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A model of hydrogen impact induced chemical erosion of carbon based on elementary reaction steps
journalor ELSEVIER
Journal of Nuclear Materials 227 (1996) 186-194
nuclear materials
A model of hydrogen impact induced chemical erosion of carbon based on elementary reaction steps M. Wittmann a,U,j. Kiippers a,b,* a
Max-Planck-lnstitut fiir Plasmaphysik, Euratom Association, 85748 Garching, Germany b Experimentalphysik VI, Universitdt Bayreuth, 95440 Bayreuth, Germany
Received 29 May 1995; accepted 29 August 1995
Abstract
Based on the elementary reaction steps for chemical erosion of carbon by hydrogen a model is developed which allows to calculate the amount of carbon erosion at a hydrogenated carbon surface under the impact of hydrogen ions and neutrals. Hydrogen ion and neutral flux energy distributions prevailing at target plates in the ASDEX upgrade experiment are chosen in the present calculation. The range of hydrogen particles in the target plates is calculated using TRIDYN code. Based upon the TRIDYN results the extent of the erosion reaction as a function of depth is estimated. The results show that both, target temperature and impinging particle flux energy distribution, determine the hydrogen flux density dependent erosion yield and the location of the erosion below the surface.
1. Introduction
Carbon is a widely used wall material in experimental fusion devices, primarily because its low-Z warrants a small radiation cooling of the plasma if contamination of the plasma from the wall material occurs. The drawback of C lies in its ability to form volatile hydrocarbons with hydrogenic particles which are the dominant species in the plasma. Accordingly, in fusion experiments and laboratory experiments as well, hydrocarbons have been detected during plasma operation. This transformation of bulk C under particle impact into hydrocarbons is termed chemical erosion, as chemical processes, rather than physical processes alone, primarily govern the overall erosion mechanism. Chemical erosion of C targets by H has been studied under materials aspects extensively in the past [1-5,19,25,26]. Most often, hydrogenic ions were used as projectiles and various types of graphites served as targets. Erosion was monitored by weight loss or detec-
* Corresponding author.
tion of volatile erosion products, predominantly methane. Erosion yields of up to 10% and the temperature range of efficient erosion, 700 to 900 K for methane, have been observed, as well as the release of methyl radicals [19] and molecular H. The elementary chemical reaction steps which lead to erosion were, however, not addressed in these investigations. In recent studies on model C : H systems compatible with UHV and surface sensitive spectroscopies these elementary reaction steps in the H atom/carbon surface chemistry have been identified. These are: 1) Thermally activated molecular H 2 release through C - H bond breaking events followed by recombinative desorption [6]. 2) Thermally induced release of methyl radicals and methane from a hydrogenated carbon substrate [6,7], a reaction step which presents a major contribution to chemical erosion. 3) Hydrogenation of CH groups with unsaturated C atoms at a partially hydrogenated C : H surface by thermal H atoms [8,9]. 4) H abstraction from CH groups with saturated C by H atoms [10]. 5) H atom impact induced chemical erosion as a consequence of the above steps 2 and 3 [10]. The present paper deals with the consequences of
0022-3115/96/$12.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0022-3115(95)00150-6
M. Wittmann, J. Kiippers/ Journal of Nuclear Materials 227 (1996) 186-194 the reaction steps 1 to 5, in particular at wall flux densities met in experimental fusion devices. The activation energies and reaction cross sections for the H / C : H surface chemistry of hydrogenated carbon deduced in the above studies were used in the present work to develop a model for chemical erosion. The procedure used in this work is as follows. The neutral and ionic H particle energy distributions faced in typical discharges in ASDEX upgrade experiments [11] are used to calculate H concentration profiles in a C target based on the TRIDYN code [12]. The C : H target defined in this way is subjected to H flux densities as found in ASDEX upgrade, and in the resulting energy dependent particle ranges the above specified elementary reactions are allowed to proceed. This then gives range dependent erosion and molecular H 2 flux densities from which the overall erosion yield as a function of temperature is calculated. This paper is subdivided into six parts. Following this introduction, Section 2 summarizes the dominating reaction paths characterizing the chemical interaction of a C : H layer with atomic H. The details have been published previously; this summary is given at the convenience of the reader. Section 3 deals with the TRIDYN calculations performed to determine the depth variation of thermal H atom effective fluxes in a macroscopic hydrogenated carbon specimen exposed to H flux densities and energies as present in experimental fusion devices. Section 4 combines the contents of Section 2 and Section 3 in developing a model allowing us to estimate the amount of hydrocarbon evolution and subsequent C contamination of the plasma resulting from chemical erosion of carbonized surfaces, i.e. first wall materials. In Section 5 the results of these model calculations are discussed, while Section 6 presents our conclusions.
2. Chemical mechanisms
The H / C : H surface chemistry is governed by few chemical reactions involving sp 2 and sp 3 C centers, radical C centers (sp x in our nomenclature) and H atoms. The combination of these reactions accounts for most of the experimentally seen features at C : H surfaces irradiated with H atoms as in plasma assisted hard C film deposition, low pressure diamond synthesis and carbonized first-wall structures in fusion experiments. The experiments performed to investigate H / C : H surface interactions are described in detail elsewhere [13]. The reader is referred to this article and the references cited therein. Therefore, only the principal aspects of the experimental work will be mentioned here.
187
In this study, C : H layers of several nm thickness were grown by ion beam deposition of hydrocarbons of 160 eV energy on a suitable substrate. Film thickness could be monitored by Auger electron spectroscopy (AES). The film composition was determined by quantitative analysis of thermodesorption products using a quadrupole mass spectrometer. H / C ratios were in between 0.4 and 0.5; limited fine adjustment could be achieved by varying the exposure parameters ion energy and surface temperature, or changing the feed gas. Surface vibrations were measured by high resolution electron energy loss spectroscopy (HREELS). All experiments were carried out under UHV conditions. Spectroscopic investigations were made in situ. The C : H films prepared in this way exhibit the essential structural features of carbon irradiated by H particles, a C network partially terminated by H, and are considered as appropriate model systems for the study of the interaction of H and surfaces of hydrogenated C materials. The reactions occurring at the surfaces of these films when exposed to thermal H atoms were studied in situ. Thermal H (or deuterium) atoms were produced by effusion from a Ta tube heated to 1900 K. From the H pressure inside the tube, the effusion geometry and the dissociation equilibrium constants at the tube temperature the flux density at the C : H surface is estimated to ca. 1 × 1013 cm-2s -1, i.e. far below the fluxes in fusion applications. The H atom source is described in detail elsewhere [14]. 2.1. Hydrogenation H R E E L spectra of C: H layers prior to H exposure show a broad band in the C - H valence region, 2800 to 3350 c m - 1, composed of C - H vibrational losses with C in aromatic sp2-hybridization and in sp3-hybridization, and, to a very small extent, in sp-hybridization. The loss energies of the v (CH, arom., sp2), /"as (CH, sp3), vs (CH, sp3), and v (CH, sp) vibrations [8,15-17] correlate very well with the respective frequencies which characterize analogous b o n d s in h y d r o c a r b o n molecules. From the loss intensities it can be inferred that C : H film surfaces contain about equal amounts of sp 2 and sp 3 C atoms with a minor contribution of sp C, similar to the C : H films found at plasma exposed C surfaces. This observation stresses the conclusion that the essential structural features of hydrogenated C are present in the C - H network of ion-beam deposited C : H films. Exposure of a C ' H layer to H atoms at or near room temperature leads to a complete removal of v (CH, sp) related losses, a reduction of v (CH, arom. sp 2) related losses and to a gain in sp3-CH related loss intensity. If this experiment is conducted with deu-
M. Wittmann, J. Kiippers/Journal of Nuclear Materials 227 (1996) 186-194
188
terium atoms, an energy loss peak at 2129 cm -1 is observed, indicating that deuterium is bound to sp 3 hybridized C only [8]. This observation leads to the conclusion that hydrogen or deuterium atoms efficiently hydrogenate sp and sp 2 C centers, i.e. unsaturated CH groups, at the surface of the C : H layer. Due to the low energy of the H atoms this hydrogenation reaction is limited to the near surface region. Control experiments using 160 eV H~- ions result in hydrogenation of a C : H layer throughout the penetration range [8]. Quantitative analysis of the HREELS data based on the rate equation - d [ C H s p 2 ] / d t = [CH sp2]~H~
\
/
\
I
C.-C-H, / I
(lb)
with [CH sp 2] the concentration of hydrogen bound to sp 2 centers, q~ the flux density of H atoms and trH the reaction cross section for hydrogenation yields a value of ~rH = 4.5 × 10 -2o m 2 [10]. In the reaction (lb) a representative sp 2 two carbon center is shown. The open bonds at the C atoms may either connect this group to the C network or may end at H atoms. As every sp 2 C is bound to one or three (in a graphitic layer) more sp 2 C, reaction (lb) produces a sp 3 C and a neighboring radical center as an intermediate which we call an spX-center and mark by an asterisk in Eqs. (lb) and (2b). A spX-center can further be hydrogenated yielding an sp3-center according to the following equations: - d [ C H spX]/dt = [CH spX]~rn qb,
(2a)
\ n + C./
(2b)
I -~ H - C I
22. Hydrogen abstraction Exposure of a H saturated C : H film to a flux of deuterium at room temperature results in isotopic exchange of H against deuterium. This can be monitored in HREEL spectra, which reveal a buildup of loss intensity at energies characteristic of sp 3 C - D stretch vibrations accompanied by isotope shifts in the fingerprint region [8]. This isotopic exchange is the result of H abstraction followed by hydrogenation as formulated in Eqs. (3) and (4): L /* -C-H+D~-C +HOg S , (3) /
-C, \
I
+D ~-C-D. I
- d[CH s p 3 ] / d t = [CH sp3]trD q~,
(5)
(la)
for the elementary reaction C=C+H~ / \
The radical carbon species is marked by an asterisk and open bonds make either connections to the carbon network or are terminated by hydrogen. The analogous processes as Eqs. (3) and (4) are observed when subjecting a C: D-layer to a flux of thermal hydrogen atoms. No isotopic effect on the reaction rates can be observed within the experimental error [18]. Thus the rate limiting, i.e. slowest, reaction step, H abstraction (Eq. (3)), has a small activation energy. As the isotope exchange reaction rate is determined by reaction (3) the differential rate equation for Eq. (3) + Eq. (4) can be formulated as
(4)
with [CH sp 3] the concentration of H bound to sp 3 hybridized C, tro the reaction cross section for H abstraction and ¢ the deuterium flux density onto the sample [18]. Quantitative analysis of the H R E E L spectral peak intensities yields tr D = 0.05 × 10 -20 m E [18]. This small value is consistent with a gas phase reaction cross section, as would be expected for an Eley-Rideal mechanism in the abstraction reaction. As H (or deuterium) on a C : H surface and in the bulk of a C : H film as well can only exist in a covalently bound state, the reaction proceeds via a close encounter of a deuterium atom from the gas phase with a covalently bound H atom in the C : H layer and subsequent H - D bond formation with simultaneous C - H bond cleavage.
2.3. Chemical erosion If a C : H surface is exposed to H atoms at elevated temperatures in the range 400 to 700 K, a reduction of C : H layer thickness is observed in AES. This process, most efficient at ca. 600 K under laboratory conditions, is not due to thermal desorption effects or the action of H molecules, as has been demonstrated in control experiments. Obviously, H atoms of thermal energies initiate the formation of volatile hydrocarbon species and thus chemically erode the C : H layer. HREEL spectra show an accompanying shift of loss intensity from sp 3 C bonded to aromatic sp 2 C bonded H. In line with the direct observation of methyl radical release from graphite or C : H layers exposed to atomic H at elevated temperatures reported from several other groups [19,20] it is supposed that radical sp X C centers formed upon H impact by abstraction (Section 2.2) can deexcite via the split-off of a neighboring methyl group. This involves cleavage of a carbon-methyl or-bond, ca. 380 kJ/mol or 4 eV, and the formation of a carboncarbon ~r-bond, ca. 190 kJ/mol or 2 eV. Thus the erosion step is endothermic by about 190 kJ/mol, in accordance with the observation that it is restricted to the elevated temperature regime.
M. Wittmann, J. Kiippers/Journal of Nuclear Materials 227 (1996) 186-194
~'H H3C"
1017
, ~/ / ~ /sp3
oH//~+H"
~
+H"
~.1015 ,,
H'7 t"H
-H2
H+
•~ 101~
CD -H2
T
189
H'l
,
10
~"H
,
J
i
1 1 , 1 ,
i
100 primaryenergy[eV]
,
•
.
.
.
.
.
.
1,000
Fig. 2. Hydrogen neutrals and ions energy distribution and flux density at ASDEX upgrade target plates.
T, kx I ~ ; H 3
J Fig. 1. Scheme of reactions initiated by thermal energy and hydrogen impact at C:H films. Fat lines represent thermally activated reaction paths. The thermal decomposition of sp x centers t o s p 2 via methyl radical split-off is described by the following rate equation: - d [ f H s p X ] / d t = [CH s p X ] k x e x p [ - E x / k T ] . (6) The experimental observation of the temperature dependent sp x t o s p 2 conversion and the erosion rate maximum could be fitted using values of k x = 1013 S- 1 and E x = 155 k J / m o l (1.6 eV) [10]. Fig. 1, adapted from [10], schematically summarizes the reactions observed at H exposed C: H films as deduced from the results so far. The upper right shows the H abstraction/hydrogenation steps (Section 2.2) converting s p 3 carbon to sp x and vice versa. The lower right indicates the activated erosion step, conversion f r o m sp x t o sO 2 with the release of a methyl radical initially in a-position relative to sp x carbon (Section 2.3). The hydrogenation sequence (Section 2.1) is shown on the left half of the reaction scheme. It c o n v e r t s sp 2 C to sp 3 via sp x. The thermal decomposition of sp x C t o sp 2 via H atom release is included in the scheme, although it is not described here explicitly. 3. TRIDYN calculations
The most important differences regarding H / C : H interaction in laboratory experiments and fusion de-
vices are the extremely high H flux densities and specific distribution of primary energies achieved in the latter. Fig. 2 illustrates neutral and ion flux energy distributions typical for plasma discharges in A S D E X Upgrade at the target plates in the diverter. These distributions exhibit characteristics typical for fusion experiments: charge exchange neutrals with increasing fluxes towards low particle energies and ions with a flux peak at the sheath potential. In the present calculation the charge exchange neutrals energy distribution was approximated by a 1 / E dependence. The ion energy distribution was approximated by a Maxwellian distribution shifted by a sheath potential of 150 V. As can be deduced from earlier experiments, chemical reactions with H atoms or ions occur only if H is slowed down to thermal energies. This rises the question how to find the effective fluxes of thermalized H atoms varying with target depth given a specific total flux density and its energy distribution,
1/\ j f L j A
5
100eV
_
+ .= ~ ~ ~ 1 ~ ~ t t 0 0 0 0
5
eV
10 15 20 25 30 35 40 45 50 depth[nm]
Fig. 3. Calculated depth profiles of hydrogen in carbon. The curves represent distinct TRIDYN runs with hydrogen primary energies ranging from 100 to 1000 eV.
M. Wittmann, J. Kiippers /Journal of Nuclear Materials 227 (1996) 186-194
190 1019 "7
E 1078
~ 1017 -o 101o -1- 10~5 E
~ 1014 .~
013
~ 1012 0
I
I
I
I
5
10
15
20
25
30
35
40
45
50
depth [nm]
Fig. 4. Calculated effective thermal flux density of hydrogen in carbon assuming a hydrogen (H ° and H +) primary energy distribution as in Fig. 2, and a total flux density of 1019 cm-2s -1. See text for details.
tial equations with the concentrations of the respective species as variables. All parameters needed, such as reaction cross sections, activation energies, and rate coefficients, are taken from experimental data except the thermal H flux densities into the individual layers which are taken from the TRIDYN results described in Section 3 and displayed in Fig. 4. In order to study the flux density dependence, these flux densities were scaled to yield different total flux densities. In the present calculation total flux densities of 1017 to 1019 particles c m - 2s- 1 have been assumed. In addition to the differential Eqs. (1), (2), (5) and (6) two further equations were included in the numerical model, which describe chemical reaction pathways of lower significance in the H flux region addressed here. These are the thermally activated decomposition of sp x centers to sp 2 via split-off of a H atom shown in the lower left part of Fig. 1. The rate equation is - d [ C H spX]/dt = [CH s p X ] k _ H e x p [ - E H / k T ]
(7) This problem can be solved in principle using the TRIDYN code that allows to calculate depth profiles based upon the binary collision model. Details of this model are given in the literature [21]. We modified the code slightly to include the possibility of generating projectile particles with a given primary energy distribution. Fig. 3 shows several hydrogen depth profiles calculated for monoenergetic hydrogen particles impinging at normal incidence at a carbon target. The H atoms are regarded as stationary as soon as their kinetic energy is below 5 eV. Clearly, the penetration depth is strongly energy dependent. Given the approximate energy distributions of H ° (atomic hydrogen) and H + as seen near the C tiles in a fusion device (Fig. 2) we arrive at a depth profile as shown in Fig. 4. As the projectile particle trajectories are followed to an end energy of 5 eV, i.e. near thermal energy, the depth variation of the H concentration profile represents the effective net flux density of thermal H particles at the implantation range in the carbon target. These H atoms then can initiate the reactions as specified in Section 2 of the present paper. TRIDYN code does not account for any differences between neutral and ionic H atoms, as their masses are regarded as equal. The results shown represent specific TRIDYN runs at depth resolutions of I nm.
4. Chemical erosion calculations
The model calculations are performed in the following way: The C : H target is cut into 1 nm thick layers oriented parallel to the surface. The chemieal reaction scheme (Section 2) is converted into a set of differen-
and the thermal decomposition of sp 3 centers to sp x with the rate equation - d [ C H s p 3 ] / d / = [CH s p 3 ] k T e x p [ - E a / k T ].
(8)
Parameters for Eq. (8) are taken from Ref. [10] with k T = 1013 s -1 and E a = 234 kJ/mol. Parameters for Eq. (7) are taken to be the gas phase values reported in the literature [22]: k.H=1013 s -1 and E . H = 1 6 7 kJ/tool. Table 1 summarizes the complete set of elementary reactions incorporated into the model including all kinetic parameters and the expressions describing differential changes in the concentrations of the sp 3, sp 2 and sp x C species in these reactions. The complete set of differential equations is solved numerically using the Rosenbrock method [23]. Each layer is treated independently during the calculation. The calculations are performed for the temperature range from 500 to 1100 K in 10 K intervals. For each layer thermal equilibrium concentrations of the respective species, rates and probabilities of methyl radical formation are calculated. This simple model does not explicitly account for any effects which may be introduced by the geometrical constraints caused by the various C atom hybridization states. Furthermore, as only the individual concentrations of the respective C species are taken into account, depth information is achieved by applying this zero-dimensional approach to each layer individually. Fig. 5 shows the calculated concentrations of sp 2 (a), sp 3 (b) and sp x (c) C as a function of target depth and temperature at a total H flux density of 1019 cm-Zs -1. sp 2 and sp 3 concentrations span the range
M. ~ittmann, J. Kiippers/Journal of Nuclear Materials 227 (1996) 186-194
I
I
,~,
~,
I
f
~
~
"eb
<.
i
<.
-4,
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I "e,.r, b
c~
'T
x
x
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192
M. Wittmann, J. Kiippers/Journal of Nuclear Materials 227 (1996) 186-194
a) sp2 carbon i ! sp2 carbon
depth [nm]
30 40
00 8 0 0 900 1000 500 600
temperature[K]
b) • 1.0
sp3 carbon
• 0.8 • 0.6 •
0.4 spo carbon
• 0.2 • 0.0
depth [nm]
40
)0 500 600 700 ow ---
temperature [Iq
c) • 0.012
spXcarbon
• 0.008 .0.004
deptt, t, ,,,,J
~
spXcarbon
further grows at the expense of sp 3 and sp x C. At temperatures well beyond 1000 K sp 2 C has become the dominating species at all target depths. At all temperatures and depths the ratio of sp x and sp 3 C is determined by the ratio of the dehydrogenation and hydrogenation cross sections. The decrease of the sp 3 fraction with increasing temperature and depth is paralleled by an equivalent decrease of the sp x fraction. At temperatures above ca. 900 K the sp x fraction increases slightly as a result of the thermally activated reaction paths converting sp 3 C to sp x. Fig. 6 shows the resulting depth and temperature variation of the methyl radical production rate at total H ( H ° + H +) flux densities of 1017 to 1019 cm-2s -1. Each plot shows a H flux density dependent maximum at temperatures ranging from 870 K at a flux density of 1017 cm-2s -1 to 1050 K at 1019 cm-2s -1. The erosion maximum naturally is located in the near surface region as a result of the higher H fluxes (compare Fig. 4). This result is in agreement with experimental evidence; at a lower H flux density of ca. 1013 cm-2s -1 the maximum temperature is ca. 620 K [10]. A set of separate calculations further demonstrated the total flux density dependence of the erosion maximum tem-
0.000 0 500 t~oo,w
temperatureIK]
Fig. 5. Calculated equilibrium fractions of sp 2 (a), sp 3 (b) and sp x (c) carbon in a C:H layer exposed to atomic hydrogen as a function of depth and temperature.
from approximately zero to one, whereas the sp x concentration does not exceed a value of about 0.011, the ratio of the dehydrogenation and hydrogenation cross sections. At low temperatures, the presence of the various carbon species is completely governed by the hydrogen induced hydrogenation and dehydrogenation processes. The extent of thermally activated reactions is negligible. As the hydrogenation cross section exceeds the dehydrogenation cross section by a factor of ca. 102, the dominating species is sp 3 hybridized C. This situation gradually changes at increasing temperatures as thermally activated reactions converting sp x carbon to sp 2 C are beginning to contribute. The lower the effective thermal H flux density, the lower the temperature where thermally activated reactions compensate for the dominating hydrogenation reaction path. Near the surface, at an effective thermal H flux density of ca. 1018 cm-2s -1, equal fractions of sp 3 and sp 2 C occur at ca. 900 K, whereas 40 nm beyond the surface, at a flux density of 1014 cm-2s -1, this ratio is found at 700 K. With increasing temperature the sp 2 C fraction
o depth [nm]
1100 zu
25
50o
600
'w
temperature
[K]
Fig. 6. Calculated methyl production rates from a C:H layer subjected to fluxes of atomic hydrogen as a function of depth and temperature at different total hydrogen flux densities: (a) 1017 c m - 2 s -1, (b) 10 TMcm-2s -I, (c) 1019 c m - 2 s -1.
M. Wittmann, .7. Kiippers /Journal of Nuclear Materials 227 (1996) 186-194 perature predicted by the model. Absolute values cannot be given, as the concentration of methyl groups in a C : H layer is not known. Methyl groups in a-position relative to the thermal decay reaction center are a chemical erosion prerequisite. Assuming a hit rate of 0.01, a total chemical erosion rate of ca. 30 C monolayers per second at maximum erosion conditions and a hydrogen flux density of 1019 cm-2s -1 were calculated. This corresponds to an effective erosion yield of 0.01 C per H atom, a value which was determined in model experiments of H exposed C : H layers [10], whereas in other laboratory experiments erosion yields of 0.1 C per H atom have been found [24].
5. Discussion The approach to model chemical erosion of C by H as used in the present study is different from the more phenomenological descriptions used previously [1-5]. The justification for the model comes from the fact that the elementary chemical reaction steps of the H / C : H interaction are now identified and the model confirms experimental results at C : H films at H flux densities available in laboratory experiments. However, there are some points which have to be addressed concerning the applicability of the model at erosion of C targets by H flux densities present in experimental fusion devices. At first one has to consider whether the C : H films resemble the relevant characteristics of H irradiated C tiles. Irrespective of the particular type of graphite used for the tile the high energy fraction of the H flux will suffice to amorphisize the surface region of the graphite. Therefore, under equilibrium conditions, in the implantation range the C tile will exhibit a structure which is very similar, if not identical, to an amorphous C : H layer. For the present flux densities and energy distributions the thickness of this layer was calculated to be about 30 nm. The TRIDYN code used is capable to handle the given implantation problem beyond the precision needed here. Therefore, we have confidence, that the gross structural features of H exposed C tile surfaces are sufficiently close to several 10 nm thick C : H films. Often, in studies on chemical erosion [1-5] transport of eroding and erosion species was a concern. In the present work, transport of H is not treated beyond the TRIDYN range, and transport of the erosion species, methyl, is neglected altogether, as for the equilibrium erosion it has no effect. The hybridization state of the C atoms in a C : H network at a given hydrogen atom flux density is governed by the temperature. For the flux densities addressed here, sp 3 C dominates up to ca. 700 K, whereas sp 2 C is the prevailing species at high temperatures
193
above 1000 K, see Fig. 5. The sp x species is present in low concentrations at all temperatures. The explanation is as follows: The hydrogenation reaction converts sp 2 to sp 3 hybridized C. Every sp 2 hydrogenation step yields one sp 3 and one sp x hybridized C atom. Due to its large hydrogenation cross section sp x C is further hydrogenated. This accounts for the low steady state concentration of the sp X species. The hydrogenation rate depends on the sp / concentration and the H flux density only, i.e. is independent of temperature. The reaction pathways leading from sp 3 to sp 2 hybridized C (with the sp x species as an intermediate) are thermally activated as in the sp 3 thermal decomposition case (Eq. (8)) or involve one activated step as in the thermal decomposition of sp x centers. Thus at low temperatures, the hydrogenation process dominates until all sp 2 C is converted to sp 3 and the C : H layer exclusively contains sp 3 hybridized C plus a small fraction of the sp X species. At high temperatures, the reaction rates of the thermally activated reactions are high enough to overcome the hydrogenation rate and to interchange the population of sp 2 and sp 3 C. Thus in a high temperature equilibrium the sp 3 fraction is negligible and sp 2 dominates besides the small sp x C fraction. In an intermediate temperature range between 700 and 1000 K, there is a smooth transition from sp 3 to sp 2 dominance. The transition temperature depends on the H atom flux density in so far as higher temperatures are needed to compensate a high flux density. In the near surface region which is exposed to the highest thermal H flux this transition is observed at higher temperatures than towards the bulk, see Fig. 5. Three arguments account for the temperature and depth dependence of the calculated methyl formation rates. Methyl radicals are formed during the thermal decay of an unsaturated C atom, sp x. This is an activated reaction, its rate strongly increasing with temperature. As the methyl radical stems from a C network bound methyl group with, of course, a s p 3 hybridized C atom, the first prerequisite for methyl release is the presence of sp 3 C. It has been shown before that this condition is met primarily at low temperatures. So a temperature optimum must exist for this reaction step (see Fig. 6 for reference). The methyl formation rate is proportional to the sp x concentration (Eq. (6)). The amount of sp x C present in the C : H layer is to a first approximation proportional to the flux density of thermal H atoms. Therefore the methyl formation rate will decrease with depth (Fig. 6) as the thermal H flux density decreases. Furthermore, the calculated results have shown a flux density dependence of the temperature where maximal erosion occurs. This temperature varies from below 900 K to 1050 K at flux densities from 1017 to 1019 cm-2s -1. It originates from the fact that the temperature where the sp 3 concentration be-
194
M. Wittmann, J. Kiippers /Journal of Nuclear Materials 227 (1996) 186-194
gins to decrease depends on the H flux density. As stated, the absolute erosion yield is not available from the present calculation as the model implies that there are always potential eroding methyl groups adjacent to a reaction center. This is certainly not the case. It might well be that a hit factor of 0.01 as used above represents a reasonable value.
6. Conclusions Laboratory results of H / C : H layer interaction clearly have demonstrated the action of processes leading to the removal of hydrocarbon species from the C : H layer. These reactions are based upon the chemical interaction of thermal H atoms leading to hydrogenation, i.e. the formation of covalent H - C bonds, and several thermally activated processes involving the breaking of H - C and C - C covalent bonds, the latter representing the actual C erosion steps. Cross sections, frequency factors, and activation energies of elementary reaction steps of the H / C : H interaction have been used together with energy dependent H implantation ranges to calculate chemical erosion of C tiles exposed to fusion relevant target plate fluxes. The results reveal a temperature and flux dependent erosion zone in a few 10 nm thick region at the surface of the target plates. The trends observed can be easily understood in terms of the reaction schemes applied in this study.
References [1] P.C. Stangeby and G.M. McCracken, Nucl. Fusion 30 (1990) 1225. [2] E. Vietzke, K. Flaskamp and V. Philipps, J. Nucl. Mater. 128&129 (1984) 545. [3] A.A. Haasz, O. Auciello and P.C. Stangeby, J. Vac. Sci. Technoi. A 4 (1986) 1179. [4] V. Philipps, E. Vietzke, M. Erdweg and F. Waelbroeck, J. Nucl. Mater. 162-164 (1989) 520.
[5] J. Roth, J. Nucl. Mater. 145-147 (1987) 87. [6] J. Biener, A. Schenk, B. Winter, C. Lutterloh, U.A. Schubert and J. Kiippers, Appl. Phys. Lett. 61 (1992) 2414. [7] J. Biener, U.A. Schubert, A. Schenk, B. Winter, C. Lutterloh and J. Kiippers, Adv. Mater. 5 (1993) 639. [8] J. Biener, A. Schenk, B. Winter, C. Lutterloh, U.A. Schubert and J. Kiippers, J. Chem. Phys. 99 (1993) 3125. [9] J. Biener, A. Schenk, B. Winter, C. Lutterloh, U.A. Schubert and J. Kiippers, Surf. Sci. 307-309 (1994) 228. [10] A. Horn, A. Schenk, J. Biener, B. Winter, C. Lutterloh, M. Wittmann and J. Kiippers, Chem. Phys. Lett. 231 (1994) 193. [11] ASDEX Upgrade staff personal communication. [12] W. M611er and W. Eckstein, TRIDYN - Binary Collision Simulation of Atomic Collisions, Max-Planck-Institut fiir Plasmaphysik IPP 9/64 (1988). [13] A. Schenk, B. Winter, J. Biener, C. Lutterloh, U.A. Schubert and J. Kiippers, J. Appl. Phys. 77 (1995) 2462. [14] J. Biener, Doctoral Thesis, Universifiit Bayreuth 1994. [15] J. Biener, A. Schenk, B. Winter, C. Lutterloh, U.A. Schubert and J. Kiippers, Surf. Sci. Lett. 291 (1993) L725. [16] J. Biener, A. Schenk, B. Winter, C. Lutterloh, U.A. Schubert and J. KiJppers, Phys. Rev. B 49 (1994) 17307. [17] J. Biener, A. Schenk, B. Winter and J. Kiippers, J, Electr. Spectr. Rel. Phenomena 64/65 (1993) 331. [18] C. Lutterloh, A. Schenk, J. Biener, B. Winter and J. Kiippers, Surf. Sci. Lett. 312 (1994) L1039. [19] E. Vietzke, K. Flaskamp, V. Phillips, G. Esser, P. Wienhold and J. Winter, J. Nucl. Mater. 145-147 (1987) 443. [20] E. Villa, J.A. Dagata, J. Horwitz, D. Squire and M.C. Lin, J. Vac. Sci. Technol. A 8 (1990) 3237. [21] W. Eckstein, Computer Simulation of Ion-Solid Interactions (Springer, Berlin, 1992). [22] D.L. Baluch, C.J. Cobos, R.A. Cox, C. Esser, P. Frank, Th. Just, J.A. Kerr, M.J. Pilling, J. Troe, R.W. Walker and J. Warnatz, J. Phys. Chem. Ref. Data 21 (1992) 411. [23] W.H. Press, S.A. Teukolsky, W.T. Vetterling and B.P. Flannery, Numerical Recipes in C, 2nd Ed. (Cambridge University Press, Cambridge, 1992). [24] A.A. Haasz and J.W. Davis, J. Nucl. Mater. 175 (1990) 84. [25] V. Philipps, E. Vietzke and M. Erdweg, J. Nucl. Mater. 162-164 (1989) 550. [26] J.W. Davis, A.A. Haasz and P.C, Stangeby, J. Nucl. Mater. 145-147 (1987) 417.
Journal of Nuclear Materials 227 (1996) 186-194
nuclear materials
A model of hydrogen impact induced chemical erosion of carbon based on elementary reaction steps M. Wittmann a,U,j. Kiippers a,b,* a
Max-Planck-lnstitut fiir Plasmaphysik, Euratom Association, 85748 Garching, Germany b Experimentalphysik VI, Universitdt Bayreuth, 95440 Bayreuth, Germany
Received 29 May 1995; accepted 29 August 1995
Abstract
Based on the elementary reaction steps for chemical erosion of carbon by hydrogen a model is developed which allows to calculate the amount of carbon erosion at a hydrogenated carbon surface under the impact of hydrogen ions and neutrals. Hydrogen ion and neutral flux energy distributions prevailing at target plates in the ASDEX upgrade experiment are chosen in the present calculation. The range of hydrogen particles in the target plates is calculated using TRIDYN code. Based upon the TRIDYN results the extent of the erosion reaction as a function of depth is estimated. The results show that both, target temperature and impinging particle flux energy distribution, determine the hydrogen flux density dependent erosion yield and the location of the erosion below the surface.
1. Introduction
Carbon is a widely used wall material in experimental fusion devices, primarily because its low-Z warrants a small radiation cooling of the plasma if contamination of the plasma from the wall material occurs. The drawback of C lies in its ability to form volatile hydrocarbons with hydrogenic particles which are the dominant species in the plasma. Accordingly, in fusion experiments and laboratory experiments as well, hydrocarbons have been detected during plasma operation. This transformation of bulk C under particle impact into hydrocarbons is termed chemical erosion, as chemical processes, rather than physical processes alone, primarily govern the overall erosion mechanism. Chemical erosion of C targets by H has been studied under materials aspects extensively in the past [1-5,19,25,26]. Most often, hydrogenic ions were used as projectiles and various types of graphites served as targets. Erosion was monitored by weight loss or detec-
* Corresponding author.
tion of volatile erosion products, predominantly methane. Erosion yields of up to 10% and the temperature range of efficient erosion, 700 to 900 K for methane, have been observed, as well as the release of methyl radicals [19] and molecular H. The elementary chemical reaction steps which lead to erosion were, however, not addressed in these investigations. In recent studies on model C : H systems compatible with UHV and surface sensitive spectroscopies these elementary reaction steps in the H atom/carbon surface chemistry have been identified. These are: 1) Thermally activated molecular H 2 release through C - H bond breaking events followed by recombinative desorption [6]. 2) Thermally induced release of methyl radicals and methane from a hydrogenated carbon substrate [6,7], a reaction step which presents a major contribution to chemical erosion. 3) Hydrogenation of CH groups with unsaturated C atoms at a partially hydrogenated C : H surface by thermal H atoms [8,9]. 4) H abstraction from CH groups with saturated C by H atoms [10]. 5) H atom impact induced chemical erosion as a consequence of the above steps 2 and 3 [10]. The present paper deals with the consequences of
0022-3115/96/$12.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0022-3115(95)00150-6
M. Wittmann, J. Kiippers/ Journal of Nuclear Materials 227 (1996) 186-194 the reaction steps 1 to 5, in particular at wall flux densities met in experimental fusion devices. The activation energies and reaction cross sections for the H / C : H surface chemistry of hydrogenated carbon deduced in the above studies were used in the present work to develop a model for chemical erosion. The procedure used in this work is as follows. The neutral and ionic H particle energy distributions faced in typical discharges in ASDEX upgrade experiments [11] are used to calculate H concentration profiles in a C target based on the TRIDYN code [12]. The C : H target defined in this way is subjected to H flux densities as found in ASDEX upgrade, and in the resulting energy dependent particle ranges the above specified elementary reactions are allowed to proceed. This then gives range dependent erosion and molecular H 2 flux densities from which the overall erosion yield as a function of temperature is calculated. This paper is subdivided into six parts. Following this introduction, Section 2 summarizes the dominating reaction paths characterizing the chemical interaction of a C : H layer with atomic H. The details have been published previously; this summary is given at the convenience of the reader. Section 3 deals with the TRIDYN calculations performed to determine the depth variation of thermal H atom effective fluxes in a macroscopic hydrogenated carbon specimen exposed to H flux densities and energies as present in experimental fusion devices. Section 4 combines the contents of Section 2 and Section 3 in developing a model allowing us to estimate the amount of hydrocarbon evolution and subsequent C contamination of the plasma resulting from chemical erosion of carbonized surfaces, i.e. first wall materials. In Section 5 the results of these model calculations are discussed, while Section 6 presents our conclusions.
2. Chemical mechanisms
The H / C : H surface chemistry is governed by few chemical reactions involving sp 2 and sp 3 C centers, radical C centers (sp x in our nomenclature) and H atoms. The combination of these reactions accounts for most of the experimentally seen features at C : H surfaces irradiated with H atoms as in plasma assisted hard C film deposition, low pressure diamond synthesis and carbonized first-wall structures in fusion experiments. The experiments performed to investigate H / C : H surface interactions are described in detail elsewhere [13]. The reader is referred to this article and the references cited therein. Therefore, only the principal aspects of the experimental work will be mentioned here.
187
In this study, C : H layers of several nm thickness were grown by ion beam deposition of hydrocarbons of 160 eV energy on a suitable substrate. Film thickness could be monitored by Auger electron spectroscopy (AES). The film composition was determined by quantitative analysis of thermodesorption products using a quadrupole mass spectrometer. H / C ratios were in between 0.4 and 0.5; limited fine adjustment could be achieved by varying the exposure parameters ion energy and surface temperature, or changing the feed gas. Surface vibrations were measured by high resolution electron energy loss spectroscopy (HREELS). All experiments were carried out under UHV conditions. Spectroscopic investigations were made in situ. The C : H films prepared in this way exhibit the essential structural features of carbon irradiated by H particles, a C network partially terminated by H, and are considered as appropriate model systems for the study of the interaction of H and surfaces of hydrogenated C materials. The reactions occurring at the surfaces of these films when exposed to thermal H atoms were studied in situ. Thermal H (or deuterium) atoms were produced by effusion from a Ta tube heated to 1900 K. From the H pressure inside the tube, the effusion geometry and the dissociation equilibrium constants at the tube temperature the flux density at the C : H surface is estimated to ca. 1 × 1013 cm-2s -1, i.e. far below the fluxes in fusion applications. The H atom source is described in detail elsewhere [14]. 2.1. Hydrogenation H R E E L spectra of C: H layers prior to H exposure show a broad band in the C - H valence region, 2800 to 3350 c m - 1, composed of C - H vibrational losses with C in aromatic sp2-hybridization and in sp3-hybridization, and, to a very small extent, in sp-hybridization. The loss energies of the v (CH, arom., sp2), /"as (CH, sp3), vs (CH, sp3), and v (CH, sp) vibrations [8,15-17] correlate very well with the respective frequencies which characterize analogous b o n d s in h y d r o c a r b o n molecules. From the loss intensities it can be inferred that C : H film surfaces contain about equal amounts of sp 2 and sp 3 C atoms with a minor contribution of sp C, similar to the C : H films found at plasma exposed C surfaces. This observation stresses the conclusion that the essential structural features of hydrogenated C are present in the C - H network of ion-beam deposited C : H films. Exposure of a C ' H layer to H atoms at or near room temperature leads to a complete removal of v (CH, sp) related losses, a reduction of v (CH, arom. sp 2) related losses and to a gain in sp3-CH related loss intensity. If this experiment is conducted with deu-
M. Wittmann, J. Kiippers/Journal of Nuclear Materials 227 (1996) 186-194
188
terium atoms, an energy loss peak at 2129 cm -1 is observed, indicating that deuterium is bound to sp 3 hybridized C only [8]. This observation leads to the conclusion that hydrogen or deuterium atoms efficiently hydrogenate sp and sp 2 C centers, i.e. unsaturated CH groups, at the surface of the C : H layer. Due to the low energy of the H atoms this hydrogenation reaction is limited to the near surface region. Control experiments using 160 eV H~- ions result in hydrogenation of a C : H layer throughout the penetration range [8]. Quantitative analysis of the HREELS data based on the rate equation - d [ C H s p 2 ] / d t = [CH sp2]~H~
\
/
\
I
C.-C-H, / I
(lb)
with [CH sp 2] the concentration of hydrogen bound to sp 2 centers, q~ the flux density of H atoms and trH the reaction cross section for hydrogenation yields a value of ~rH = 4.5 × 10 -2o m 2 [10]. In the reaction (lb) a representative sp 2 two carbon center is shown. The open bonds at the C atoms may either connect this group to the C network or may end at H atoms. As every sp 2 C is bound to one or three (in a graphitic layer) more sp 2 C, reaction (lb) produces a sp 3 C and a neighboring radical center as an intermediate which we call an spX-center and mark by an asterisk in Eqs. (lb) and (2b). A spX-center can further be hydrogenated yielding an sp3-center according to the following equations: - d [ C H spX]/dt = [CH spX]~rn qb,
(2a)
\ n + C./
(2b)
I -~ H - C I
22. Hydrogen abstraction Exposure of a H saturated C : H film to a flux of deuterium at room temperature results in isotopic exchange of H against deuterium. This can be monitored in HREEL spectra, which reveal a buildup of loss intensity at energies characteristic of sp 3 C - D stretch vibrations accompanied by isotope shifts in the fingerprint region [8]. This isotopic exchange is the result of H abstraction followed by hydrogenation as formulated in Eqs. (3) and (4): L /* -C-H+D~-C +HOg S , (3) /
-C, \
I
+D ~-C-D. I
- d[CH s p 3 ] / d t = [CH sp3]trD q~,
(5)
(la)
for the elementary reaction C=C+H~ / \
The radical carbon species is marked by an asterisk and open bonds make either connections to the carbon network or are terminated by hydrogen. The analogous processes as Eqs. (3) and (4) are observed when subjecting a C: D-layer to a flux of thermal hydrogen atoms. No isotopic effect on the reaction rates can be observed within the experimental error [18]. Thus the rate limiting, i.e. slowest, reaction step, H abstraction (Eq. (3)), has a small activation energy. As the isotope exchange reaction rate is determined by reaction (3) the differential rate equation for Eq. (3) + Eq. (4) can be formulated as
(4)
with [CH sp 3] the concentration of H bound to sp 3 hybridized C, tro the reaction cross section for H abstraction and ¢ the deuterium flux density onto the sample [18]. Quantitative analysis of the H R E E L spectral peak intensities yields tr D = 0.05 × 10 -20 m E [18]. This small value is consistent with a gas phase reaction cross section, as would be expected for an Eley-Rideal mechanism in the abstraction reaction. As H (or deuterium) on a C : H surface and in the bulk of a C : H film as well can only exist in a covalently bound state, the reaction proceeds via a close encounter of a deuterium atom from the gas phase with a covalently bound H atom in the C : H layer and subsequent H - D bond formation with simultaneous C - H bond cleavage.
2.3. Chemical erosion If a C : H surface is exposed to H atoms at elevated temperatures in the range 400 to 700 K, a reduction of C : H layer thickness is observed in AES. This process, most efficient at ca. 600 K under laboratory conditions, is not due to thermal desorption effects or the action of H molecules, as has been demonstrated in control experiments. Obviously, H atoms of thermal energies initiate the formation of volatile hydrocarbon species and thus chemically erode the C : H layer. HREEL spectra show an accompanying shift of loss intensity from sp 3 C bonded to aromatic sp 2 C bonded H. In line with the direct observation of methyl radical release from graphite or C : H layers exposed to atomic H at elevated temperatures reported from several other groups [19,20] it is supposed that radical sp X C centers formed upon H impact by abstraction (Section 2.2) can deexcite via the split-off of a neighboring methyl group. This involves cleavage of a carbon-methyl or-bond, ca. 380 kJ/mol or 4 eV, and the formation of a carboncarbon ~r-bond, ca. 190 kJ/mol or 2 eV. Thus the erosion step is endothermic by about 190 kJ/mol, in accordance with the observation that it is restricted to the elevated temperature regime.
M. Wittmann, J. Kiippers/Journal of Nuclear Materials 227 (1996) 186-194
~'H H3C"
1017
, ~/ / ~ /sp3
oH//~+H"
~
+H"
~.1015 ,,
H'7 t"H
-H2
H+
•~ 101~
CD -H2
T
189
H'l
,
10
~"H
,
J
i
1 1 , 1 ,
i
100 primaryenergy[eV]
,
•
.
.
.
.
.
.
1,000
Fig. 2. Hydrogen neutrals and ions energy distribution and flux density at ASDEX upgrade target plates.
T, kx I ~ ; H 3
J Fig. 1. Scheme of reactions initiated by thermal energy and hydrogen impact at C:H films. Fat lines represent thermally activated reaction paths. The thermal decomposition of sp x centers t o s p 2 via methyl radical split-off is described by the following rate equation: - d [ f H s p X ] / d t = [CH s p X ] k x e x p [ - E x / k T ] . (6) The experimental observation of the temperature dependent sp x t o s p 2 conversion and the erosion rate maximum could be fitted using values of k x = 1013 S- 1 and E x = 155 k J / m o l (1.6 eV) [10]. Fig. 1, adapted from [10], schematically summarizes the reactions observed at H exposed C: H films as deduced from the results so far. The upper right shows the H abstraction/hydrogenation steps (Section 2.2) converting s p 3 carbon to sp x and vice versa. The lower right indicates the activated erosion step, conversion f r o m sp x t o sO 2 with the release of a methyl radical initially in a-position relative to sp x carbon (Section 2.3). The hydrogenation sequence (Section 2.1) is shown on the left half of the reaction scheme. It c o n v e r t s sp 2 C to sp 3 via sp x. The thermal decomposition of sp x C t o sp 2 via H atom release is included in the scheme, although it is not described here explicitly. 3. TRIDYN calculations
The most important differences regarding H / C : H interaction in laboratory experiments and fusion de-
vices are the extremely high H flux densities and specific distribution of primary energies achieved in the latter. Fig. 2 illustrates neutral and ion flux energy distributions typical for plasma discharges in A S D E X Upgrade at the target plates in the diverter. These distributions exhibit characteristics typical for fusion experiments: charge exchange neutrals with increasing fluxes towards low particle energies and ions with a flux peak at the sheath potential. In the present calculation the charge exchange neutrals energy distribution was approximated by a 1 / E dependence. The ion energy distribution was approximated by a Maxwellian distribution shifted by a sheath potential of 150 V. As can be deduced from earlier experiments, chemical reactions with H atoms or ions occur only if H is slowed down to thermal energies. This rises the question how to find the effective fluxes of thermalized H atoms varying with target depth given a specific total flux density and its energy distribution,
1/\ j f L j A
5
100eV
_
+ .= ~ ~ ~ 1 ~ ~ t t 0 0 0 0
5
eV
10 15 20 25 30 35 40 45 50 depth[nm]
Fig. 3. Calculated depth profiles of hydrogen in carbon. The curves represent distinct TRIDYN runs with hydrogen primary energies ranging from 100 to 1000 eV.
M. Wittmann, J. Kiippers /Journal of Nuclear Materials 227 (1996) 186-194
190 1019 "7
E 1078
~ 1017 -o 101o -1- 10~5 E
~ 1014 .~
013
~ 1012 0
I
I
I
I
5
10
15
20
25
30
35
40
45
50
depth [nm]
Fig. 4. Calculated effective thermal flux density of hydrogen in carbon assuming a hydrogen (H ° and H +) primary energy distribution as in Fig. 2, and a total flux density of 1019 cm-2s -1. See text for details.
tial equations with the concentrations of the respective species as variables. All parameters needed, such as reaction cross sections, activation energies, and rate coefficients, are taken from experimental data except the thermal H flux densities into the individual layers which are taken from the TRIDYN results described in Section 3 and displayed in Fig. 4. In order to study the flux density dependence, these flux densities were scaled to yield different total flux densities. In the present calculation total flux densities of 1017 to 1019 particles c m - 2s- 1 have been assumed. In addition to the differential Eqs. (1), (2), (5) and (6) two further equations were included in the numerical model, which describe chemical reaction pathways of lower significance in the H flux region addressed here. These are the thermally activated decomposition of sp x centers to sp 2 via split-off of a H atom shown in the lower left part of Fig. 1. The rate equation is - d [ C H spX]/dt = [CH s p X ] k _ H e x p [ - E H / k T ]
(7) This problem can be solved in principle using the TRIDYN code that allows to calculate depth profiles based upon the binary collision model. Details of this model are given in the literature [21]. We modified the code slightly to include the possibility of generating projectile particles with a given primary energy distribution. Fig. 3 shows several hydrogen depth profiles calculated for monoenergetic hydrogen particles impinging at normal incidence at a carbon target. The H atoms are regarded as stationary as soon as their kinetic energy is below 5 eV. Clearly, the penetration depth is strongly energy dependent. Given the approximate energy distributions of H ° (atomic hydrogen) and H + as seen near the C tiles in a fusion device (Fig. 2) we arrive at a depth profile as shown in Fig. 4. As the projectile particle trajectories are followed to an end energy of 5 eV, i.e. near thermal energy, the depth variation of the H concentration profile represents the effective net flux density of thermal H particles at the implantation range in the carbon target. These H atoms then can initiate the reactions as specified in Section 2 of the present paper. TRIDYN code does not account for any differences between neutral and ionic H atoms, as their masses are regarded as equal. The results shown represent specific TRIDYN runs at depth resolutions of I nm.
4. Chemical erosion calculations
The model calculations are performed in the following way: The C : H target is cut into 1 nm thick layers oriented parallel to the surface. The chemieal reaction scheme (Section 2) is converted into a set of differen-
and the thermal decomposition of sp 3 centers to sp x with the rate equation - d [ C H s p 3 ] / d / = [CH s p 3 ] k T e x p [ - E a / k T ].
(8)
Parameters for Eq. (8) are taken from Ref. [10] with k T = 1013 s -1 and E a = 234 kJ/mol. Parameters for Eq. (7) are taken to be the gas phase values reported in the literature [22]: k.H=1013 s -1 and E . H = 1 6 7 kJ/tool. Table 1 summarizes the complete set of elementary reactions incorporated into the model including all kinetic parameters and the expressions describing differential changes in the concentrations of the sp 3, sp 2 and sp x C species in these reactions. The complete set of differential equations is solved numerically using the Rosenbrock method [23]. Each layer is treated independently during the calculation. The calculations are performed for the temperature range from 500 to 1100 K in 10 K intervals. For each layer thermal equilibrium concentrations of the respective species, rates and probabilities of methyl radical formation are calculated. This simple model does not explicitly account for any effects which may be introduced by the geometrical constraints caused by the various C atom hybridization states. Furthermore, as only the individual concentrations of the respective C species are taken into account, depth information is achieved by applying this zero-dimensional approach to each layer individually. Fig. 5 shows the calculated concentrations of sp 2 (a), sp 3 (b) and sp x (c) C as a function of target depth and temperature at a total H flux density of 1019 cm-Zs -1. sp 2 and sp 3 concentrations span the range
M. ~ittmann, J. Kiippers/Journal of Nuclear Materials 227 (1996) 186-194
I
I
,~,
~,
I
f
~
~
"eb
<.
i
<.
-4,
C~
I "e,.r, b
c~
'T
x
x
x
II
LI
II
0
o ¢)
II
~
~ II
IL II
~,.~
.=. 0
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= +•
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=
i
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¢)
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=
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-~/--~--
l
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II
191
192
M. Wittmann, J. Kiippers/Journal of Nuclear Materials 227 (1996) 186-194
a) sp2 carbon i ! sp2 carbon
depth [nm]
30 40
00 8 0 0 900 1000 500 600
temperature[K]
b) • 1.0
sp3 carbon
• 0.8 • 0.6 •
0.4 spo carbon
• 0.2 • 0.0
depth [nm]
40
)0 500 600 700 ow ---
temperature [Iq
c) • 0.012
spXcarbon
• 0.008 .0.004
deptt, t, ,,,,J
~
spXcarbon
further grows at the expense of sp 3 and sp x C. At temperatures well beyond 1000 K sp 2 C has become the dominating species at all target depths. At all temperatures and depths the ratio of sp x and sp 3 C is determined by the ratio of the dehydrogenation and hydrogenation cross sections. The decrease of the sp 3 fraction with increasing temperature and depth is paralleled by an equivalent decrease of the sp x fraction. At temperatures above ca. 900 K the sp x fraction increases slightly as a result of the thermally activated reaction paths converting sp 3 C to sp x. Fig. 6 shows the resulting depth and temperature variation of the methyl radical production rate at total H ( H ° + H +) flux densities of 1017 to 1019 cm-2s -1. Each plot shows a H flux density dependent maximum at temperatures ranging from 870 K at a flux density of 1017 cm-2s -1 to 1050 K at 1019 cm-2s -1. The erosion maximum naturally is located in the near surface region as a result of the higher H fluxes (compare Fig. 4). This result is in agreement with experimental evidence; at a lower H flux density of ca. 1013 cm-2s -1 the maximum temperature is ca. 620 K [10]. A set of separate calculations further demonstrated the total flux density dependence of the erosion maximum tem-
0.000 0 500 t~oo,w
temperatureIK]
Fig. 5. Calculated equilibrium fractions of sp 2 (a), sp 3 (b) and sp x (c) carbon in a C:H layer exposed to atomic hydrogen as a function of depth and temperature.
from approximately zero to one, whereas the sp x concentration does not exceed a value of about 0.011, the ratio of the dehydrogenation and hydrogenation cross sections. At low temperatures, the presence of the various carbon species is completely governed by the hydrogen induced hydrogenation and dehydrogenation processes. The extent of thermally activated reactions is negligible. As the hydrogenation cross section exceeds the dehydrogenation cross section by a factor of ca. 102, the dominating species is sp 3 hybridized C. This situation gradually changes at increasing temperatures as thermally activated reactions converting sp x carbon to sp 2 C are beginning to contribute. The lower the effective thermal H flux density, the lower the temperature where thermally activated reactions compensate for the dominating hydrogenation reaction path. Near the surface, at an effective thermal H flux density of ca. 1018 cm-2s -1, equal fractions of sp 3 and sp 2 C occur at ca. 900 K, whereas 40 nm beyond the surface, at a flux density of 1014 cm-2s -1, this ratio is found at 700 K. With increasing temperature the sp 2 C fraction
o depth [nm]
1100 zu
25
50o
600
'w
temperature
[K]
Fig. 6. Calculated methyl production rates from a C:H layer subjected to fluxes of atomic hydrogen as a function of depth and temperature at different total hydrogen flux densities: (a) 1017 c m - 2 s -1, (b) 10 TMcm-2s -I, (c) 1019 c m - 2 s -1.
M. Wittmann, .7. Kiippers /Journal of Nuclear Materials 227 (1996) 186-194 perature predicted by the model. Absolute values cannot be given, as the concentration of methyl groups in a C : H layer is not known. Methyl groups in a-position relative to the thermal decay reaction center are a chemical erosion prerequisite. Assuming a hit rate of 0.01, a total chemical erosion rate of ca. 30 C monolayers per second at maximum erosion conditions and a hydrogen flux density of 1019 cm-2s -1 were calculated. This corresponds to an effective erosion yield of 0.01 C per H atom, a value which was determined in model experiments of H exposed C : H layers [10], whereas in other laboratory experiments erosion yields of 0.1 C per H atom have been found [24].
5. Discussion The approach to model chemical erosion of C by H as used in the present study is different from the more phenomenological descriptions used previously [1-5]. The justification for the model comes from the fact that the elementary chemical reaction steps of the H / C : H interaction are now identified and the model confirms experimental results at C : H films at H flux densities available in laboratory experiments. However, there are some points which have to be addressed concerning the applicability of the model at erosion of C targets by H flux densities present in experimental fusion devices. At first one has to consider whether the C : H films resemble the relevant characteristics of H irradiated C tiles. Irrespective of the particular type of graphite used for the tile the high energy fraction of the H flux will suffice to amorphisize the surface region of the graphite. Therefore, under equilibrium conditions, in the implantation range the C tile will exhibit a structure which is very similar, if not identical, to an amorphous C : H layer. For the present flux densities and energy distributions the thickness of this layer was calculated to be about 30 nm. The TRIDYN code used is capable to handle the given implantation problem beyond the precision needed here. Therefore, we have confidence, that the gross structural features of H exposed C tile surfaces are sufficiently close to several 10 nm thick C : H films. Often, in studies on chemical erosion [1-5] transport of eroding and erosion species was a concern. In the present work, transport of H is not treated beyond the TRIDYN range, and transport of the erosion species, methyl, is neglected altogether, as for the equilibrium erosion it has no effect. The hybridization state of the C atoms in a C : H network at a given hydrogen atom flux density is governed by the temperature. For the flux densities addressed here, sp 3 C dominates up to ca. 700 K, whereas sp 2 C is the prevailing species at high temperatures
193
above 1000 K, see Fig. 5. The sp x species is present in low concentrations at all temperatures. The explanation is as follows: The hydrogenation reaction converts sp 2 to sp 3 hybridized C. Every sp 2 hydrogenation step yields one sp 3 and one sp x hybridized C atom. Due to its large hydrogenation cross section sp x C is further hydrogenated. This accounts for the low steady state concentration of the sp X species. The hydrogenation rate depends on the sp / concentration and the H flux density only, i.e. is independent of temperature. The reaction pathways leading from sp 3 to sp 2 hybridized C (with the sp x species as an intermediate) are thermally activated as in the sp 3 thermal decomposition case (Eq. (8)) or involve one activated step as in the thermal decomposition of sp x centers. Thus at low temperatures, the hydrogenation process dominates until all sp 2 C is converted to sp 3 and the C : H layer exclusively contains sp 3 hybridized C plus a small fraction of the sp X species. At high temperatures, the reaction rates of the thermally activated reactions are high enough to overcome the hydrogenation rate and to interchange the population of sp 2 and sp 3 C. Thus in a high temperature equilibrium the sp 3 fraction is negligible and sp 2 dominates besides the small sp x C fraction. In an intermediate temperature range between 700 and 1000 K, there is a smooth transition from sp 3 to sp 2 dominance. The transition temperature depends on the H atom flux density in so far as higher temperatures are needed to compensate a high flux density. In the near surface region which is exposed to the highest thermal H flux this transition is observed at higher temperatures than towards the bulk, see Fig. 5. Three arguments account for the temperature and depth dependence of the calculated methyl formation rates. Methyl radicals are formed during the thermal decay of an unsaturated C atom, sp x. This is an activated reaction, its rate strongly increasing with temperature. As the methyl radical stems from a C network bound methyl group with, of course, a s p 3 hybridized C atom, the first prerequisite for methyl release is the presence of sp 3 C. It has been shown before that this condition is met primarily at low temperatures. So a temperature optimum must exist for this reaction step (see Fig. 6 for reference). The methyl formation rate is proportional to the sp x concentration (Eq. (6)). The amount of sp x C present in the C : H layer is to a first approximation proportional to the flux density of thermal H atoms. Therefore the methyl formation rate will decrease with depth (Fig. 6) as the thermal H flux density decreases. Furthermore, the calculated results have shown a flux density dependence of the temperature where maximal erosion occurs. This temperature varies from below 900 K to 1050 K at flux densities from 1017 to 1019 cm-2s -1. It originates from the fact that the temperature where the sp 3 concentration be-
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gins to decrease depends on the H flux density. As stated, the absolute erosion yield is not available from the present calculation as the model implies that there are always potential eroding methyl groups adjacent to a reaction center. This is certainly not the case. It might well be that a hit factor of 0.01 as used above represents a reasonable value.
6. Conclusions Laboratory results of H / C : H layer interaction clearly have demonstrated the action of processes leading to the removal of hydrocarbon species from the C : H layer. These reactions are based upon the chemical interaction of thermal H atoms leading to hydrogenation, i.e. the formation of covalent H - C bonds, and several thermally activated processes involving the breaking of H - C and C - C covalent bonds, the latter representing the actual C erosion steps. Cross sections, frequency factors, and activation energies of elementary reaction steps of the H / C : H interaction have been used together with energy dependent H implantation ranges to calculate chemical erosion of C tiles exposed to fusion relevant target plate fluxes. The results reveal a temperature and flux dependent erosion zone in a few 10 nm thick region at the surface of the target plates. The trends observed can be easily understood in terms of the reaction schemes applied in this study.
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