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Hydrogen-induced defects and multiplication of dislocations in Palladium
Journal of Alloys and Compounds xxx (2015) xxx–xxx
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Hydrogen-induced defects and multiplication of dislocations in Palladium J. Cˇízˇek ⇑, O. Melikhova, I. Procházka Charles University in Prague, Faculty of Mathematics and Physics, V Holešovicˇkách 2, CZ-180 00 Praha 8, Czech Republic
a r t i c l e
i n f o
Article history: Available online xxxx Keywords: Palladium Hydrogen Defects Positron annihilation Hardness
a b s t r a c t In the present work positron lifetime spectroscopy was employed for investigation of hydrogen-induced defects in Pd. Well annealed polycrystalline Pd samples were electrochemically charged with hydrogen and the development of defects with increasing hydrogen concentration was investigated. At low concentrations (a-phase region, xH < 0.017 H/Pd) hydrogen loading introduced vacancies surrounded by hydrogen atoms and characterized by a positron lifetime of 200 ps. When the hydrogen concentration exceeded 0.017 H/Pd the a-phase transformed into the hydrogen rich a0 -phase. This generated dislocations characterized by a positron lifetime of 170 ps. Dislocations can accommodate a large volume mismatch between the a and the a0 -phase. Hardness testing revealed that absorbed hydrogen made Pd harder. In the a-phase region hardness increased due to solid solution hardening caused by dissolved hydrogen. Dislocations created by the a to a0 -phase transition caused strain hardening which led to an additional increase of hardness. Ó 2015 Elsevier B.V. All rights reserved.
1. Introduction Palladium (Pd) is able to absorb relatively large amount of hydrogen and can be charged with hydrogen easily [1]. This makes Pd–H an ideal model system for investigation of hydrogen absorption, diffusion and interaction with defects in the metal lattice. Hydrogen occupies octahedral interstitial sites in the fcc Pd lattice and causes lattice expansion. Above the critical temperature of 295 °C hydrogen is fully soluble in Pd up to the atomic ratio of 1.0 H/Pd [1]. At lower temperatures there is a miscibility gap where the Pd–H system consists of a mechanical mixture of two phases: the a-phase with lower hydrogen content and the hydrogen-rich a0 -phase [2]. Both these phases exhibit fcc structure and differ by the hydrogen content only, i.e. by the average number of octahedral sites occupied by hydrogen [1]. The lattice parameters of the a and the a0 -phase are incommensurable and their volume misfit is as high as 10% [1]. At ambient temperature the miscibility gap extends from the hydrogen concentration 0.017 H/Pd up to 0.58 H/Pd [2]. It has been reported that lattice defects are introduced into Pd ¯ kuma [3] observed by hydrogen loading. In particular Fukai and O extraordinary high vacancy concentration in a Pd annealed at a high hydrogen pressure of 5 GPa. Cheng et al. [4] found that the
⇑ Corresponding author. Tel.: +420 221912788. ˇ ízˇek). E-mail address: [email protected] (J. C
dislocation density in a cold rolled Pd–H is remarkably enhanced compared to a pure Pd subjected to the same deformation. The enhancement of the defect density in Pd containing hydrogen can be understood in the terms of reduction of the defect formation energies by segregating hydrogen proposed by Kirchheim [5]. The hydrogen-induced defects were usually characterized indirectly by X-ray diffraction measurements of the lattice contraction for vacancies [3] or by the line shape analysis of X-ray diffraction profiles in the case of dislocations [4]. Positron lifetime (LT) spectroscopy [6] is a unique non-destructive technique which enables direct probing of open volume defects on the atomic scale. In the present work LT spectroscopy was employed for characterization of hydrogen-induced defects in Pd. The LT defect studies were combined with hardness testing to monitor changes of mechanical properties of Pd loaded with hydrogen.
2. Experimental Polycrystalline Pd (99.95% purity) specimens with dimensions 10 10 0.25 mm3 were firstly annealed at 1000 °C for 2 h in a vacuum to remove virtually all defects introduced during previous casting and shaping. Subsequently the specimens were step-by-step electrochemically charged with hydrogen in a cell filled with electrolyte consisting of a mixture of H3PO4 and glycerine (volume ratio 1:2). Hydrogen loading was performed at ambient temperature using a galvanostat and applying constant current pulses between a Pt counter electrode (anode) and the Pd sample (cathode). The current density on the sample was kept at 0.3 mA/ cm2. The hydrogen concentration introduced into the sample was calculated from the transported charge using the Faraday’s law. Hydrogen is very mobile in the
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Pd lattice even at room temperature. The room temperature hydrogen diffusion coefficient in Pd is 4 1011 m2 s1 [7]. Hence, the mean hydrogen diffusion length in Pd during the period of 1 h is as high as 0.4 mm. Since the electrochemical charging of the samples took several hours one can expect that the hydrogen concentration equilibrates by diffusion and becomes uniform across the whole sample. A digital positron lifetime (LT) spectrometer [8] with excellent time resolution of 145 ps (FWHM of the resolution function) was employed for LT investigations. At least 107 positron annihilation events were accumulated in each LT spectrum which was subsequently decomposed into individual components using a maximum likelihood procedure [9]. A 22Na2CO3 positron source (1.5 MBq) deposited on a 2 lm thick Mylar foil was always forming a sandwich with two identically treated Pd specimens. The source contribution in the LT spectra was determined using a well annealed Pd sample. It consisted of two components with the lifetimes of 368 ps and 1.5 ns, and the corresponding intensities of 8% and 1% which come from positrons annihilated in the Na2CO3 source spot and the covering Mylar foil, respectively. The source components were always subtracted from the LT spectra. A Struers Durascan 2 hardness tester was used for the Vickers hardness (HV) measurements. Hardness of hydrogen loaded samples was measured using the load of 0.5 kg applied for 10 s.
3. Results and discussions The annealed Pd sample exhibits a single component LT spectrum with the lifetime sB = (110.1 ± 0.5) ps. This lifetime agrees well with the calculated bulk lifetime for Pd [10]. Hence, one can conclude that the defect density in the annealed sample is very low, below the sensitivity threshold of PAS. Virtually all positrons in the annealed Pd are annihilated in the free state, i.e. delocalized in the lattice and not trapped at defects. The LT spectra of the Pd samples loaded with hydrogen can be well fitted by two exponential components. The dependence of the positron lifetimes s1, s2 resolved in the LT spectra on the hydrogen concentration xH introduced into the sample is plotted in Fig. 1a. The shorter component with the lifetime s1 < sB represents a contribution of free positrons delocalized in the lattice. Note that shortening of the lifetime s1 is due to positron trapping at defects as described by the simple trapping model [11]. The longer component with the lifetime s2 can be attributed to positrons trapped at defects since its lifetime is higher than sB. This component appeared in hydrogen-loaded sample already after the first loading step (xH = 0.005 H/Pd). It means that these defects were created by hydrogen loading. The intensity I2 of this component plotted in Fig. 1b grows with increasing hydrogen content in the sample. It testifies to increasing concentration of hydrogen-induced defects. In the a-phase region (xH < 0.017 H/Pd) the lifetime s2 is approximately 200 ps. This value is close to the lifetime of 209 ps calculated for Pd vacancy using the self-consistent electron density and the generalized gradient approximation for the electron-positron correlation (LMTO-GGA approach) [10]. Hence, in the a-phase region hydrogen loading introduces vacancies. Slightly
shorter value of s2 200 ps measured in the experiment is likely due to hydrogen atoms bound to vacancies. Similar effect, i.e. shortening of positron lifetime due to hydrogen atoms attached to vacancy, was observed also in Nb loaded with hydrogen [12]. In Pd the shortening of the positron lifetime is smaller in magnitude compared to Nb indicating that hydrogen atoms are located farther away from the vacancy. Determination of the exact structure of the vacancy-hydrogen complexes in Pd requires ab-inito theoretical calculations which are out of the scope of this work. In the two-phase field (xH > 0.017 H/Pd) the lifetime s2 gradually decreases down to 170 ps which is close to the lifetime of 160 ps reported for positrons trapped at dislocations in Pd [13]. Hence in the two-phase field hydrogen loading introduces not only vacancies but also dislocations. Since positrons trapped at both these defects contribute to the defect component the observed decrease of s2 is due to increasing population of dislocations. To separate the contribution of positrons trapped at hydrogeninduced vacancies and dislocations the LT spectra were in further analysis decomposed into tree components: (i) the free positron component with the lifetime s1, (ii) the dislocation component with the lifetime s2 fixed at 160 ps and (iii) the vacancy component with the lifetime s3 fixed at 200 ps. Results of the three-component decomposition are presented in Fig. 2. The intensity I3 of positrons trapped at vacancies rises sharply already in the a-phase field while the dislocation component with the intensity I2 arises in the two-phase field only. Hence the a to a0 -phase transition generates dislocations because dislocations allow for accommodation of the large volume misfit (10%) between the a and the a0 -phase [14]. Fig. 3a shows the concentration of hydrogen-induced vacancies cV calculated from the LT results using the three-state simple trapping model [15]
cV ¼
1 I2 I3 1 1 I3 1 1 þ ; mV I1 s3 s2 I 1 sB s3
ð1Þ
where mV = 1014 s1 is the specific positron trapping rate typical for vacancies in metals [15]. The density of dislocations qD was calculated from the three-state trapping model as well
qD ¼
1 I2 I3 1 1 I2 1 1 þ m D I 1 s2 s3 I1 sB s2
ð2Þ
using the specific trapping rate for dislocations mD = 0.5 104 m2 s1 [15]. Fig. 3b shows the dislocation density plotted as a function of the hydrogen concentration in the sample. From inspection of Fig. 3a it becomes clear that in the a-phase field hydrogen loading introduces vacancies and the concentration of hydrogen-induced vacancies increases up to 8 ppm measured
Fig. 1. Results of the two-component decomposition of LT spectra: positron lifetimes s1, s2 (a) and the intensity I2 of positrons trapped at defects (b) plotted as a function of the hydrogen concentration xH in the sample. Dashed line shows position of the phase boundary between the a-phase region and the two-phase field.
Please cite this article in press as: J. Cˇízˇek et al., J. Alloys Comp. (2015), http://dx.doi.org/10.1016/j.jallcom.2014.12.155
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Fig. 2. Results of the three-component decomposition of the LT spectra: the dependence of the positron lifetimes (a) and the intensities (b) of LT components on the hydrogen concentration in the sample.
Fig. 3. The concentration of hydrogen-induced vacancies (a) and the dislocation density (b) plotted as a function of the hydrogen concentration in the sample.
Fig. 4. (a) The dependence of hardness on the hydrogen concentration and (b) the hardness plotted as a function of the square root of the dislocation density. The inset shows the hardness in the two-phase field correlated with the square root of the dislocation density.
at xH = 0.017 H/Pd. This concentration can be compared with the equilibrium concentration of vacancies
cV;eq ¼ eSf =k eEf =kT ;
ð3Þ
where T is the thermodynamic temperature, k is the Boltzmann constant and Sf and Ef denote the vacancy formation entropy and enthalpy, respectively. Using Sf = (2–3) k which holds for most of metals [16] and Ef = 1.68 eV [17] one obtains that at the ambient temperature the equilibrium vacancy concentration in Pd is extremely small and falls into the range (1–3) 1028. Hence the
vacancy concentration measured in the a phase exceeds the equilibrium concentration by many orders of magnitude. Using Eq. (3) one can easily calculate that to get the equilibrium concentration of vacancies of 8 ppm which was measured in experiment Ef has to be decreased down to 0.4 eV. Thus, hydrogen absorbed in the a-phase decreased the vacancy formation energy roughly by 1.3 eV. This value is comparable with the reduction of the vacancy ¯ kuma in a high formation energy in Pd measured by Fukai and O pressure hydrogen gas loading experiment [3]. Fig. 3b shows that the dislocation density strongly increases in the range of hydrogen concentrations xH = 0.1–0.2 H/Pd and finally
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saturates at qD 2 1014 m2. Hence, in the two-phase field dislocations are introduced by plastic deformation caused by the a to a0 -phase transition. From comparison of Fig. 3a and b one can realize that the increase of vacancy concentration in the two-phase field is correlated with the increase of dislocation density. Hence, the plastic deformation produces not only dislocations but also non-equilibrium vacancies created by crossing dislocations. The development of hardness with increasing hydrogen concentration in the sample is plotted in Fig. 4a. In general absorbed hydrogen makes Pd harder but the slope of hardening in the a-phase region is much higher than in the two-phase field. It indicates that hardening mechanism in the a-phase region is different from that in the two-phase field. Fig. 4b shows the dependence of HV on the square root of hydrogen concentration. In the a-phase pffiffiffiffiffi region HV xH testifying that the solid solution hardening [18] by hydrogen absorbed in the interstitial sites is the dominating hardening mechanism. From the LT studies we know that in the two-phase filed dislocations are introduced by the a to a0 -phase transition. Dislocations cause strain hardening which leads to an additional increase of HV visible in Fig. 4. The yield stress increment by dislocations is governed by the Taylor relation [19] and is proportional to the square root of dislocation density. Since hardness is approximately proportional to the yield stress HV in the two phase field is expected to be proportional to the square root of dislocation density. To test it HV in the two-phase field was correlated with the square root of dislocation density measured by the LT spectroscopy and the correlation plot is presented in the inset in Fig. 4b. Obviously the measured dependence pffiffiffiffiffiffi is consistent with the linear relationship HV qD expected for the strain hardening [20]. 4. Conclusions Bulk polycrystalline Pd specimens were electrochemically charged with hydrogen and hydrogen-induced defects were characterized by the positron lifetime spectroscopy. In the a-phase region (xH < 0.017 H/Pd) hydrogen loading created vacancies because hydrogen segregating at vacancies significantly reduced the vacancy formation energy. Moreover, hydrogen absorbed in
the octahedral interstitial sites of the Pd lattice caused remarkable solid solution hardening. In the two-phase field (xH > 0.017 H/Pd) the a to a0 -phase transition introduced dislocations which accommodated a large volume mismatch between the a and a0 -phase. The hardness of the sample increased further in the two-phase field due to strain hardening caused by dislocations. Acknowledgement This work was supported by the Czech Science Foundation (project P108-13-09436S). References [1] T.B. Flanagan, W.A. Oates, Annu. Rev. Mater. Sci. 21 (1991) 269–304. [2] T.B. Massalski (Ed.), Binary Alloy Phase Diagrams, ASM, Metals Park, OH, 1993, pp. 158–181. ¯ kuma, Phys. Rev. Lett. 73 (1997) 1640–1643. [3] Y. Fukai, N. O [4] Y.Z. Chen, H.P. Barth, M. Deutges, C. Borchers, F. Liua, R. Kirchheim, Scr. Mater. 68 (2013) 743–746. [5] R. Kirchheim, Acta Mater. 55 (2007) 5129–5138. [6] P. Hautojärvi (Ed.), Positrons in Solids, Springer-Verlag, Berlin, 1979. [7] J. Völkl, G. Alefeld, in: G. Alefeld, J. Völkl (Eds.), Hydrogen in Metals I, SpringerVerlag, Berlin, 1978, pp. 321–348. [8] F. Becˇvárˇ, J. Cˇízˇek, I. Procházka, J. Janotová, Nucl. Instrum. Methods A 539 (2005) 372–385. [9] I. Procházka, I. Novotny´, F. Becˇvárˇ, Mater. Sci. Forum 255–257 (1997) 772–774. [10] J.M. Campillo Robles, E. Ogando, F. Plazaola, J. Phys.: Condens. Matter 19 (2007) 176222 (20pp). [11] R. West, in: P. Hautojärvi (Ed.), Positrons in Solids, Springer-Verlag, Berlin, 1979, pp. 89–144. ˇ ízˇek, I. Procházka, F. Becˇvárˇ, R. Kuzˇel, M. Cieslar, G. Brauer, W. Anwand, R. [12] J. C Kirchheim, A. Pundt, Phys. Rev. B 69 (2004) 224106. ˇ ízˇek, I. Procházka, Acta Phys. Pol., A 125 (2014) 752–755. [13] O. Melikhova, J. C [14] E. Ho, H.A. Goldberg, G.C. Weatherly, F.D. Manchester, Acta Metall. 27 (1979) 841–853. [15] P. Hautojärvi, C. Corbel, in: A. Dupasquier, A.P. Mills (Eds.), Proceedings of the International School of Physics ‘‘Enrico Fermi’’, Course CXXV, IOS Press, Varena, 1995, pp. 491–532. [16] H.J. Wollenberger, in: R.W. Cahn, P. Haasen (Eds.), Physical Metallurgy, vol. 2, Elsevier, Amsterdam, 1983, pp. 1146–1721. [17] M. Doyama, J.S. Koehler, Acta Metall. 24 (1976) 871–879. [18] J.W. Martin, Precipitation Hardening, Elsevier, Amsterdam, 1998, pp. 79–125. [19] G.I. Taylor, Proc. R. Soc. London A 145 (1934) 362–387. [20] E. Nes, Prog. Mater. Sci. 41 (1997) 129–193.
Please cite this article in press as: J. Cˇízˇek et al., J. Alloys Comp. (2015), http://dx.doi.org/10.1016/j.jallcom.2014.12.155
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jalcom
Hydrogen-induced defects and multiplication of dislocations in Palladium J. Cˇízˇek ⇑, O. Melikhova, I. Procházka Charles University in Prague, Faculty of Mathematics and Physics, V Holešovicˇkách 2, CZ-180 00 Praha 8, Czech Republic
a r t i c l e
i n f o
Article history: Available online xxxx Keywords: Palladium Hydrogen Defects Positron annihilation Hardness
a b s t r a c t In the present work positron lifetime spectroscopy was employed for investigation of hydrogen-induced defects in Pd. Well annealed polycrystalline Pd samples were electrochemically charged with hydrogen and the development of defects with increasing hydrogen concentration was investigated. At low concentrations (a-phase region, xH < 0.017 H/Pd) hydrogen loading introduced vacancies surrounded by hydrogen atoms and characterized by a positron lifetime of 200 ps. When the hydrogen concentration exceeded 0.017 H/Pd the a-phase transformed into the hydrogen rich a0 -phase. This generated dislocations characterized by a positron lifetime of 170 ps. Dislocations can accommodate a large volume mismatch between the a and the a0 -phase. Hardness testing revealed that absorbed hydrogen made Pd harder. In the a-phase region hardness increased due to solid solution hardening caused by dissolved hydrogen. Dislocations created by the a to a0 -phase transition caused strain hardening which led to an additional increase of hardness. Ó 2015 Elsevier B.V. All rights reserved.
1. Introduction Palladium (Pd) is able to absorb relatively large amount of hydrogen and can be charged with hydrogen easily [1]. This makes Pd–H an ideal model system for investigation of hydrogen absorption, diffusion and interaction with defects in the metal lattice. Hydrogen occupies octahedral interstitial sites in the fcc Pd lattice and causes lattice expansion. Above the critical temperature of 295 °C hydrogen is fully soluble in Pd up to the atomic ratio of 1.0 H/Pd [1]. At lower temperatures there is a miscibility gap where the Pd–H system consists of a mechanical mixture of two phases: the a-phase with lower hydrogen content and the hydrogen-rich a0 -phase [2]. Both these phases exhibit fcc structure and differ by the hydrogen content only, i.e. by the average number of octahedral sites occupied by hydrogen [1]. The lattice parameters of the a and the a0 -phase are incommensurable and their volume misfit is as high as 10% [1]. At ambient temperature the miscibility gap extends from the hydrogen concentration 0.017 H/Pd up to 0.58 H/Pd [2]. It has been reported that lattice defects are introduced into Pd ¯ kuma [3] observed by hydrogen loading. In particular Fukai and O extraordinary high vacancy concentration in a Pd annealed at a high hydrogen pressure of 5 GPa. Cheng et al. [4] found that the
⇑ Corresponding author. Tel.: +420 221912788. ˇ ízˇek). E-mail address: [email protected] (J. C
dislocation density in a cold rolled Pd–H is remarkably enhanced compared to a pure Pd subjected to the same deformation. The enhancement of the defect density in Pd containing hydrogen can be understood in the terms of reduction of the defect formation energies by segregating hydrogen proposed by Kirchheim [5]. The hydrogen-induced defects were usually characterized indirectly by X-ray diffraction measurements of the lattice contraction for vacancies [3] or by the line shape analysis of X-ray diffraction profiles in the case of dislocations [4]. Positron lifetime (LT) spectroscopy [6] is a unique non-destructive technique which enables direct probing of open volume defects on the atomic scale. In the present work LT spectroscopy was employed for characterization of hydrogen-induced defects in Pd. The LT defect studies were combined with hardness testing to monitor changes of mechanical properties of Pd loaded with hydrogen.
2. Experimental Polycrystalline Pd (99.95% purity) specimens with dimensions 10 10 0.25 mm3 were firstly annealed at 1000 °C for 2 h in a vacuum to remove virtually all defects introduced during previous casting and shaping. Subsequently the specimens were step-by-step electrochemically charged with hydrogen in a cell filled with electrolyte consisting of a mixture of H3PO4 and glycerine (volume ratio 1:2). Hydrogen loading was performed at ambient temperature using a galvanostat and applying constant current pulses between a Pt counter electrode (anode) and the Pd sample (cathode). The current density on the sample was kept at 0.3 mA/ cm2. The hydrogen concentration introduced into the sample was calculated from the transported charge using the Faraday’s law. Hydrogen is very mobile in the
http://dx.doi.org/10.1016/j.jallcom.2014.12.155 0925-8388/Ó 2015 Elsevier B.V. All rights reserved.
ˇ ízˇek et al., J. Alloys Comp. (2015), http://dx.doi.org/10.1016/j.jallcom.2014.12.155 Please cite this article in press as: J. C
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Pd lattice even at room temperature. The room temperature hydrogen diffusion coefficient in Pd is 4 1011 m2 s1 [7]. Hence, the mean hydrogen diffusion length in Pd during the period of 1 h is as high as 0.4 mm. Since the electrochemical charging of the samples took several hours one can expect that the hydrogen concentration equilibrates by diffusion and becomes uniform across the whole sample. A digital positron lifetime (LT) spectrometer [8] with excellent time resolution of 145 ps (FWHM of the resolution function) was employed for LT investigations. At least 107 positron annihilation events were accumulated in each LT spectrum which was subsequently decomposed into individual components using a maximum likelihood procedure [9]. A 22Na2CO3 positron source (1.5 MBq) deposited on a 2 lm thick Mylar foil was always forming a sandwich with two identically treated Pd specimens. The source contribution in the LT spectra was determined using a well annealed Pd sample. It consisted of two components with the lifetimes of 368 ps and 1.5 ns, and the corresponding intensities of 8% and 1% which come from positrons annihilated in the Na2CO3 source spot and the covering Mylar foil, respectively. The source components were always subtracted from the LT spectra. A Struers Durascan 2 hardness tester was used for the Vickers hardness (HV) measurements. Hardness of hydrogen loaded samples was measured using the load of 0.5 kg applied for 10 s.
3. Results and discussions The annealed Pd sample exhibits a single component LT spectrum with the lifetime sB = (110.1 ± 0.5) ps. This lifetime agrees well with the calculated bulk lifetime for Pd [10]. Hence, one can conclude that the defect density in the annealed sample is very low, below the sensitivity threshold of PAS. Virtually all positrons in the annealed Pd are annihilated in the free state, i.e. delocalized in the lattice and not trapped at defects. The LT spectra of the Pd samples loaded with hydrogen can be well fitted by two exponential components. The dependence of the positron lifetimes s1, s2 resolved in the LT spectra on the hydrogen concentration xH introduced into the sample is plotted in Fig. 1a. The shorter component with the lifetime s1 < sB represents a contribution of free positrons delocalized in the lattice. Note that shortening of the lifetime s1 is due to positron trapping at defects as described by the simple trapping model [11]. The longer component with the lifetime s2 can be attributed to positrons trapped at defects since its lifetime is higher than sB. This component appeared in hydrogen-loaded sample already after the first loading step (xH = 0.005 H/Pd). It means that these defects were created by hydrogen loading. The intensity I2 of this component plotted in Fig. 1b grows with increasing hydrogen content in the sample. It testifies to increasing concentration of hydrogen-induced defects. In the a-phase region (xH < 0.017 H/Pd) the lifetime s2 is approximately 200 ps. This value is close to the lifetime of 209 ps calculated for Pd vacancy using the self-consistent electron density and the generalized gradient approximation for the electron-positron correlation (LMTO-GGA approach) [10]. Hence, in the a-phase region hydrogen loading introduces vacancies. Slightly
shorter value of s2 200 ps measured in the experiment is likely due to hydrogen atoms bound to vacancies. Similar effect, i.e. shortening of positron lifetime due to hydrogen atoms attached to vacancy, was observed also in Nb loaded with hydrogen [12]. In Pd the shortening of the positron lifetime is smaller in magnitude compared to Nb indicating that hydrogen atoms are located farther away from the vacancy. Determination of the exact structure of the vacancy-hydrogen complexes in Pd requires ab-inito theoretical calculations which are out of the scope of this work. In the two-phase field (xH > 0.017 H/Pd) the lifetime s2 gradually decreases down to 170 ps which is close to the lifetime of 160 ps reported for positrons trapped at dislocations in Pd [13]. Hence in the two-phase field hydrogen loading introduces not only vacancies but also dislocations. Since positrons trapped at both these defects contribute to the defect component the observed decrease of s2 is due to increasing population of dislocations. To separate the contribution of positrons trapped at hydrogeninduced vacancies and dislocations the LT spectra were in further analysis decomposed into tree components: (i) the free positron component with the lifetime s1, (ii) the dislocation component with the lifetime s2 fixed at 160 ps and (iii) the vacancy component with the lifetime s3 fixed at 200 ps. Results of the three-component decomposition are presented in Fig. 2. The intensity I3 of positrons trapped at vacancies rises sharply already in the a-phase field while the dislocation component with the intensity I2 arises in the two-phase field only. Hence the a to a0 -phase transition generates dislocations because dislocations allow for accommodation of the large volume misfit (10%) between the a and the a0 -phase [14]. Fig. 3a shows the concentration of hydrogen-induced vacancies cV calculated from the LT results using the three-state simple trapping model [15]
cV ¼
1 I2 I3 1 1 I3 1 1 þ ; mV I1 s3 s2 I 1 sB s3
ð1Þ
where mV = 1014 s1 is the specific positron trapping rate typical for vacancies in metals [15]. The density of dislocations qD was calculated from the three-state trapping model as well
qD ¼
1 I2 I3 1 1 I2 1 1 þ m D I 1 s2 s3 I1 sB s2
ð2Þ
using the specific trapping rate for dislocations mD = 0.5 104 m2 s1 [15]. Fig. 3b shows the dislocation density plotted as a function of the hydrogen concentration in the sample. From inspection of Fig. 3a it becomes clear that in the a-phase field hydrogen loading introduces vacancies and the concentration of hydrogen-induced vacancies increases up to 8 ppm measured
Fig. 1. Results of the two-component decomposition of LT spectra: positron lifetimes s1, s2 (a) and the intensity I2 of positrons trapped at defects (b) plotted as a function of the hydrogen concentration xH in the sample. Dashed line shows position of the phase boundary between the a-phase region and the two-phase field.
Please cite this article in press as: J. Cˇízˇek et al., J. Alloys Comp. (2015), http://dx.doi.org/10.1016/j.jallcom.2014.12.155
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Fig. 2. Results of the three-component decomposition of the LT spectra: the dependence of the positron lifetimes (a) and the intensities (b) of LT components on the hydrogen concentration in the sample.
Fig. 3. The concentration of hydrogen-induced vacancies (a) and the dislocation density (b) plotted as a function of the hydrogen concentration in the sample.
Fig. 4. (a) The dependence of hardness on the hydrogen concentration and (b) the hardness plotted as a function of the square root of the dislocation density. The inset shows the hardness in the two-phase field correlated with the square root of the dislocation density.
at xH = 0.017 H/Pd. This concentration can be compared with the equilibrium concentration of vacancies
cV;eq ¼ eSf =k eEf =kT ;
ð3Þ
where T is the thermodynamic temperature, k is the Boltzmann constant and Sf and Ef denote the vacancy formation entropy and enthalpy, respectively. Using Sf = (2–3) k which holds for most of metals [16] and Ef = 1.68 eV [17] one obtains that at the ambient temperature the equilibrium vacancy concentration in Pd is extremely small and falls into the range (1–3) 1028. Hence the
vacancy concentration measured in the a phase exceeds the equilibrium concentration by many orders of magnitude. Using Eq. (3) one can easily calculate that to get the equilibrium concentration of vacancies of 8 ppm which was measured in experiment Ef has to be decreased down to 0.4 eV. Thus, hydrogen absorbed in the a-phase decreased the vacancy formation energy roughly by 1.3 eV. This value is comparable with the reduction of the vacancy ¯ kuma in a high formation energy in Pd measured by Fukai and O pressure hydrogen gas loading experiment [3]. Fig. 3b shows that the dislocation density strongly increases in the range of hydrogen concentrations xH = 0.1–0.2 H/Pd and finally
ˇ ízˇek et al., J. Alloys Comp. (2015), http://dx.doi.org/10.1016/j.jallcom.2014.12.155 Please cite this article in press as: J. C
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J. Cˇízˇek et al. / Journal of Alloys and Compounds xxx (2015) xxx–xxx
saturates at qD 2 1014 m2. Hence, in the two-phase field dislocations are introduced by plastic deformation caused by the a to a0 -phase transition. From comparison of Fig. 3a and b one can realize that the increase of vacancy concentration in the two-phase field is correlated with the increase of dislocation density. Hence, the plastic deformation produces not only dislocations but also non-equilibrium vacancies created by crossing dislocations. The development of hardness with increasing hydrogen concentration in the sample is plotted in Fig. 4a. In general absorbed hydrogen makes Pd harder but the slope of hardening in the a-phase region is much higher than in the two-phase field. It indicates that hardening mechanism in the a-phase region is different from that in the two-phase field. Fig. 4b shows the dependence of HV on the square root of hydrogen concentration. In the a-phase pffiffiffiffiffi region HV xH testifying that the solid solution hardening [18] by hydrogen absorbed in the interstitial sites is the dominating hardening mechanism. From the LT studies we know that in the two-phase filed dislocations are introduced by the a to a0 -phase transition. Dislocations cause strain hardening which leads to an additional increase of HV visible in Fig. 4. The yield stress increment by dislocations is governed by the Taylor relation [19] and is proportional to the square root of dislocation density. Since hardness is approximately proportional to the yield stress HV in the two phase field is expected to be proportional to the square root of dislocation density. To test it HV in the two-phase field was correlated with the square root of dislocation density measured by the LT spectroscopy and the correlation plot is presented in the inset in Fig. 4b. Obviously the measured dependence pffiffiffiffiffiffi is consistent with the linear relationship HV qD expected for the strain hardening [20]. 4. Conclusions Bulk polycrystalline Pd specimens were electrochemically charged with hydrogen and hydrogen-induced defects were characterized by the positron lifetime spectroscopy. In the a-phase region (xH < 0.017 H/Pd) hydrogen loading created vacancies because hydrogen segregating at vacancies significantly reduced the vacancy formation energy. Moreover, hydrogen absorbed in
the octahedral interstitial sites of the Pd lattice caused remarkable solid solution hardening. In the two-phase field (xH > 0.017 H/Pd) the a to a0 -phase transition introduced dislocations which accommodated a large volume mismatch between the a and a0 -phase. The hardness of the sample increased further in the two-phase field due to strain hardening caused by dislocations. Acknowledgement This work was supported by the Czech Science Foundation (project P108-13-09436S). References [1] T.B. Flanagan, W.A. Oates, Annu. Rev. Mater. Sci. 21 (1991) 269–304. [2] T.B. Massalski (Ed.), Binary Alloy Phase Diagrams, ASM, Metals Park, OH, 1993, pp. 158–181. ¯ kuma, Phys. Rev. Lett. 73 (1997) 1640–1643. [3] Y. Fukai, N. O [4] Y.Z. Chen, H.P. Barth, M. Deutges, C. Borchers, F. Liua, R. Kirchheim, Scr. Mater. 68 (2013) 743–746. [5] R. Kirchheim, Acta Mater. 55 (2007) 5129–5138. [6] P. Hautojärvi (Ed.), Positrons in Solids, Springer-Verlag, Berlin, 1979. [7] J. Völkl, G. Alefeld, in: G. Alefeld, J. Völkl (Eds.), Hydrogen in Metals I, SpringerVerlag, Berlin, 1978, pp. 321–348. [8] F. Becˇvárˇ, J. Cˇízˇek, I. Procházka, J. Janotová, Nucl. Instrum. Methods A 539 (2005) 372–385. [9] I. Procházka, I. Novotny´, F. Becˇvárˇ, Mater. Sci. Forum 255–257 (1997) 772–774. [10] J.M. Campillo Robles, E. Ogando, F. Plazaola, J. Phys.: Condens. Matter 19 (2007) 176222 (20pp). [11] R. West, in: P. Hautojärvi (Ed.), Positrons in Solids, Springer-Verlag, Berlin, 1979, pp. 89–144. ˇ ízˇek, I. Procházka, F. Becˇvárˇ, R. Kuzˇel, M. Cieslar, G. Brauer, W. Anwand, R. [12] J. C Kirchheim, A. Pundt, Phys. Rev. B 69 (2004) 224106. ˇ ízˇek, I. Procházka, Acta Phys. Pol., A 125 (2014) 752–755. [13] O. Melikhova, J. C [14] E. Ho, H.A. Goldberg, G.C. Weatherly, F.D. Manchester, Acta Metall. 27 (1979) 841–853. [15] P. Hautojärvi, C. Corbel, in: A. Dupasquier, A.P. Mills (Eds.), Proceedings of the International School of Physics ‘‘Enrico Fermi’’, Course CXXV, IOS Press, Varena, 1995, pp. 491–532. [16] H.J. Wollenberger, in: R.W. Cahn, P. Haasen (Eds.), Physical Metallurgy, vol. 2, Elsevier, Amsterdam, 1983, pp. 1146–1721. [17] M. Doyama, J.S. Koehler, Acta Metall. 24 (1976) 871–879. [18] J.W. Martin, Precipitation Hardening, Elsevier, Amsterdam, 1998, pp. 79–125. [19] G.I. Taylor, Proc. R. Soc. London A 145 (1934) 362–387. [20] E. Nes, Prog. Mater. Sci. 41 (1997) 129–193.
Please cite this article in press as: J. Cˇízˇek et al., J. Alloys Comp. (2015), http://dx.doi.org/10.1016/j.jallcom.2014.12.155