Grain-Boundary Diffusion of Helium in Palladium with Submicron-Grained Structure Zhiganov A.N., Kupryazhkin A.Ya. Department of Molecular Physics, Urals State Technical University, Yekaterinburg, Russia Abstract. Helium diffusion in polycrystalline palladium sample with submicron-grained structure (the grain size is ∼150 nm) was investigated with the method of gas thermal desorption from previously saturated in gas phase sample. The dependences of the helium solubility in the sample upon the saturation pressure have the typical shape of saturation curve with clear expressed “plateau”. The obtained dependences of the effective helium diffusion coefficient have high temperature (400÷508) K (1) and low temperature (293÷400) K (2) branches that can be described with ( ) D1,2 = D0 exp − E1D,2 kT exponents. In the range of linear dependence of the helium solubility upon the saturation pressure (2.5 bar) the low temperature branch is featured with the migration energy E 2D =(0.0036±0.0015) eV, when the high temperature branch corresponds to the migration energy E1D =(0.33±0.03) eV. The migration energies at the “plateau” of the dependence of the helium solubility upon the saturation pressure (20 bar) are E 2D =(0.0052±0.005) eV in the low temperature region and E1D =(0.18±0.01) eV in the high temperature region. The helium diffusion and solubility mechanisms are discussed. DESCRIPTION OF THE SAMPLE AND THE MEASUREMENT PROCEDURE The study of the gas diffusion in ultra small pores when the size of a grain boundary is comparable with the sizes of the atoms, is interesting in connection with investigation of the gas-surface interactions. The present work studies helium diffusion in polycrystalline palladium with the submicron size of the grains. For the present investigations we have chosen a palladium sample of purity 99.99 % which was kindly submitted for the researches by prof. R.R. Mulyukov. The submicron-grained structure of the sample was prepared by severe plastic deformations to the true logarithm power e=7 by the torsion technique under the quasi-hydrostatic pressure with a device similar to the Bridgman's anvil [1]. Investigations of the microstructure of the samples analogous to the one used in this work were performed using the transmission electron microscope JEM 2000EX. From the transmission electron microscopy data it was obtained, that after the severe plastic deformation the samples get highly dispersed structure saturated with dislocations and with the average grain size of 150 nm and the width of the grain boundaries up to 0.6 nm. The sample had shape of a plate with thickness h = (6.1±0.3) 10-3 cm, total area of the surface S = (2.5±0.1) cm2 and mass m = (90.9±0.1) mg. The technique of experiment [2] involves saturation of a sample in the saturation chamber at desired temperature T and saturation pressure P, tempering the dissolved helium in the sample by sharp cooling down to room temperature, transferring the sample from the saturation chamber to the desorption chamber and measurement of the helium desorption at the same temperature T. The measuring system is constructed on the basis of modernized mass spectrometer MI-1201 B. To increase the helium sensitivity of the system we used a quasi-static (with respect to helium) exhaust schedule of the mass spectrometer achieved by the use of a getter pump, which provides absorption of all the residual gases except for helium up to 10-6 Pa [3]. The calibration of the measuring system was performed by the method of double expansion of known quantity of helium from the calibrated chamber [3]. The time interval of the sample saturation was determined experimentally. CP663, Rarefied Gas Dynamics: 23rd International Symposium, edited by A. D. Ketsdever and E. P. Muntz © 2003 American Institute of Physics 0-7354-0124-1/03/$20.00 The effective helium diffusion coefficient Deff was determined from processing of the desorption curves according to the solution of the desorption problem for gas desorption from a saturated sample having form of an infinite plate, into vacuum (1). J( t ) = 8SC eff Deff ∞ h π 2 (2k + 1)2 D eff ∑ exp − k =0 h2 t (1) EXPERIMENTAL RESULTS The measurements were carried out at various saturation temperatures T and saturation pressures P. This had allowed taking dependencies of the effective diffusion coefficient Deff and the effective solubility Ceff upon the saturation temperature. To eliminate the influence of the high temperature annealing on the measurement results the reiterated measurings were performed at the low temperatures. The error of determination of the coefficient Deff was ≤ 7%. The helium solubility in the sample was calculated from the data on complete desorption of the sample. The error of determination of the solubility was ≤ 10%. The experimental dependencies of Ceff in grain boundaries of submicron-grained palladium and Deff upon the saturation pressure are given on Fig. 1, 2 for helium desorption from the previously saturated sample. Two temperature branches may be observed at the curves of dependence of the diffusion coefficient (Fig. 3) and the solubility of helium upon the saturation temperature. The high temperature branch corresponds to the (400÷508) K region and the low temperature branch corresponds to the (293÷400) K region. The diffusion coefficient Deff and the solubility of helium Ceff dependences upon saturation temperature follow the exponents (2). ( exp(− E ) kT ) Deff 1,2 = Deff 0 exp − E1D,2 kT C eff 1,2 = C eff 0 P 1,2 (2) The values of the parameters of the helium diffusion in the palladium sample with submicron-grained structure are shown in Table 1. Ceff , 1016 cm-3 2 -1 -2 -3 -4 1 0 10 20 P, bar FIGURE 1. Dependence of the effective helium solubility in the sample upon the pressure of saturation at the saturation temperatures: 1 - 387 K; 2 - 403 K; 3 - 433 K; 4 - approximation. D -9 eff , 2 10 cm s -1 3 2 -1 -2 -3 -4 1 0 10 20 P, bar FIGURE 2. Dependence of the effective coefficient of helium diffusion in the sample upon the pressure of saturation at the saturation temperatures: 1 - 387 K; 2 - 403 K; 3 - 433 K; 4 – approximation. ln(Deff ) 500 400 300 T, K -19 Deff , cm2s-1 -8 10 -1 -2 -3 -20 -9 10 -21 2.0 2.4 2.8 3.2 1000/T, 1/K FIGURE 3. Dependence of the effective coefficient of helium diffusion on the sample upon the temperature of saturation at the saturation pressures: 1 – P = 20 bar; 2 - P = 2.5 bar; 3 – approximation. TABLE 1. The Values of Parameters of the Helium Diffusion in the Palladium Sample with Submicron-Grained Structure ∆T, K P, bar 293÷400 2.5 400÷508 2.5 293÷400 20 400÷508 20 Deff 0, cm2s-1 (0.98 )⋅ 10 (1.1 )⋅10 (9.3 )⋅10 (3.9 )⋅10 +1.1 −0.09 +0.9 − 0.5 +1.6 −1.4 +1.1 −0.9 ED, eV −9 0.0036 ± 0.0015 −5 0.33 ± 0.03 −9 0.052 ± 0.005 −9 0.18 ± 0.01 The solution energies of helium were determined from processing of dependences of the helium solubility upon the saturation E 2S temperature and are E1S = (− 0.025 ± 0.008) eV at the low temperature branch and = (0.086 ± 0.008) eV at the high temperature branch. DISCUSSION According to the data of the research of palladium samples prepared by the same technique as for this work, by means of the positron lifetime measurements [4] and the magnetic susceptibility [5], these samples have sufficiently high concentration of vacancy and vacancy clusters (up to 6-12 vacancies [5]) in comparison with the undeformed polycrystalline samples. In accordance with the data of [5], there are two typical anneal temperatures. The annealing at the temperature T=473 K leads to almost double increase of the grain size, because of annealing of the lineages of the grains, and, according to [4], after the annealing at this temperature the vacancy cluster concentration decreases down to the detection limit of the method. The second typical annealing temperature is ∼823 K. The assembling recrystallization is observed at this temperature, and, therefore, according to [5], the vacancy concentration decreases down to the values which are typical for the undeformed palladium polycrystalline samples. According to our measurements, values of Deff and Ceff at temperatures up to 508 K do not depend on sample annealing and, correspondingly, on the grain size. Therefore, it seems that helium solubility in the lineages of the grains is negligibly small. The helium atom solution energies for palladium determined from the lattice static approach [6] are 0.52 eV for the solution in vacancy and 3.68 eV for the solution in interstitial position. This allows us to neglect the dissolution of helium atoms in interstitial positions of the palladium lattice (in the grain volume) and realization of the interstitial mechanism of helium diffusion in our experiments. The saturated positions in the palladium sample with submicron-grained structure may be positions of defectless grain boundaries, vacancies, divacancies and vacancy clusters in the large tilt grain boundaries, which have been created during the deformation and do not anneal at the low temperatures. The effective solubility is sum of the helium solubilities in all the solution positions: C eff (T , P ) = C gb + C v + C div + C nv . (3) Here C v , C div , C vn , C gb are the helium solubilities in vacancies, divacancies, vacancy clusters in grain boundary and in the defectless grain boundaries of polycrystalline, respectively. As it follows from the measurements presented in this work, helium solubility isotherms have typical shape of the saturation curve with clear expressed “plateau” (Fig. 1). Such behavior of the effective solubility dependence upon the saturation pressure indicates complete filling of certain traps (positions of dissolution) at the surface or the near-surface region of grain boundaries. We can write the dependence of Ceff upon the saturation pressure and temperature, which correspond to the curves observed in the experiment: Ceff (P ,T ) = 4 C * Γ (T )P ∑ 1 +k Γk (T )P , k =1 (4) k Here summation is performed over all types of the solution positions (vacancies, divacancies, vacancy clusters in grain boundary and in the defectless grain boundaries of polycrystalline), C *k is the concentration of the solution positions of type k, Γk is constants for the solution positions of type k that does not depend on pressure. The effective volume of the polycrystalline grain boundaries is relatively large. This is especially true for the polycrystalline with submicron-grained structure. Because of the large values solution energy for helium atoms in the defectless grain boundary Γgb (4) are much smaller then values of Γk corresponding to the other solution positions. So in the whole range of the used saturation pressures, the full saturation of the defectless grain boundaries was not achieved and the condition C *gb >> C gb (P ) was true. From processing of experimental curves we can determine only the effective values for the case when only one type of the solution positions dominates. Assuming this, we get the approximation of equation (4) when only one term of the sum remains. Then, C *k =1 = C *eff = (2.0±0.2)⋅1016 cm-3 is concentration of the traps mainly saturated with helium. The C *eff is the same for the all investigated saturation temperatures. Because the concentrations C* of the positions saturated with helium, do not depend on temperature (see Fig. 1), it seems that C * ≈ C nv , which is also confirmed by the value of the helium solution energy E1P = (− 0.025 ± 0.008) eV at the low saturation temperatures (293÷400 K). The latter may be compared with the helium adsorption energy at solid-state surfaces [7]. At the higher saturation temperatures the total solubility of helium is affected with the solution in simpler defects, including vacancies and/or defectless grain boundaries. The solution energy in these defects is higher, and, therefore, the effective helium solution energy in the sample increases to E2P = (0.086 ± 0.008) eV . The diffusion of gas atoms can be explained by several mechanisms: the vacancy diffusion, the diffusion of the vacancy clusters, the divacancy diffusion mechanism and, at last, the grain boundary diffusion. It seems, that the most likely diffusion mechanisms are the monovacancy diffusion, the divacancy diffusion and the diffusion via the defectless grain boundaries featured by the trapping of the atoms in the vacancy clusters at the large tilt boundaries. These clusters do not anneal at the investigated temperatures [4]. Assuming realization of these mechanisms in the experiment, we can, similarly to [8], obtain the equation for the effective diffusion coefficient from the random walk theory: D gb C gb + Ddiv C div + Dv C v DC Deff = ∑ i i ≈ . C eff i C eff (5) Here C i C eff is multiplier, which equals fraction of the time a gas atom spends in solution position of type i; Di is the coefficient of helium diffusion via the positions of type i. In our case considerable contribution to the effective diffusion coefficient comes from the terms D gb , which corresponds to the diffusion via the defectless grain boundaries and Ddiv , Dv , which describe the diffusion via the divacancies and monovacancies of the near-surface region of the grains. The value of the coefficient for diffusion via vacancy clusters in the grain boundary is negligibly small because of the clusters has low mobility; therefore we neglect this term in the numerator of (5). Similarly to [8], we can find, that ( ) ( ) Ci Ci* − Ci (P ) Li exp − EiS kT = , 3 C eff S * ( ) − − C C P L exp E kT ∑ k k k k ( k =1 ) ( ) (6) where summation in the denominator is over all the position types (monovacancies, divacancies, vacancy clusters and defectless grain boundaries); C k0 is concentration of the positions of type k; E kS is the energy of the helium solution in the position of type k; Lk is multiplier which does not depend on pressure. At low occupancy of the solution positions (at the low saturation pressure), so that C *k −C k (P ) ≈ C *k , where C k (P ) corresponds to expression (4) for the k-type solution position, the effective diffusion coefficient Deff (Fig. 2) does not strongly vary with saturation pressure. As the saturation temperature increases, the equation (6) predicts transition from diffusion via divacancies at the low temperatures to the monovacancy diffusion and/or defectless grain boundaries diffusion at the higher temperatures, which corresponds to (5) (Fig. 3, curve 2). As the saturation pressure increases, value of denominator in (5) decreases in accordance with (6), along with the increase of the vacancy clusters saturation. At the same time, Deff increases (Fig. 3, curve 1) and achieves the “plateau” (Fig. 2). The analysis of the change of the migration energy requires additional investigations. CONCLUSION It is shown, that the method of the helium thermal desorption from the polycrystalline samples previously saturated in gas phase, which is used in this work, has high sensitivity, that allows determination of the concentration of the saturated positions from helium solubility in the sample. From the carried out analysis of solution mechanisms, it seems, that helium solution in polycrystalline palladium with submicro-grained structure at 293÷508 K occurs mainly in vacancy clusters at the large tilt grain boundaries. It is confirmed by the solution energy value, which may be compared with helium adsorption energy at solid-state surfaces. At low occupancy of the solution positions (the low saturation pressures) and the low temperatures the helium diffusion is conditioned mainly by the divacancy mechanism with trapping of the atoms in the vacancy clusters at the grain boundaries. At the high temperatures the main mechanism is the monovacancy diffusion and/or defectless grain boundaries diffusion with the same traps. The filling of the traps with helium atoms as the saturation pressure increases leads to smoothing of the potential relief for the diffusing helium atoms and to increase in the effective diffusion coefficient. Improvement of understanding of the diffusion mechanisms on atomistic level requires additional investigations. ACKNOWLEDGMENTS The authors are grateful to prof. R.R. Mulyukov for the polycrystalline sample kindly submitted for the research. REFERENCES 1. 2. 3. 4. 5. 6. Mulyukov, R.R., and Starostenkov, M.D., Acta Met. Sinica, 13, 301-309 (2000). Dudorov, A.G., and Kupryazhkin, A.Ya., Zhurnal Tekhnicheskoi Fiziki, 68, 85-89 (1998). A.Ya. Kupryazhkin and A.Yu. Kurkin. Fizika Tverdogo Tela, 35, 3003-3007 (1993). Würschum, R., Kübler, A. et. al., Ann. de Chim. - Sci. des Mat, 21, 471-482. (1996). Rempel, A.A., Gusev, A.I. et. al. 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