

large clusters regime where surface coverage is dominated by large H clusters. In

this regime, sudden variations of desorption parameters when H surface coverage

increases are qualitatively described by the model

kinetic of H desorption from W surface may be not second-order.

Quantitative descriptions of adsorption, diffusion and clustering of H on W surface

however strongly depend on W-H interatomic potential, and better assessment of

W-H potential for W-H interactions on W surface is thus required, e.g. with DFT.

Summary