MSU LIBRARlES n v RETURNING MATERIALS: Place in book drop to remove this checkout from your record. FINES will be charged if book is returned after the date stamped below. get 2 7 fl???) PERHEAIION MEMBRANES FOR.TRITIUH.EXIRACTION FROH.LIQUID METAL GOOLANTS EN FUSION REACTORS BY Cheazone Hsu A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemical Engineering 1987 uqa;gé\ “"" ' sl‘ ‘ Copyright by GHEAZONE HSU 1987 ABSTRACT PERHEAIION MEMBRANES FOR.TRITIUH EXTRACTION FROM LIQUID HEIAL.COOLANTS IN FUSION REACTORS BY Cheazone Hsu Tritium separation from liquid lithium and lithium-lead alloy (17L183Pb) at low concentrations is an important problem in fusion technology. This research investigates the use of permeation membranes for tritium extraction from liquid breeders in fusion reactors. Palladium-coated metal membranes provide an excellent option for tritium extraction from liquid breeders. This method is attractive because of low contamination, continuous operation, and low cost. For extracting tritium from liquid lithium in a fusion reactor, palladium- coated zirconium is the cheapest window, its fixed capital cost is 8.0 NS for extracting 1 wppm tritium from lithium and is inversely proportional to tritium concentration. For extracting tritium from liquid l7Li83Pb at .26 prb, the cheapest window is palladium-coated vanadium, its fixed capital cost is only 2.6 M$, and the tritium holdup is negligible. Techniques for coating an adherent palladium film on clean membrane surfaces are important. Among membrane metals suggested, zirconium is perhaps the most difficult to coat because of its chemical reactivity. An electroless plating method has been developed to coat palladium on a zirconium surface. Surface activation is crucial to this technique. Thermodynamic concentration limits and kinetic concentration limits of C, N and 0 in Li and in l7Li83Pb are calculated based on projections of the limiting mechanism for carbide, nitride, and oxide formation on membrane surfaces. The study shows that oxygen concentration limits for all likely membranes (Zr, Nb & V) are thermodynamically limited. A hot- gettering startup is required before putting a permeation window into operation. A new experimental analysis technique is proposed for determining hydrogen and hydrogen isotope permeabilities through palladium-coated membranes; data required are hydrogen bulk gas pressures and permeation fluxs. A gas permeation apparatus has been built to perform these experiments at pressures between 10-2 and 10.4 Pa. The results show that deuterium permeabilities in zirconium are 2.00x10'6exp(59/T)i20% g- mol/m.s.Pa1/2, somewhat higher than the values calculated from diffusivity and solubility. The experimental data obtained favor the applicability of permeation windows for fusion reactors. ACKNOWLEDGMENTS I would like to express my deep gratitude to my research advisor, Professor Robert E. Buxbaum, for his insight, encouragement, and financial support. Many thanks are due to the technicians in the DER machine shop and to Robert Welton of the Cyclotron National Laboratory; without their help, the apparatus could not be well set up. I also want to thank Dr. Anderson, Dr. Wilkinson and the other faculty & Staff of the Chemical Engineering Department, Dr. Reinhard in Electrical Engineering, and Dr. Solin in Physics. I am also greatly indebted to my elder brother, George, for his encouragement and financial support. Special thanks are also due to my parents and my parents-in law for babysitting my children. Their help allowed me to concentrate my study; their love is endless. Finally, many thanks to my wife, Shu-Hui, for her patience, encouragement, and love. TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES CHAPTER 1: 1-1. 2 1- 3-5. 3-6. REVIEW OF POSSIBLE SEPARATION PROCESSES Introduction Separation processes 1-2-1. Mechanical separations Solvent extraction . Solid absorption . Gas sparging (gas stripping) . Vacuum degassing Permeation through permeable metal membranes Comparisons of separation processes References \lO‘U‘v'FUJN -2- -2- -2- -2- -2- -2- rehuardraha METAL WINDOW CONCEPT AND DESIGN Introduction Palladium thickness Tritium extraction flux 2-3-1. Tritium diffusion flux in liquid metal 2-3-2. Tritium permeation flux in the membrane 2-3-3. Tritium oxidation rate on the palladium surface 2 3 4. Tritium extraction flux Helium content Design considerations Fixed capital cost, tritium holdup, and overall cost References MASS TRANSFER OF CARBON, NITROGEN, AND OXYGEN IN A PERMEATION WINDOW Introduction Distribution coefficient Thermodynamics of impurity in liquid and membrane 3-3-1. Carbon 3-3-2. Nitrogen 3-3-3. Oxygen Distribution coefficients of C, N, and O in Li and in l7Li83Pb Thermodynamic concentration limits of C, N, and O in Li and in 17Li83Pb Kinetic concentration limits in liquids . Distillation, crystallization, and cold trapping Ho >6 X I-‘HVNO‘UIPPWWNH 33 34 34 35 35 42 43 45 53 61 3-7. CHAPTER 7: NH 7- 7- APPENDIX 1: A1-1. Al-2. Pretreatment steps Symbols Greek letters Abbreviations References EXPERIMENTS 0F PALLADIUM COATING ON ZIRCONIUM Introduction Experiments Immersion plating results Electroless plating results References PERMEATION MODEL USED TO ANALYZE EXPERIMENTAL DATA Surface oxides and hydrogen sticking coefficients Hydrogen permeation model through palladium-coated membranes at low pressures 5-2-1. Without oxygen provided in the downstream 5-2-2. With oxygen provided in the downstream Validity of the technique 5-3-1. Data by Koffler et a1. 5-3-2. Data by Balovnev 5-3-3. Data by Young 5-3-4. Effectiveness of data analysis technique References EXPERIMENTAL MEASUREMENTS OF DEUTERIUM PERMEATION THROUGH PALLADIUM-COATED ZIRCONIUM MEMBRANES Introduction Apparatus Calibration of D20 collection system Experimental procedure Sample descriptions and experimental conditions Results 6-6-1. Deuterium permeability in zirconium 6-6-2. The sticking coefficient of deuterium on palladium References SUMMARY OF CONCLUSIONS AND SUGGESTIONS FOR FUTURE RESEARCH Summary of conclusions by chapter Suggestions for future research DIFFUSIVITIES AND SOLUBILITIES OF NON-METALLIC ELEMENTS IN LIQUID METALS Li, 17Li83Pb, AND STRUCTURAL METALS Diffusivities of non-metallic elements in liquid metals and structural metals Solubilities of non-metallic elements in liquid metals and structural metals References 107 108 108 113 115 116 116 119 122 125 126 127 129 131 132 137 143 APPENDIX 2: A2-l. A2-2. A2-3. A2-4. A2-5. APPENDIX 3: A3-l. A3-2. IMPURITY CONCENTRATION LIMITS FOR CONTAINMENT COMPOUND FORMATION IN THE LIQUID TRITIUM BREEDER- BLANKET OF A FUSION REACTOR Introduction Mathematics of impurity mass transfer Solubilities, diffusivities and mass transfer coefficients Concentration limits in the lithium coolant of a fusion reactor Startup procedure References PERMEABILITIES OF HYDROGEN AND ITS ISOTOPES THROUGH PALLADIUM AND ZIRCINIUM Palladium Zirconium References 145 146 147 151 152 159 161 162 163 164 167 Table Table Table Table Table Table Table LIST OF TABLES Intermetallic diffusivities and projected inter- metallic thicknessfor Zr-Pd, Nb-Pd, V-Pd, and SS-Pd for 30 years operation Diffusion coefficients and solubilities of tritium in metals The resistance of tritium separation from the breeder fluid at 450°C and 0.0015 m thick membrane Flux, window size, helium content, and cost The free energies of formation for carbides, nitrides, and oxides of liquid metals and structural metals for membrane and for fusion blanket Distribution coefficients of C, N, and 0 between Li and structural metals Thermodynamic constants in the non-metallic element concentration equation, Eq. (3-27), in liquid lithium below which compound do not form. Controlling limits in Li for surface compound formation on the membrane of a permeation window 'Controlling limits in l7Li83Pb for surface compound formation on the membrane of a permeation window Formation pressure of palladium oxide Hydrogen permeability in palladium Permeation flux of deuterium through a palladium- coated zirconium Deuterium permeabilities in zirconium Sticking coefficient The diffusivities of carbon, nitrogen, and oxygen in structural metals Diffusivities of carbon, nitrogen, and oxygen in Li and in 17L183Pb Solubilities of carbon, nitrogen, and oxygen in structural metals Solubilities of carbon, nitrogen, and oxygen in Li and in 17Li83Pb Thermodynamic values of non-metallic element concen- trations in liquid lithium required to form surface compounds Controlling limits for the impurity compound forma- tion on the structural surface of liquid lithium breeder fusion blanket The diffusivity of hydrogen in a-Zirconium The solubility of hydrogen in a-zirconium 15 20 23 24 37 46 54 64 64 89 105 117 120 123 132 135 137 141 154 154 165 165 LIST OF FIGURES Fig. 1-1 Tritium permeation route 9 Fig. 2-1 The main tritium flows 27 Fig. 3-1 Carbon distribution coefficients between liquid l7Li83Pb and structural metals, Kc; Kc is calculated from Eq. (3-17). 47 Fig. 3-2 Nitrogen distribution coefficients between liquid 17Li83Pb and structural metals, Kn; Kn is calculated from Eq. (3-21). 48 Fig. 3-3 Oxygen distribution coefficients between 17Li83Pb and structural metals, K ; K0 is calculated from Eq. (3-24). 49 0 Fig. 3-4 Carbon distribution coefficients between liquid metals and membranes Zr, Nb, and V; where Lin is l7Li83Pb. 50 Fig. 3-5 Nitrogen distribution coefficients between liquid metals and membranes Zr, Nb, and V 51 Fig. 3-6 Oxygen distribution coefficients between liquid metals and membranes Zr, Nb, and V 52 Fig. 3-7 Thermodynamic concentration limits of carbon in 17Li83Pb, xct; a thermodynamic concentration limit is the maximam concentration in the liquid at which compounds do not form on a membrane surface; Xct is calculated from Eq. (3-13), assuming the dilute carbon phase would obey Sieverts' law. 55 Fig. 3-8 Thermodynamic concentration limits of nitrogen in l7Li83Pb, xnt; Xnt is calculated from Eq. (3-22), assuming the dilute nitrogen phase would obey Sieverts' law. 56 Fig. 3-9 Thermodynamic concentration limits of oxygen in 17Li83Pb, xot; X0t is calculated from Eq. (3-25), assuming the dilute oxygen phase would obey Sieverts' law. 57 Fig. 3-10 Thermodynamic concentration limits of carbon in liquid metals for membranes Zr, Nb, and V 58 Fig. 3-11 Thermodynamic concentration limits of nitrogen in liquid metals for membranes Zr, Nb, and V 59 Fig. 3-12 Thermodynamic concentration limits of oxygen in liquid metals for membranes Zr, Nb, and V 60 Fig. 3-13 Carbon concentration limits in Li for membranes Zr, Nb, and V; where XCt and Xck are carbon thermodynamic concentration limit and kinetic concentration limit, respectively; for any membrane, the upper concentration is the true limit. 65 Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. 3-14 3-15 3-16 3-17 3-18 53-19 3-20 5-1 5-2 5-3 6-5 6-6 Nitrogen concentration limits in Li for membranes Zr, Nb, and V; where Xnk and xnt are nitrogen kinetic and thermodynamic concentration limits, respectively; for any membrane, the upper concentration is the true limit. 66 Oxygen concentration limits in Li for membranes Zr, Nb, and V; where X0k and X0t are oxygen kinetic and thermodynamic concentration limits, respectively; for any membrane, the upper concentration is the true limit. 67 Carbon concentration limits in l7Li83Pb for membranes Zr, Nb, and V 68 Nitrogen concentration limits in 17L183Pb for membranes Zr, Nb, and V 69 Oxygen concentration limits in 17Li83Pb for membranes Zr, Nb, and V 70 Gettering time required for Lithium breeder fusion blanket at different window temperatures; window life time is 10 years and the initial impurity concentration is at 2 appm. 74 Gettering time required for l7Li83Pb breeder fusion blanket at different window temperatures; window life time is 10 years and the initial impurity concentration is at 2 appm. 75 Hydrogen permeation through a palladium-coated membrane; oxygen is not provided in the downstream. 90 Hydrogen permeation through a palladium-coated membrane; sweep gas containing oxygen flows over downstream. 91 P/J vs. J plot of hydrogen permeation through palladium membranes using data of Koffler et a1. 98 P/J vs. J plot of hydrogen permeation through palladium membranes using data of Bolovnev 101 P/J vs. J plot of hydrogen permeation through palladium membranes using data of Young 103 Deuterium permeation apparatus 109 Main vacuum chamber 110 D20 pressure in the mass spectrometer chamber against 020 amount in the cold trap; leak valve open 3.75 turns. 114 Deuterium permeation flux through palladium-coated zirconium membranes; where o: 423°C, 0: 363°C, D: 323°C. 118 Temperature dependence of deuterium permeability in zir- conium. e - 2.00x10-6exp(59/T)i20% g-mol DZ/m.s.Pa1/2° Dz-Zr the straight line, O - 2.97x10-8exp(1880/T) g-mol D2-Zr D2/m.s.Pa1/2, is obtained from the product of the geometric means for diffusivity and solubility data. 121 Sticking coefficients of hydrogen and deuterium on palladium surface; where o: HZ-Pd, o: D2-Pd. 124 xi Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. A1-1 A1-2 Al-3 A1-4 A2-1 A2-2 A2-3 A2-4 Diffusivities of carbon, nitrogen, and oxygen in structural metals 133 Diffusivities of carbon, nitrogen, and oxygen in Li and 17Li83Pb 136 Solubilities of carbon, nitrogen, and oxygen in structural metals 138 Solubilities of carbon, nitrogen, and oxygen in Li and 17L183Pb 142 Carbon concentration limits in a liquid lithium breeder- blanket contained by vanadium for different operation times; transport kinetics determines true limits. 155 Temperature dependence of the carbon concentration limit for 10 years operation of a liquid lithium breeder-balnket contained by vanadium; vanadium carbide will not form if initial concentration lies in the lower-right region. 156 Carbon concentration limits for 10 years operation of a liquid lithium breeder-blanket. For any structural metal, the upper concentration is the true limit. 157 Nitrogen concnentration limits for 10 years operation of a liquid lithium breeder-blanket. Thermodynamic limits for Mo and Cr are very high and are not plotted in the figure. For any structural metal, the upper concentration is the true limit. 158 CHAPTER 1: REVIEW OF POSSIBLE SEPARATION PROCESSES l-l. Int 0 u n Fusion reactors based on the deuterium-tritium fuel cycle will have to breed their own tritium to be cost effective because of the high price of tritium, about 20 M$/kg [1]. For a 1000 MWe fusion reactor, for example, the tritium required is 180 kg/yr; without its own tritium breeding system, the tritium cost would be 3.6 G$/yr, which is too expensive for competitive power generation. Liquid metals have been proposed as tritium breeding materials for commercial fusion power reactors. The advantages of liquid metal breeder-blankets are: possible high temperature operation (especially with vanadium alloy blankets), high breeding ratios, high cross sections for fast and slow neutrons, high fluidity and thermal conductivity [2]. Further, liquid metal use simplifies fusion reactor design because the same liquid metal can serve as the tritium breeder, the heat transfer fluid, and the tritium transfer fluid. For these reasons, the ANL "Blanket Comparison and Selection Study Final Report" [3] suggests liquid-metal-cooled reactor designs as the most attractive. The trade- offs with l7Li83Pb use are: alloys allow easier tritium extraction and have lower fire/explosion hazards. Pure lithium, however, has a higher breeding ratio, a lower density, a lower melting point, lower corrosiveness (by a factor of 10), and a lower tritium leakage rate. Also, Li-6 enrichment is unnecessary with lithium. Tritium is radioactive with a half-life of 12.26 years and is likely to permeate through containment materials. To contain the radiactivity at an acceptable level, 1000 ci/yr [4], the tritium concentration in the liquid metal needs to be extremely low, around 1 ppm (by weight) in lithium, and 1 ppb or less in 17Li83Pb. At these concentrations, tritium inventory in a lithium breeder-blanket is below a kilogram and is negligible in a l7Li83Pb blanket. For the forseeable future, safety remains the primary consideration for keeping low tritium concentrations in liquid metal. 1-2. e o o e ses Tritium bred in fusion power reactor blankets will have to be extracted from the breeding materials and refueled into the plasma chamber. Tritium extraction is crucial to a liquid-metal breeder blanket design. At concentrations in the ppm range or below, very few separation processes offer any promise for extracting tritium from lithium or l7Li83Pb. A number of workers have examined possible processes, and summaries have been presented by Buxbaum [5], by Watson [6], and by Johnson [7]. In this section a full range of separation processes will be reviewed. 1-2-1. Me a a a t ons Mechanical separations, e.g. filtration, are not applicable because tritium is dissolved in the liquid lithium and 17Li83Pb at the temperatures and concentrations of irterest. 1-2-2. 0 s at o a d o d t Fractional distillation and any vaporation process for separating tritium from liquid metals are not economical because required equipment sizes at all temperatures of interest (14000C or less) are prohibitively large. Buxbaum projected a distillation tower diameter of 77 meters is required for tritium separation from liquid lithium at 1000°C [8]. I Crystallization and cold trapping are not applicable since the tritium solubility in Li or 17Li83Pb is greater than 1 wppm at temperatures near the melting points of Li and l7Li83Pb [9], [10]. Natesan and Smith [11] reported that, by incorporating a separate liquid metal (NaK) loop with niobium as a permeable membrane, a tritium concentration 1 wppm can be reached by cold trapping the secondary metal at 30°C. Experimental studies are needed of tritium-NaK thermodynamics, and of precipitation and decomposition kinetics of tritide in the cold trap. 1-2-3. So ve ext action Liquid-liquid solvent extraction of tritium from lithium using molten salts was reported by Maroni et a1. [12]. A slip stream of lithium from the fusion blanket is contacted with molten salt. Tritium transfers to the salt and is removed by electrolysis. The recommended salt is 22LiF-31LiCl-47LiBr (by mole percent) [13], which melts at 445°C and has a tritium volumetric distribution coefficient of 3.5. The possibility of using this salt to extract tritium from l7Li83Pb is being studied in Argonne National Laboratory [14]. Although the tritium transfer characteristics are favorable, the low tritium concentration in lithium requires large solvent amounts, large contactors, and large electrode areas. It was estimated that, at a tritium breeding rate of 60 g/hr and a tritium recovery efficiency of 90%, the extractor capacity and the number of extractor would be about 23 mB/hr and 30, respectively [13]. Researchers at Los Alamos Scientific Laboratory have investigated tritium extraction using low melting point metal eutectics containing yttrium, lanthanium, or cerium, [15], [16]. These metal eutectics have higher tritium distribution coefficients than molten salts, but the prices are higher. Also, solvent contamination of the lithium may present problems. The cost for solvent extraction of tritium from lithium has been estimated at about 40 M$ [17]. 1-2-4. Solid absorption Absorption employing solid sorbents can be considered as a modification of the cold trap concept. In 1954 Salmon proposed that zirconium and titanium were good solid sorbents [18]. However, yttrium appears preferrable to these [19], [20], [21]. Buxbaum [19] showed that, a tritium recovery system using yttrium as the sorbent, requires at least three identical absorber vessels and a major expenditure in tritium holdup. The cost was estimated at about 30 M$ which is relatively inexpensive. The author is not aware of any data for tritium separation from liquid 17L183Pb. One uncertainty with solid absorption is the structural stability of yttrium on repeated thermal cycling; thus, sorbent operation life appears marginal [8]. 1-2-5. Waving). The tritium pressures over lithium at the low concentrations expected in fusion power reactors will be extremely low, thus the inert gas sparging rate required for tritium removal would be excessive. For example, a tritium pressure of 1.5x10.6 Pa in the lithium breeding fluid requires gas sparging rate of 1.4x108 m3/s to separate 0.5 kg tritium [6]. However, with liquid 17L183Pb, inert gas sparging may be an acceptable technology due to the low tritium solubility (high tritium pressure). It was estimated that a helium flow rate about 104 m3/s could purge tritium from l7L183Pb at 450°C and at tritium concentration of 0.5 wppb (part per billion, by weight); and with the addition of 10 Pa hydrogen into the purge gas, the gas flow would be reduced to about 100 m3/s [24]. The tritium recombination rate on the liquid metal surface is still unkown, however, and the total cost is estimated at 50 MS [17]. 1-2-6. V e n Vacuum degassing as a method of tritium separation from a liquid 17L183Pb breeding blanket was proposed by Badger, Flute, and Sze et al. [25], [26], [27], and by Tseng and Johnson [28]. Degassing tritium from droplet sprays, from thin films, and from a stirred pool were compared. It appears that degassing from a droplet spray is better because of the higher transport area. 1-2-7. Pe ea 0 throu h a metal membrane Tritium permeation through a metal window provides a very attractive option for tritium separation from lithium or l7Li83Pb because of low contamination, low cost, and continuous operation. Watson [6] evaluated the tritium recovery from fusion blanket lithium and suggested that an attractive window composition would be niobium-coated palladium. Buxbaum proposed that zirconium would be a better membrane material than niobium for tritium separation from lithium because of zirconium's higher permeability and lower price. Hsu and Buxbaum [2] present more detail about the principles of permeation window operation, and the choices for window design for tritium extraction from Li and 17Li83Pb. A typical permeation window resembles a series of shell & tube heat exchangers with a slipstream of Li or l7Li83Pb flowing through the window and an inert gas containing oxygen flowing past the palladium- coated downstream surface. Extremely low tritium pressures should be achieveable. Tritium diffuses through the window membrane and is oxidized and desorbed as T20. The tritium oxidation produces the very low downstream pressures that drive the flux. Fig. 1-1 shows the tritium permeation route. LiT dissoved in liquid Li ” or l7Li83Pb T Pd film I Y . O O. ] (X) 02 W Sweep gas containing Sweep gas containing 02 O2 and T20 Fig; 1-1 Tritium permeation route. 10 1-3. Com a ons 0 se aration rocesses Among all the separation processes discussed above, mechanical separations are not applicable in principle. Fractional distillation involves excessive process equipment sizes. Crystallization is not applicable because of low crystallization rates at temperatures above melting points of liquid metals. Cold trapping coupling with membrane permeation, solvent extraction, and solid absorption have their pros and cons in separating tritium from liquid lithium. Solid absorption may have significant advantages in terms of cost and contamination. Helium sparging and vacuum droplet degassing are possible methods for tritium separation from liquid 17Li83Pb, but the cost is high and experimental demonstrations are needed. Tritium permeation through a metal window provides a very good option for tritium separation from lithium and l7Li83Pb. This method is attractive because of low contamination, low cost, and continuous operation. Furthermore, it is more modular than other separation designs, containing few moving parts and requiring minimal operator attention. A modular system approach offers more flexibility in design and operation. 11 References [1] [2] [3] [4] [6] [7] [3] [9] [10] [11] [12] [13] [14] [15] [15] [17] [18] [19] R.C. Weast, ed., CRC Handbook of Chemistry and Physics (CRC Press, 63rd. edn., Boca Raton, Fla., 1982) p.B-20. C. Hsu and R.E. Buxbaum, J. Nucl. Mater. 141-143 (1986) 238. D.L. Smith, G.D. Morgan et al., Blanket Comparison and Selection Study Final Report, Argonne National Laboratory Report, ANL/FPP- 84-1 (September 1984). D. Steiner and A.P. Fraas, Nucl. Safety, 13 (1972) 353. R.E. Buxbaum, Sep. Sci. Technol. 18 (1983) 1251. J.S. Watson, An evaluation of the methods for recovering tritium from the blankets or coolant systems of fusion reactors, Oak Ridge National Laboratory Report, ORNL-TM-3794 (1972). E.F. Johnson, AIChE J. 23 (1977) 617. R.E. Buxbaum, The separation of tritium from the liquid lithium breeder-blanket of a fusion reactor; the use of yttrium as a getter, PhD Dissertation, Princeton University, 1981. P.F. Adams, M.G. Down, P. Hubberstey, and R.J. Pulham, J. Less- Common Met. 42 (1975) 325. R.E. Buxbaum, J. Less-Common Met. 97 (1984) 27. K. Natesan and D.L. Smith, Nucl. Technol. 22 (1974) 138. V.A. Maroni, R.D. Wolson, and G.E. Staahl, Nucl. Technol. 25 (1975) 83. W.F. Calaway, Nucl. Technol. 39 (1978) 63. Private communication with V.A. Maroni in April 1986. D.H.W. Carstens, J. Nucl. Mater. 73 (1978) 50. D.H.W. Carstens, J. Less-Common Met. 61 (1978) 253. P.A. Finn, Fusion Technol. 8 (1985) 904. O.N. Salmon, cited in letter from J.F. Flagg to L. Tonks (March 4, 1954). R.E. Buxbaum and E.F. Johnson, Nucl. Technol. 49 (1980) 307. [20] [21] [22] [23] [24] [25] [26] [27] [28] 12 S.D. Clinton and J.S. Watson, Proceeding of the 7th Symposium on Engineering Problem of Fusion Research, Vol. 2, IEEE pub. no. 77CH1267-4-NPS (1977) p. 1647. P. Hubberstey, P.F. Adams, and R.J. Pulham, Proceedings Intl. Conf. Radiation Effects and Tritium Technol. for Fusion Reactors Vol. 3, Gatinburg, TN (1976) p. 270. B. Badger et al., WITAMIR- A University of Wisconsin Tandem Mirror Reactor Design, UWFDM-400 (1980). D.K. Sze, Fusion Technol. 8 (1985) 887. P.A. Finn and D.K. Sze, Fusion Technol. 8 (1985) 693. G. Pierni, R. Baratti, A.M. Polcaro, P.F. Ricci, and A. Viola Fusion Technol. 8 (1985) 2121. R.E. Plute, E.M. Larsen, Nucl. Technol./Fusion, 4 (1983) 407. B. Badger et al., A tokamak reactor design study, UMFDM-330, University of Wiscosin (1979). H.H. Tseng and E.F. Johnson, The applicability of fan spray nozzels to stripping insoluble gases from viscous liquids, Plasma Physics Laboratory Report, PPPL-2026, Princeton University, (1983). CEAPTERZ: METAL WINDOW CONCEPT AND DESIGN l3 14 2-1. I uc on This chapter examines the economics and design characteristics of tritium extraction from liquid lithium and 17Li83Pb using permeable metal windows. This process is important because tritium control is a main problem with liquid-metal tritium breeders for nuclear fusion. Permeation metal windows can extract tritium from liquid breeders as an oxygen-containing sweep gas flows over palladium-coated downstream surface. Palladium is chosen because of its catalytic properties and high tritium permeability. The palladium coating technique, developed by Hsu and Buxbaum [1], is described in Chapter 4. Permeation membranes have successfully removed tritium from liquid sodium [2] and hydrogen from zirconium [3], and have pumped hydrogen at high vacuum [4]. 2-2. h ess The first window design problem is the palladium coating thickness. This is determined by the rate of palladium diffusion into the substrate. Also, palladium-substrate interdiffusion rates determine whether annealing is a feasible method for absorbing surface oxides and nitrides to activate the window surface. For palladium-coated zirconium windows, it is calculated that annealing at 500°C should be practical for removing impurities [5] since the diffusion coefficients for oxygen and nitrogen are much greater than those for intermetallic formation. Also, experimental evidence [3] suggests that relatively thick layers of Zrde have no appreciable effect on hydrogen permeability. These 15 contentions are strongly supported by the experimental results in Chapter 6. Using similar correlations to those in [5], we calculate the intermetallic diffusivities for palladium-niobium, palladium-vanadium, palladium-nickel, and palladium-stainless steel. The required palladium coating thicknesses for 30 years operation are predicted and listed in Table 2-1. From the data in Table 2-1, a 5.6 pm thick palladium coating on zirconium gives a safety factor of three times at 450°C. Interdiffusion rates appear manageable for all important window compositions; observations of niobium-platinum interdiffusion [6] suggest that these predictions are similar to observations. Still, uncertainty in these estimations is 500%. Careful interdiffusion rate measurements are needed before final choices are made on window design or operation temperatures. However, errors in the diffusion predictions may be managed by modest changes in the operation temperatures. Table 2-1 Intermetallic diffusivities and projected intermetallic thickness for Zr-Pd, Nb-Pd, V-Pd, and SS-Pd for 30 years operation Metal D, m2/s Thickness, m 400°C 450°C 500°C 550°C 600°C Zr-Pd 7.2x10'4exp(-5100/RT)* 1.5x10'° 5.6x10'° 1.3x10'5 4.9x10‘51.2x10'4 Nb-Pd 1.2x10'3exp(-67380/RT) 2.2x10‘8 1.3x10’7 5 7x10'7 2.0x10'67.0x10'° V-Pd 7.2x10'4exp(-63094/RT) 7.8x10'8 4.0x10'7 1.6x10'6 5.7x10'°1.7x10'5 Ni-Pd 6.2x10'5exp(-59757/RT) 8.5x10'8 4.0x10‘: 1.5x10'° 5.0x10'61.4x10'5 -7 - -5 5 -4 SS-Pd 7.2x10-4exp(-59327/RT) 9.2x10 4.3x10 1.6x10 5.3x10' 1.5x10 * where R equals 1.987 cal/g-atom.°K. 16 2-3. Tritism_ertreetienlflur For tritium extraction through a permeation membrane, the flux is calculated by equating the tritium diffusion flux in the liquid metal, the permeation flux through the membrane, and the reaction rate on the palladium. Detailed calculations follow: 2-3-1. Irigium diffusion flux in liquid metal Tritium diffusion flux in liquid metal is calculated by: J£ - k AC - k (CT - CT’up) , (2-1) D N k _ _I£E_§b , (2_2) .8 .33 NSh - .023 NR6 NSC (2-3) where J2 is the tritium diffusion flux in liquid metal, g-atoms/m2.s; k is the mass transfer coefficient, m/s; CT is the bulk concentration of tritium in liquid metal, g-atoms/m3; C is the tritium concentration T,up on the upstream surface of a permeation membrane; is the diffusion DT£ coefficient of tritium in liquid metal, m2/s; d is the effective 17 diameter for the flowing metal, m; NSh’ NRe’ and NSc are the Sherwood number, the Reynold number, and the Schmidt number, respectively. The relation between pressure and concentration of tritium in liquid metal can be expressed by the appropriate Sieverts' constant: _'1_ KS - 1/2 . (2-4) where K8 is Sieverts' constant, prm/Pal/z; and PT is the tritium 2 pressure in liquid metal, Pa. The Sieverts' constant for tritium in liquid lithium is approximately [7] KS - 3.71 exp(10104/RT) , (2-5) where R is the gas constant, 1.987 cal/g-atom.°K; and T is the 0 temperature, K. Buxbaum's [8] theoretical/experimental correlation of the Sieverts' constant of tritium in liquid lithium-lead l7Li83Pb is approximately: KS - 11.4 exp(-l2300/RT) . (2-6) Substituting Eq. (4) into Eq. (1), yields 18 1/2 1/2 J,Z - (1/3)k KS p, ( PT2 - 9T2 up ) _ 1/2 _ 1/2 _ < l/Rl ) < PT2 PT2,up ) . (2 7) The tritium atomic weight (3 g/g-atom) and liquid metal density p2 in g/cm3 are put in Eq. (2-7) to make the units consistent; PT up is the 2! tritium pressure on the upstream surface of permeation membrane, Pa. In the above, R1 equals 3/(kKsp2) and can be called the tritium transport Pal/z/g-atom; it is calculated from the . . . 2 re51stance in liquid metal, m .5. known operation temperature and liquid metal velocity. For instance, if T - 450°C, d - 0.0254 m and velocity is 3 m/s; then k - 7.90x10.7 m/s in lithium and 3.55x10-3 m/s in 17Li83Pb. For this case, R equals 15 and 1 4.6x104 m2.s.Pa1/2/g-atom in lithium and in 17L183Pb, respectively, tritium transport resistance in 17Li83Pb is much greater than in lithium because of the differences in KS. 2-3-2. Tr t um ermeatio ux the membrane Tritium permeation flux in the membrane is calculated by: (2-8) 19 where Jm is the tritium permeation flux in the membrane, g-atoms/m2.s; DTm is the tritium diffusion coefficient in the membrane, m2/s; CTm is the tritium concentration in the membrane, g-atoms/ms; and dCTm/dx is the tritium concentration gradient across the permeation membrane. The solubility of tritium in the membrane follows the relation. Tm ' 1/2 » (2-9) T2,m where S is the tritium solubility (i.e. Sieverts’ constant) in the membrane, g-atoms/m3.Pa1/2;and PT m is the tritium partial pressure in 2, the membrane, Pa. substituting Eq. (2-9) into Eq. (2-8) gives 1/2 1/2 1/2 dPT2,m PT2,up ' PT2,dn J - - D S '_——-———_' - D S m Tm Tm dX Tm Tm AX 1/2 1/2 PT2,up ' PT2,dn ' R . (2'10) 2 where P and P T2,up T dn are the pressures of tritium on the upstream and 2 ! the downstream membrane surfaces, respectively; and AX is the membrane thickness, m. The tritium transport resistance in the permeation 20 membrane, R2, equals AX/DS. Diffusion coefficients and solubilities of _tritium in the membranes are listed in Table 2-2. Table 2-2 Diffusion coefficients and solubilities of tritium in metals Metal Dr mils Sig-atom31m3,Pal/2 References Zr 2.7x10-8exp(-5940/RT)* 2.8x102exp(7l35/RT) [9], [101 Nb 2.9x10'8exp(-2444/RT) 1.3x10'1exp(11028/RT) [11] v 1.7x10'8exp(-994/RT) 1.4x10'1exp(6935/RT) [11] Ni DS - 1.5x10-7exp(-12916/RT) [11] ss 0s - 1.4x10'ngp(-15760/RT) [111 * where R equals 1.987 cal/g-atom.°K. 2-3-3. T t oxidatio rate on the alladium surface The tritium oxidation rate on the palladium surface can be calculated from Berkheimer & Buxbaum's model [12] of data from Engel & Kuipers [13] for hydrogen adsorption on a palladium surface Ad T + O P. (OT) T20 Ads Ads slow Ads fast (g) The rate constant for the slow step was reported as 10 K - 4x10- exp(-7000/RT) , (2-11) 21 where K is the rate constant, m2/atom.s. Thus, the reaction rate was approximately K C C __J.‘_._n_Q._ t - g d“ , (2-12) A where r is the reaction rate, g-mol TZO/m2.s; CT dn is the surface concentration of tritium on the palladium surface, atoms/m2; CO dn is the surface concentration of adsorbed oxygen on the palladium surface, atoms/m2, and NA is the Avogadro's number. For oxygen adsorption on palladium at 450°C, oxygen partial pressures in the range of 10 to 0.001 Pa are high enough that the palladium surface becomes saturated with oxygen atoms. In this pressure range, there are approximately 0.25 oxygen atoms per surface palladium atom (1018 oxygen atoms/m2). The maximum oxygen pressure here is picked as low enough that bulk palladium oxide will not form. The following equation holds for the fractional coverage of hydrogen on palladium [l2] -6 1/2 9 2.8x10 PTZ’dn exp(9947/RT) , (2-13) where 8 is the fractional coverage of tritium on the palladium surface, atoms tritium/atom of surface palladium. Combining Eqs. (2-11), (2-12), and (2-13) gives r - K C C - 7.4x10- P T,dn O,dn T dn exp(2947/RT) . (2-14) If r is in g-atoms tritium/m2.s, then Eq. (2-14) will be 1/2 T dn -5 1/2 2’ r - 2x7.4x10 PT dn exp(2947/RT) - R 2’ 3 P (2-15) The reaction resistance R3 is [l/(2x7.4x10'5)] exp(-2947/RT). Combining Eqs. (2-10) and (2-15) yields P1/2 T2,up Jm - r - R, + R: . (2-16) The flux is proportional to the square root of upstream pressure. 2-3-4. Tritium extraction flux The tritium extraction flux J is calculated by equating Jg, Jm, and 1/2 J - J1 - Jm - r - R1 + R2 + R3 (2-17) 23 or or J - Ks (R1 + R2 + R,) (2-18) Transport resistances R1, R2, and R3 are listed in Table 2-3 for operation at the conditions considered in section 2-3-1, and with a 0.0015 m thick membrane. Table 2-3 The resistance of tritium separation from the breeder fluid at 450°C and 0.0015 m thick membrane Resistance, m2,s,Pa1/2/g-atom Maggri§i_2§_mgmbrane Zr Nb V Ni SS R1 (in lithium) 15 15 15 15 15 (in l7Li83Pb) 4.6x104 4.6x104 4.6x10“ 4.6x104 4.6x104 32 87 1000 1.0x104 7.8xlo7 6.3x108 R3 866 866 866 866 866 For tritium extraction from liquid lithium breeder blankets, the transport resistance in the liquid , R1, is negligible. Tritium oxidation at the palladium surface limits transport for the most attractive lithium-based windows, Zr-Pd, but membrane diffusion limits transport for all the others. The liquid-phase transfer resistance, R1, limits the separation rate when lithium-lead alloy (l7Li83Pb) is used with windows of Zr-Pd, Nb-Pd, or V-Pd. The extraction flux at tritium concentrations of interest are calculated at 450°C and results are listed in Table 2-4. 24 Table 2-4 Flux, window size, helium content, and cost Table 2-4a. For tritium separation from lithium at 1 wppm, 450°C Material Flux Area Helium Fixed Tritium Overall g-atoms/m2.s m2 content capital holdup cost appm MS MS MS Zr-Pd 2.6x10‘7 7.5x103 230 8.0 4.8 12.8 Nb-Pd 1.2x10'7 1.6x10A 1.3 78.5 0.02 78.5 V-Pd 2.1x10.8 9.5x104 0.06 110 0.02 110 Ni-Pd 2.9x10'12 6.5xlo8 2x10'S 5.5x105 0.2 5.5x105 SS-Pd 3.6x10'13 5.5x109 10’5 3.4x106 1.5 3 4x106 Table 2-4b. For tritium separation from lithium at 5 wppm, 450°C Material Flux Area Helium Fixed Tritium Overall g-atoms/m2.s m2 content capital holdup cost appm MS MS MS Zr-Pd 1.3x10'6 1.5x103 1140 1.6 4.8 6.4 Nb-Pd 6.0x10'7 3.2x105 6.5 15.7 0.02 15.7 V-Pd 10le7 1.9x104 0.3 22 0.02 22 Ni-Pd 1.5x10’11 1.3x108 4x10‘4 1.1x105 0.2 1.1x10S SS-Pd 1.8x10'12 1.1x109 2xlo‘4 6.8x10S 1.5 6.8x10S Table 2-4c. For tritium separation from lithium-lead 17Li83Pb at 0.00026wppm, 450°C Material Flux Area Helium Fixed Tritium Overall g-atoms/m2.s m2 content capital holdup cost appm MS MS MS Zr-Pd 2.6x10'6 7.4x102 2125 0.9 4.8 5.7 Nb-Pd 2.5x10'° 7.7x102 11 4.9 0.02 4.9 V-Pd 2.1xlo'6 9.2x102 0.2 2.6 0.02 2.6 Ni-Pd 1.5x10'9 1.3x106 0.04 888 0.2 888 SS-Pd 1.9x10'lo 1.0x107 0.02 5364 1.5 5365.5 25 2-4. e ent The permeation window will contain fairly large amounts of tritium, some of which will decay to helium 3. The helium content is calculated as follows: 6CH§(t,X) - A C (x) + a D 8CH§(t,X) at T T He 8X ’ (2-19) where CHe(t,X) is the helium content, g—atoms/m3; AT is the tritium decay constant, 1.8x10'9 5-1; CT(X) is the steady state concentration of . . . 3 tritium in the membrane, g-atoms/m3; a is the surface area of 1 m membrane with thickness of 0.0015 m, (l/.0015) m2; DHe is the helium diffusion coefficient in the membrane metal, mz/s [14]; t is time, s; and aCHe(t,X)/6X is the helium concentration gradient across the membrane. Table 2-4 lists the helium contents after 30 years operation. Carpenter [15] observed void in zirconium following helium implantation to 10 appm. If zirconium is assumed to behave like niobium, strengthening will be expected at helium contents as high as 1675 appm [16]. From Table 2-4, we do not expect helium embrittlement of the membrane to be a problem with any of the window design recommendations in Section 2-6. 26 2-5. Dgsign cgnsiderations The main tritium flows are shown in Fig. 2-1. A slip-stream of blanket fluid flows past the permeation window. Flow rates of blanket fluid and sweep gas are adusted by control valves. T20 is recovered in a cold trap or in a molecular sieve bed, then eletrolyzed and fed in a tritium-deuterium isotopic separator. The concentrations of non-metallic elements such as carbon, nitrogen, and oxygen in liquid breeders must be kept below certain levels to prevent permeation barrier formation on the membrane surface which would affect the permeation window performance. A blanket fluid purification loop may be useful for this. Buxbaum [8] projects that oxygen levels in a liquid 17Li83Pb breeding blanket could be managed with a cold trap loop. Prevention of other surface compound formation may be achieved by a tailored start-up procedure described by Hsu and Buxbaum [17], and in more detail in Chapter 3 and Appendex 3. A typical permeation window for fusion reactor use might resemble a shell & tube heat exchanger with the tubes made of palladium-coated Zr, Nb, or V. Since the shell will have to be compatible with liquid breeders, the same structural metals for the fusion blanket could serve as the shell metals here [18]. Floating head design is probably advantageous to reduce stress resulting from thermal and concentration gradients. The design and construction of these exchangers (with zirconium tube at least) is a developed technology in the chemical industry [19]. 27' Ezmcousop azwxm: can“ taco .mzosm emanate came one Hum .mam 11' .111. 4 1:1V fl can E:__o= 4 . a. unau.uaq . . . Ecuuonc_ EDLCousoo ‘1 nsswudub “can «duo Amadeuuuoa lll'. cauouocoo Eouum . - _uoncuucou FL LTII # — )ovc~> fil com Boos—sod :9 aIDADaJ zo erodes: an L3 amou uauocooz ‘ \ concom so“) o>~o> acuucou h rm]. it 28 For use with a liquid breeder blanket, the palladium will probably be coated inside the tubes and the liquid metal will flow outside. The main reasons for this is decreasing window size by placing the larger transport resistance is on the side with the greater area. Similarly, the breeder material which flows through the outside shell should have reduced pressure drops and enhanced turbulent transport. 2-6. t st t oldu and ve a cost Window size is the most important factor in estimating the overall cost of a permeation window. In lieu of significant optimization, tubes of 0.0254 m diameter and 0.0015 wall are chosen, this is twice the ASTM standard for zirconium in low pressure operation. For tritium extraction from a 1000 MWe (3300 MWt) fusion reactor (167 g-atoms/day), the membrane surface areas are calculated as follows: A _ (167 g-atomslday) [(86400 s/day )( J, g-atoms/m2.s)] . (2-20) . . 2 . . where A, the membrane surface area of a permeation Window, m , is listed in Table 2-4. The overall cost of a permeation window includes fixed capital cost and tritium holdup cost. Since the permeation window resembles a shell & tubes heat exchanger, a first-approximation method is to use the charts and tables for heat exchanger cost estimation in "Plant Design and Economics for Chemical Engineers" by Peters and Timmerhaus [l9]. 29 Fixed capital cost should be the same as for heat exchangers with a factor of 1.7 added to correct these data for inflation since 1979. For example, the estimated shell & tube cost for a zirconium window designed for tritium extraction at 1 wppm in lithium is 5 MS, and the palladium cost is about 3 M$ (a factor of 2 is included here to cover the plating cost). Similar estimations can be made for Nb-Pd, V-Pd, Ni-Pd, and SS- Pd windows, the results are listed in Table 2-4. The tritium holdup cost, $2/curie (0.06 M$/g-atom tritium), contributes a major portion of overall cost for Zr-Pd windows because of the high tritium solubility in zirconium. The tritium holdup costs are calculated as follows C$ - B v C , (2-21) m Tm,ave where 1/2 1/2 P T2,dn T2,up + P C _ CTm.up I CIm,dn _ Tm,ave 2 . 2 (2-22) Here, G$ is the tritium holdup cost, M$; B is the tritium price, 0.06 M$/g-atom; Vm is the membrane volume, m3; and C is the average Tm,ave tritium concentration in the membrane, g-atoms/m3. Estimations of tritium holdup cost are listed in Table 2-4 along with overall cost; overall cost equals tritium holdup cost plus window fixed capital cost. 30 From Table 2-4 Zr-Pd is currently the cheapest window for tritium recovery from liquid lithium. An overall cost analysis shows that 1 wppm operation is preferable to 5 wppm for use in liquid lithium because the additional window costs are more than balanced by blanket tritium inventory savings. Helium embrittlement should not be a problem, except at very high tritium concentration (>5 wppm) and very high window lifetimes. For tritium recovery from liquid lithium-lead, l7Li83Pb, higher concentrations would be better economically, but the environmental (tritium leak) problem requires concentrations about 0.26 wppb [20]. As shown in Table 2-4, V-Pd windows have the lowest cost at this concentration, but Zr-Pd and Nb-Pd are also acceptable. 31 Rgigienges [1] [2] [3] [4] [5] [6] [7] [3] [9] [10] [11] [12] C. Hsu and R.E. Buxbaum, J. Electrochem. Soc. 132 (1985) 2419. E.F. Hill, Feasibility Study-"Removal of Tritium from Sodium during the MDEC Process by Oxidative Diffusion" research performed at Argonne West, DOE document N707Tl830035, DOE Contract P.O. 31-109-38-6163 (1982). A. Sawatzky and G.A. Ledoux in: Proc. 2nd International Congress on Hydrogen in Metals, Paris, France, June 1977. J.R. Young, Rev. Sci. Instrum. 34 (1963) 374. C.L. Stokes and R.E. Buxbaum, "Use of a Palladium Coating to Remove H-isotopes from Zirconium Fuel Rods in CANDU-PHW Reactors", presented at the Annual North Central Region Student Chapter Conference of AICHE, April 1984. J.H. Devan (ORNL), private conversion concerning unpublished interdiffusion observations, May 9, 1985. F.J. Smith, A.M. La Gamma de Bastistoni, G.M. Begun and F.J. Land, in: Proc. 9th Sysm. on Fusion Technology (Pergamon Press, Oxford, England, 1976) p. 325. R.E. Buxbaum, J. Less Comm. Met. 97 (1984) 27. J. Volkl and G. Alefeld, "Diffusion of Hydrogen in Metals", Topics in Applied Physics, Hydrogen in Metals I (Springer Verlag, New York, 1978) p. 321. E.A. Gulbransen and K.F. Andrew, Met. Trans. AIME (1955) 136. S.A. Steward, "Review of Hydrogen Isotope Permeability Through Materials", UCRL-5344l, Lawrence Livermore National Laboratory (1983). G.D. Berkheimer and R.E. Buxbaum, J. Vac. Sci. Technol. A3 (1985) 412. T. Engel and H. Kuipers, Surf. Sci. 90 (1979) 181. W.D. Wilson and C.L. Bisson, J. Nucl. Mater. 53 (1954) 154. G.J. Carpenter, Radiation Effect 19 (1973) 189. J.A. Donavan, R.J. Burger, and R.J. Arsennault, Met. Trans. AIME 12A (1981) 1917. [17] [13] [19] [20] 32 C. Hsu and R.E. Buxbaum, "Impurity concentration limits for containment compound formation in the liquid lithium tritium breeding blanket of a fusion reactor", submitted to J. Nucl. Mater, 1987. D.L. Smith and G.D. Morgan et al., Blanket comparison and selection study final report, Argonne National Laboratory Report, ANL/FPP-84-1 (September 1984). M.S. Peters and K.D. Timmerhaus, "Plant Design and Economics for Chemical Engineers", 3rd ed., McGraw Hill (1980) p. 632. D.K. Sze, "Tritium Recovery from Lin", liquid metal tritium process workshop, Argonne National Laboratory, February 1986. CHAPTER3: MASS TRANSFER OF CARBON, NITROGEN, AND OXYGEN IN A PERMEATION WINDOW 33 3-1. u on High concentrations of non-metallic elements in the liquid metal breeder fluid, e.g. carbon, nitrogen, and oxygen (hereafter called impurities), could adversely affect the performance of a permeation window, forming oxide, carbide, or nitride layers which would slow the tritium extraction flux. Therefore, the impurity concentration levels in the liquid breeders should be tightly controlled before putting a permeation window into operation. This chapter analyzes the thermodynamics and kinetics of impurity mass transfer between a liquid breeder and a membrane or wall, and suggests pretreatment steps as a possible solution. 3-2. Distribution coefficient Thermodynamics determines the direction of impurity mass transfer between a liquid breeder and a permeation membrane. The distribution coefficient is defined as (x )p/n K _ im (3-1) i X. ’ 1£ where K1 is the impurity distribution coefficient; Xim and X1 are 2 equilibrium impurity concentrations in the membrane and in the liquid breeder, respectively, appm; n and p are the numbers of impurity atoms in a molecule of impurity-membrane compound and impurity-liquid 35 compound, respectively. For instance, n is 1 for the solid compound ZrC and p is 2 for the liquid compound Li2C2. Thus, for carbon distribution between lithium and zirconium, p/n is 2. A condensed phase analog to Sieverts' behavior is expected, so carbon concentration in lithium at equilibrilium should be proportional to the square of concentration in zirconium. This definition for the distribution coefficient is the only source of differences between the results below and those of Smith and Natesan [1]. 3-3. Thermodynamics of impurity in liquid and membrane This section develops general thermodynamic equations for impurity distribution coefficients and the thermodynamic concentration limits in liquid breeders in contact with any structural or membrane metal so that no new nonmetallic phase appears. 3-3-1. Carbon The only stable compound formed by carbon in lithium is Li C 2 2 LI(2) + C(g) : 1/2 L12C2 ; a carbon phase would thus obey Sieverts’ law. Concentrations are predicted by balancing the chemical potentials 36 * o * -,uLi-RTlnaLi-pC -RTlnPC + l/2pL1202+ 1/2RTln7LiZCZ+ 1/2 RTlnXLiZCZ- 0 , (3-2) where p's are chemical potentials, cal/g-atom; 7Li C and XLi C are the 2 2 2 2 activity coefficient and concentration of Li2C2, respectively; T is the is the carbon pressure, atm; and a is the lithium o 0 temperature, K, P Li C activity, approximately 1. The standard state equation for the reaction of solid carbon with liquid lithium is * * * * AF1/2L12C2‘ 1/2 ”Lizcz' “Li'”c ' (3'3) where, s o * AFC - pC- ”C . (3-4) * Here p8 and pC are chemical potentials of gaseous and solid carbon, * respectively; AF1/2Li2C is the free energy of formation of l/2Li2C2 at 2 S the standard state, cal/g-atom C; and AFC is the free energy difference between solid carbon and gas carbon at 1 atm, cal/g-atom. Free energies of formation for carbides, nitrides, and oxides for several important fusion blanket and membrane materials are listed in Table 3-1. 37 Table 3-1 The free energies of formation for carbides, nitrides, and oxides of liquid metals and structural metals for membrane and for fusion blanket. Qeenound AF*. cellseeEee Ce N. 0 Eefereeeee... 1/2 L12C2 -7800 + 7.11 [1] ZrC -44100 + 2.21 [1] szc -46000 + 1.01 [1] v20 -35200 + 1.11 [1] TiC -43700 + 2.251 [1] M02C -1136O - 2.261 [2] l/6Cr2306 -12550 - 2.781 [3] Li3N -41110 + 33.61 [4] ZrN -87000 + 22.21 [1] Nb2N -65100 + 22.21 [1] VZN -31500 + 11.11 [3] TiN -80400 + 22.11 [1] MOZN -l6470 + 15.171 [1] Cr2N -29440 + 17.251 [3] Li20 -144350 + 32.81 [1] 1/2 21:02 ~130400 + 22.41 [1] NbO -100000 + 21.6T [3] v90 -127000 + 47.31 [1] PhD -52372 + 23.81 [5] TiO -129390 + 22.771 [3] 1/2 Moo2 -67200 + 19.01 [1] 1/3 Cr203 -90000 + 20.781 [3] 38 Combining Eqs. (3-3) and (3-4) gives * s * O * AF - AF - 1/2p - p - p . (3-5) l/2L1262 C Li2C2 C Li From Eq. (3-2), this becomes * s AFl/2Li2C2 - AFC - RTlnaLi+ RTlnPC-1/2RTln’yL12C2-l/2RTlnXL12C2 (3-6) The following is true [1], [6] because lithium and lithium carbide are largely immiscible, sat 7 - 1 . (3'7) L12C2 /XL12C2 Eq. (3-6) becomes * s 'ZAFl/ZLiZC + 2 AF C sat 2 2 2 . - a P exp , (3-8) XL12C2 XL12C2 Li C RT where XEItC is the saturation concentration of Li2C2 in lithium, which 2 2 is half of the carbon solubility in lithium, appm. The solubilities of carbon, nitrogen, and oxygen in Li, l7Li83Pb, and membrane metals are listed in Appendix 1. 39 Similarly, for the reaction of carbon with a membrane metal, when a separate carbide phase is in equilibrium with the membrane, “C(g) + mM(S) 2 Man(s) , then, to good approximation, a M(s) m n(s) * o * “Mmcn ' “”0 ' m“M lnPc - ' nRT . (3-9) where AF* * * * M C ' ”M C ’ n"C 'm“M (3°10) m n m n Combining Eqs. (3-4) and (3-10), gives * s * O * AFM C - nAFC - ”M C - an - mpM , (3-11) m n m n and substituting this into Eq. (3-9) yields * s l/nAFMan -AFC P - exp (3-12) RT 40 This is the carbon pressure at which a stable carbide forms on the membrane metal. Combining Eqs. (3-8) and (3-12), gives the equivalent carbon concentration in lithium at that temperature. * 'k 2 2/“AFM C ' 2AFl/2L12C2 X - 2 - 2( sat ) a exp m n ct XL1202 XL1262 Li RT * * 2AFl/nM C ' 2AF1/2Li C - xsat a2 exp 9 n 2 2 (3-13) c£ Li RT ' where xzjt and Xct are the carbon solubility in the lithium and the thermodynamic concentration limit of carbon in the lithium, respectively, appm. If the carbon concentration in a lithium breeder is maintained at a value greater than xct’ a stable carbide will eventually form on the membrane surface. Such films would be expected to slow the tritium permeation flux. Because the only stable carbon compound in liquid 17Li83Pb is Li2C2 [4], Eq. (3-13) is also applicable to the thermodynamic carbon concentration limits for membranes in contact with 17Li83Pb. Here, however, the lithium activity is estimated as [6] aLi - 1.1 exp(-7000/T) . (3-14) The distribution coefficient of carbon between liquid and membrane is derived by an approach similar to that of Smith and Natesan [1]. If carbon in membrane is below saturation, the following reaction 41 n0 Man (dissolved in M) (8) + 1“4(9) 2 leads, at equilibrium, to * o * sat "Man- an- mpM nlnPC+ lnXM C - lnXM C - RT . (3-15) m n m n Combining Eqs. (3-11) and (3-15) gives Fs AF* sat n HA C- MmC .. ————B - XM C xM C PC exP R1 ' (3 1°) The distribution coefficient of carbon, Kc, is then calculated from Eqs. (3-1), (3-8), and (3-16) * * (Xsat)2/n 2AF1/2Li C - ZAFl/nM C K _ cm 2 2 m n (3_17) c sat 2 exp RT ' xcfl aLi Note that this differs from the equations of Smith & Natesan [l] by the factor of p/n in the definition of Kc’ Eq. (3-1). An abbreviated derivation of Eq. (3-13) follows. Eq. (3-1) is rewritirn as (Xsat)2/n cm _ xct - -——7;:-——- . (3 18) 42 Combining Eqs. (3-17) and (3-18) gives * * 2AF - 2AF sat 2 1/anCn 1/2Li202 xct ' xci aLi ex? 5-* RT ' (3‘19) which is identical to Eq. (3-13). 3-3-2. Nitrogen The only stable compound for nitrogen dissolved in Li or l7Li83Pb is L13N l 2 N + 3 Li 4 Li N / 2 «— 3 The nitrogen distribution coefficient, Kn’ is obtained by the method in Section 3-3-1 sat 1/2 3 * an Xn£ PN2 aLi exp(-AFL13N/RT) , (3-20) and * * (xsat)1/n AFLi N - AFM N K nm exp 3 m (3_21) n Xsat 3 RT ’ n2 aLi 43 where Xsat and Xsat nm n2 are the nitrogen solubilities in the membrane, and in the liquid, respectively, appm. The thermodynamic concentration limit of nitrogen in the liquid is, to good approximation * * xnt - zit aii exp MmN Li3N . (3-22) 3-3-3. Oxygen For oxygen dissolved in Li or in 17Li83Pb, the stable compounds are Li20 and PbO. 2Li + 1/20 N- (8) 2(a) Li2°02) ' Pb(£) + 1/202(g) Z Pb0(£) The equilibrium concentration of oxygen in liquid breeder, X02, can be calculated by the method in Section 3-3-1 X _ Xsat l/2 [a2 * * 02 PO Li exp(- AFLiZO/RT) + an exp(-AFPbO/RT)] , (3-23) 02 2 where Xiit is the oxygen solubility in the liquid, appm; PO is oxygen 2 pressure, atm; and aLi and an are activities of Li and Pb in the liquid, respectively. In liquid lithium, aLi and an are l and 0, respectively. In liquid 17Li83Pb, a can be estimated by Eq. (3-14), Li and an can be estimated by [6] 1' 2x11 Pb ' 1- xLi ' a where XLi is the mole fraction of Li in 17Li83Pb, .17. As in Section 3-3-1, the oxygen distribution coefficient in the liquid, K0, is expressed as sat l/n - l * om ) exp[ nAFM 0 /RT K - 2 — m n — * o sat X02 [ aLiexp(- AFLiZO/RT> + an exp(- AFPbO/RT)] (X 9 (3'24) *- where xzjt is the oxygen solubility in the membrane, appm. The oxygen thermodynamic concentration limit can be estimated by AF* * AF* 1* l/nM 0 ' Li 0] [ l/nM 0 ' A PbO] m n 2 m n + an exp RT _ xsat a2 ex ot o! p (3-25) 45 3-4. u o coe cient o C N and O and n Li83Pb The coefficients for carbon, nitrogen, and oxygen distribution between Li and various metals, as calculated from Eqs. (3-17), (3-21), and (3-24), are all of the form Ki - A exp(B/T) , (3-26) where A and B are constants listed in Table 3-2 and T is in oK. The distribution coefficients between 17Li83Pb and structural metals are calculated using the C, N, and O solubilities in 17Li83Pb (calculated in Appendix 1). These are plotted in Figs. 3-1, 3-2, and 3- 3, respectively. These figures show very high distribution coefficients for carbon and nitrogen in most structural metals. The distribution coefficient for oxygen in most structural metals is below 1. Figs. 3-4, 3-5, and 3-6, for C, N, and 0 respectively, compare distribution coefficients of possible membrane materials Zr, Nb, and V, in Li and in l7Li83Pb. The distribution coefficients of C and N are higher in 17Li83Pb than in Li. In general, C and N will migrate to structural or membrane metals while 0 will migrate to breeder fluids. 46 Table 3-2 Distribution coefficients of C, N, and 0 between Li and structural metals K - A exp(B/T)* 1 System A B Sy§£em A B Li-C-Zr 7.50x1017 -l4940 Li-N-Ti 5.73x101 21410 Li-C-Nb 6.00x1011 6815 Li-N-Mo 2.7lx101 -l7506 Li-C-V 2.13x106 27580 Li-N-Cr 4.50x10A -17571 Li-C-Ti 1.46x108 22636 Li-O-Zr 4.00x10‘1 -2359 Li-C-Mo 1.39x1013 -33472 Li-O-Nb 1.08x102 -l9567 Li-C-Cr 1.24x1013 -19049 Li-O-V 3.74::10"4 -5255 Li-N-Zr 5.35x10O 27626 Li-O-Ti 2.09x102 -2867 Li-N-Nb 1.71x10'1 14872 Li-O-Mo 6.71x10O -48115 Li-N-V 2.45x103 -2880 Li-O-Cr 2.00x10'1 -22696 * 1 in °K. ln(Kc) $ 9 ii 10‘ -10. '50 r 1 l T l I B 1 12 IE L8 2 22 1.4 1000/T (1/K) Fig. 3-1 Carbon distribution coefficients between liquid 17Li83Pb and structural metals, Kc; Kc is calculated from Eq. (3-17). 110 -a- Zr + Nb 95- + V + In 80- -0— Mo -+— Cr [n(Kn) 1.4 1.5 1.8 2 2.2 1000/T (1/K) Fig. 3-2 Nitrogen distribution coefficients between liquid 17Li83Pb and structural metals, Kn; Kn is calculated from Eq. (3-21). 49 ln(Ko) ‘80 I I r I I I .8 I 1.2 1.6 1.8 2 2.2 1.4 1000/T (1/K) Fig. 3-3 Oxygen distribution coefficients between 17Li83Pb and structural metals, K0; K0 is calculated from Eq. (3-24). 50 90 -e— Zr-Lin + Nb-UPb 30. + V-Lin -+- Zr-Li 70‘ + Nb-Li —+— V-Li 60.. ’8 6 5‘" E 404 30. 20- 10- 0 l l T 1 T l .8 1 1.2 1.6 1.8 2 2.2 1.4 1000/T (1 /K) Fig. 3-4 Carbon distribution coefficients between liquid metals and membranes Zr, Nb, and V; where Lin is l7Li83Pb. "0 —a— Zr-LPb + Nb-Lin + V-Lin 90‘ + Zr-Li + Nb-U -+- V-Li 7o] '8 3‘, E 50‘ / 3o. 10‘ o4roe9r6fl4r’O’uorw4raa4y—ra4yrvwdo '10 I I I I I I .8 1 I 2 1.4 1.6 I 8 22 1000/T (1 /K) Fig. 3-5 Nitrogen distribution coefficients between liquid metals and membranes Zr, Nb, and V. 52 |n(Ko) -a— Zr-Lin + Nb-Lin + V-Lin + Zr-Li -e— Nb-Li -+— H] -204 -30+ '40 r I I I j I .8 1 1.2 1.5 1.8 2 2.2 1.4 1000/T (1/K) Fig. 3-6 Oxygen distribution coefficients between liquid metals and membranes Zr, Nb, and V. 53 3-5. e o ami once t atio im'ts of and i and 11141113122 The thermodynamic concentration limits of carbon, nitrogen, and oxygen in lithium, calculated from Eqs. (3-13), (3-22), and (3-25), can be expreesed in the form Xit - A exp(B/T) , (3-27) where A and B are constants; and T is in oK. Table 3-3 lists constants calculated for various systems. The thermodynamic concentration limits in l7Li83Pb can also be calculated and the results are plotted in Figs. 3-7, 3-8, and 3-9. These figures show that carbon and nitrogen have very low concentration limits for all the structural metals. For membrane materials Zr, Nb, and V, Figs. 3-10, 3-11, and 3-12 show the differences of concentration limits in Li and in l7Li83Pb for carbon, nitrogen, and oxygen, respectively. 54 Table 3-3 Thermodynamic constants in the non-metallic element concentration equation, Eq. (3-27), in liquid lithium below which compound do not form * A exp(BZT), in appm Cempound A B Compound A B NbO 1010 17640 Cr23C6 90 -8670 v90 4.28x108 4070 ZrC 13300 -40420 Moo2 280 34160 TiC 14000 -40020 Cr203 680 22690 Nb2N 67010 -16930 Zro2 1550 2360 v,N ' 250 -40 110 1860 2870 M02N 1950 7850 Nb2C 3990 -42340 Cer 5550 1020 v,C 4410 -31460 ZrN 67020 -27950 Mozc 90 -7470 TiN 63700 -24630 * T in OK. 55 +V +1": +Mo ln ts ' (-kbAb/Vb)(3600) . (3-37) where tg is the gettering time, hrs; X12 is the impurity controlling limit in the breeder liquid. Pretreatment differs from window operation in that much higher temperatures are used. Presumably these higher temperatures will forstall excessive impurity buildups at the structure-liquid interface. Eq. (AZ-l3) is used to check whether the impurity concentration in blanket metal surface is saturated with carbon or nitrogen O Zkbxifl t1/2 . (3-38) 1/2 g (Dimfl) Xim4>< N Xim(tg)|x-O XLi XL12C2 XM C III“ sat XM 0 mn N nk n2 sat n2 nm sat nm N XX XX nt ok 02 sat 02 0t NNNN Y(t) 77 carbon kinetic concentration limit in a breeder liquid, appm carbon concentration in a breeder liquid, appm carbon solubility in a liquid breeder, appm carbon concentration in a membrane, appm carbon solubility in a membrane, appm carbon thermodynamic concentration limit in a breeder liquid, appm initial impurity concentration in a fusion blanket, appm a impurity controlling limit in a breeder liquid, appm impurity concentration in a membrane, appm impurity solubility in a membrane, appm a impurity concentration in a blanket structural metal at liquid-structure surface after gettering, appm mloe fraction of lithium in the lithium-lead alloy L1202 concentration in a liquid breeder Man concentration in a membrane saturation concentration of Man in a membrane, l/n of carbon solubility in a membrane nitrogen kinetic concentration limit ina breeder liquid, appm nitrogen concentration in a liquid breeder, appm nitrogen solubility in a liquid breeder, appm nitrogen concentration in a mebrane, appm nitrogen solubility in a membrane, appm nitrogen thermodynamic concentration limit in a liquid breeder, appm oxygen kinetic concentration limit in a liquid breeder, appm oxygen concentration in a liquid breeder, appm oxygen solubility in a liquid breeder, appm oxygen thermodynamic concentration limit in a liquid breeder, appm a factor in Eqs. (3-28) and (3-29) G ek e er AF* free energy of formation, cal/g-atom p* chemical potential, cal/g-atom 1 activity coefficient p liquid breeder density, kg/m3 n liquid viscosity, kg/m.s Abbreviations Cr chromium Li lithium Lin l7Li83Pb, a lithium-lead alloy with and .83 mole fraction lead Mo molybdenum Nb niobium Ti titanium Zr zirconium 78 .17 mole fraction lithium 79 Re e en es [1] [2] [3] [4] [5] [5] [7] [8] D.L. Smith and K. Natesan, Nucl. Technol. 22 (1974) 392. L.L. Seigle, C.L. Chang, and T.P. Sharma, Metall. Trans. 10A (1979) 1223. M.W. Chase, J.L. Curnutt, H. Prophet, J.R. Downey, Jr., JANAF Thermochemical Tables, 1975 Supplement, J. Phys. Chem. Ref. Data 4, No. l (1975). M.W. Chase, J.L. Curnutt, J.R. Downey, Jr., R.A. McDonald, A.N. Syverud, and E.A. Valenzuela, JANAF Thermochemical Tables, 1982 Supplement, J. Phys. Chem. Ref. Data 11, No. 3 (1982). M.W. Chase, J.L. Curnutt, H. Prophet, R.A. McDonald, and A.N. Syverud, JANAF Thermochemical Tables, J. Phys. Chem. Ref. Data 3, No. 2 (1974). R.E. Buxbaum, J. Less-Common Met. 97 (1984) 27. D.L. Smith and G.D. Morgan et al., Blanket Comparison and Selection Study Final Report, Argonne National Report, ANL/FPP-84-l (1984). C. Hsu and R.E. Buxbaum, "Impurity concentration limits for containmene compound formation in the liquid lithium tritium breeding blanket of a fusion reactor", submitted to J. Nucl, Mater., 1987. m4: EXPERIHENTS OF PALLADIUM COATING 0N ZIRCONIUM 80 81 4-1. mm For extracting tritium from liquid lithium or l7Li83Pb, a palladium coating on the membrane catalyzes the oxidative reaction which causes the very low pressures that drive the flux. Chapter 2 suggests that Zr is the best membrane material for extracting tritium from the lithium, V and Nb are good membrane materials for extracting tritium from the 17Li83Pb. Therefore techniques for coating palladium on the membrane surface is important. Among the materials suggested, zirconium is perhaps the most difficult to coat an adherent palladium film because of its chemical reactivity. Currently the following metals can be plated on zirconium: Ni, Fe, Cu, Sn, Cr, and Ag. Schicker et al. [1], [2] described nickel and iron electrodeposition on zirconium following pretreatment by mechanical descaling, alkaline cleaning, and chemical etching. After electrodeposition, the sample was baked at 200°C to prevent blistering. Kohan [3] reported immersion plating of nickel, copper, and tin on zircaloy-2 using a pretreatment of vapor blasting, cathodic alkaline cleaning, and pickling. Thicknesses up to 7 pm were deposited by this method. Saubestre [4] studied nickel and copper electroplating on zirconium a cathodic pretreatment in a suitable electrolyte. Wax et al. [5] proposed the electroplating of copper, nickel, and chromium on zirconium using an activation solution of ammonium biflouride and sulfuric acid; and Donaghy [6], [7] holds two patents on processes for electroplating and electroless plating of these same metals. Recently Dini et al. [8] published electroplating nickel, silver, and chromium on 82 zirconium, and showed adhesion was improved by a postplating heat treatment at 700°C in constrained geometry or by mechanical treatments such as surface thread or knurling. At least two dozen formulations for palladium plating baths have been suggested or patented. But no technique has been published for either electroplating or nonelectrolytic plating palladium on zirconium. 4-2. Experiments The following two palladium bath formulations were selected for this study. First, the immersion plating solution that Johnson [9] used to plate palladium on copper, brass, beryllium-copper, phosphor-bronze, and nickel-silver was used. The composition was PdCl 5 g/l; HCl 2! (38%), 200 ml/l. The temperature was 25°C. Second, the electroless palladium bath solution of Pearlstein and Weightman [10] was used. The composition was PdClz, 2 g/l; HCl (38%), hml/l; NHAOH (28%), 160 ml/l; NaH2P02.H20, 10 g/l. The temperature and the pH value were 50°C and 9.8, respectively. The surface pretreatment was as follows. 1. The sample, zirconium disk with surface area 10 cm2 was machined from a zirconium bar of purity of 99.8%. 2. Surface grinding and polishing were used to removed some surface scale and oxide. 83 3. Detergent washing and solvent cleaning with trichloroethylene were used to remove surface oil and grease. 4. The sample was given a cathodic alkaline cleaning. (Composition: NaOH, 35 g/l; Na3P04, 10 g/l. pH value: 12. Temperature: 90°C. Time: 3 min. Cathodic current density: 0.1 A/cmz. Voltage: 4 V). 5. The sample was given a water rinse. 6. The sample was given an "acid pickling" [11]. (Composition: HNO3 70%, 10 parts; HF 49%, 1 part; H20, 10 parts. Temperature: 25°C. Time: 0.5 min). 7. Another water rinse was given. 8. The sample was given an activation etching. (Composition: NH4HF2’ 15 g/l; H2804, 1 g/l. Temperature: 25°C. Time: 1, 2, 3, 6 or 10 min). 9. A final water rinse was given. 10. Then, the palladium plating was applied. Immersion plating was tried with and without activation etching step in the surface pretreatment. 4-3. Immersion plating results Because the positive potential of zirconium is higher than that of palladium, the palladium ions can theoretically replace atoms of the zirconium substrate in solution by immersion plating. For this process, zirconium atoms must be simultaneously oxidized and dissolved as ions into the solution while palladium ions in solution deposit onto the zirconium substrate. It is found, however, that immersion plating (using a PdClz-HCl solution) does not coat the zirconium surface. Without the activation etching prior to immersion plating, a possible explanation is that an oxide film stopped the replacement reaction. Zirconium, being a reactive metal, quickly forms a stable film of surface oxide when the pickled surface is exposed to air or water. Although the thickness of surface oxide is less 0.0025 pm [12], it may be thick enough to stop atomic replacement. With the activation etching in the surface pretreatment, a thin film of zirconium hydride was formed on the surface and there was still no replacement reaction. 4-4. Electroless plating results The surface was activated for electroless plating of palladium on zirconium by forming an adherent, electrically conducting film of black zirconium hydride using a solution containing 15 g/l NHAHF2 and 1 g/l H 304. Zirconium Hydride provides an improved surface for palladium 2 deposition because it, like palladium, is a face-centered cubic structure [13]. Activation etching times of 1, 2, 3, 6, and 10 minutes 0 . . . were tested at 25 C, and it was found that at least 3 minutes is necessary to form an adherent palladium deposit. About 9 pm of zirconium was etched off after 3 minutes of activation at 25°C. Adhesion was determined by scratching through the coating with a sharp blade; the surface showed no lifting or peeling when viewed under a microscrope. Adhesion was also evaluated by a heat-quenching test 85 [14]: the sample was heated in a vacuum oven to 200°C at a rate of 30°C/hr, and was then immersed in room temperature water. No flaking, peeling, or blistering was observed. An adherent palladium coating 5 pm thick was achieved after 3 hour plating at 50°C. 86 W [1] [2] [3] l4] [5] [6] [7] [3] [9] [10] [11] [12] [13] [14] W.C. Schickner, J.G. Beach, and C.L. Faust, J. Electrochem. Soc. 100 (1953) 289. W.C. Schickner, J.G. Beach, and C.L. Faust, Met. Finish. 52 (1954) 57. L.R. Kohan, Met. Finish. 57 (1959) 68. E.B. Saubestre, J. Eletrochem. Soc. 106 (1959) 305. D.E. Wax and R.L. Cowan, U.S. Patent 40,017,368, April 12,1977. R.E. Donaghy, U.S. Patent 4,093,756. June 6, 1978. R.E. Donaghy, U.S. Patent 4,137,131, January 30,1979. J.W. Dini, H.R. Johnson, and A. Jones, J. Less-Common Met. 79 (1981) 261. R.W. Johnson, J. Electrochem. Soc. 108 (1961) 632. F. Pearlstein and R.F. Weightman, Plating 56 (1969) 1151. Metal Finishing Guidebook Directory, (Metals and Plastics Publications, Hackensack, New Jersey, 1984) p. 168. T.L. Barr, J. Vac. Sci. Technol. 14 (1977) 660. J. Fitzwilliam, A. Kaufmann, and C. Squire, J. Chem. Phys. 9 (1941) 678. Standard Test Methods for Adhesion of Metallic coatings, ASTM B 571-79, American Society for Testing and Materials, Philadelphia (1984). CHAPTERS: PERMEATION MODEL USED TO ANALYZE EXPERIMENTAL DATA 87 5-1. Surface oxides and hydrogen sticking coefficients The hydrogen sticking coefficient on a pure zirconium surface (without oxide) is very low, causing a very high surface resistance for hydrogen permeation through a zirconium membrane. Lin and Gilbert [1] reported that hydrogen sticking on zirconium is in the order of 10.4 at 500°C. The hydrogen sticking coefficient on a palladium surface is much higher. Berkheimer and Baxbaum [2] reported hydrogen sticking coefficients on palladium surface are about .01 at 500°C. Thus, the hydrogen permeability is easier to measure in palladium than in zirconium. Hydrogen permeability data are listed in Appendix 3. Zirconium oxides form easily on a clean zirconium surface [3]. Palladium is more oxidation-resistant than zirconium. The maximum oxygen pressure to avoid the surface oxide formation on palladium can be calculated from the data given in Ref. [4] 3 ln P - -18843/T + 6.681nT - 6.39x10’ T - 17.07 - 4.72x104/T2 I (5.1) where P is the oxygen pressure, atm; T in OK. Table 5-1 lists the maximum oxygen pressures at which palladium oxides are not formed. 89 Table 5-1 Formation pressure of palladium oxide Temperature, 0C P atm Temperature, 0C P 02, 02, atm 250 4.39x10'7 450 2.09x10'2 300 1.33x10'5 500 1.27x10'1 350 2.30x10'“ 550 6.10x10'1 400 2.61x10'3 600 2.44x100 5-2. Hydrogen permeation through membranesaat low presaurea This section describes an analysis technique to obtain hydrogen permeabilities through palladium membranes or palladium-coated membranes at low upstream pressures. Figs. 5-1 and 5-2 show hydrogen permeation through palladium-coated membranes without and with oxygen provided in the downstream, respectively. Upstream hydrogen molecules strike the palladium surface, some of them diffuse through the membrane, and then desorb as hydrogen molecules or water, depending if oxygen is provided in the downstream. 90 Upstream hydrogen .0 H2 \ \% \T'f": Pd film W // we» Downstream hydrogen Fig. 5-1 Hydrogen permeation through a palladium- coated membrane; oxygen is not provided in the downstream. 91 Upstream hydrogen 0..., \\‘—YT Pd film H%X\Y:\\ Pd film + ‘— Sweep gas containing 02 Sweep gas containing 02 and H20 Fig. 5-2 Hydrogen permeation through a palladium-coated membrane; sweep gas containing oxygen flows over downstream. 92 5-2-1. W u x v ded the do st eam If oxygen is not provided in the downstream, the hydrogen flow flux can be expressed by [2], [5] J - aup(Pb.up' Pa.up) (5-2) 1/2 (2”MRTb,up ) 1/2 - 1/2 Q $11.11) P§.dn) (5 3) - AX - adn(P§.dn' Pb.dn) 5 4 - 1/2 9 ( - ) (ZWMRTb’dn) 2 . where J is the hydrogen flow flux, g-mol H2/m .5, cup and adn are hydrogen sticking coefficients on the upstream and the downstream palladium, respectively; Pb up and Pb dn are hydrogen bulk gas pressures in the upstream and in the downstream, respectively, Pa; PS u and Ps ,dn are hydrogen pressures on the upstream and downstream surfaces, respectively, Pa; M is the hydrogen molecular weight, kg/g-mol; R is the o . . gas constant, 8.314 J/g—mol. K, Tb,up and Tb,dn are gas temperatures in the upstream bulk phase and the downstream bulk phase, respectively, oK; 93 e is the hydrogen permeability of the membrane, g-mol Hz/m.s.Pa1/2; and AX is the membrane thickness, m. Rewriting Eqs. (5-2), (5-3), and (5-4) in terms of hydrogen transport resistances gives Pb u - Ps u J - R (5-5) 1 P1/2 P1/2 .up - s.dn - —§ R - (5-6) 2 P - P _ s,an b,dn , (5_7) 3 where R1 is the hydrogen transport resistance from the upstream gas phase surface to the upstream surface, Pa.s.m2/g-mol H2 1/2 (2rMRT ) R _ a b.up . ; (5-8) up l/2 R2 is the hydrogen trnsport resistance in the membrane, Pa .s.m2/g-mol R = . (5-9) 94 and R3 is the hydrogen transport resistance from the downstream surface to the downstream gas phase, Pa.s.m2/g-mol H2 1/2 (ZWMRTb.dn) R - . (5-10) 3 adn Eqs. (5-8) and (5-10) show that Rl equals R3 if Tb,dn equals Tb,up and if adn equals aup' Combining Eqs. (5-5), (5-6), and (5-7) to remove surface pressures yields 1/2 1/2 (P - R J) - (P + R J) R2 This is an useful expression for hydrogen permeation through a membrane. If the transport process is diffusion-controlled, the surface effect is negligible and Eq. (5-11) becomes the standard (Sieverts') permeation equation P1/2 _ P1/2 J - b.upR b.dn ’ (5-12) 2 which applies to cases of high sticking coefficient, low hydrogen permeability, or thick membranes. 95 5-2-2. With oxygen provided in the downstream If oxygen is provided in the downstream, then the hydrogen is oxidized and desorbed as water, the steady state flux is expressed similarly to Eqs. (5—5) to (5-7): Pb up ' Ps,up J - ‘ R (5-5) 1 P1/2 _ P1/(21 .. AME—H (5'6) 2 Fifi. - R , (5'13) 3 where R3 is hydrogen oxidation resistance on the palladium, Pal/2.8.m2/g-mol H2 (Chapter 2). Combining Eqs. (5-6) and (5-13) gives P1/2 _ S u - J §;;*§:- . (5 14) Combining Eqs. (5-5) and (5-14), we obtain the following expression for hydrogen permeation through a membrane with oxidation on the downstream surface 96 1/2 > R1 and R3, so that Eq. (5-15) becomes 1/2 Pb u J - —-—P— . (5-16) R2 Rewriting Eq. (5-15) gives: P _Lim _ 2 _ J R1+ (R2+R3) J . (5 17) From Eq. (5-17), a plot of experimental Pb up/J vs. J at constant temperature should be a straight line, where R1 and (R2+R3) can be determined from the slope and the intercept. Sticking coefficients and hydrogen permeabilities of the membrane can then be estimated using Eqs. (5-8) and (5-9), respectively. This analysis technique assumes that sticking coefficeints is independent of pressure, which is true for hydrogen-Pd below 0.1 Pa [3]. To obtain permeabilities and sticking coefficients by this method, two measureable factors are required: hydrogen upstream bulk pressure and flow flux through the membrane. The data analysis technique may also apply to other gas-metal systems, providing that gas is dissociated adsorption on metal surfaces. 97 5-3. Validipy of tha tephnigue Hydrogen permeation data in palladium obtained by Koffler et al. [5], by Balovnev [6], and by Young [7] are used to check if the above is useful for analyzing permeabilities and sticking coefficients. 5-3-1. Data_by Koffler et al. Koffler et al. [6] measured hydrogen permeation through a 5.08x10'4 m thick palladium membrane at temperatures between 23 and 436°C, and pressures between 3.9x10.3 and 6.7x10-1 Pa. When we plot Pb up/J vs. J at 208°C, Fig. 5-3, it shows a slope of 1.3 and an intercept of 1.0, the values of (R2 + R3) and R1 are thus R2+ R3 - (slope)1/2- (1.3x10“/10‘6)1/2 - 1.14x105 Pal/2.3.m2/g-mol H2 and R - 1.0xlO4 Pa.s.m2/g—mol H l 2 This experiment appears significantly diffusion-controlled, R < cows so um» co Imuwcch H a H a . II >~r> Fl o>am> . J . —F J Im.oeotuuomMI tobacco A popsmzo mmme Eaaua> .umam mam: > Esauw> can: a can» use a v uuomaxdm A fimfioocuzg I ---I-I-uls < a 4. cod» " > :aoEuaa . unfit . . o>H > odaEam . - A .111 _ _ uuHHouusou _ . h ouaumuooaoh filJr . aoumhm gene .11 r N a l afina mcwgm30c ou lawl Manson «sauna; ecu xaaaam Coaoa u mean > cowunuom Op 4 nonzero < > IL swam u~a30005tszh ouauxHa cowzxo .comu< nor mlemU 110 Main Vacuum Chamber Heat'——“-~.~ Shield Window Disc -_—\\\\\\N LIL Thermocouple 12H “ILJ‘ A; ‘ l 1 Fig. 6-2 Main vacuum chamber. 111 The main vacuum chamber and deuterium chamber were two four way crosses of 4 inch and 1.5 inch pipes, respectively. The vacuum chamber of the quadruple mass spectrometer was a 1.5 inch 6 way cross, all made by Varian. Sorption pumps were used for roughing the pressure to below 10"2 torr. Varian and Perkin-Elmer 20 l/s ion pumps pumped the system down to 10.9 torr. The combination of sorption pumps and ion pumps reduced contamination of chambers. The valves connecting the ion pumps and vacuum chambers were 1.5 inch bakeable all-metal valves with 2.75 inch conflat flanges. Deuterium gas from a D2 cyclinder passed through a palladium-thimble purifier into the deuterium chamber. A leak valve between the deuterium chamber and the main vacuum chamber was used to regulate the deuterium input. A quadruple mass spectrometer (Balzers QMG 064) was connected to the main vacuum chamber to monitor the total pressures and partial pressures and to analyze the amount of D20 which was collected in the sample collection system. A Varian leak valve between the sample collection system and the vacuum chamber of mass spectrometer was used to analyze the sample collection system. A dual- conductor feedthrough made by Huntington was welded to the deuterium permeation window. A dc-power supply (Sorensen DCR-B) conducted adjustable currents to the permeation window, heating it resistively. A thermocouple and temperature controller (Omega D921) was used to control the temperatures during permeation measurements. A gas mixture of argon and oxygen passed over the downstream surface of a membrane, sweeping away the D20 (which desorbed from the membrane surface) and brought it 112 to a D O collection system. Fig. 6-2 shows a detail of the permeation 2 window in the main vacuum chamber. The palladium-coated zirconium membrane (0.02 m in diameter and, .002 m thick with a 2 pm palladium coating on both sides) was connected to a window holder by conflat flanges. A stainless steel heat shield plate welded to conflat flange encircled the permeation window to reduce the high-temperature radiation heat loss. The vacuum chambers and sample collection system were wrapped in heating tapes to bake out the system. A cold trap was used to collect D20 sample during the permeation process. 113 6-3. Calibration of the D20 collection system A variable leak valve (Varian 951-5106) was used to adjust the gas flow into the mass spectrometer vacuum chamber from the sample collection system. To calibrate the D20 collection system, a known amount of D20 was injected into the cold trap at dry ice temperature, then the D20 collection system was pumped down to 0.2 torr to reduce the background pressure. The cold trap was then warmed to 60°C by immersing it into a hot oil bath, the temperatures of the connecting tubes between the cold trap and the leak valve were also maintained above 60°C by regulating heating tapes to avoid condensation of D20 vapor. After a steady state pressure in the sample collection system was reached and recorded, the leak valve was opened and the D20 pressure in the mass spectrometer was measured. A plot of D20 pressures vs. D20 amount in the cold trap is shown in Fig. 6-3. 114 6 I l I I 3 § ‘1’ 4" d o H O N c Q III-I O Q) S .. m 2 In 0) H OI I—I .- (U '04 4.1 H (U 0.; o - I ' ' 0 10 20 30 Volume of 020 (ALL) Fig. 6-3 D20 pressure in the mass spectrometer chamber against 020 amount in the cold trap; leak valve open 3.75 turns. 115 6-4. W The experimental procedure was as follows. 1. The vacuum system (including deuterium chamber, mass spectrometer vacuum chamber, and main vacuum chamber) were pumped to 5x10"3 torr using sorption pumps. 2. The ion pumps were turned on after the system pressure reached -3 5x10 torr. 3. The vacuum system was baked out at 200°C for 48 hours. The system pressure reached 10'9 torr after about 50 hours. This was the system background pressure. 4. The palladium coating was activated by annealing the permeation window at 350°C for 10 hours at background pressure (please see Table 5- 1), the D20 collection system was pumped periodically and sweep gas flowed over the downstream membrane to complete the activation. 5. The temperature controller was set at desired temperatures. 6. The deuterium pressure in the main vacuum chamber was controlled by regulating the leak valve. The sweep gas flowed over the permeation window at the desired rate. A soap bubble flowmeter and a Matheson flowmeter were used to monitor the sweep gas flow rate. 7. 020 sample was collected during the permeation process. 8. At the end of permeation process, the amount of D O in the sample 2 collection system was analyzed. 116 6-5. Sample dascripriona and experiment conditions Palladium was coated on both sides of a zirconium membrane, 0.002 m thick and .02 m in diameter, by applying the electroless plating technique in Chapter 4. The sample was tightly sealed between mini- conflat flanges which were welded to inconel tubes. A leak detector was used to test if the sample assembly was leak-proof. The experiments 2 2 3 were performed at pressures of 2.67x10- , 1.33x10- , 2.67x10- , and 6.67x10’“ Pa, and at temperatures of 323, 363, and 423°C. A stainless steel disc replaced the palladium-coated membrane as a blank test of the eqiupment operation. The blank test produced D20 pressures of 6.3x10.8 mbar after 50 hours at 2.67x10m2 Pa, indicating negligible O2 permeation during the blank test. Nonetheless, this permeation was substracted from all subsequent data. 6-6. Results The amounts of D20 collected and the deuterium permeation flux are shown in Table 6-1. The plot of P /J vs. J D2 D2 D2 is shown in Fig. 6-4. 117 Table 6-1 Permeation flux of deuterium through a palladium-coated zirconium PD2, Permeation flux, JDZ, PD2/JD2 Pa g-mol DZ/s.m2 Pa.s.m2/g-mol D2 323°C 363°C 423°C 323°C 363°C 423°C 2.67xlo'2 5.3xlo’S 46le5 4.3x10'5 5.0x102 5.8x102 6.2x102 1.33x10'2 3.4x10'S 3.0x10'5 2.7x10‘5 3.9x102 4.4x102 4.9x102 2.67:.10"3 1.23.10"5 9.9x10'6 9.0x10‘6 2.2x102 2.7x102 3.0x102 6.67x10'“ 3r8x10'6 2.8xlo‘6 2.5xlo‘° 1.8x102 2.4xlo2 2.7x102 , LIP—“Wm, 118 3 I 1 I l r - 1 d AN o H o E I .. o \ N E m w - a. N O H N - n '1 \ N O m C 0 n I 1 I l 0 20 40 60 JD2 (10.6 g-mol D2/m2.s) Fig. 6-4 Deuterium permeation flux through palladium-coated zirconium membranes; where 0: 423°C, 0: 363°C,D: 323°C. 119 6-6-1. Deute um e eabil t 1 con um From the method in Chapter 5, the deuterium permeability in zirconium and deuterium sticking coefficient on palladium are as follows. From Eq. (5-9) R — + ________ Pal/2.3.m2/g-mol D2 , where AXPd - palladium film thickness, 4x10.6 m (both sides), and AXZr - zirconium thickness, 2x10.3 m. The deuterium permeability in palladium, QD ~Pd’ is estimated from 2 hydrogen permeability in palladium (Appendix 3) l ___ -7 @Dz-Pd - 2.2x!2 x10 exp(-1885/T) g-mol Dz/m.s.Pa 1/2 The downstream reaction resistance, R3, is calculated from Chapter 2, R - 1.35x104 exp(-l483/T) m2.s.Pal/2/g-mol D 3 2 The slope of P /J vs. J plot should yield R , deuterium D2 D2 D2 2 permeability in zirconium can then be calculated, listed in Table 6-2, 120 and plotted in Fig. 6-5 along with the values from deuterium diffusivity and solubility in zirconium (Appendix 3). The measured permeabilities are slightly higher than the values obtained from product of geometric- mean diffusivity and geometric-mean solubility of deuterium in zirconium. As expected, they also show that permeabilities are not strongly temperature-dependent. Table 6-2 Deuterium permeabilities in zirconium Temperature, From solubility & diffusivity Experimental results oC g-mol DZ/m.s.Pa1/2 g-mol D2/m.s.Pa1/2 323 .96x10'° 2.41x10'° 363 .79xlo'6 1.87x10'6 423 .62x10'6 2.33mlo'° A least square fitting to our experimental results suggests that the permeability of deuterium in a zirconium is CD -Zr - 2.00x10'6exp(59/1) 120% g-mol/m,s.Pa1/2 2 121 10" I ' ' NA \ H m m m -5 __ ‘- E 10 \ N G H 8 I 1. Cl 3‘ 0 >1 Si -5 '- ~I 10 '- -a .o m m E H m m - I ’ I ' 10 7 104 1.5 1.6 1'7 1000/T (1/K) Fig. 6-5 Temperature dependence of deuterium permeability in zirconium. 4D _Zr a 2.00x10'6exp(59/T):20% g-mol D2/m.s.Pa1/2° 2 I the straight line, OD -Zr = 2.97xlO-8exp(1880/T) g-mol D2/m.s.Pa 2 is obtained from the product of the geometric means for diffusivity and solubility data. 1/2 122 6-6-2. The sticking poefficient of deuterium on palladium Sticking coefficients for deuterium on palladium are estimated from the intercept of the PD /JD vs. JD plot and Eq. (5—8) 2 2 2 1/2 (2rMRTb,up) . 2 intercept - R1 - “up Pa.s.m /g-mol D2 where Tb up is the upstream gas temperature, 3000K; M is the deuterium molecular weight, 0.004 kg/g-mole; R is the gas constant, 8.314 J/g- mol.K. The sticking coefficient, aup’ is listed in Table 6-3, and plotted in Fig. 6-6 along with hydrogen sticking coefficient on palladium. The deuterium sticking coefficient on palladium is of the order of 10'2. While the sticking coefficient of gas on a metal surface is a complex function of temperature, surface coverage, and geometric effects, these measurements are similar to those measured previously [2], [3], [4]. In all, the data obtained are not unreasonable, suggesting favorably the applicability of permeation windows for fusion reactors and the cost estimations in Chapter 2. Table 6-3 Sticking coefficient 123 Temperarure. oC Sticking coefficient * HZ-Pd Dz-Pd 208 5.5x10-4 ..... 323 ----- 5.4x10 363 ----- 3.9x10 380 6.5xlo'2 ..... 423 ----- 3.34x10 600 5.3x10'3 ------ * values from Chapter 5. Sticking coefficient 124 C 600 500 400 300 200 10'1 I I I I I O C . C 10'2 - ‘ O 10’3 - - O 10'4 . l ‘ ' ‘ 1.1 1.5 1.9 2.3 1000/T (l/K) Fig. 6-6 Sticking coefficients of hydrogen and palladium surface; where o: H2-Pd, o: Dz-Pd. deuterium on 125 References [1]- [2] [3] [4] A.A. Gokhale and D.L. Johnson, in Proc. 2nd Intl Conf. on Environmental Degration of Engineering Materials, VPI, Blacksburg, VA (1981) p. 113. G.D. Berkheimer and R.E. Buxbaum, J. Vac. Sci. Technol. A3 (1985) 412. G.A. Somorjai, Chemistry in two dimensions: surfaces, Conell University Press, Ithaca, New York, 1981. M.W. Roberts and C.S. Mckee, Chemistry of the metal-gas interface, Oxford University Press, Oxford, 1978. CHAPTER7: SUMMARY OF CONCLUSIONS AND SUGGESTIONS FOR FUTURE RESEARCH 126 127 7-1. S ar of cone usio 3 Cha ter 1. Liquid lithium and liquid lithium-lead alloy, l7Li83Pb are the most promising liquid tritium breeders for fusion reactors. Successfulness of separating tritium from liquid breeders is a key factor deciding the possibility of commercializing fusion reactors. Palladium-coated metal membrane provides an excellent option for tritium extraction from liquid breeders. 2. Oxidative diffusion through a palladium-coated membrane can extract tritium economicaly from liquid breeders at low concentrations. For extracting tritium from Li and 17L183Pb, Zr-Pd and V-Pd are the cheapest membranes, respectively, but Nb-Pd membrane is not far behind. 3. Thermodynamic concentration limits of C, N, and O in Li and l7Li83Pb are derived to be for carbon, 2AFl/n Man ’ZAFl/z 112C2 exp . (3‘13) RT X _ sat a2 ct c2 Li 128 for nitrogen, * M N Li N sa 6 3 Xnt ' Kn! aLi ex? for oxygen, * * AF - AF _ Xsat 3 l/n MmOn L120 Xot 02 8Li exp RT I (3'22) AF* AF* l/n M 0 ' PbO + a exp m n Pb RT (3-25) The kinetic concentration limits of C, N, and O in Li and in l7Li83Pb can be calculated from Eq. (3-28) 1/2 sat (Dimfl) xim X. 1k * 2kw [:1/2 + It Y(t)dt] 0 (3-28) The controlling limits of C, N, and O in liquid Li and in 17Li83Pb are listed in Table 3-3. A hot-gettering startup step, detailed in Chapter 3, is required to prevent the surface compound formation on the membrane. 129 4. An electroless plating method has been developed to coat palladium on a zirconium surface. Surface activation is crucial to this technique. 5. A method has been proposed to obtain hydrogen permeability in palladium-coated membranes and to obtain hydrogen sticking coefficient on a palladium surface. Measurable data must include hydrogen bulk gas pressure and permeation flux. 6. A gas permeation apparatus has been built with system pressure of 10- torr to measure deuterium permeation flux through palladium-coated zirconium. The results show that deuterium permeabilities in zirconium I are in the same order of magnitude as values obtained from diffusivity and solubility. The deuterium sticking coefficient on palladium are also determined. 7-2. Suggestions for future research 1. There is no any experimental measurements of tritium in Li and l7Li83Pb permeation through a palladium-coated membrane. These data are required before a permeation window can be used to separate tritium in fusion reactors. 2. More experimental work is required to measure permeabilities of hydrogen in palladium-coated vanadium and palladium-coated niobium. 130 Techniques for coating palladium on niobium and vanadium need to be developed. 3. The mechanical stability of a palladium film after long time operation at high temperatures needs to be investigated. 4. Tritium diffusivity in l7Li83Pb needs to be experimentally determined. 5. Optimization of permeation membranes, operation temperatures, mechanical design of membrane tubes, and cost would be helpful. APPENDICES APPENDIX 1: DIFI'USIVITIES AND SOLUBILITIES OF NON-METALLIC ELEMENTS IN LIQUID METALS L1 AND 17Li83Pb AND STRUCTURAL METALS 131 Al-l. structurai metals 132 Diffusivities of non-metaliic elements in liquid metals and Diffusivities of carbon, nitrogen, and oxygen in structural metals are updated [1]* [26], listed and plotted in Table Al-l and Fig. Al-l, respectively. Table Al-l The diffusivities of carbon, nitrogen, and oxygen in structural metals _§y§tem Diffuaivity. EEL§ References Nb-C 4.0x10'7exp(-l6610/T)* [1] V-C 8.8x10'7exp(-l3990/T) [2] Mo-C 2.8x10'8exp(-8380/T) [3], [4] Cr—C 4.0x10‘5exp(-19630/T) [5] Zr-C 2.0x10'7exp(-18230/T) [6], [7] Ti-C 3.0x10'7exp(-10070/T) [8] a-Fe-C 1.7x10-7exp(-9390/T) [9], [10] Nb-N 8.6x10'7exp(-l756O/T) [11], [12] V-N 4.2x10-6exp(-17850/T) [2], [12]»[14] Mo-N 4.0x101exp(-14210/T) [15] Cr-N 7.0x10-8exp(-l6l30/T) [16], [17] Zr-N 5.0x10'8exprl9210/T) [18], [19] Ti—N 2.1x10'5exp(-26930/T) [20] a-Fe-N 1.3x10'7exp(-8830/T) [9] Nb-O 2.1x10'6exp(-13540/T) [21] v-0 2.5x10'6exp(-14840/T) [2], [13], [14], [22] Mo-O 3.0x10'6eXp(-15600/T) [23] Cr-O 8.0x10'6expr-16700/T)** Zr-O 6.6x10'6exp(-22140/T) [24] Ti-O 4.5x10'5exp(-24160/T) [25] a-Fe-O 4.0x10‘5expr-20080/Tl [261 * where T in 0K ** estimated from geometric mean of diffusivities of carbon and nitrogen. 133 -10 10 I I I I I I I I I I I l l l I I I in Fe in M0 in Ti _15 — in Nb in V in V in M0 in Cr in M0 in Nb in Cr 0 in Fe N in Cr C in Zr 0 N O 10 10‘20 ' in Zr in Zr in T1 Diffusivity (mz/s) ' I I I I I I /o . v 4’ Z in Ti -25 1 I l I l l I I 1 I l l l I I I I 10 1000/T (l/K) Fig. Al-l Diffusivities of carbon, nitrogen, and oxygen in structural metals. 134 The diffusivities of carbon, nitrogen, and oxygen in liquid metals can be calculated by the hydrodynamical theory which was proposed by Buxbaum and Tentoni [27], [28]: KB T 7 9 (Al-1) ii 4flprc [ l - .112(T/Tm)1/2 ] where KB is Boltzman's constant, 1.38x10.23 J/OK; Tm is the melting point of liquid metal, oK; rc is covalent radius, 9x10.ll m for carbon, 11 11 7x10- m for nitrogen, and 6.6x10' m for oxygen [29]; p is liquid metal viscosity, kg/m.s. The lithium viscosity has been reported as [30] p - 1.0xlo'3 exp(3.44- .7368lnT+ 253.1/1) . (Al-2) The lead viscosity was interpolated from the data given in Ref. [31] linb - -2.5lx10'31- 4.384 . (Al-3) The viscosity of lithium-lead alloy can be calculated by the equation as follows 1m‘1in ‘ XLi 1n“Li + XPb 1n“Pb ' (Al'a) 135 The diffusivities of carbon, nitrogen, and oxygen in lithium and l7L183Pb are calculated, listed, and plotted in Table A1-2, and Fig. Al- 2, respectively. Table Al-2 Diffusivities of carbon, nitrogen, and oxygen in Li and in 17Li83Pb §ya§am Diffusivity. m22§ 250°C 350°C 450°C 550°C 650°C 750°C C-Li 1.44xlo'8 2.14x10'8 2.97x10'8 3.92x10'8 5.00::10'8 6.20x10'8 N-Li 1.86xlo'8 2.75x10'8 3.82x10'8 5.04:.10‘8 6.43x10'8 7.98xlo'8 O-Li 1.97xlo‘8 2.92x10'8 4.05xlo‘8 5.35x10'8 6.82x10‘8 8.46xlo'8 C-Lin 2.96xlo'9 4.56x10'9 6.78x10'9 9.83x10'9 1.40x10‘8 1.96xlo'8 N-Lin 3.8lxlo‘9 5.86x10'9 8.71x10'9 1.26xlo'8 1.80x10'8 2.52::10'8 O-Lin 4.04xlo'9 521le9 924le9 1.34xlo'8 1.9lx10'8 2.68xlo'8 136 10'9 - ' l 7 l ' T ' ; I C 4 I- '1 10.8 {_- '2 5 :I 5; - 1 \ NE 1- + _ O-Li . 3* N—Li -; C-Li -H g 10'7 :' '1 m - ‘ II-I '- «I "-1 ,_ - Q l- _ O-Lin I __ N-Lin . L C-Lin 'l -6 L J L J l J l 10 .8 1.2 1.6 2.0 2.4 1000/T (l/K) Fig. A1-2 Diffusivities of carbon, nitrogen, and oxygen in Li and 17Li83Pb. 137 Al-2. ub ties of on-metal elements 1 li uid metals and structural_aetals Solubilities of non-metallic elements in structural metals are updated [33]» [35], listed, and plotted in Table Al—3 and Fig. Al-3, respectively. Table Al-3 Solubilities of carbon, nitrogen, and oxygen in structural metals System Solubiligyirappm Rararappaa____ C-Zr 1.00x1011exp(-27680/T) [33] C-Nb 4.89x107exp(-l7760/T) [34] C-V 9.70x104exp(-3124/T) [34] C-Mo 4.57x107exp(-3124/T) [34] C-Ti 1.43x106exp(-5158/T) [34] C-Cr 3.32x107exp(-13840/T) [34] N-Zr 3.62x105exp(-321/T) [34] N-Nb 1.16x104exp(-2054/T) [34] N-V 6.23x105exp(-2921/T) [34] N-Mo 5.34x104exp(-9959/T) [34] N-Ti 3.69x106exp(-3125/T) [34] N-Cr 2.52x108exp(-16550/T) [34] o-z: 3.82x105 [34] O-Nb 1.12x105exp(-l909/T) [34] o-v l.6lx105exp(-1185/T) I34] O-Mo 3.51x108exp(-27900/T) [35] O-Ti 3.90x105 [34] O-Cr 2.56x106exp(-15350/T) [34] Solubilities (appm) 138 10 Zr V Nb 10 Ti Fe Fe Fe Cr 10’ MO Cr MO Cr Nb C O C N N C O C 10‘ - 10' 1000/T (l/K) Fig. A1—3 Solubilities of carbon, nitrogen, and oxygen in structural metals. 139 Although there have been many studies of solubilities of carbon, nitrogen, and oxygen in lithium, but solubilities in l7Li83Pb have not been experimentally determined. Buxbaum [36] in his solution thermodynamic analysis of non-metallic elements in lead-rich Li-Pb mixtures proposed the following equation to calculate the solubilities in 17Li83Pb 24 55“ )(°Lin' aLi)Nav sat _ (Ai)(2.4x10- i-Lin ln(X -) i-Ll R T ) - ln(X , (Al-5) sat sat . . . . . where Xi-Li and Xi-Lin are solubilities of non-metallic elements in lithium and l7Li83Pb, respectively, appm; 0L1 and aLin are surface tension of Li and l7Li83Pb, respectively, dyne/cm; Nav is the Avogadro's number; A1 is the surface area of the dissolved compound, A2; R is the gas constant, 1.987 cal/g-atom.°K; T is temperature, 0K; and 2.4x10-24 is a factor to convert surface tension unit from dyne/cm to cal/82. Since the primary forms of dissolved non-metallic elements in l7Li83Pb is compound dissolved in the liquid, the most simple way of calculating surface area of dissolved compounds is to use the Van der Waals radii of anions A. - 4xr? , (Al-6) l l 140 Where ri is 1.6 A for carbon atoms, 1.5 A for nitrogen atoms, and 1.4 A for oxygen atoms [37]. The surface tension of 17Li83Pb can be calculated by: XL 0.25 x 0.25 4 + _£b_£b__.) , (Al_7) a . - p . ( Lle Lle pLi pr where XLi and X are mole fractions of Li and Pb in Lin alloy, Pb respectively; and pLin, and pr are densities of Lin alloy, Li, pLi’ and Pb, respectively, g/cm3. The surface tensions and densities of Li and Pb can be interpolated from data given in Ref. [39] 6L1 - 473- .16T , dyne/cm, T in °R , (Al-8) an - 499- .0751 , (Al-9) -4 3 . o pLi - .5628- 1.01x10 T g/cm , T in K , (Al-10) and ppb - 10.678- 1.317x10’31 . (Al-ll) The density of Lin can be calculated as follows [40] ”Lin ' (MW)Lin / VLin ’ (Al'lz) v - x v + x v (Al-l3) Lin Li Li Pb Pb ’ 141 V - (MW) Li (Al-l4) Li / pLi ’ and V b - (MW) (Al-15) P Pb / pr V and V Where VLin’ Li’ Pb are molar volume of Lin, Li, and Pb, respectively, cm3/g-mole. Solubilities of carbon, nitrogen, and oxygen in 17Li83Pb can then be calculated, listed in Table Al-4, and plotted in Fig. Al-4, respectively, along with solubilities in pure lithium. Table Al-4 Solubilities of carbon, nitrogen, and oxygen in Li and in l7Li83Pb Syaram Solubility.iappm Referencea__ C-Li 1.85x106exp(-3885/T) [34] N-Li 2.1x107exp(-4852/T) [41] O-Li 2.9x105exp(-4662/T) [34] 250°C 350°C 450°C 550°C 650°C 750°C C-Lin 6.01xlo1 2.31x102 6.14x102 1.29x103 2.30x103 3.67x103 N-Lin 1.53x102 7.76x102 2.52x103 6.14x103 1.24x104 2.17xlo4 O-Lin 4.22x100 1.99x101 6.10x10l 1.43x102 2.78x102 4.76x102 Solubility (appm) 142 I I I I I I r 10° - n N-Li _. C-Li a 2 N-Lin 10 I. . '— C-Lle O-Li O-Lin 100 L 1 I 1 I l .8 1.2 1.6 2.0 2.4 1000/T (l/K) Fig. A1-4 Solubilities of carbon, nitrogen, and oxygen in Li and l7Li83Pb. 143 References [1] [2] [3] [4] [5] l6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] P. Son, S. Ihara, M. Amiyake, and T. Sano, J. Japan. Inst. Met. 31 (1967) 998. R.C. Svedberg and R.W. Buckman, Jr., Intl. Met. Rev. No. 5 & 6 (1980) 223. V.Y. Schchelkonogov, L.N. Aleksandrov, V.A. Piterimov, and V.S. Mordyuk, Fiz. Metl. Metalloved 25 (1968) 80. H. Kimura, Mater. Sci. Eng. 24 (1976) 171. S.V. Zemskii and B.P. Pyakhin, Fiz. Metal. Metalloved, 23 (1967) 913. V.S. Zotov and A.P. Tsedilkin, Phys. Met. Metall. 47 (1975) 103. R.P. Agarwala and A.R. Paul, J. Nucl. Mater. 58(1975) 25. R.C. Weast (ed.), Handbook of Chemistry and Physics (Chemical Rubber Company, Cleveland, 63th. edn., 1982) p. F-58. J.R.G.de Silva and Rex B. Melellan, Mater. Sci. Eng. 26 (1976) 83. 0.6. Homan, Acta Metall. 12 (1964) 1071. Raymond J. Farraro and Rex B. Mecllan, Mater. Sci. Eng. 33 (1978) 113. J. Keinnonen, J. Raisanen, and A. Anttila, Appl. Phys. A34 (1984) 49. R. Farraro and R.B. McLellan, Mater. Sci. Eng. 39 (1979) 47. F.J.M. Boratto and R.E. Reed-Hill, Scripta Metall. 11 (1977) 1107. A. Anttila and J. Hirvonen, Appl. Phys. Lett. 33 (1978) 394. M.J. Klein, J. Appl. Phys. 38 (1967) 167. J. Keinonen, J. Raisanen, and A. Anttila, Appl. Phys. A35 (1984) 227. C.J. Rosa and W.C. Hafel, J. Electrochem. Soc. 115 (1968) 467. A. Anttila, J. Raisanen, and J. Keinonen, J. Less-Common Met. 96 (1984) 257. A. Anttila, J. Raisanen, and J. Keinonen, Appl. Phys. Lett. 42 (1983) 498. B. Gunther and O. Kanert, Acta Metall. 31 (1983) 909. [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] 144 R.E. Tate, G.R. Edwards, and E.A. Hakkila, J. Nucl. Mater. 29 (1969) 154. I.G. Ritchie and A. Atrens, J. Nucl. Mater. 67 (1977) 254. D. David, G. Beranger, and E.A. Garcia, J. Electrochem. Soc. 130 (1983) 1423. R. Balow and P.J. Grundy, J. Mater. Sci. 4 (1967) 797. M.A. Hoffman and G.A. Carlson, Calculation techniques for estimating the pressure losses for conducting fluid flows in magnetic fields, USAEC Report, UCRL-SlOlO (1971). L.B. Tentoni and R.E. Buxbaum, The diffusivities of nitrogen, oxygen and hydrogen in pure liquid metals, presented at the 2nd. Intl. Conf. on Fusion Reactor Mater. (ICFRM-2), Chicago, April 1986. L.B. Tentoni, The diffusivities of gases in pure liquid metals, Master of Science Thesis, Michigan State University, 1984. L. Pauling, The Nature of the Chemical Bond, (Cornell University Press, Ithaca, New York, 3rd edn., 1960) p. 224. E.B. Shpilrain, Y.A. Soldatenko, V.A. Fomin, V.A. Sarchenko, A.M. Belova, D.N. Kagon, and I.F. Dramova, High Temp. 3 (1965) 870. R.C. Weast (ed.), Handbook of Chemistry and Physics (Chemical Rubber Company, Cleveland, 63th. edn., 1982) p. F-44. R.C. Reid, J.M. Prausnitz, and T.K. Sherwood, The Properties of Gases and Liquids (Mcgraw Hill, New York, 3rd edn., 1976) p. 460. V.S. Zotov and A.P. Tsedilkin, Phys. Met. Metall. 47 (1979) 103. D.L. Smith and K. Natesan, Nucl. Technol. 22 (1974) 392. 5.0. Scrivastava and L.L. Seigle, Metall. Trans. 5 (1974) 49. R.E. Baxbaum, J. Less-Common Met. 97 (1984) 27. L. Pauling, The Nature of the Chemical Bond (Cornell University Press, Ithaca, New York, 3rd edn., 1960) p. 260. R.C. Reid, J.M. Prausnitz, and T.K. Sherwood, The Properties of Gases and Liquids (McGraw Hill, New York, 3rd edn., 1976) p. 616. R.C. Weast (ed.), Handbook of Chemistry and Physics (Chemical Rubber Company, Clevelend, 63th. edn., 1982) P. F-26, B-245. R.C. Reid, J.M. Prausnitz, and T.K. Sherwood, The Properties of Gases and Liquids (McGraw Hill, New York, 3rd edn., 1976) p. 86. APPENDIX 2 : IHPURITY CONCENTRATION LIMITS FOR CONTAINMENT COHPOUND FORMATION IN THE LIQUID TRITIUM BREEDER-BLANKET OF A FUSION REACTOR 145 146 A2-l. I t od on Liquid lithium is possibly the most attractive tritium breeder fluid for fusion reactors. However, impurity concentrations in lithium must be tightly controlled because compound formation on structural metals (carbides, nitrogen, and oxides of Zr, Nb, V, Cr, Mo, a-Fe, or Ti) adversely affects their mechanical properties. This appendix discusses the kinetics and thermodynamics of compound formation on fusion reactor structural metals, and suggests concentration limits for carbon and nitrogen in lithium. A structural material must be compatible with liquid lithium while maintaining integrity during long exposures to thermal cycling and intense irradiation. This criterion suggests alloys of Zr, Nb, V, Cr, Mo, Ti, and a-Fe as good candidates. While these metals are highly resistant to pure liquid lithium, the presence of carbon, nitrogen, or oxygen can cause corrosion. For example, niobium containing 200 ppm oxygen is readily attacked by lithium at 600°C as a result of oxygen extraction into the lithium [l], [2]. Loss of structural integrity can also result when non-metallic elements transfer to the structure forming compounds that spall. An example is the very high rate of vanadium corrosion in liquid sodium containing above 5 ppm oxygen [2], [3]. One solution to this problem is to coat the inside of reactor channels with a low diffusivity, high resistance ceramic; CaO for example. This method is suggested to lessen structural fatigue, but it is currently a long way from demonstration. Alternately, the impurity concentration must be maintained below various thermodynamic and kinetic limits. __A 11““... 147 The distribution coefficient (the equilibrium ratio of non-metallic element concentration in the structure to that in the lithium ) determines the direction of non-metallic element exchange. Smith and Natesan [2], [4] predicted from this that oxygen transport corrosion was manageable with lithium breeder-blankets, but that carbon and nitrogen transport presented problems. This appendix extends their work on carbon and nitrogen to include the kinetics of transport from fusion reactor lithium; we thus find new lower startup concentration limitations, and suggest a startup procedure for prolonging reactor lifetimes. A2-2. Mathematics of impurity mass transfer The impurity mass transfer rate from a turbulent fluid to a solid channel wall is expressed by Ji - k [Ci£(t)- Ci£(t)|x_o] , (A2-1) where J1 is the impurity mass transfer rate, g-atoms/s.m2; k is the liquid phase impurity mass transfer coefficient, m/s; Ci2(t) is the impurity concentration in the bulk liquid, g-atoms/m3; and Ci£(t)|x=0 is the impurity concentration in the liquid at the wall. In the solid, 148 2 aCim(X,t) - D 6 Cim(x’t) 6t im ax2 I (A272) where Cim(x’t) is the impurity concentration in the solid, g-atoms/m3; and Dim is the diffusivity in the solid, mZ/s. Eq. (A2-1) and (A2-2) are solved together by differentiating Eq. (AZ-2) 2 _a _ 9.. (62-3) Thus, 22_F aF/at — D , (AZ-4) im ax2 where F E BCim(X,t)/6X , (AZ-5) and the pseudo-steady state boundary condition is aCim(X,t) k [Ci£(t) - Ci£(t)|x-O] - - Dim 6X lx=-0 - -Dim Flx=0 '(A2-6) Where thermodynamics limits transport, the concentrations are set as by Smith & Natesan [2], [4]. However, for the kinetically limited 149 case (i.e. where thermodynamics strongly favors transport), Ci£(t)|x_0~ 0, and Eq. (A2-6) is, approximately, F|x_0 a - k Ci£(t)/Dim , (A2-7) o where Ci2(t) - C12 exp(-Askt/V) . (AZ-8) Here, Cifi is the initial bulk concentration of impurity in the lithium, g-atoms/m3; As is the channel surface area, m2; and V is the lithium volume in the breeder blanket, m3. Solving by Laplace Transformation [5] produces kc °e'°t 1/2 F(X,t)- - —§l§———— e ‘[('°/Dim) X] erfc[ 51/2 - (- a t)1/2] im 2(Dimt) 1/2 + e(‘a/Dim) X erfc[ x 1/2 + (-at)1/2] ,(A2-9) 2(Dimt) where a - Ask/V . (AZ-10) This is differentiated and integrated to solve for Cim(X,t), because, aCim(X,t) 2 8t im 0 0505 xiv (AZ-ll) 150 t Thus, Cim(x’t) - i0 Dim(aF/6X)dt . (A2 12) The impurity concentration in the solid at the liquid surface [6] is thus k C° ii 1/2 t Cim(x’t)|x-O - 1/2 [2 t - a Jo Y(t)dt ] , (A2-l3) (Dir) m m 2n+l n+1 n+.5 -at E (:1) (a) t _ where Y(t) - e n!(2n+l) (A2 14) n-O For larger t, Y(t) is negligible, Eq. (A2-12) can then be used to solved for the kinetic impurity concentrations by setting Cim(t)|x-O to the impurity solubility in the structure metal. Thus, the initial impurity concentration in lithium for surface compound formation after operation time t is: 1/2 sat Cik - (Dimfl) Cim ; k[2 tl/z- a I: Y(t)dt] (D. «)1/2 x5at 1m 1m or X. - , (A2-15) 1k 2k [ 1:”2 + It Y(t)dt] 0 151 sat and Xsat where Cim im are the impurity solubilities in the structure metal with units of g-atoms/m3 and appm, respectively; Cik and Xik are the kinetic concentration limits in the liquid with units of g-atoms/cm3 and appm, respectively. This limit is proportional to impurity solubility divided by mass transfer coefficient, and to the square-root of solid phase diffusivity. A2-3. Solubilities, diffusivities and mass trapafer coefficients To solve for Eq. (A2-l4) for kinetic concentration limits, we need to know the channel surface area, the breeder liquid volume, the solid solubilities and diffusivities, and the liquid mass transfer coefficient. The following values appear reasonable at the present time for a 1000 MWe fusion power reactor [7]: a surface area of 4x104 1112 a lithium volume of 220 m3, a lithium flow rate of 1 m/s, a channel diameter of 0.2 m, and a magnetic field of 6 tesla. A recently updated collection of the solubilities and diffusivities of carbon, nitrogen, and oxygen in liquid lithium and solid Zr, Nb, V, Cr, Mo, and Ti has been listed in Appendix 1. The impurity mass transfer coefficient is then calculated as: N D. E ___:h 119 , (A2-l6) 152 where NSh is the Sherwood number; D11 is the impurity diffusivity in the liquid and has presented in Appendix 1, m2/s; and d is the channel diameter, m. For lithium flowing in a fusion reactor at 450°C, the Hartmann number MH is 6x104 and the Reynolds number NRe is 3.1x105. The criterion of Hoffman and Carlson MH > NRe/SOO predicts a laminar slug-flow [8], [9]. The Sherwood number can then be calculated [10], [11]. A2-4. Concentration limits in the lithium coplant of a fusiop reaptor Eq. (A2-15) calculates the kinetic impurity concentration limits in the lithium only where the impurity distribution coefficient is high enough that the liquid impurity concentration at the surface is negligible compared to the bulk concentration. Otherwise thermodynamics affects, and eventually determines, the impurity concentration limit. Thus, whichever concentration is higher -the thermodynamic or kinetic limit- this concentration is a conservative limit of allowed impurity in startup lithium. Figs A2-1 to A2-4 plot updated thermodynamic concentration limits (from updated solubility and free energy of formation data [2], [12]+[15], Table A2—1) along with the result of Eq. (A2-15). For carbon in liquid lithium contained by vanadium at 450°C, Fig. A2-l shows that vanadium carbide is not formed for 10 years operation if the carbon concentration is below 0.0055 appm. This is much greater than the thermodynamic limit, 5.6le16 appm; thus, this is 153 a kinetically limited case. Fig. A2-2 shows that kinetics limits the 10 year operation concentration at all temperatures of interest for this system. Not all impurity-fluid-structure combinations are kinetically limited; as shown in Figs. A2-3 and A2-4, the nitrogen concentration limit for vanadium, for example, is controlled by thermodynamics. Also, oxygen concentration limits for the metals considered, as shown in Fig. A2-5, are very high and manageable. Table A2-2 lists the controlling mechanism for surface compound formation on the structural metals. Overall, vanadium, molybdenum, and chromium allow the highest impurity concentrations in liquid lithium, suggesting that they are particularly attractive as structural metals for liquid lithium cooled fusion reactors . 154 Table A2-l Thermodynamic values of non-metallic element concentrations ip liguid Lithium reguireg tp form surface compounds * A 982182111_ia_a228ll Compound A B Compound A B NbO 1010 17640 Cr2306 90 -8670 v,0 4.28x108 4070 th 13300 -40420 Moo2 280 34160 TiC 14000 -40020 Ct,o3 680 22690 szN 67010 -16930 th2 1550 2360 V2N 250 -40 TiO 1860 2870 M02N 1950 7850 Nb,c 3990 -42340 Ct,N 5550 1020 v20 4410 -31460 th 67020 -27950 M02C 90 -7470 TiN 63700 -24630 [a inn-ME“. * where T in oK. Table A2-2 Controlling limits for the impurity compound formation on the structural surface of liguid lithium breeder fusion blanket Impurity, Structural metal Controlling limit carbon Nb, Ti, V, Zr kinetic Cr, Mo thermodynamic nitrogen Nb, Ti, Zr kinetic Cr, Mo, V thermodynamic oxygen Cr, Mo, Nb, Ti, V, Zr thermodynamic 155 10 I I I I ._—:Kinetic concentration ' limit ' ‘ --6Thermodynamic concentration I 750°C limit " 2 10° .. . 650°C _ 0. 550°C «‘3‘ - 450°C .— 5 350°C '3 _ 3; 10’ - _ H .5 ' ' I: .— 3 - u -6 2 1° - -l U c 0 - ._ U 8 U h -I c _ 3 10’ — — t; 750 °,c --------------------- U '- .- 10-12 - q _ 550°C ...................... _ I l. I I -, - - 10 10 2 10 ‘ 10 ° 10 ’ 10 2 Time (year) Fig. A2-l. Carbon concentration limits in a liquid lithium breeder- blanket contained by vanadium for different operation times; transport kinetics determines true limits. Carbon concentration in lithium (appm) 156 1 10 l U 1 I I r I U l ' 16z — - 16" - - — -w — ’I” d I 16“ - //” _ L. / .. I / — I - [I 16'“ _ I, —« _ /// ___—:Kinetic concentratiom _ /’ limit _ ./ -11 / . 10 .. / ----:Thermodynam1c .1 / . . . [I concentration 11mlt _ I 10.20 l 1 J l l I l L l J 250 350 450 550 650 750 850 Temperature (”C) Fig. A2-2. Temperature dependence of the carbon concentration limit for 10 years operation of a liquid lithium breeder-balnket contained by vanadium; vanadium carbide will not form if initial concentration lies in the lower-right region. 157 Carbon concentration in lithium (appm) 10 I I I l I T U T V I I l I I V l I b - -2 - 10 - q I- d -s 10 - .. 1610: : - d -1~- '- 10 " —I - H -u '- 10 P .. - \ \‘\\‘ V '- ‘ ss‘ - \\ “Rx ' -zz' —:Kinetic \\ \1“ - 10 " concentration \ \‘é‘ - ' limit “ ‘¢~ . - . ‘~ ‘:~ T1 ” ---:Thermodynam1c \ ~ '1 - . . . \ Zr .. -16 concentration 11mlt ~‘ ~ Nb 10 _ .1 n l l I l 4 L l l l 1 I I l 4 l l 0.9 1.1 1.3 1.5 1.7 1000/T UK") Fig. A2-3. Carbon concentration limits for 10 years operation of a liquid lithium breeder-blanket. For any structural metal, the upper concentration is the true limit. -M‘m 158 3 . 10 I I I l ”T I’ I I I I I I I I I I I - ----------------------- v - a - - o. o. 33 10° - - 5 ~ - E .. u - H 10': - - r: 0'4 H - 0H s - ‘ H -s c 10 " ' o 0:, - - ca 13 - ‘ C 8 10°: _ ._. C 0 U " '- I: 0 n _- o» .0 -iz - - :3 10 _‘ —: Kinetic . \ ~ Cr - .... concentration \\ \Ti 2 - limit \\ " ----: Thermodynamic ‘\ "' concentration limit \\ Zr "' 1615 I I I l I I I l I I I l I I I l I 0.9 1.1 1.3 1.5 1.7 lOOO/T(°K") Fig. A2-4. Nitrogen concnentration limits for 10 years operation of a liquid lithium breeder-blanket. Thermodynamic limits for Mo and Cr are very high and are not plotted in the figure. For any structural metal, the upper concentration is the true limit. 159 A2-5. W For practical fusion reactor use, the kinetic concentration limits, although higher than the thermodynamic limits in many cases, will often require a tailored startup procedure. For example, liquid lithium contained by vanadium (Li-C-V system) requires an initial carbon concentration below 0.023 appm if vanadium carbide formation is to be forstalled for 10 years operation at 550°C. Since this purity is not available commercially, a high temperature gettering startup is needed. Carbon gettering at 750°C from an initial carbon concentration of 2 appm (an arbitrary available value) appears acceptable as a gettering step. Eqs. (A2-8) and (A2-13) show that circulating the lithium in the blanket at 750°C for 10 hours should reduce the carbon concentration from 2 appm to 0.00016 appm while increasing the carbon concentration at the vanadium surface to 610 appm. This is far below the carbon solubility in vanadium at 750°C (4580 appm) or 550°C (2180 appm), we show below that regular operation at 550°C should be possible. To check whether vanadium carbide forms on the surface after 10 years operation at 550°C following the above start-up procedure, the post-gettering carbon concentration profile in the solid is used in solving Eq. (A2-15). This produces a somewhat lower kinetic concentration limit, 0.017 appm, but this is well above the concentration in the lithium, 0.00016 appm, which results from 10 hours gettering. Therefore this appears as an attractive technique for 160 preventing the vanadium carbide formation. The reactor can now operate at 550°C assuming no additional carbon is introduced. While a similar start-up procedure should allow the use of any of the other suggested structural metals, it should be noted that corrosion is not the only factor determining fusion material suitability. 161 References [1] [2] [3] [4] [5] [6] [7] [3] [9] [10] [11] [12] [13] [14] [15] E.B. Hoffman, "Effects of oxygen and nitrogen in the corrosion resistance of columbium to lithium at elevated temperatures" 0RNL-2675, Oak Ridge National Laboratory, 1959. D.L. Smith and K. Natesan, Nucl. Technol. 22 (1974) 392. D.L. Smith, Met. Trans. 2 (1971) 579. K. Natesan, J. Nucl. Mater. 115 (1983) 251. H.S. Carslaw and J.C. Jaeger, Conduction of Heat in Solids (Oxford University Press, London, 1959) p. 62. M. Abrawitz and I.A. Stegun, Handbook of Mathematical Functions with Formula, Graphs, and Mathematical Tables (National Bureau of Standards, Wasington, D.C., 1972). Based on the upcoming TPSS Study at Argonne National Laboratory, as of August 1986. M.A. Hoffman and G.A. Carlson, Calculation techniques for estimating the pressure losses for conducting fluid flows in magnetic fields, USAEC Report, UCRL-SlOlO (1971). S. Malang and D.L. Smith, Modeling of liquid-metal corrosion deposition in a fusion reactor blanket, Argonne National Laboratory Report, ANL/FPP/TM-l92 (1984). M.A. Hoffman, Magnetic field effects on the heat transfer of potential fusion reactor coolants, Lawrence Livermore Laboratory Report, UCRL-73993 (1972). R.N. Lyon, Chem. Engr. Prog. 47 (1951) 75. M.W. Chase, Jr., J.L. Curnutt, J.R. Downey, Jr., R.A. McDonald, A.N. Syverud, and E.A. Vanenzuela, JANAF thermochemical tables, 1982 Supplement, J. Phys. Chem. Ref. Data, Vol. 11, No. 3 (1982). M.W. Chase, Jr., J.L. Curnutt, H. Prophet, R.A. McDonald, and A.N. Syverud, JANAF thermochemical tables, 1975 Supplement, J. Phys. Chem. Ref. Data, Vol. 4, No. l (1975). H. Jehn and P. Ettmayer, High Temperature-High Pressures, 8 (1976) 83. L.L. Seigle, C.L. Chang, and T.P. Sharma, Metall. Trans. 10A (1979) 1223. APPENDIX 3 : PERMEABILITIES OF HYDROGEN AND ITS ISOTOPES THROUGH PALLADIUM AND ZIRCONIUM 162 163 Palladium-coated zirconium is a good membrane material for a permeation window as described in Chapter 2. Palladium, with its catalytic properties for hydrogen oxidation, has very high hydrogen permeability. Zirconium, among the membrane materials suggested, has the highest hydrogen permeability. A3-l. Palladium The palladium-hydrogen system has been well studied. Volkl and Alefeld reviewed hydrogen diffusivity data and the more reliable results are quite consistent [I] D - 2.90x10‘7 exp(-2670/T) , (As-1) where D is hydrogen diffusivity in palladium, m2/s; and T is in OK. Recently Steward of LLNL [2], in his review of hydrogen isotope permeability through materials, suggested that the most reliable data for hydrogen permeation in palladium are by Koffler et al. [3] and by Balovnev [4]. The permeability obtained by Koffler et al. is a - 2.2x10'7exp(-l885/T) , (AB-2) 164 with pressures from 0.04 to 7 Pa and temperatures from 23 to 436 0C, where Q is hydrogen permeability in palladium, g-mol H2/m.s.Pa1/2, T is in OK. The permeability equation by Balovnev is a - 8.1x10-7exp(-1860/T) , (AB-3) 5 with pressures from 3x10- to 7x10'2 Pa and temperatures from 100 to 620 °c. A3-2. Zirconium The diffusion and solution of hydrogen in zirconium are well studied and the most updated collection of data are listed in Tables A3- 1 and A3-2, where the difoS1V1tY and solubility (ie Sieverts' constant) are expressed as D - A exp(B/T) , (A3'4) and S - A exp(B/T) , (A3-5) 2 . . . . 3 1/2_ where D is diffusivity , m /s, S is solubility, g-mol H2/m .Pa , A . . o and B are constants; and T is in K. 165 Table A3-l The diffusivity of hydrogen in a-Zirconium D - ex B m2 References A B 1.80xio'7 -5064 [5] 4.68x10‘8 -2990 [6] 5.00xio'7 -5800 [7] 3.64xio'8 -4284 [8] 7.00x10‘7 -5355 [9] 2.65x10'7 -4573 [10] 2.17x10'7 -4217 [11] 4.15xio'7 -4711 [12] 7.14x10'8 -3562 [13] 1.09xio'7 -s737 [14] 7 geometric mean of diffusivities, D - 1.70x10- exp(-4630/T)i70% m2/s. Table A3-2 The solubility of hydrogen in a-zirconium A exp(B/T), g-mol H2/m3.l’a1/2 References A B 1.88x10'1 6541 [15] 2.81xio'1 7700 [16] 2.60x10'l 6247 [17] 4.32x10'1 5959 [18] 6.13x10'1 5939 [19] 6.15x10'1 5435 [20] 9.80x10'2 7398 [21] 3.26xio'1 6190 [22] 1.20x10‘1 7172 [23] geometric mean of solubilities, S - 2.47x10-1exp(6510/T)i120% g-mol HZ/m3.Pa1/2. 166 The permeability can be obtained from diffusivity and solubility o - D s , (A3-6) 1/2. where T is permeability, g-mol H2/m.s.Pa Thus, the hydrogen permeability in zirconium can be estimated from Tables A3-l and A3-2 a - [(1.70xlO-7exp(-4630/T))(2.47x10-1exp(6510/T))] 1/2. - 4.20x10'8exp(1880/T)i270% g-mol Hz/m.s.Pa (A3-7) The only experimental measurement of hydrogen permeation in zirconium (without palladium film) previous to this study is by Gokhale and Johnson [24] °2r-H - l.17x104exp(-27730/T)i30% g-mol/m.s.Pal/2, (A3-8) at pressures from 3.32 to 33.2 Pa and temperatures from 527 to 727°C. 167 References [1] J. Volkl and G. Alefeld, Diffusion in solids: Recent Developments, Nowick and Burton (ed.) (Academic Press, New York, 1976) p. 247. [2] S.A. Steward, Review of hydrogen isotope permeability through materials, Lawrence Livermore National Laboratory Report, UCRL-5433l (1983). [3] S.A. Koffler, J.B. Hudson, and G.S. Ansell, Trans. AIME 245 (1969) 1735. [4] Y.A. Balovnev, Russian J. Phys. Chem. 48 (1974) 409. [5] G.U. Greger, H. Munzel, W. Kunz and A. Schwierczinski, J. Nucl. Mater. 88 (1980) 15. [6] J. Volkl and G. Alefeld, Diffusion of hydrogen in metals, topics in applied physics, Hydrogen in Metals I (Spring Verlag, New York, 1978) p. 321. [7] F.M. Mazzolai and J. Ryll-Nardzewsi, J. Less-Common Met. 49 (1976) 323. [8] J.H. Austin, T.S. Elleman and K. Verghese, J. Nucl. Mater. 51 (1974) 321. [9] J.J. Kearns, J. Nucl. Mater. 43 (1972) 380. [10] G.R. Cupp and P. Flubacher, J. Nucl. Mater. 6 (19620 213. [11] A. Sawatzki, J. Nucl. Mater. 2 (1960) 62. [12] M. Someno, Nippon Kinzoku Gakkaishi 24 (1960) 249. [13] M.W. Mallet and W.M. Albrecht, J. Electrochem. Soc. 104 (1957) 142. [14] E.A. Gulbransen and K.F. Andrew, J. Electrochem. Soc. 101 (1954) 561. [15] K. Watanabe, J. Nucl. Mater. 136 (1985) 1. [16] M. Nagasaka and T. Yamashina J. Less-Common Met. 45 (1976) 53. [17] F. Ricca and T.A. Giorgi, J. Phys. Chen. 71 (1967) 3627. [18] J.J. Kearns, J. Nucl. Mater. 22 (19767) 292. [19] W.H. Erickson, J. Electrochem. Technol. 4 (1966) 205. [20] D. Hardie, J. Nucl. Mater. 17 (1960) 88. 168 [21] L.D. LaGrange, L.J. Dykstra, J.M. Dixson, and U. Merten, J. Phys. Chem. 63 (1959) 2035. [22] C.E. E115 and A.D. Mcquillan, J. Inst. Met. 85 (1956-7) 89. [23] E.A. Gulbransen and K.F. Andrew, Met. Trans AIME (1955) 136. [24] A.A. Gokhale and D.L. Johnson, in: Proc. 2nd Intl Conf. on Environmental Degration of Engineering Materials, VPI, Blacksburg, Va (1981) p. 113. ”[11111]![1'][1|1111[