CHINESE JOURNAL OF PHYSICS
VOL. 24, NO. 3
AUTUMN 1986
Deuterium Recombination on Surfaces of Stainless Steel and Gold
Jin-Gor Chang ( @ g %)
Department of Applied Physics, Chung Cheng Institute of Technology,
Ta-Shi, Taiwan 33500
(Received 14 March 1986)
The recombination and reemission of deuterium implanted
into a stainless steel surface has been studied at temperatures from
300 to 600 °K . The recombination coefficient is found to increase by more than two orders of magnitude as the natural surface
oxide layer is removed. By constrast for gold the recombination
coefficient is independent of surface treatment. It is pointed out
that the so-called recombination coefficient must involve surface
diffusion, true recombination and desorption. Moreover, this
paper suggestes that the recombination step may not be the rate
limiting process at all.
I. INTRODUCTION
Recombination of hydrogen on a surface to form molecules and its re-emission into
free space is an important process in the recycling of fuel from the walls of a magnetically
confined thermonuclear reactor. The rate of the combined recombination and re-emission
process $r (molecules cm-* s-’ ) is generally taken’ to be proportional to the square of the
volume concentration c (atoms cmV3 ) of H atoms at the surface and written in the form
$I* = 2akr c2.
Here kr is a constant of proportionality termed the recombination coefficient and the
factor 2 allows for each emerging molecule containing two atoms. The roughness factor
(J is included to represent the ratio of the true surface area to nominal aera; for an atomically flat surface u would be unity. Many experimental studies2y3 have the hydrogen
introduced into the near surface region by ion-implantation, the hydrogen then diffusing
back to the surface. Alternatively4 the hydrogen is introduced by permeation under the
influence of a pressure gradient across a foil. In general the re-emission flux #r is measured
by the rise of gas pressure monitored in the surrounding chamber. Near surface volume
concentration c can be measured directly by a nuclear reaction technique2r4 or inferred
145
._
4L.z
146
DEUTERIUM RECOMBINATION ON SURFACES OF STAINLESS STEEL AND GOLD
from some assumed mode13T4 of the process whereby hydrogen is introduced. There has
been no attempt to measure surface roughness factor u so the monitoring of flux $, and
surface concentration c leads to a measure of 2ukr. The majority of published results are
measurements on a stainless steel surface. While of little fundamental significance steel
is the constructional material of choice for thermonuclear reactor vessels and therefore
of practical significance.
Wilson’ points out that these published values of 2ak, range over four orders of
magnitude from a value of 1O-29 cm4 se& to 4 X 10m2 ’ cm4 se& for room temperature
targets. Direct measurements of 2ukr in thermonuclear plasma devices617 are at about
1o-27 cm4 se? for room temperature. it is generally acknowledged that this range of
values relates to differing surface conditions. The lowest values2Y3 l4 are for steel in an
“as-received” condition where oxide layers are certainly present. The highest values’ T9 y1 ’
are for surfaces that have been baked and sputter cleaned so that oxide layers are presumably absent. The intermediate values observed in plasma devices697 are probably appropriate to a surface that has been subject to some cleaning from plasma discharges. The
actual value of 2uk, is quite important to the operation of plasma devices such as TFTR
when titanium is used because models 1 ’ show that for the lowest values of 2ukr much of
the available tritium inventory will become locked in the device walls after some sixty days
of operation.
The present work is a further study of this recombination process on steel with various
surface pre-treatments designed to reduce oxide coverage. The aim was to confirm that
removal of the oxide is intimately related to the observation of high recombination rates.
For comparison we have also performed a limited series of measurements on gold for which
oxide layers should be absent.
II. EXPERIMENTAL APPROACH
The experiments were performed on stainless steel and gold using 10 kev D; beams
to introduce hydrogen into the surface by implantation. Deuterium was used to assist with
discrimination of signals over backgrounds of residual H, . D; was assumed to dissociate
at impact on the surface so that each 10 kev D; ion behaved like two 5 kev D+ ions. This
assumption has been commonly made by others’2,1 3y1 4 and was confirmed to be valid
in a previous experiment”. The general procedure was to measure the re-emission flux
@r by the pressure rise at mass 4 (D, ) in the vacuum chamber surrounding the target. The
surface concentration was determined indirectly from a model for the implantation process
introduced previously by Thomas et al.* Direct measurements of the implanted D depth
distribution performed previously by a nuclear reaction technique 2 show that the concentration c (atoms cme3) of deuterium is constant to some depth R approximately equal
to projectile range. Thus R. c is equal to the area1 concentration of deuterium in the near
surface region. The change of this area1 concentration with time is governed by the
equation.
--_-_
147
JIN-GOR CHANG
WC) =
R
dt
dc = a$+L2uk,c2
dt
+DZ .
(2)
Here ad is a rate of increase due to implantation with $ being the incident flux of deuterium
(D’ cm-* s-l ) and CY the fraction retained (or unity minus the fraction kinematically reflected). The second term of equation (2) is simply the flux of re-emission defined by Eq. 1.
The third term represents diffusion into the bulk with D being diffusion coefficient, and
s being concentration gradient into the bulk. Direct measurement of concentration
gradient for D’ implanted into stainless steel2 suggests that the diffusion term is in practice
smaller than the other factors of Eq. 2 so that it may be neglected. Solving Eq. 2 for the
case where concentration c is zero at time t equal to zero one arrives 2 at a flux #r of recombined and re-emitted atoms given by
$r =
20krc2
= 2akrc; [
exp (t/r) - 1
exp (t/T) + 1
I’
(3)
where
and
T = R/2 (ar$20kJw
(5)
Here cm is the maximum surface concentration obtained ast t + 00. For a situation where
the concentration has been allowed to build up to its maximum value cm and then t = 0
the projectile beam is turned off so 4 = 0 the solution to Eq. (2) gives2 a re-emission flux
declining with time t of the form
#r = 2ukrc* = 2ukrc; [ 1 + t/27] -*
(6)
where 7 is again defined by Eq. 5. Re-emission C#I* gives rise to a pressure rise of the
appropriate species in the vessel surrounding the target so that partial pressure p(t) of
deuterium due to re-emission is related to re-emission rate @r(t) by
p(t) =
qt)% .
(7)
Where A is the area of the target bombarded and S is the speed at which the chamber is
pumped. By monitoring re-emission (by means of ifrssure rise) as a fraction of time after
the beam is turned on, or after it is turned off, and / iitting Eq. 3 or Eq. 6 (as appropriate)
2
to the data we can obtain r and hence 2ukr. This approach was used previously and shown
to give the same value of 2akl as was obtained using Eq. 1 with a direct measure of c (by
a nuclear reaction technique) and @Jo.
, .._
-.
,
148
.
DEUTERIUM RECOMBINATION ON SURFACES OF STAINLESS STEEL AND GOLD
A complete description of the deuterium concentration would require inclusion of a
trapping term in Eq. 2. This has been omitted on the grounds that the equation is designed
only to describe mobile deuterium. When a beam is first directed at a target there may be
creation of traps by radiation damage so that the second term of Eq. 2 representing the
increase of mobile deuterium by implantation may not be correct. If implantation is
continued to a saturation condition where re-emission becomes invariant with time then
presumably a saturation density of traps and of trapped deuterium concentration will have
been arrived at. When the beam is turned off, and re-emission is described by Eq. 6 then
one might presume trap occupancy would remain invariant with time. For this reason the
data presented here is based on the decay of re-emission after bombardment as described
by Eq. 6 and we ignore the question of permanently trapped deuterium. Tests show that
a target that has been subject to some preliminary bombardment exhibits increases and
decreases of re-emission consistent with, respectively, equations 3 and 6 with the same
time constant in both cases. Moreover, previous work2 in a similar experiment shows that
the value of 2ak1 derived via the time constant T is the same as a direct measure via equation
1. Thus we argue that the trapped or immobile deuterium can be properly neglected in the
present experiment.
In studying re-emission using pressure rise of mass 4 (D, ) components there are two
further potential problems to bear in mind. Firstly the signal during ion bombardment
will include a component representing kinematically reflected D that has recombined on
the chamber walls after reflection, This can be identified as the initial signal on commencement of bombardment. In the present study we have used only the decay of signal after
bombardment is commenced so that reflection is not present. A second factor is that some
of the re-emitted deuterium shows up as mass 3 (HD) molecules. These may be due to
recombination of implanted D with residual H on the target surface or due to isotopic
exchange when D2 impacts on the chamber wall where H 2
time constants for both mass 3 (HD) and mass 4
(D,
In reality the problem of implantation, diffusion,
recombintion
pee formulations provide an operational definition of
th_,,
recombination rate coefficient consistent with observations and comparable with other
definitions of the same quantity. The principal purpose of the present work is to investigate
how 2ukr defined in this manner varies with bombardment of the surface and with surface
composition.
JIN-CQR CHANG
149
III. EXPERIMENTAL PROCEDURE FOR STUDIES OF STAINLESS STEEL
The experimental procedures are based on the previous work.’ 5 The ion beam is
obtained from an r-f source, accelerated to 10 kev, mass selected to provide D;, collimated
to an area of 0.16 cm* and directed onto a target. Typical projectile fluxes were in the
range 1 to 5 X 10’ 4 D’ cm-* s-’ . The target was contained in a uhv (10-l O torr) chamber
pumped at a speed of 6 liters/set. Pressure of deuterium in the chamber was monitored
with a quadrupole residual gas analyzer. In general, we record only signals at mass 4 which
we take to represent D, formed by recombination and re-emission on the surface. Target
materials were industrial type 301 stainless steel shim stock of 0.005 cm thickness and high
purity, polycrystalline gold of 0.0025 cm thickness. Preliminary target preparation
consisted only of ultrasonic cleaning with solvents to remove organic materials and
particulate contamination. Target temperatures could be valied from 300” K to 600°K
with a resistive heater. Projectile beam flux to the target was measured as a current. Dtails
of the equipment are essentially the same as the previous experiments on gold’ 5.
The general experimental procedure was to establish the desired target temperature,
direct the projectile beam onto the target and follow rise of the mass 4 re-emission signal
until it became constant, then interrupt the projectile beam and observe the pressure signal
as it decayed to background levels. The decay signal was shown to be consistent with the
form of Eq. 6 and a value of r determined. We take the distance R, representing the
assumed depth of the implant, to be equal to the projectile range which from the work of
Andersen and Zeigler’ 6 is 360 A. The factor is 1 - RN where RN is the particle reflection
coefficient which we take as 0.12 from the review of Tabata et al.’ 7 With these factors we
use Eq. 5 to derive a value of 2okr. In general terms the raw data is quite similar to that
shown previously2 so there is no need to reproduce it here.
A general problem with this type of experiment is initial drifts of partial pressure
signals due presumably to deuterium adsorption and D-H interchange on the chamber
walls. To avoid these disturbances each experimental run was proceeded by one or more
test runs on a secondary target sample; these tests were continued until the data was reproducible.
The initial observations on a virgin steel target gave recombination coefficients
generally similar to the data of Thomas, Young, Braun and co-workers 2 73 y4. As cumulative
dose to the target increased the time constant for decay after cessation of bombardment
decreased. This by Eq. 5 is interpreted as an increase of 2ak,. After a cumulative dose
of about 5 X 1 O1 a D’ ions cm* the decay time r and the recombination rate 2okr stabilized
at a value more than two orders of magnitude higher than the initial observations. It was
anticipated that this dose had caused substantial erosion of the natural surface oxide layer.
Assuming that erosion of stainless steel can be approximated by the rate for D’ erosion of
Ni and taking that value from the tabulations of LMatsunami et al.,’ 8 the dose of 5 X 1 0 ’ 8
D+cm-* will have eroded approximately IOnm of the surface which is approximately 8 the
thickness of the natural oxide layer on steel. We also tested the effect of bombarding a
virgin surface with 5 kev Ar’ to a dose of 4 X 10 ’ 6 Ar’ cm-* which according to sputtering
150
DEUTERIUM RECOMBINATION ON SURFACES OF STAINLESS STEEL AND GOLD
data’ * should erode the same thickness as 5 X 10’ a cme2 of D ’. The recombination
coefficient 2akr from this spot was identical to that for a surface bombarded with 5 X 10’ 8
D’ cm-‘.
In order to determine what change had occurred to the sample it was removed from the
apparatus and placed in a separate system where the Auger spectrum of the surface could
be recorded. Since the sample transfer was through air it is inevitable that some oxygen
(and perhaps other contaminants) will absorb on the surface. Nevertheless the Auger signals
showed substantially less oxygen on the bombarded regions than on the virgen surface
(38% of atomic composition compared with 46%). We then performed a mild sputter
cleaning of the surface with a 5 kev Ar’ beam with a dose that is calculated to remove
approximately a monolayer of material and therefore would remove the contaminants
picked up during air transfer. After this treatment the areas bombarded during the experiments showed no oxygen at all while the virgin surface still showed 45% of the atomic
composition as being oxygen. After extended sputter erosion with 5 kev Ar’ the Auger
spectra from the bombarded and unbombarded regions were identical with no significant
oxygen present. We conclude from this series of tests that the high recombination
coefficients associated with the extended D’ bombardment or with surfaces sputter cleaned
with Ar’ are for surfaces where the oxide layer has been removed. Due to the close proximity of Cr and Fe Auger lines it was not possible to determine what changes had occurred
to the Cr concentrations. However, since it is generally agreed that the oxide layer on stainless steel is a chromium oxide layer it is a reasonable assumption that the sputtering action
of the projectiles had removed both the oxygen and the enhanced chromium density expected on the surface.
For all subsequent studies on steel we prebombarded the sample with 5 kev D’ to a
dose of 5 x 10’ 8 D’ cm-’ to erode the natural surface oxide layer. The beam was then
turned off for 30 minutes or more to allow mobile deuterium to diffuse out of the surface
as indicated by decay of the mass 4 signal to its background level. Subsequently the experimental bombardment was commenced, the rise, equilibrium and fall of the re-emission
signal recorded and 2ukr derived in the manner described previously. The time delay
between pre-bombardment and experiment did not effect the data; presumably the oxide
formed by oxygen adsorption from the residual gas was insignificant. Cycling of target
temperature to 600°K between pre-bombardment and the experimental measurement was
employed to drive out deuterium trapped during pre-bombardment ; this also did not effect
the measured 2ukr. Various beam fluxes were used to confirm the relationship of 2ukr to
@J given in Eq. 5. Various different samples from the same source were used and gave
identical results.
The data for steel are given in Fig. 1 in comparison with data from various other
authors. We show results for an oxide covered surface and results for two different samples
where the oxide had been removed by preliminary bombardment. Accuracy limitations due
to random errors was assessed by the reproducibility of the data. We regard random error
as less than * 7%. Systematic errors are due to limitations of projectile beam density
measurements and the spread of values in the tabulations’ 6 of range R and reflection
i-L-....-,..
.
.
,_,,
JIN-GOR CHANG
FIG. 1
151
Recombination coefficient 2ok, for stainless steel shown as a function of inverse temperature.
Present data for sputter cleaned targets are shown as closed squares; for an as-received target data
is shown as a cross. A line is drawn through the data points on the assumption that the Arrhenius
equation (Eq. 8) is valid. All other data points represent measured values by other authors: (a)
Braun et al.,4 ; (b) Thomas et al.,’ ; (c) Wilson and Baskes’ ; (d) Kerst’ ; (e) Myers and Wampler’ ’ ;
(f) Young et a13.
coefficient RN ’ 7. The estimated systematic error is + 25%.
IV. EXPERIMENTAL PROCEDURES FOR THE STUDY OF GOLD
As a comparison with steel we also performed a series of similar measurements on gold
for which, of course, no oxide layer nor other chemically bonded contaminant is expected.
The experimental procedures were essentially the same as that for steel.
At room temperatures and slightly above we found that the initial signal on commencement of bombardment is invariant with dose and clearly not represented by Eq. 3 of our
model. As an example we show the raw data at room temperature in Fig. 2. In this
particular case we have added the re-emission determined by the mass 4 signal (D2) to the
re-emission from the smaller mass 3 (HD) to get total re-emission signal. The behavior
shown in Fig. 2 is similar to that for stainless steel at 77°K where implanted deuterium is
trapped and the signal S, is due only kinematic reflection. After a dose of about 6 X 10’ 7
152
DEUTERIUM RECOMBINATION ON SURFACES OF STAINLESS STEEL AND GOLD
D’ cme2 in Fig. 2 the traps are saturated and re-emission occurs. The signal S2 is appropriate to saturated re-emission. The re-emission signal at saturation was shown to be equal
in magnitude to the saturated re-emission from steel; for the latter case re-emission is’ ’
100%. Thus saturated re-emission from room temperature gold is also lOO%, the signal
S, is proportional to incident beam flux, and the ratio S, IS2 is equal to reflection
coefficient. Evaluating S, /S, from Fig. 2 we determine the reflection coefficient of 5 kev
D’ on Au to be 0.23 which is consistent with measurements by other techniques.’ ’
FLUENCE
FIG. 2
: 1017 D/c,,,*)
The deuterium re-emission signal as a function of dose for D’ impact on Au at 300°K.
The behavior of Fig. 2 is observed for temperatures up to 350°K with the transition
from reflection to re-emission occurring at lower doses as temperature increases. For
measurements at 410°K or above we observe re-emission to commence immediately the
beam is incident on the target so that trapping no longer occurring. We note the work of
Bugeat et al.,’ ’ on trapping of implanted D in single crystal gold which suggests that the
implanted D is at an interstitial site adjacent and bonded to a vacancy. At a temperature
above 350 °K the vacancy-interstitial D complex becomes mobile and diffuses.
Our
observations on the onset of re-emission are consistent with the work of Bugeat et al.’ ’
For temperatures where trapping is significant and the implanted D is not mobile it
is clearly inappropriate to describe re-emission behavior by equations 3 or 6. At temperatures where the D is mobile, however, we can again use our formulation to determine 2okr.
The primary objective was to determine whether the decay times in re-emission were dependent on the cumulative dose of D’ or on sputter cleaning with D’. No such effects were
found and the measured value of 2akl, shown in Fig. 3, were reproducibile under all
circumstances.
L-.
__
~_
ia_“.
JIN-GOR CHANG
..
153
.
;
I
2
l"?'h.PERAT"RE
FIG. 3
I
3
(OK)
Recombination coefficient 2ukr for gold shown as a function of inverse temperature. A line is
drawn through the data points on the assumption that the Arrhenius equation (Eq. 8) is valid.
V. DISCUSSION
Measurements of 2 okr for stainless steel are shown in Fig. 1 compared with a variety
of data from other authors. There is a set of data by Braun et a1.,4 by Thomas et al.,* and
by Young et a1.3 that are in essential agreement and span a wide temperature range. It is
our contention that all of these represent values appropriate to an oxide covered surface.
One data point taken from the present experiment, before significant target sputtering had
occurred, is shown and is consistent with this data set. There are also individual data points
by Wilson,’ Kerst,’ Myers,” and co-workers. For the work of Myers et al.” and Wilson
et a1.8 the experimental procedures involved substantial preliminary bombardment of the
sample surface so that oxide layers should have been substantially removed. These data are
also much higher than that of Braun, Thomas and Young2P3 F4 tending to confirm our
contention that removal of the oxide increases the value of 2 okr. The data of Wilson, Kerst
and Myers do not, however, agree with our measurements being two to three orders of
magnitude higher. It is noted that these previous determinations involved fitting of rather
sophisticated modelling codes to re-emission during bombardment. Use of the codes
requires assumption of other parameters, such as diffusion coefficient, that are taken from
other sources and are appropriate to unbombarded materials. If, as seems likely, radiation
-.’
DEUTERIUM RECOMBINATION ON SURFACES OF STAINLESS STEEL AND GOLD
154
damage occurs then these assumed values are likely to be wrong and the derived values of
2akr are also incorrect. It is not at all clear whether the difference between our work and
that of Wilson,’ Kerst,9 MyerslO and co-workers is due to the nature of the models used
to analyze data or whether it represents an actual difference in 2okr. There are also
measurements by Howe and Langley6 and by Dylla et al.,’ of a value for 2uk, appropriate
to the walls of a tokamak reactor; these data are in general agreement with the present
work. These tokamak reactor device walls had received substantial cumulative bombardment by hydrogen isotopes and therefore might be expected to exhibit similar behavior to
the samples used in the present experiment.
Our data for the gold target shown in Fig. 3 would appear to be the first for this
material and there are no other results with which comparison is possible.
The data shown in Fig. 1 and 3 are plotted on the assumption that they should fit an
Arrhenius equation of the form
2uk, = A e x p
(8)
Fitting this equation to our data we find that the activation energy E, is 0.25 ev for stainless steel and 0.29 ev for gold; pre-exponential factors A are respectively 4 X 1O-23 cm4 s-l
and 1.1 X 10ez3 cm4 s-l.
The recombination process studied here and in similar experiments is not a single
mechanism, as its definition implies, but rather must involve three distinct steps. D atoms
on the surface must first diffuse to arrive in close proximity with each other, then recombine, and finally desorb as a molecule. The measured coefficient kr is a rate for the
combined three steps process; it does not refer to the recombination step alone. Indeed the
rate limiting process may not be the recombination step at all. Doll and Freeman20 have
recently considered recombination of C and 0 on Pt and argue that the surface diffusion
step is the rate limiting process and the other two steps are instantaneous by comparison.
It is instructive to compare the present measured rate coefficient with the corresponding
coefficients in a gas phase reaction. One must first realized that equation 1 implies a two
body reation D + D + D2 ; this is in fact energetically impossible since the binding energy
of the molecule must be removed by the mediation of some third body. The recombination
process must, in its simplest form, be a three body reaction like D + D + A + D2 + A.
Formulating the rate for such a process in terms of deuterium concentration c and third
body concentration N, one uses the standard expression: dc
- =
dt
k3NAc2
(9)
d
c
where k3 in the three body rate coefficient and dt is the volume rate of recombination.
Now, our original expression in Eq. 1 is a surface rate. If we write surface concentration as
v = cs where 6 is the effective depth over which recombination occurs then the rate of
molecular re-emission from the surface is 20 dvldt where again the factor 2 is because each
molecule removes two atoms. Thus we can formulate the re-emitted flux as follows:
“.I
.~.
JIN-GOR CHANG
dC
= 206 - = 20 k3 N, cz
dt
15.5
(10)
Comparing Eq. 1 with Eq. 9
kr = 6 k3 N,
.
(11)
There is regrettably no published data on a three body recombination process in the gas
phase involving two D atoms and a constituent of steel. However, Hasted” states that
three body rates k3 will be in the range lo-** to 1O-32 cm6 P’ . If we take the depth 6 over
which recombination can occur to be 10v8 cm and assume the value of N, is the number
density of steel of the order 1 023 atom cme3 then our calculated value of kr from Eq. 10 is
of the order 10-l 3 to 10-l 7 cm4 s-’ . This is some ten or more orders of magnitude larger
than the measurements presented in Fig. 1. Clearly there is no comparison at all between
my rough estimate based on gas phase data with the measurements of surface recombination
in this work or indeed by any other author. We would conclude that the quantity kr
studied in our experiment is not a recombination rate at all and, following Doll and Freeman, speculate that our measurement may be representative of the surface diffusion that
must occur before recombination takes place.
VI. CONCLUSION
The measured recombination coefficients on stainless steel are dependent on the condition of the surface. If the natural oxide layer is remvoed then 2ukr increases by two
orders of magnitude to a value consistent with that obtained on the walls of an operating
thermonuclear plasma device. Using these new values and Baskes” model for the TFTR
tokamak device we would conclude that tritium retention in the TFTR walls will be
acceptably small provided the surface oxide layer is removed by some preliminary discharge
cleaning procedure.
We have pointed out that the so-called recombination coefficient measured in this and
in previous experiments is in fact a sum of a diffusion, a recombination and a desorption
mechanism. Comparison with gas phase recombination data suggests strongly that of these
three contributing mechanisms recombination is not rate limiting step at all. It is quite
possible that this and other experiments which purport to measure recombination are in fact
monitoring surface diffusion.
ACKNOWLEDGEMENTS
I would like to express my sincere appreciation to Dr. E. W. Thomas, whose cordial
instruction made this work possible. Financial support from the Ministry of National
h__
156
DEUTERIUM RECOMBINATION ON SURFACES OF STAINLESS STEEL AND GOLD
Defense, Republic of China, is much appreciated.
REFERENCES
1.
2.
3.
4.
5.
6.
7.
.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
._...
I Ali-khan, K.J. Dietz, F. G. Waelbroeck and P. Wienhold, Journal of Nuclear Materials,
76 & 77, 337 (1978).
E. W. Thomas, I. G. Petrov, and M. Braun, Journal of Applied Physics, 53, 6365
(1982).
R. Young, E. W. Thomas and B. Emmoth, Journal of Nuclear Materials, 111 & 112,
642 (1982).
M. Braun, B. Emmoth, F. Waelbroeck and P. Wienhold, Journal of Nuclear Materials
93 & 94, 861 (1980).
K. L. Wilson, Journal of Nuclear Materials, 103 & 104, 453 (1981).
H. Howe and R. A. Langley, J. Vat. Sci. Technol. Al, 1435 (1983).
H. F. Dylla, J. L. Cecchi, and R. J. Knize, Princeton Plasma Physics Laboratory Report
PPPL-2046, December (1983).
K. L. Wilson and M. I. Baskes, Journal of Nuclear Materials, 111 & 112, 622 (1982).
R. A. Kerst, Journal of Nuclear Materials 103 & 104, 439 (1981).
S. M. Myers and W. R. Wampler, Journal of Nuclear Materials, 111 & 112, 579 (1982).
M. I. Baskes, quoted from reference [ 31.
E. W. Thomas, Journal of Applied Physics 51, 1176 (1980).
C. M. Braganza, S. K. Erents, E. S. Hotston, and G. M. McCracken, Journal of Nuclear
Materials, 76 & 77, 298 (1978).
R. S. Blewer, R. Behrisch, B. M. U. Scherzer, and R. Schulz, Journal of Nuclear
Materials, 76 & 77, 305 (1978).
J. G. Chang, Proc. Natl. Sci. Count. ROC (A) 9, No. 1, 14 (1985).
H. H. Andersen and J. F. Ziegler, “Hydrogen Stopping Powers and Ranges in all Elements ”, New York, Pergamon Press, pp. 32 (1975).
T. Tabata, R. Ito, Y. Itikawa, N. Itoh, and K. Morita, “D ata on the Backscattering
Coefficients of Light Ions from Solids”, IPPJ-AM-18, Nagoya, Japan, Nagoya University (1981).
N. Matsunami, Y. Yamamura, Y. Itikawa, Y. Kazumata, S. Miyagawa, N. Itoh, K.
Morita and R. Shimizu, “E nergy Dependence of Sputtering Yields of Monatomic
Solids”, IPPJ-AM-14, Nagoya, Japen, Nagoya University (1980).
J. P. Bugeat and E. Ligeon, Proceedings of the 2nd International Congress on “Hydrogen in Metals”, Princeton, Pergamon Press, B-27 (1977).
J. D. Doll and D. L. Freeman, Surf. Sci. 134,769 (1983).
J. B. Hasted, Physics of Atomic Collisions, Butterworth Press, London, 12 (1964).
/