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1H NMR spectra and echoes in Pd–H and Pd–Ag–H alloys
Journal of Alloys and Compounds 450 (2008) 22–27
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H NMR spectra and echoes in Pd–H and Pd–Ag–H alloys G. Lasanda ∗ , P. B´anki, M. Bokor, K. Tompa
Research Institute for Solid State Physics and Optics, Hungarian Academy of Sciences, PO Box 49, H-1525 Budapest, Hungary Received 18 August 2006; received in revised form 24 October 2006; accepted 25 October 2006 Available online 4 December 2006
Abstract The paper presents the experimental results of rigid-lattice proton magnetic resonance spectra and second moments in Pd–H, Pd0.90 Ag0.10 –H, Pd0.80 Ag0.20 –H, Pd0.75 Ag0.25 –H, and Pd0.65 Ag0.35 –H alloys at T = 2.4 K in a wide hydrogen concentration range. Free induction decay (FID), solid and inhomogeneous echoes were detected and interpreted. The interpretation based on dipole–dipole interaction of homogeneously distributed proton spin system is satisfactory at high hydrogen concentration, but an inhomogeneous field of paramagnetic origin (most probably coming from Fe impurities) plays the dominant role at small hydrogen content. An unexpected correlation was found between the macroscopic magnetic susceptibility and the second moment coming from the inhomogeneous internal field. © 2006 Published by Elsevier B.V. Keywords: Metal hydrides; Hyperfine interactions; Magnetic measurements; Nuclear resonances
1. Introduction Our goal is to survey the hydrogen location in Pd–H and Pd–Ag–H systems and its dependence on the hydrogen and silver concentration. We used 1 H NMR spectroscopy to get information on the hydrogen occupancy of the octahedral interstitial lattice sites. We carried out the NMR line-shape measurements at a temperature low enough to reach the rigid-lattice state in order to avoid the effects of hydrogen diffusion. To fulfill our goal set above, we made 1 H NMR experiments on Pd–H and Pd–Ag–H systems at temperatures as low as 2.4 K and varied H/M ratios from 0.04 to maximum H/M using our technology for hydrogen introduction [1]. No rigid-lattice proton NMR results have been reported to make it possible to determine the hydrogen occupation in Pd–H system and this is especially true for H/M values lower than 0.2. The lowest temperature of the published measurements was 4.2 K [2]. To our knowledge, no proton NMR line-shape investigations have been published on Pd–Ag–H systems in the literature. We report here our results on the mentioned metal–hydrogen systems based on 1 H NMR free induction decay (FID) and echo
∗
Corresponding author. Tel.: +36 1 3922222x3386; fax: +36 1 3922215. E-mail address: [email protected] (G. Lasanda).
0925-8388/$ – see front matter © 2006 Published by Elsevier B.V. doi:10.1016/j.jallcom.2006.10.118
measurements made in a wide range of H/M (minimum = 0.04 and maximum = 0.6) at temperature T = 2.4 K. 1.1. Palladium and palladium–hydrogen systems Palladium–hydrogen was the first and probably is the most frequently investigated metal–hydrogen system. The results concern the occupation [3,4], the motion, the electronic structure [5], etc. of hydrogen in the metallic lattice and the macroscopic properties of Pd and Pd–H alloys. As far as the magnetic results are concerned, palladium is a strongly enhanced itinerant paramagnet, the measured static spin susceptibility of which exceeds the Pauli susceptibility χ by an order of magnitude [6] with a maximum at around 80 K [7–10]. The χ of the Pd matrix depends strongly on the temperature [11]. The local magnetic field measured by NMR Knight shift at the sites of 105 Pd nuclei in Pd metal at a fixed frequency [12,13] shows a correlation with the Pd magnetic susceptibility [7] in the temperature range of 4.2–300 ◦ K. The susceptibility of Pd is extremely sensitive to iron impurities [9] (raising the iron concentration from 1 to 3 ppm causes a marked rise of χ below 10 K). The value of local magnetic moment of electronic origin is estimated to be of 11.3 B (Bohr magneton) in a Pd alloy containing 1% Fe at 100 K [11,14]. The magnetic moments associated with iron impurities are local according to M¨ossbauer experiments on very dilute solution of 57 Fe in palladium at T < 4.2 K [15].
G. Lasanda et al. / Journal of Alloys and Compounds 450 (2008) 22–27
The effective magnetic moment of 57 Fe was found to be about 12.6 B and its spin is 13/2. It appears evident that the spin of the iron impurity polarizes the palladium matrix in its vicinity to give an enhanced local moment. 1.2. Introduction of hydrogen Hydrogen absorbed in palladium occupies octahedral sites of the face centered cubic (fcc) metal lattice [3,4]. The interstitial hydrogen produces a 4.4 eV wide electronic band centered 1 eV below the bottom of palladium-derived d bands in the Pd–H system [5]. The electrons added by the interstitial hydrogen fill the d-band holes at EF as well as extra s-p band states that are pulled down below EF [5]. This latter result also explains why the number of added electrons (0.6) in Pd–H exceeds the number of d-band holes (0.36) in palladium [16]. The theoretical calculation of the rigid-lattice proton dipolar second and fourth moments (M2 and M4 ) of the 1 H NMR line for fcc lattice is given for instance in [17]. The rigid-lattice dipolar M2 of Pd–H system gives M2 = 10.75 × 10−8 T2 for H/M = 1, with contributions of the resonant and nonresonant nuclei and the lattice expansion caused by the introduced hydrogen taken into account. The 1 H NMR experimental results on Pd–H system are published in papers [2,18–21]. The only analysis of line shape for polycrystalline Pd (foil samples, H/M = 0.70–0.81) appeared in the paper of Avram and Armstrong [2]. They used the solid echo pulse sequence to escape the recovery time problem and found that the characteristic echo shape can be represented by an empirical function of f(t) = f(0) exp(−a2 t2 )J3/2 (bt)/(bt)3/2 , where J3/2 (bt) is a Bessel function of the first kind, a and b are adjustable parameters and f(0) is normalization constant (later we will refer to f(t) as Avram–Armstrong empirical function). The authors assumed that proton–proton dipolar contribution to spectrum shape is dominant. Their theoretical calculations showed that the calculated M2 and M4 were higher than measured even at T = 40 K. They ascribed the effect to phonon-assisted tunneling of hydrogen atoms and found the acceptable agreement between calculated and measured M2 and M4 values at temperatures around 4 ◦ K. 1.3. The effect of silver alloying-addition The Pd–Ag alloys are probably the simplest and consequently the best representatives of the chemically disordered alloys; they were subjects of widespread experimental and theoretical investigations. The atom radii of the two alloying elements are nearly the same in this system. Pd and Ag form homogeneous solid solution of fcc structure in the whole concentration range of the alloying addition silver. The hydrogen solubility for the pure metals differs by many orders of magnitude, so the (probably binomial) local distribution of the constituents exerts strong effect on the microscopic physical properties too. The hydrogen solubility in Pd–Ag alloys decreases with increasing silver concentration. The magnetic susceptibility of pure Pd is reduced by both silver and hydrogen addition and demonstrates
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the change in electronic structure. Starting with the pure palladium, the paramagnetic susceptibility of the nonordered solution decreases with increasing silver content and reaches zero at about 60 at.% Ag. At higher silver content, the susceptibility is slightly negative (see [22,23] and references therein). No data on the chemical impurity content, especially that of the transition metal impurities of the investigated samples (except in [21]), are given in the literature. 2. Experimental 2.1. Sample parameters and preparation Lumps of palladium were used (purity 99.95 wt%, Goodfellow) with main quoted impurities Ag: 50, Pt: 40, Rh and Si: 20, Fe, Cu, and Pb: 10, Al, Ca, Mn, and Na: 1 ppm. The alloys were prepared with silver (purity 99.99 wt%, Goodfellow) of main quoted impurities Bi, Mg: 1, Fe: 2, Au: 5, Pb: 10, and Cu: 20 ppm. The samples were mixed and alloyed by induction melting under reduced argon pressure of 8 × 104 Pa. To reach homogeneity, the ingots were re-melted three times. Binary Pd–Ag alloys of 10, 20, and 35 at.% Ag content were produced and cold-rolled in five to seven steps to a thickness of 15–20 m. The steps of cold rolling were separated by surface cleaning in 6M HCl and annealing at 700 ◦ C also in the case of pure palladium sample. The palladium silver foil Pd0.75 Ag0.25 , 0.025 mm thick (with purity of Pd: 74.99% and Ag: 24.93%, Johnson Matthey GmbH) had main quoted impurities Pt: 454, Ir: 34, Fe: 142, and Cu: 22 ppm. Sandwich-type samples consisting of a few foils were made with Teflon spacers for the NMR measurements.
2.2. Hydrogen introduction A complementary unit to the spectrometer was constructed to produce in situ hydrogen charging or discharging. The Pd and Pd–Ag samples contained in a glass tube and inserted into the probe coil of the pulse spectrometer were connected with vacuum and high-purity hydrogen systems. Thus, the samples could be exposed to controlled hydrogen atmosphere and temperature in a similar way as reported in [24]. As in addition to the known NMR methods, the in situ measurement of hydrogen concentration in the samples was used [25] as well as what is operative in minute time range and makes the NMR method applicable for the simultaneous measurements of NMR parameters and characteristic hydrogen content in equilibrium state.
2.3. Methods of NMR measurements The NMR experiments and data acquisition were accomplished by a Bruker SXP 4–100 spectrometer at 1 H resonance frequencies of 27.7 and 82.5 MHz. The recovery time of the NMR spectrometer at frequency 27.7 MHz after the π/2 pulse was 7 s. FID, solid echo, and Hahn echo signals were detected. The (π/2)X (pulse with shorthand X, the (π/2)X –τ–(π/2)X pulse sequence with shorthand X–τ–X and (π/2)X –τ–(π/2)Y pulse sequence with shorthand X–τ–Y were used in the investigation. The appropriate responses to pulse sequences are: FID to a single X pulse, Hahn echo or inhomogeneous echo (HE) to the X–τ–X pulse sequence and solid echo (SE) to an X–τ–Y pulse sequence. When it was possible to fit the initial part of FID by an empirical function or to describe the X–τ–Y echo around its maximum by an analytical function with sufficient precision, then the M2 was determined by taking the second time derivative of the signal envelope −
[d2 Mx (t, τ)/dt 2 ]t=τ , Mx (τ, τ)
where the Mx (t, τ) is echo amplitude as a function of time t and inter-pulse delay τ.
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G. Lasanda et al. / Journal of Alloys and Compounds 450 (2008) 22–27
Fig. 1. 1 H NMR FID (solid lines), X–τ–Y (solid lines) and X–τ–X (dashed lines) echo signals (upper row) measured for Pd0.90 Ag0.10 –H alloys at ν0 = 27 MHz and T = 2.4 K. First column: H/M = 0.04; second column: H/M = 0.60. Lower row: relative echo signal amplitudes of X–τ–Y (triangles) and X–τ–X (squares) experiments normalized by FID signal amplitudes. In X–τ–X echo experiments, the signal following the second X pulse has the general character of a derivative of free induction decay. The M2 can be determined in this case by a procedure proposed by Mansfield [26] and not detailed here.
3. Results 1H
NMR signals of the investigated Pd–Ag–H alloys are demonstrated by Fig. 1 for the Pd0.90 Ag0.10 –H alloy at low (H/M = 0.04) and at high (H/M = 0.6) hydrogen concentrations. The FID and echo signals can be described by Avram–Armstrong empirical function (Fig. 1a and c). The higher amount of Ag and low H/M leads to Gaussian line shapes, at the high H/M ratios the line shapes are still described by the Avram–Armstrong empirical function. The X–τ–X and X–τ–Y echo amplitudes ratio (Fig. 1b) for the H/M = 0.04 and close pulse spacing (τ = 15–20 s) is ≈0.4 for all alloys. The echo amplitudes become equal for the Pd–H sample at τ = 40 s. The increasing silver content of alloys leads to the growth of , the Pd0.65 Ag0.35 –H0.04 the echo amplitudes becomes equal at τ = 100 s. The same trend is valid for higher H/M ratios (Fig. 1d).
3.1. Evaluation of second moments The FID of the Pd–H0.04 sample (ν0 = 28.153 MHz and T = 2.4 K) follows Avram–Armstrong empirical function. The second derivative of the fitted function taken t = 0 gives the second moment value M2 = (14.7 ± 0.05) × 10–8 T2 . The semi-log plot of the smoothed FID and linear approximation extended to t = 0 gives M2 = (14.2 ± 0.05) × 10–8 T2 as evaluated by the usual procedure [27–29]. FID of the Pd–H0.59 sample, fitted by Avram–Armstrong empirical function [30] gives M2 = (7.6 ± 0.5) × 10–8 T2 . The semi-log plot of FID signal versus t2 gives M2 = (7.8 ± 0.3) × 10–8 T2 . As it could be seen above, the two different methods used to determine the M2 values of the measured FID signals gave identical results within the error. The value of M2 of the FID, in spite of loss of initial part due to recovery time can be determined with precision 3–5% by this method. Second moments of the 1 H NMR signals depend on the applied resonance frequencies (ν1 = 28.153 MHz, ν2 = 82.55 MHz for Pd H samples measured at T = 2.4 K) as can be seen on Fig. 2. The FID signals for Pd–H samples for low H/M = 0.04 give unexpectedly high M2 values (17.8 × 10–8 T2
G. Lasanda et al. / Journal of Alloys and Compounds 450 (2008) 22–27
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Fig. 2. Second moment of 1 H NMR signals vs. H/M for Pd–H samples (T = 2.4 K). Open circles: ν0 = 28.153 MHz. Solid circles: ν0 = 82.55 MHz. Error bars represent ±5% for M2 values. The standard error of H/M is smaller than ±1%. The lines are guides to the eye.
at 82.55 MHz and 14.5 × 10−8 T2 at 28.153 MHz), higher than that calculated for homogeneous distribution of protons and H/M = 1. 3.2. Correlation between second moments and quadrate of susceptibilities We found strong correlation between the second moment M2 of the 1 H NMR signals and the quadrate of susceptibility 2 for Pd χm 1−x Agx –H alloys with H/M = 0.04 when investigating their dependence on the silver content x of the samples (Fig. 3). The large deviation in case of the Pd0.75 Ag0.25 alloy is caused by a higher Fe impurity content (142 ppm) than that of the other samples (10 ppm for x = 0 and <10 ppm for x = 0.10, 2 cor0.20, and 0.35). As can be seen on the insert, the M2 − χm relation is impaired by dipolar contribution of protons to M2 at the increased hydrogen concentration of H/M = 0.17, in spite of the fact that we subtracted the value M2 = 1.58 × 10−8 T2 corresponding to homogeneous distribution of protons in Pd–H. As we found out, the correlation is completely lost at H/M = maximum.
Fig. 4. Second moments of 1 H NMR lines generated by X–τ–Y pulse sequence for Pd1−x Agx –H alloys (T = 2.4 K, τ = 15 s, ν0 = 27.7 MHz). Heavy line: calculated dipolar contribution to M2 for homogeneous distribution of hydrogen atoms occupying the octahedral sites in an fcc lattice of a = 0.4004 nm. Squares: x = 0, circles: x = 0.10, up triangles: x = 0.20, down triangles: x = 0.25 and diamonds: x = 0.35. Error bars represent ±5% for M2 values. The standard error of H/M is smaller than ±1%. The lines are guides to the eye.
3.3. Hydrogen distribution The comparison of M2 values for samples of various silver content (Fig. 4) measured as a function of H/M with the dipolar M2 contribution calculated for homogeneous hydrogen distribution (line, Fig. 4) reveals the presence of inhomogeneous contribution to M2 . The magnitude of this inhomogeneous component decreases with increasing H/M and with increasing silver content. The most remarkable deviation from homogeneous distribution occurs at H/M = 0.04 for the Pd–H system. The deviation decreases to zero for Pd0.65 Ag0.35 alloy within 5% of error. 4. Discussion
Fig. 3. The correlation between second moment M2 of 1 H NMR lines and 2 for Pd quadrate of susceptibility χm 1−x Agx –H alloys with H/M = 0.04. Insert: 2. H/M = 0.17. Triangles: second moment, heavy line: χm
The appearance of X–τ–X echoes proves the presence of an inhomogeneous magnetic field in addition to the dipolar field of hydrogen nuclei for the studied samples of different H/M levels and silver concentrations (Fig. 1). The equality of the X–τ–Y and the X–τ–X echo amplitudes measured for long τ values (Fig. 1) means that these NMR signals are generated by the interaction of the nuclear spin system with inhomogeneous local fields [31]. The M2 values are extremely high for the Pd–H system at resonance frequencies ν0 = 27.7 MHz (H/M = 0.04) and ν0 = 82.55 MHz (H/M < 0.2) (Fig. 2), compared to the theoretical value of M2 = 10.11 × 10−8 T2 calculated for dipolar proton–proton contribution and H/M = 1. The dependence of M2 on the resonance frequency at low H/M refers to a dominant
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G. Lasanda et al. / Journal of Alloys and Compounds 450 (2008) 22–27
paramagnetic effect. The proton–proton dipolar term becomes increasingly prevalent over this inhomogeneous contribution with increasing H/M (Fig. 4). Increasing silver concentration has the same result, because both hydrogen and silver addition lowers the susceptibility of the host palladium metal. Starting with the pure palladium, the paramagnetic susceptibility decreases with introduced hydrogen and reaches zero at about H/M = 0.60 [23]. The origins of the inhomogeneous magnetic field can be identified as the consequence of local magnetic moments of the iron impurities. We presumed homogeneously distributed Fe impurities (cFe = 10 ppm) and protons (H/M = 0.04) to estimate the effect exerted on protons by inhomogeneous magnetic fields coming from Fe impurities in Pd–H samples. This low amount of absorbed hydrogen decreases the susceptibility of the palladium matrix only negligibly [32]. The effective local moment of the Fe atom is 11.3 B in this case. The paramagnetic dipolar field of a localized electron decreases to a value comparable to the magnitude of nuclear dipolar field of protons (with closest separation of 0.283 nm) at the distance of 7.75 nm from an iron impurity. There are 1.2 × 105 palladium atoms, 480 hydrogen atoms and roughly only one Fe atom in this volume. All protons of the sample are therefore exposed to the paramagnetic field of Fe impurities, which is stronger than the proton–proton dipolar field. The dipolar contribution of hydrogen atoms homogeneously distributed (H/M = 0.04) gives a second moment term of M2II = 0.37 × 10−8 T2 . The interaction with Pd nuclei results in M2IS = 0.011 × 10−8 T2 . The total theoretical second moment of a PdH0.04 system is then M2 = M2II + M2IS = 0.38 × 10−8 T2 . The measured M2 of the FID signal is 14.5 × 10−8 T2 at ν0 = 27.7 MHz, which cannot come from dipolar contributions of resonant and nonresonant nuclei. The experimental second moments of 1 H NMR lines deviate mostly from the theoretical value calculated for homogenous hydrogen distribution for the Pd–H system at the lowest hydrogen concentration (H/M = 0.04). The deviation diminishes rapidly and the measured values converge to the calculated ones as H/M increases to its maximum possible and/or as the silver concentration grows (Fig. 4), as a general trend for each Pd1−x Agx –H alloy. Second moments measured for the highest silver-concentration sample Pd0.65 Ag0.35 –H show no deviation from the theoretical values calculated for homogeneous hydrogen distribution even for H/M = 0.04. The above detailed consequences of increasing hydrogen and silver concentrations support also the concept that the absorbed hydrogen occupies the octahedral lattice sites homogeneously. We find that homogeneous hydrogen distribution is unambiguously proven by our results for high silver concentration (x = 0.35) when the observable effects of the local field of iron impurities are negligible even at the lowest hydrogen concentration studied. We could obtain further indications to homogeneous hydrogen distribution by the comparison of the silver concentration dependences of NMR-line second moments and susceptibility squares (Fig. 3). The 1 H NMR signal for Pd–H at very low con-
centration of absorbed hydrogen (H/M = 0.04) is formed mainly by inhomogeneous field of paramagnetic origin (most probably of Fe impurities). Negligible role of proton–proton dipolar con2 tribution is confirmed by strong correlation between M2 and χm (Fig. 3). Dipolar contribution of greater hydrogen concentrations causes apparent deviation from correlation besides decreasing 2 (Fig. 3) and the correlation disappears completely at maxχm imum H/M as found. These results confirm also that there is no hydrogen clustering at H/M = 0.04 in Pd1−x Agx –H alloys (0 ≤ x ≤ 0.35) similarly to the above interpretation of M2 data summarized in Fig. 4 because it would lead to nonnegligible deviation from correlation. 5. Conclusion The main conclusion of our work is that the interpretation of the rigid-lattice second moments in Pd–H and Pd–Ag–H systems in the wide H/M range is impossible without invoking the effects of paramagnetic (mostly Fe) impurities. The effect is substantial at small H/M values. The proton–proton dipolar contribution to the second moment of the 1 H NMR lines gives a satisfactory agreement between the measured and calculated values at high H/M, but the existence of X–τ–X echoes shows that the effect of paramagnetic impurities is nonzero in this case too, similarly to the contribution of spin-lattice relaxation time [33]. Acknowledgement The work was supported by the Hungarian Research Fund (OTKA) under the Grant T31994. References [1] K. Tompa, P. B´anki, M. Bokor, G. Lasanda, Europhys. Lett. 53 (2001) 79–85. [2] H.E. Avram, R.L. Armstrong, J. Phys. C: Solid State Phys. 20 (1987) 6305–6314. [3] J.E. Worsham Jr., M.K. Wilkinson, C.G. Shull, J. Phys. Chem. Solids 3 (1957) 303–310. [4] P.P. Davis, E.F.W. Seymour, D. Zamir, W.D. Williams, R.M. Cots, J. Less Common Met. 49 (1976) 159–168. [5] D.E. Eastman, J.K. Cashion, A.C. Switendick, Phys. Rev. Lett. 27 (1971) 35–38. [6] L.W. Roeland, J.C. Wolfrat, D.K. Mark, M. Springford, J. Phys. F: Met. Phys. 12 (1982) L267–L272. [7] F.E. Hoare, J.C. Matthews, Proc. R. Soc. Lond. A212 (1952) 137– 142. [8] H.C. Jamieson, F.D. Manchester, J. Phys. F: Met. Phys. 2 (1972) 323– 336. [9] S. Foner, R. Doclo, E.J. McNiff Jr., J. Appl. Phys. 39 (1968) 551–552. [10] W. Gerhardt, F. Razavi, J.S. Shilling, D. H¨user, J.A. Mydosh, Phys. Rev. 24 (1981) 6744–6746. [11] A.M. Clogston, B.T. Matthias, M. Peter, H.J. Williams, E. Corenzwit, R.C. Sherwood, Phys. Rev. 125 (1962) 541–552. [12] M. Takigawa, H. Yasuoka, J. Phys. Soc. Jpn. 51 (1982) 787–793. [13] J.A. Seitchik, A.C. Gossard, V. Jaccarino, Phys. Rev. 136 (1964) A1119–A1125. [14] D.W. Budworth, F.E. Hoare, J. Preston, Proc. R. Soc. Lond. A257 (1961) 250–260. [15] P.P. Craig, D.E. Nagle, W.A. Steyert, R.D. Taylor, Phys. Rev. Lett. 9 (1962) 12–14.
G. Lasanda et al. / Journal of Alloys and Compounds 450 (2008) 22–27 [16] F.M. Mueller, A.J. Freeman, J.O. Dimmock, A.M. Furdyna, Phys. Rev. B: Condens. Matter. 1 (1970) 4617–4635. [17] A. L¨osche, Kerninduktion Berlin, 1959, p. 461 (A. Л¨eшe: Ядeрhая Иhдyкция Моcква, 1963). [18] R.E. Norberg, Phys. Rev. 86 (1952) 745–751. [19] W. Spalthoff, Z. Phys. Chem. (Frankfurt) 29 (1961) 258–276. [20] T. It´o, T. Kadowaki, Phys. Lett. 54 (1975) 61–62. [21] S.R. Kreitzman, R.L. Armstrong, Phys. Rev. B: Condens. Matter. 25 (1982) 2046–2049. [22] J.D. Fast, Interaction of Metals, Gases, vol. 2, Philips Technical Library, ed., Macmillan, 1971. [23] E. Wicke, H. Brodowsky, H. Zuchner, Hydrogen in palladium and palladium alloys, in: J. Alefeld, J. Vokl (Eds.), Topics in Applied Physics, Hydrogen in Metals II, vol.29, Springer-Verlag, Berlin, 1978, p. 128.
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[24] P. Brill, J. Voitl¨ander, Ber. Bunsenges. Phys. Chem. 77 (1973) 1097–1103. [25] K. Tompa, P. B´anki, M. Bokor, G. Lasanda, L. Vasaros, J. Alloys Compd. 350 (2003) 52–55. [26] P. Mansfield, Phys. Rev. 137 (1965) A961–A974. [27] W.W. Waren, R.F. Norberg, Phys. Rev. 154 (1967) 227–286. [28] M. Engelsberg, R.F. Norberg, Phys. Rev. B: Condens. Matter. 5 (1972) 3395–3406. [29] N. Boden, M. Gibb, Mol. Phys. 27 (1974) 1359–1371. [30] H.E. Avram, R.L. Armstrong, J. Phys. C: Solid State Phys. 17 (1984) L89–L92. [31] G. Bonera, M. Galimbery, Solid State Commun. 4 (1966) 589–591. [32] A. Narath, J. Appl. Phys. 39 (1968) 553–555. [33] M. Bokor, P. B´anki, G. Lasanda, K. Tompa, J. Alloys Compd. 404–406C (2005) 238–242.
1
H NMR spectra and echoes in Pd–H and Pd–Ag–H alloys G. Lasanda ∗ , P. B´anki, M. Bokor, K. Tompa
Research Institute for Solid State Physics and Optics, Hungarian Academy of Sciences, PO Box 49, H-1525 Budapest, Hungary Received 18 August 2006; received in revised form 24 October 2006; accepted 25 October 2006 Available online 4 December 2006
Abstract The paper presents the experimental results of rigid-lattice proton magnetic resonance spectra and second moments in Pd–H, Pd0.90 Ag0.10 –H, Pd0.80 Ag0.20 –H, Pd0.75 Ag0.25 –H, and Pd0.65 Ag0.35 –H alloys at T = 2.4 K in a wide hydrogen concentration range. Free induction decay (FID), solid and inhomogeneous echoes were detected and interpreted. The interpretation based on dipole–dipole interaction of homogeneously distributed proton spin system is satisfactory at high hydrogen concentration, but an inhomogeneous field of paramagnetic origin (most probably coming from Fe impurities) plays the dominant role at small hydrogen content. An unexpected correlation was found between the macroscopic magnetic susceptibility and the second moment coming from the inhomogeneous internal field. © 2006 Published by Elsevier B.V. Keywords: Metal hydrides; Hyperfine interactions; Magnetic measurements; Nuclear resonances
1. Introduction Our goal is to survey the hydrogen location in Pd–H and Pd–Ag–H systems and its dependence on the hydrogen and silver concentration. We used 1 H NMR spectroscopy to get information on the hydrogen occupancy of the octahedral interstitial lattice sites. We carried out the NMR line-shape measurements at a temperature low enough to reach the rigid-lattice state in order to avoid the effects of hydrogen diffusion. To fulfill our goal set above, we made 1 H NMR experiments on Pd–H and Pd–Ag–H systems at temperatures as low as 2.4 K and varied H/M ratios from 0.04 to maximum H/M using our technology for hydrogen introduction [1]. No rigid-lattice proton NMR results have been reported to make it possible to determine the hydrogen occupation in Pd–H system and this is especially true for H/M values lower than 0.2. The lowest temperature of the published measurements was 4.2 K [2]. To our knowledge, no proton NMR line-shape investigations have been published on Pd–Ag–H systems in the literature. We report here our results on the mentioned metal–hydrogen systems based on 1 H NMR free induction decay (FID) and echo
∗
Corresponding author. Tel.: +36 1 3922222x3386; fax: +36 1 3922215. E-mail address: [email protected] (G. Lasanda).
0925-8388/$ – see front matter © 2006 Published by Elsevier B.V. doi:10.1016/j.jallcom.2006.10.118
measurements made in a wide range of H/M (minimum = 0.04 and maximum = 0.6) at temperature T = 2.4 K. 1.1. Palladium and palladium–hydrogen systems Palladium–hydrogen was the first and probably is the most frequently investigated metal–hydrogen system. The results concern the occupation [3,4], the motion, the electronic structure [5], etc. of hydrogen in the metallic lattice and the macroscopic properties of Pd and Pd–H alloys. As far as the magnetic results are concerned, palladium is a strongly enhanced itinerant paramagnet, the measured static spin susceptibility of which exceeds the Pauli susceptibility χ by an order of magnitude [6] with a maximum at around 80 K [7–10]. The χ of the Pd matrix depends strongly on the temperature [11]. The local magnetic field measured by NMR Knight shift at the sites of 105 Pd nuclei in Pd metal at a fixed frequency [12,13] shows a correlation with the Pd magnetic susceptibility [7] in the temperature range of 4.2–300 ◦ K. The susceptibility of Pd is extremely sensitive to iron impurities [9] (raising the iron concentration from 1 to 3 ppm causes a marked rise of χ below 10 K). The value of local magnetic moment of electronic origin is estimated to be of 11.3 B (Bohr magneton) in a Pd alloy containing 1% Fe at 100 K [11,14]. The magnetic moments associated with iron impurities are local according to M¨ossbauer experiments on very dilute solution of 57 Fe in palladium at T < 4.2 K [15].
G. Lasanda et al. / Journal of Alloys and Compounds 450 (2008) 22–27
The effective magnetic moment of 57 Fe was found to be about 12.6 B and its spin is 13/2. It appears evident that the spin of the iron impurity polarizes the palladium matrix in its vicinity to give an enhanced local moment. 1.2. Introduction of hydrogen Hydrogen absorbed in palladium occupies octahedral sites of the face centered cubic (fcc) metal lattice [3,4]. The interstitial hydrogen produces a 4.4 eV wide electronic band centered 1 eV below the bottom of palladium-derived d bands in the Pd–H system [5]. The electrons added by the interstitial hydrogen fill the d-band holes at EF as well as extra s-p band states that are pulled down below EF [5]. This latter result also explains why the number of added electrons (0.6) in Pd–H exceeds the number of d-band holes (0.36) in palladium [16]. The theoretical calculation of the rigid-lattice proton dipolar second and fourth moments (M2 and M4 ) of the 1 H NMR line for fcc lattice is given for instance in [17]. The rigid-lattice dipolar M2 of Pd–H system gives M2 = 10.75 × 10−8 T2 for H/M = 1, with contributions of the resonant and nonresonant nuclei and the lattice expansion caused by the introduced hydrogen taken into account. The 1 H NMR experimental results on Pd–H system are published in papers [2,18–21]. The only analysis of line shape for polycrystalline Pd (foil samples, H/M = 0.70–0.81) appeared in the paper of Avram and Armstrong [2]. They used the solid echo pulse sequence to escape the recovery time problem and found that the characteristic echo shape can be represented by an empirical function of f(t) = f(0) exp(−a2 t2 )J3/2 (bt)/(bt)3/2 , where J3/2 (bt) is a Bessel function of the first kind, a and b are adjustable parameters and f(0) is normalization constant (later we will refer to f(t) as Avram–Armstrong empirical function). The authors assumed that proton–proton dipolar contribution to spectrum shape is dominant. Their theoretical calculations showed that the calculated M2 and M4 were higher than measured even at T = 40 K. They ascribed the effect to phonon-assisted tunneling of hydrogen atoms and found the acceptable agreement between calculated and measured M2 and M4 values at temperatures around 4 ◦ K. 1.3. The effect of silver alloying-addition The Pd–Ag alloys are probably the simplest and consequently the best representatives of the chemically disordered alloys; they were subjects of widespread experimental and theoretical investigations. The atom radii of the two alloying elements are nearly the same in this system. Pd and Ag form homogeneous solid solution of fcc structure in the whole concentration range of the alloying addition silver. The hydrogen solubility for the pure metals differs by many orders of magnitude, so the (probably binomial) local distribution of the constituents exerts strong effect on the microscopic physical properties too. The hydrogen solubility in Pd–Ag alloys decreases with increasing silver concentration. The magnetic susceptibility of pure Pd is reduced by both silver and hydrogen addition and demonstrates
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the change in electronic structure. Starting with the pure palladium, the paramagnetic susceptibility of the nonordered solution decreases with increasing silver content and reaches zero at about 60 at.% Ag. At higher silver content, the susceptibility is slightly negative (see [22,23] and references therein). No data on the chemical impurity content, especially that of the transition metal impurities of the investigated samples (except in [21]), are given in the literature. 2. Experimental 2.1. Sample parameters and preparation Lumps of palladium were used (purity 99.95 wt%, Goodfellow) with main quoted impurities Ag: 50, Pt: 40, Rh and Si: 20, Fe, Cu, and Pb: 10, Al, Ca, Mn, and Na: 1 ppm. The alloys were prepared with silver (purity 99.99 wt%, Goodfellow) of main quoted impurities Bi, Mg: 1, Fe: 2, Au: 5, Pb: 10, and Cu: 20 ppm. The samples were mixed and alloyed by induction melting under reduced argon pressure of 8 × 104 Pa. To reach homogeneity, the ingots were re-melted three times. Binary Pd–Ag alloys of 10, 20, and 35 at.% Ag content were produced and cold-rolled in five to seven steps to a thickness of 15–20 m. The steps of cold rolling were separated by surface cleaning in 6M HCl and annealing at 700 ◦ C also in the case of pure palladium sample. The palladium silver foil Pd0.75 Ag0.25 , 0.025 mm thick (with purity of Pd: 74.99% and Ag: 24.93%, Johnson Matthey GmbH) had main quoted impurities Pt: 454, Ir: 34, Fe: 142, and Cu: 22 ppm. Sandwich-type samples consisting of a few foils were made with Teflon spacers for the NMR measurements.
2.2. Hydrogen introduction A complementary unit to the spectrometer was constructed to produce in situ hydrogen charging or discharging. The Pd and Pd–Ag samples contained in a glass tube and inserted into the probe coil of the pulse spectrometer were connected with vacuum and high-purity hydrogen systems. Thus, the samples could be exposed to controlled hydrogen atmosphere and temperature in a similar way as reported in [24]. As in addition to the known NMR methods, the in situ measurement of hydrogen concentration in the samples was used [25] as well as what is operative in minute time range and makes the NMR method applicable for the simultaneous measurements of NMR parameters and characteristic hydrogen content in equilibrium state.
2.3. Methods of NMR measurements The NMR experiments and data acquisition were accomplished by a Bruker SXP 4–100 spectrometer at 1 H resonance frequencies of 27.7 and 82.5 MHz. The recovery time of the NMR spectrometer at frequency 27.7 MHz after the π/2 pulse was 7 s. FID, solid echo, and Hahn echo signals were detected. The (π/2)X (pulse with shorthand X, the (π/2)X –τ–(π/2)X pulse sequence with shorthand X–τ–X and (π/2)X –τ–(π/2)Y pulse sequence with shorthand X–τ–Y were used in the investigation. The appropriate responses to pulse sequences are: FID to a single X pulse, Hahn echo or inhomogeneous echo (HE) to the X–τ–X pulse sequence and solid echo (SE) to an X–τ–Y pulse sequence. When it was possible to fit the initial part of FID by an empirical function or to describe the X–τ–Y echo around its maximum by an analytical function with sufficient precision, then the M2 was determined by taking the second time derivative of the signal envelope −
[d2 Mx (t, τ)/dt 2 ]t=τ , Mx (τ, τ)
where the Mx (t, τ) is echo amplitude as a function of time t and inter-pulse delay τ.
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G. Lasanda et al. / Journal of Alloys and Compounds 450 (2008) 22–27
Fig. 1. 1 H NMR FID (solid lines), X–τ–Y (solid lines) and X–τ–X (dashed lines) echo signals (upper row) measured for Pd0.90 Ag0.10 –H alloys at ν0 = 27 MHz and T = 2.4 K. First column: H/M = 0.04; second column: H/M = 0.60. Lower row: relative echo signal amplitudes of X–τ–Y (triangles) and X–τ–X (squares) experiments normalized by FID signal amplitudes. In X–τ–X echo experiments, the signal following the second X pulse has the general character of a derivative of free induction decay. The M2 can be determined in this case by a procedure proposed by Mansfield [26] and not detailed here.
3. Results 1H
NMR signals of the investigated Pd–Ag–H alloys are demonstrated by Fig. 1 for the Pd0.90 Ag0.10 –H alloy at low (H/M = 0.04) and at high (H/M = 0.6) hydrogen concentrations. The FID and echo signals can be described by Avram–Armstrong empirical function (Fig. 1a and c). The higher amount of Ag and low H/M leads to Gaussian line shapes, at the high H/M ratios the line shapes are still described by the Avram–Armstrong empirical function. The X–τ–X and X–τ–Y echo amplitudes ratio (Fig. 1b) for the H/M = 0.04 and close pulse spacing (τ = 15–20 s) is ≈0.4 for all alloys. The echo amplitudes become equal for the Pd–H sample at τ = 40 s. The increasing silver content of alloys leads to the growth of , the Pd0.65 Ag0.35 –H0.04 the echo amplitudes becomes equal at τ = 100 s. The same trend is valid for higher H/M ratios (Fig. 1d).
3.1. Evaluation of second moments The FID of the Pd–H0.04 sample (ν0 = 28.153 MHz and T = 2.4 K) follows Avram–Armstrong empirical function. The second derivative of the fitted function taken t = 0 gives the second moment value M2 = (14.7 ± 0.05) × 10–8 T2 . The semi-log plot of the smoothed FID and linear approximation extended to t = 0 gives M2 = (14.2 ± 0.05) × 10–8 T2 as evaluated by the usual procedure [27–29]. FID of the Pd–H0.59 sample, fitted by Avram–Armstrong empirical function [30] gives M2 = (7.6 ± 0.5) × 10–8 T2 . The semi-log plot of FID signal versus t2 gives M2 = (7.8 ± 0.3) × 10–8 T2 . As it could be seen above, the two different methods used to determine the M2 values of the measured FID signals gave identical results within the error. The value of M2 of the FID, in spite of loss of initial part due to recovery time can be determined with precision 3–5% by this method. Second moments of the 1 H NMR signals depend on the applied resonance frequencies (ν1 = 28.153 MHz, ν2 = 82.55 MHz for Pd H samples measured at T = 2.4 K) as can be seen on Fig. 2. The FID signals for Pd–H samples for low H/M = 0.04 give unexpectedly high M2 values (17.8 × 10–8 T2
G. Lasanda et al. / Journal of Alloys and Compounds 450 (2008) 22–27
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Fig. 2. Second moment of 1 H NMR signals vs. H/M for Pd–H samples (T = 2.4 K). Open circles: ν0 = 28.153 MHz. Solid circles: ν0 = 82.55 MHz. Error bars represent ±5% for M2 values. The standard error of H/M is smaller than ±1%. The lines are guides to the eye.
at 82.55 MHz and 14.5 × 10−8 T2 at 28.153 MHz), higher than that calculated for homogeneous distribution of protons and H/M = 1. 3.2. Correlation between second moments and quadrate of susceptibilities We found strong correlation between the second moment M2 of the 1 H NMR signals and the quadrate of susceptibility 2 for Pd χm 1−x Agx –H alloys with H/M = 0.04 when investigating their dependence on the silver content x of the samples (Fig. 3). The large deviation in case of the Pd0.75 Ag0.25 alloy is caused by a higher Fe impurity content (142 ppm) than that of the other samples (10 ppm for x = 0 and <10 ppm for x = 0.10, 2 cor0.20, and 0.35). As can be seen on the insert, the M2 − χm relation is impaired by dipolar contribution of protons to M2 at the increased hydrogen concentration of H/M = 0.17, in spite of the fact that we subtracted the value M2 = 1.58 × 10−8 T2 corresponding to homogeneous distribution of protons in Pd–H. As we found out, the correlation is completely lost at H/M = maximum.
Fig. 4. Second moments of 1 H NMR lines generated by X–τ–Y pulse sequence for Pd1−x Agx –H alloys (T = 2.4 K, τ = 15 s, ν0 = 27.7 MHz). Heavy line: calculated dipolar contribution to M2 for homogeneous distribution of hydrogen atoms occupying the octahedral sites in an fcc lattice of a = 0.4004 nm. Squares: x = 0, circles: x = 0.10, up triangles: x = 0.20, down triangles: x = 0.25 and diamonds: x = 0.35. Error bars represent ±5% for M2 values. The standard error of H/M is smaller than ±1%. The lines are guides to the eye.
3.3. Hydrogen distribution The comparison of M2 values for samples of various silver content (Fig. 4) measured as a function of H/M with the dipolar M2 contribution calculated for homogeneous hydrogen distribution (line, Fig. 4) reveals the presence of inhomogeneous contribution to M2 . The magnitude of this inhomogeneous component decreases with increasing H/M and with increasing silver content. The most remarkable deviation from homogeneous distribution occurs at H/M = 0.04 for the Pd–H system. The deviation decreases to zero for Pd0.65 Ag0.35 alloy within 5% of error. 4. Discussion
Fig. 3. The correlation between second moment M2 of 1 H NMR lines and 2 for Pd quadrate of susceptibility χm 1−x Agx –H alloys with H/M = 0.04. Insert: 2. H/M = 0.17. Triangles: second moment, heavy line: χm
The appearance of X–τ–X echoes proves the presence of an inhomogeneous magnetic field in addition to the dipolar field of hydrogen nuclei for the studied samples of different H/M levels and silver concentrations (Fig. 1). The equality of the X–τ–Y and the X–τ–X echo amplitudes measured for long τ values (Fig. 1) means that these NMR signals are generated by the interaction of the nuclear spin system with inhomogeneous local fields [31]. The M2 values are extremely high for the Pd–H system at resonance frequencies ν0 = 27.7 MHz (H/M = 0.04) and ν0 = 82.55 MHz (H/M < 0.2) (Fig. 2), compared to the theoretical value of M2 = 10.11 × 10−8 T2 calculated for dipolar proton–proton contribution and H/M = 1. The dependence of M2 on the resonance frequency at low H/M refers to a dominant
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G. Lasanda et al. / Journal of Alloys and Compounds 450 (2008) 22–27
paramagnetic effect. The proton–proton dipolar term becomes increasingly prevalent over this inhomogeneous contribution with increasing H/M (Fig. 4). Increasing silver concentration has the same result, because both hydrogen and silver addition lowers the susceptibility of the host palladium metal. Starting with the pure palladium, the paramagnetic susceptibility decreases with introduced hydrogen and reaches zero at about H/M = 0.60 [23]. The origins of the inhomogeneous magnetic field can be identified as the consequence of local magnetic moments of the iron impurities. We presumed homogeneously distributed Fe impurities (cFe = 10 ppm) and protons (H/M = 0.04) to estimate the effect exerted on protons by inhomogeneous magnetic fields coming from Fe impurities in Pd–H samples. This low amount of absorbed hydrogen decreases the susceptibility of the palladium matrix only negligibly [32]. The effective local moment of the Fe atom is 11.3 B in this case. The paramagnetic dipolar field of a localized electron decreases to a value comparable to the magnitude of nuclear dipolar field of protons (with closest separation of 0.283 nm) at the distance of 7.75 nm from an iron impurity. There are 1.2 × 105 palladium atoms, 480 hydrogen atoms and roughly only one Fe atom in this volume. All protons of the sample are therefore exposed to the paramagnetic field of Fe impurities, which is stronger than the proton–proton dipolar field. The dipolar contribution of hydrogen atoms homogeneously distributed (H/M = 0.04) gives a second moment term of M2II = 0.37 × 10−8 T2 . The interaction with Pd nuclei results in M2IS = 0.011 × 10−8 T2 . The total theoretical second moment of a PdH0.04 system is then M2 = M2II + M2IS = 0.38 × 10−8 T2 . The measured M2 of the FID signal is 14.5 × 10−8 T2 at ν0 = 27.7 MHz, which cannot come from dipolar contributions of resonant and nonresonant nuclei. The experimental second moments of 1 H NMR lines deviate mostly from the theoretical value calculated for homogenous hydrogen distribution for the Pd–H system at the lowest hydrogen concentration (H/M = 0.04). The deviation diminishes rapidly and the measured values converge to the calculated ones as H/M increases to its maximum possible and/or as the silver concentration grows (Fig. 4), as a general trend for each Pd1−x Agx –H alloy. Second moments measured for the highest silver-concentration sample Pd0.65 Ag0.35 –H show no deviation from the theoretical values calculated for homogeneous hydrogen distribution even for H/M = 0.04. The above detailed consequences of increasing hydrogen and silver concentrations support also the concept that the absorbed hydrogen occupies the octahedral lattice sites homogeneously. We find that homogeneous hydrogen distribution is unambiguously proven by our results for high silver concentration (x = 0.35) when the observable effects of the local field of iron impurities are negligible even at the lowest hydrogen concentration studied. We could obtain further indications to homogeneous hydrogen distribution by the comparison of the silver concentration dependences of NMR-line second moments and susceptibility squares (Fig. 3). The 1 H NMR signal for Pd–H at very low con-
centration of absorbed hydrogen (H/M = 0.04) is formed mainly by inhomogeneous field of paramagnetic origin (most probably of Fe impurities). Negligible role of proton–proton dipolar con2 tribution is confirmed by strong correlation between M2 and χm (Fig. 3). Dipolar contribution of greater hydrogen concentrations causes apparent deviation from correlation besides decreasing 2 (Fig. 3) and the correlation disappears completely at maxχm imum H/M as found. These results confirm also that there is no hydrogen clustering at H/M = 0.04 in Pd1−x Agx –H alloys (0 ≤ x ≤ 0.35) similarly to the above interpretation of M2 data summarized in Fig. 4 because it would lead to nonnegligible deviation from correlation. 5. Conclusion The main conclusion of our work is that the interpretation of the rigid-lattice second moments in Pd–H and Pd–Ag–H systems in the wide H/M range is impossible without invoking the effects of paramagnetic (mostly Fe) impurities. The effect is substantial at small H/M values. The proton–proton dipolar contribution to the second moment of the 1 H NMR lines gives a satisfactory agreement between the measured and calculated values at high H/M, but the existence of X–τ–X echoes shows that the effect of paramagnetic impurities is nonzero in this case too, similarly to the contribution of spin-lattice relaxation time [33]. Acknowledgement The work was supported by the Hungarian Research Fund (OTKA) under the Grant T31994. References [1] K. Tompa, P. B´anki, M. Bokor, G. Lasanda, Europhys. Lett. 53 (2001) 79–85. [2] H.E. Avram, R.L. Armstrong, J. Phys. C: Solid State Phys. 20 (1987) 6305–6314. [3] J.E. Worsham Jr., M.K. Wilkinson, C.G. Shull, J. Phys. Chem. Solids 3 (1957) 303–310. [4] P.P. Davis, E.F.W. Seymour, D. Zamir, W.D. Williams, R.M. Cots, J. Less Common Met. 49 (1976) 159–168. [5] D.E. Eastman, J.K. Cashion, A.C. Switendick, Phys. Rev. Lett. 27 (1971) 35–38. [6] L.W. Roeland, J.C. Wolfrat, D.K. Mark, M. Springford, J. Phys. F: Met. Phys. 12 (1982) L267–L272. [7] F.E. Hoare, J.C. Matthews, Proc. R. Soc. Lond. A212 (1952) 137– 142. [8] H.C. Jamieson, F.D. Manchester, J. Phys. F: Met. Phys. 2 (1972) 323– 336. [9] S. Foner, R. Doclo, E.J. McNiff Jr., J. Appl. Phys. 39 (1968) 551–552. [10] W. Gerhardt, F. Razavi, J.S. Shilling, D. H¨user, J.A. Mydosh, Phys. Rev. 24 (1981) 6744–6746. [11] A.M. Clogston, B.T. Matthias, M. Peter, H.J. Williams, E. Corenzwit, R.C. Sherwood, Phys. Rev. 125 (1962) 541–552. [12] M. Takigawa, H. Yasuoka, J. Phys. Soc. Jpn. 51 (1982) 787–793. [13] J.A. Seitchik, A.C. Gossard, V. Jaccarino, Phys. Rev. 136 (1964) A1119–A1125. [14] D.W. Budworth, F.E. Hoare, J. Preston, Proc. R. Soc. Lond. A257 (1961) 250–260. [15] P.P. Craig, D.E. Nagle, W.A. Steyert, R.D. Taylor, Phys. Rev. Lett. 9 (1962) 12–14.
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