1 + VOl/kiS,
5.2. Bulk diffusion, solubility and trapping of hydrogen and graphite at elevated temperatures
5.2.1. Diffusion
The high temperature behaviour of hydrogen in graphite has recently been reviewed by Causey [112].
There have been many attempts to measure the diffu-sion coefficient of the hydrogen isotopes in graphite, and the reported values have varied tremendously.
The different experimental techniques used by the researchers are discussed here and the results for the diffusivities are shown in Fig. 13. Elleman [147] used pyrolytic carbon microspheres with internal cores of lithium aluminate enriched in the 6Li isotope in his experiments. The particles were placed in a nuclear reactor at room temperature to generate tritium from the n-a reaction. Diffusivities were determined from breakthrough times during isothermal anneals.
Elleman reported a diffusion coefficient of D = 700 exp (-3.25 eV/kT) cm2/s over the temperature range 1073-1473 K. Rohrig et al. [148] used the release rate of tritium from nuclear graphites during isother-mal anneals to determine the diffusivity of tritium in graphite. They reported the diffusion coefficient to be given by D = 0.04 exp(-2.78 eV/kT) cm2/s.
Causey et al. [149] used a recoil injection technique to measure the tritium diffusion coefficient in pyrolytic carbon. The diffusion coefficient for laminar pyro-lytic carbon was reported t o b e D = 3.3 x 102
x exp (-4.3 eV/kT) cm2/s. For silicon doped pyrolytic carbon, the coefficient was given D = 1.1 X 10"3
x exp(-2.3 eV/kT)cm2/s. For low temperature isotropic pyrolytic carbon, two different diffusion coefficients were determined, depending on whether hydrogen was used in the gas sweeping over the samples during the isothermal anneals. The porosity in the isotropic
3 - Saeki [152]
4 - Malka et al. [150]
.1 7 5 - Rohrig et al. [148]
1 0 " 6 - C a u s e y [112]
7 - Moritaetal. [146]
8 - Tanabe and Watanabe [154]
1 ( l'i al i i i i i ' ' ' '
0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 103<T(K)
FIG. 13. Arrhenius plot of the diffusivity of tritium in graphite by various investigators [112, 146-154].
material was given as the cause for the larger apparent diffusion coefficient, and isotropic exchange with trapped tritium was suggested as a possible explanation for the enhanced release when hydrogen was used in the sweep gas. Malka et al. [150], in experiments similar to those performed by Rohrig et al. [148], used nuclear graphite, with the tritium production due to activatidn of lithium impuri-ties in the graphite. Their diffusion coefficient of D = 8.3 X 103 exp(-3.8 eV/kT) cm2/s is also shown in Fig. 13. Saeki [151] examined the effect of neutron irradiation on the release rate of tritium from different types of graphites. In a subsequent study [152] on the release of tritium from irradiated graphite, Saeki used isothermal anneals to determine the diffusivity of tritium in graphite. The graphite was ground to a powder to remove the effects of grain orientation. The curve shown in Fig. 13 is for natural graphite with relatively large powder size, and the equation is given by D = 3.8 x 10"4 exp(-2.22 eV/kT) cm2/s. For the nuclear graphite, the activation energy for the diffusion was seen to increase with neutron fluence. In a third study [153], Saeki examined the effect of the degree of preferred orientation of the grains in pyrolytic carbon
on the tritium diffusion coefficient. He reported two different diffusion coefficients with very different acti-vation energies. An actiacti-vation energy of 2.7 eV was given for the highly oriented material and 1.1 eV for the isotropic carbon. This difference was proposed to be caused by radial pores in the isotropic material.
Saeki proposed the difference to be due to a more rapid diffusion along the basal planes than that which is possible along the prism planes. The highly oriented material, with the basal planes aligned with the exter-nal surface, would require a greater diffusion distance before the tritium could be released from the carbon.
Morita et al. [146] recently used elastic recoil depth profile analysis to measure diffusion during hydrogen implantation into graphite at 300-1000 K. Tanabe and Watanabe [154] subsequently examined deuterium retention in graphite exposed to D° at 460-1323 K by means of re-emission and thermal desorption tech-niques. They obtained results similar to those of Morita et al. and determined a diffusion coefficient of D = 2.1 x lO"12 exp(-0.45 eV/kT) cm2/s for hydrogen saturated graphite. These results, also shown in Fig. 13, differ markedly from the other data and have not yet been fully explained. Differences in the various experimental methods used to obtain the data summarized in Fig. 13 may be primarily responsible for the differences in the reported hydrogen concentra-tion in graphite, and variaconcentra-tions in the sample materials and hydrogen loading methods may also be important.
1.0
10'
10''
1 0 ' o
1 0 '
10
1 - Causey et al. [149]
2 - Atsumi et al. [155]
3-Causey [112]
(D
(2)
i5 _1_
0.55 0.60 0.65
_L_
0.70 0.75 10VT (K)
0.80 0.85 0.90
FIG. 14. Arrhenius plot of the solubility of hydrogen isotopes in graphite.
5.2.2. Solubility
An apparent deuterium solubility in pyrolytic carbon was reported by Causey et al. [149]. In this study, laminar pyrolytic carbon samples were exposed to tritium gas at different temperatures and pressures.
The amount of absorbed deuterium was determined by subsequent outgassing through a calibrated mass spectrometer. Because of the slow inward diffusion and the large diffusion distance in this non-porous material, equilibrium saturation of the samples could not be reached. This non-equilibrium condition meant that the values determined for the solubility were based on the earlier measured diffusion coefficient, and any errors in that measurement would have carried over to the solubility. The solubility was reported to be 5.1 x 10-8exp(+1.45eV/kT)atomfraction/atm"2. An Arrhenius plot of these data and the other solubility results is shown in Fig. 14.
Atsumi et al. [155] recently measured the solubility of deuterium in ISO 88 graphite at temperatures between 1123 and 1323 K and pressures between
2.5 x 102 Pa and approximately 1.3 x 104 Pa.
Although not stated in the paper, it appears that the solubility values were determined by pressure changes in a constant volume chamber measured by a capacitance manometer. The solubility was reported to be given by S = 6.44 x 10"5 exp(+0.2 eV/kT) atom fraction per atm"2. As predicted by Sievert's law, the results were seen to scale linearly with the square root of pressure.
The reported temperature dependence of the solubility is shown in Fig. 14, together with two additional data points determined in experiments at 1273 and 1473 K with 1 atm pressure. Deuterium containing 1 % tritium was used in the experiments performed with POCO AXF-5Q graphite. Both data sets show a negative heat of solution, suggesting bonding of the hydrogen iso-topes to the graphite.
The study by Atsumi et al. [155] appears to give the best estimate for the hydrogen isotope solubility in graphite. This expression is:
S = 6.44 x 10"5 exp(+0.2 eV/kT) atom fraction/atm"2
25. .
x _ Gas Pressure = 0 66 Pa Time = 1.5 h
— , „ DIFFUSE Code Result
r> 20
-JJ e
i
-o 15 - X c / g /
c / 2 10 • /
a* r a /
E /
?
5" /
900 1000 1100 1200 1300 MOO 1500 1600 1700 1600 1000 Temperature (K)
FIG. 15. Tritium retention in POCO AXF-5Q graphite as a function of temperature 1156].
The best estimate for the diffusivity comes from the combination of the solubility results by Atsumi et al.
[155] and the inward migration rates reported by Causey et al. [156] for POCO AXF-5Q graphite. In the latter study, the inward migration rate was analysed using the DIFFUSE [37] computer code to determine the product of diffusivity and solubility. The effect of trapping was included in this analysis. The diffusivity is given by
D = 0.93 exp(-2.8 eV/kT) cm2/s 5.2.3. Trapping
The review of the diffusion data for hydrogen iso-topes in graphite and pyrolytic carbon reveals great disparities in the reported values, sometimes as great as four to five orders of magnitude. The primary reason for these measured differences is trapping. The magni-tude of the effect of trapping on the apparent diffusion coefficient was demonstrated in the recent studies by Causey and co-workers [156, 157], In these studies with Papyex and POCO AXF-5Q graphite, samples were exposed to 0.66 Pa neutral gas pressure. Results for the experiments performed at 0.66 Pa and a fixed time of 1.5 h are shown in Fig. 15. It can be seen that the tritium retention initially rises with increasing temperature, but then decreases with increasing tem-perature. Above 1500 K, the inward migration rate is not fast enough to replace the atoms that escape from the traps, and the net result is less than 100% filling of the traps. Below 1500 K, there was not sufficient time during the 1.5 h experiments for the tritium to diffuse completely into the 10 pim grains and fill
the traps. The DIFFUSE computer [37] code was used to analyse these data, and it was determined that the trap energy was 4.3 eV with an intrinsic trap density of 17 appm for this graphite.
The trap energy of 4.3 eV is the same as that given for the bond energy between hydrogen and carbon in typical hydrocarbons [158]. These sites are thought to be on the prism planes along the crystalline edges [159, 160]. Neutron damage is thought to significantly increase the concentration of these trapping sites.
6. SUMMARY
The theory for hydrogen trapping and release in metals is quite well developed, although there is still some controversy regarding the form of the molecular recombination coefficient. However, there are large gaps in the database for the three most popular metallic plasma facing materials: beryllium, molybdenum and tungsten. A wealth of data and modelling have been generated over the last decade for interaction of hydrogen with carbon based materials. However, there are still major discrepancies between various measure-ments, and the modelling has reached only the phenomenological level.
ACKNOWLEDGEMENT
This work was supported in part by the United States Department of Energy, under Contract No.
DE-AC04-76DP00789.
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W. ECKSTEIN, J. BOHDANSKY, J. ROTH Max-Planck-Institut fur Plasmaphysik, Euratom-IPP Association,
Garching bei Miinchen, Germany
ABSTRACT. The paper reviews empirical formulas used to describe the dependence of the sputtering yield on the projectile energy and the angle of incidence. Values of the parameters of plasma relevant materials are given in a table.
New information on the dependence of the sputtering yield on Maxwellian bombardment and on the surface roughness is described, as well as new results on energy and angular distributions of sputtered atoms. Finally, the sputtering of compounds and alloys is discussed as well as the bombardment of elements by non-volatile species.
The paper reviews first some of the semi-empirical formulas for the sputtering yield for light and heavy ions as presented in Ref. [1]; these are based on a more fundamental investigation of the sputtering process by Sigmund [2] limited to heavy ion sputtering. Then, recent developments are discussed in greater detail. A more recent overview on physical sputtering with special regard to the fusion reactor technology is given by Roth [3].
1. SPUTTERING YIELD