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AC electrical resistance measurements of PdHx samples versus composition x
Journal of Alloys and Compounds 486 (2009) 55–59
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jallcom
AC electrical resistance measurements of PdHx samples versus composition x Paolo Tripodi a,∗ , Daniele Di Gioacchino b , Jenny Darja Vinko a a b
H.E.R.A. SRL - Hydrogen Energy Research Agency, Corso della Repubblica 448, 00049 Velletri, Italy INFN-LNF – National Institute of Nuclear Physics – National Laboratory of Frascati, Via Enrico Fermi 40, 00044 Frascati, Italy
a r t i c l e
i n f o
Article history: Received 29 December 2008 Received in revised form 7 July 2009 Accepted 8 July 2009 Available online 16 July 2009 Keywords: PdHx Four probe AC electrical resistance Phase transitions
a b s t r a c t A brief introduction on the transport properties of PdHx system will be presented. The resistance ratio method is the most frequent technique used to measure the interstitial loading of hydrogen atoms into palladium. Using this technique a series of AC electrical resistance measurements of PdHx , demonstrating a stoichiometric values x > 1 obtained by electrochemical method at room temperature and pressure is presented. A full description of the used electrochemical method for preparing the samples PdHx with composition x > 1 and the analysis to determine the achieved composition will be presented. Conclusions on the electrical resistance of PdHx versus composition x and correlated physical phenomena have been done. In particular, these studies show the importance of the electrochemical processes efficiency. In order to have an accurate calculation of x value, precise efficiency amplitude estimation is needed. Our analysis underline the systematic underestimation of the x value in the well known PdHx relative electrical resistance versus x at room temperature as reported in literature. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Hydrogen and its isotopes dissolve in many metals and occupy interstitial sites in the host lattice producing an expansion of the lattice. Each interstitial hydrogen atom causes displacement of the metal atoms from their original sites while its electrons fill the electronic band of the metal at the Fermi energy level EF . This gives rise to a series of changes in physical properties of the hosting metal [1,2]. In this framework palladium is an intensely studied metal, for much of its peculiarities [3,4] like the capacity to adsorb large amount of hydrogen and the superconducting transition temperature in function of hydrogen composition. Generally, for palladium, the 4d10 state should be completely filled but in reality the 10 electrons are shared between two zones and the EF intersects the 4d and the broad 5sp bands [3–5]. There are 0.36 electrons in the 5sp band [5] and equal number of positive holes of unfilled state in the d shell. For this reason palladium absorbs hydrogen very strongly. In particular, interstitial hydrogen atoms affect the electrical resistance of the host metal [6–8]. New electron scattering centers are produced in metallic hydrides when interstitial vacancies are occupied by H(D,T) producing a new optical phonon band. This leads to a change in the
∗ Corresponding author. Tel.: +39 39 27868142; fax: +39 06 97258656. E-mail address: [email protected] (P. Tripodi). 0925-8388/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2009.07.052
resistance which can manifest itself even at room temperature. In the case of palladium this is the most important contribution considered in the overall changes observed. The relative resistance R(x)/Ro versus composition x [4] is shown in Fig. 1 where Ro is the pure Pd resistance and x is the molar ratio H/Pd. At room temperature, changing the composition x, the PdHx system exhibits several phases. The ␣ phase is present for composition in the range 0 < x < 0.05, while a coexisting ␣ +  phases exist for composition in the range 0.05 < x < 0.7. Then the  phase between 0.7 < x < 0.9 of the composition range is produced until the ␥ phase starts producing a  + ␥ phase in the composition range of 0.9 < x < x␥ and finally for composition x > x␥ with x␥ > 1 only the ␥ phase exists [9,10]. As would be expected the temperature coefficient of resistivity, , changes with hydrogen composition x in palladium. Information regarding the values range of the coefficient for corresponding composition x is well known [7,8]. In Refs. [9,10] an indication of a new phase transition in PdH system loaded at very high H composition, x > 1, is shown and is here reported in Figs. 2 and 3. In fact, the steep variation of the resistivity temperature coefficient in a short range of composition x, characterizes a strong evidence for a phase transition in PdH. During the transition, the softening of the optical phonons lattice elastic constant (due to the movement of hydrogen in the sub-lattice) lowers the same optical phonon energy, so that, these optical phonons begin to give a contribution to the resistivity value.
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P. Tripodi et al. / Journal of Alloys and Compounds 486 (2009) 55–59 2. Experimental method
Fig. 1. Relative resistance of PdHx versus composition x at constant temperature T = 300 K.
Fig. 2. The temperature coefficient of resistance for PdHx , in function of hydrogen composition x [9]. The horizontal axes x has been reverted for a better comparison with Fig. 2. In this measurement the temperature coefficient reached a maximum value of = 14.0 × 10−3 K−1 . For pure palladium at composition x = 0 the temperature coefficient is = 3.7 × 10−3 K−1 .
Hydrogen is loaded into the palladium lattice using an electrochemical cell. This electrochemical hydrogen absorption process is used preferentially over physical absorption (via H2 as pressure) for one primary reason: this method allows higher composition to be achieved at room temperature and atmospheric pressure in respect to the other processes. The cell geometry consists of two parallel platinum square plates (100 mm × 100 mm × 0.05 mm) as anode electrodes, separated by 10 cm of electrolyte. The cathode was palladium wires (50 m diameter, length in the range 4–6 cm), placed in the middle between the two anodes. This unusual geometry and a short loading time were adopted in order to maximize the hydrogen loading into palladium cathode and to minimize the transfer of anodically produced species to the cathode. The attainment of very high loading levels is found to be critically dependent on controlling the impurities in the electrolyte. In our case, this is done using standard microelectronic industry clean procedures in all steps of the processes in a clean class 100 environment. The electrolyte consisted of strontium sulfate (SrSO4 ) dissolved in 18 M cm water (10−5 M) giving a slightly acidic solution (5.0 < pH < 6.5). The electrolysis required a DC current from 5 mA up to 50 mA. During the electrolysis the four probe AC resistance measurements of the palladium cathode were taken using an RCL meter at 1 KHz sinusoidal current. Highly loaded PdHx samples were electrochemically stabilized by adding (10−5 M) mercurous sulfate (Hg2 SO4 ) to the electrolyte. With this procedure the coated cathodes are found to be resistant to hydrogen de-loading for periods of months at room temperature and room pressure. The Pd–Hg “alloy” forms an amalgam that covers the palladium surface and the depth of this “coating” is hundreds of nanometers, so that the effect of the resistance decrease, due to this coating, is negligible. The final purpose of the alloy layer is to inhibit the hydrogen diffusion inside the palladium surface and at the same time to avoid hydrogen recombination. Hence, the composition x of PdHx sample is stable in time. There is another important intermediate effect of the alloy during the loading process. At the beginning, the Pd–Hg amalgam, only partially covers the cathode surface and goes preferentially in the de-loading defect points. This avoids the recombination of the atomic hydrogen absorbed into palladium lattice that diffuses on the surface in those defects producing H2 hydrogen molecules escaping from the cathode. For this reason a basic effect of stoichiometric ratio increase is obtained. Important characterization of the sample is the measurement of the average final stoichiometric value x. In order to obtain the x value, it is necessary to know the value of hydrogen and palladium moles. Palladium moles are measurable with a sensitivity of about 1 mol, but due to the low weight of hydrogen moles inside the palladium sample these measurements for hydrogen are not simple. For this purpose we have defined an electrochemical method, destructive however, for the measurement of stoichiometric ratio x in PdHx sample, based on the relative resistance R(x)/Ro measurements. This technique can be used as a standard method for the measurement of R(x)/Ro versus x as described below.
3. Analysis In order to obtain the functional of the relative resistance R(x)/Ro versus composition x as shown in Fig. 1, the composition x must be calculated since it is a variable not directly measurable. In Fig. 1, the plot of relative resistance versus x is time independent, while during the hydrogenation or dehydrogenation electrochemical process the time is a fundamental variable to calculate the total electrical charge Q[C] passing through the electrode. The Q[C] value is connected to x value. The x calculation using time, electrochemical current and some experimental constrain of relative resistance is described below and consequently, also the desired functional of relative resistance versus composition. The experimental data used for the composition x calculation are:
1. The behavior of R(x)/Ro versus x of the PdHx (Fig. 1), where Ro represents the pure palladium electrical resistance, has three experimental constraints: Fig. 3. The temperature coefficient of resistance of PdHx in function of time during a slight hydrogen leakage (elapsed time) [10]. After the hydrogen loading, the sample was not perfectly stabilized in order to have a hydrogen leak and hence a change in composition x. Each experimental point represents a measurement of in the temperature range 273–373 K. In these measurements the exact composition x, is not known, but x > 1 is present at the beginning of the experiment, i.e. when the elapsed time () is in the range [0 s < < 9 × 104 s]. It is interesting to note that the temperature coefficient of resistance reaches a maximum value of = 30.4 × 10−3 K−1 .
R(x) =1 Ro
for x = 0;
R(x) = 1.07 Ro
for x = 0.05
(1a)
(1b)
P. Tripodi et al. / Journal of Alloys and Compounds 486 (2009) 55–59
Fig. 4. Relative resistance of PdHx sample versus electrical current during the absorption process. Three regions are defined: region III where the ␣ phase is present and the calculated efficiency of absorption is very high; region II where the ␣, ␣ +  and  phases are present and the efficiency assumes a very low value; the region I where there are the phases ,  + ␥ and ␥ with efficiency close to zero.
that represents the composition value at which the  phase starts, i.e. the transition composition between ␣ and ␣ +  phase; R(x) = 1.76 for x = 0.78 Ro
(1c)
that represents the composition value in  phase where the electrical resistance has the maximum value; 2. The electric charge Q passing through the electrodes during the hydrogenation or dehydrogenation of PdHx samples is proportional to the amount of H moles that enter or exit Pd lattice. For the composition calculation a variable ε measured in C−1 named efficiency has been defined as follows: ε=
x Q
(1)
57
as the ratio between the variation of composition x and the corresponding amount of electrical charge Q transferred through the electrodes. During the hydrogen loading, when the palladium is the cathode, two reactions take place on the cathode surface; the hydrogen absorption inside the lattice and the hydrogen recombination. The relative resistance of PdHx versus total electric charge passing through the electrodes is shown in Fig. 4. In the phase ␣, at the beginning of electrochemical hydrogen loading process, an efficiency ε = 0.893 is found, because the R(x)/Ro = 1.07 at x = 0.05 is reached for a corresponding total electrochemical current Q = 0.056 C. Consequently, introducing the parasitic efficiency εH representing the quantity of electrochemical charge producing molecular hydrogen H2 , the value εH = 0.107 has been calculated. In this region the ratio between the two efficiencies is ε/εH = 8.35. Thus, the electrochemical current contributes to the composition with efficiency almost 8 times greater than the efficiency of the parasitic reaction. Furthermore, repeating the calculation in the ␣ +  phase region starting at x = 0.05 and ending at the maximum value of relative resistance (experimental constrain with x = 0.78, Eq. (1c)) the values ε = 0.060 and εH = 0.940 are obtained. Here the efficiency ratio is completely reversed giving a value ε/εH = 0.063. Only a small fraction of the electrochemical current contributes to the composition x, almost the totality of electrochemical charge yields the parasitic effect of H2 gas formation, the parasitic efficiency is almost 15 times greater then the efficiency ε. The estimation of efficiency ε in the region at higher composition becomes very difficult because the parasitic efficiency is very high εH ≈ 1. Unfortunately, this is the region where the calculation of efficiency is most important in order to calculate the final composition x. On the other hand, at high composition, the anodic process involves mainly the hydrogen absorbed into palladium sample, so that a more accurate x value can be obtained. After the loading procedure reached the maximum composition in reason of the boundary condition settled, the stripping of hydrogen is obtained inverting the polarity of electrochemical cell using the palladium electrode as anode. During the hydrogen deloading three reactions take place on the anode surface: hydrogen adsorption and oxygen recombination related to the electrochem-
Fig. 5. Relative resistance of PdHx sample versus electrical current during the adsorption process. In the region I where the ␥,  + ␥ and  phases are present, the calculated total efficiency is very high; region II where the ␣, ␣ +  and  phases are present and the region III where there is the ␣ phase.
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P. Tripodi et al. / Journal of Alloys and Compounds 486 (2009) 55–59
ical current provided to the electrodes; hydrogen recombination producing H2 molecules independent from the electrochemical current. In this anodic process, the third parasitic effect plays an important role especially at high composition. Analyzing Fig. 5, three regions are evident: region I in the interval [D–C], where the ␥,  + ␥ and  phases are present; region II in the interval [C–B] where the present phases are ␣, ␣ +  and  and region III in the interval [B–A] where the phase ␣ is present. The measurement of ε in the region III gives ε = 0.05 which is way too low for calculation of the final x value. The oxygen recombination is the dominant process in this region, the parasitic process of hydrogen recombination is negligible and the adsorption of hydrogen is strongly dependent on the hydrogen diffusion coefficient in palladium lattice. The absorbed hydrogen must diffuse from the inner lattice up to the palladium surface. Then in this region, the efficiency for the oxygen recombination named εO yields εO = 0.95, whereas ε = 0.05 and εH ≈ 0. The region II must be considered for a more accurate evaluation of ε. In the interval [C–B] the electric charge is Q = 1.425 C and comparing this data with the experimental constrains (1b) and (1c), we find an efficiency value ε = 0.533 and consequently εO = 0.467. In this region the contribution of the parasitic efficiency is present but negligible (still modest εH > 0) because of the low value of composition x. On the contrary, this parasitic efficiency gives an important contribution to the calculation of composition x in the region I, where composition x is very high and εH » ε. Here, if no voltage is applied to the electrodes, spontaneous and fast hydrogen deloading always takes place. In this case having no electrochemical current passing through the electrode the parasitic efficiency is mathematically enormous εH → ∞ because the large quantity of hydrogen absorbed in the palladium recombines on the surface. Moreover, to consider the amount of hydrogen lost by the parasitic effect, the following consideration for the εT (total efficiency) calculation have been evaluated: the efficiency ε in the region I assumes higher values, almost close to the unit, where the efficiency of oxygen recombination is very low in respect to the values in the region II. From the previously calculated efficiency ratio the following relationship εH > 15ε has been found for composition x < 0.78 then assuming the value εH = ε in the region I and assuming a total efficiency εT for this region as εT = ε + εH . This is still a strongly conservative estimation since the hydrogen recombination in this region is very high due to the superficial diffusion of adsorbed hydrogen atoms. With this ε estimation, the following composition x calculation in the region I has been performed. It can be assumed, with an acceptable under-estimation error of the total efficiency, that the two efficiencies, ε and εH , have same constant value inside the region I, which is the initial value of ε = 0.53. Hence, the average total efficiency in the region I, analyzing Fig. 4 results εT = 1.06. In Fig. 6 the behavior of efficiencies ε, εH and εT versus composition in the region I are shown. The efficiency ε in this region I is ε = 0.53 for composition x = 0.78, being the average value calculated in the region II. At the maximum x value, ε reaches the unit (1 C−1 ), i.e. x = Q. A linear behavior has been considered as a first order approximation of an exponential behavior. Exponential behavior of εH starting from εH = 0 at composition x = 0.78 and becoming very high (εH → ∞) at the maximum x value has been considered. Using the definition εT = ε + εH with εH = ε, the under-estimation of εT is evident. From this calculated εT value, the final mean x value is obtained. The electric charge in the zone I, from the point (C) to the point (D), is Q = 0.281 C. Hence, the mole number of the hydrogen absorbed in the sample for the zone I gives x = 0.298. Now, as stated in item (1c), the composition of the sample is x = 0.78. Therefore the final composition is xf = 0.78 + 0.298 = 1.078.
Fig. 6. Indicative efficiencies behavior in the region I during the electrochemical stripping of hydrogen. ε is related to the measured electrochemical hydrogen adsorption process; εH is associated to the parasitic hydrogen loss by H2 gas recombination; εT represents the average total efficiency.
For the pointed composition calculation for each electric charge measurement in the region I, the following equation has been used xi = (ε + εH ) · qi = εT · qi
(2)
where the xi is the pointed composition, qi is the pointed electric charge transferred and εT is the total efficiency in the region I. Using this method, the curves of relative resistance R(x)/Ro versus composition x have been produced as shown in Fig. 7. In Fig. 7 only relative resistance corresponding to the composition ratio x > 0.78 are plotted, because for lower composition such behavior it is well known. The data plotted in Fig. 7 is calculated in the following way: • The AC electrical resistance of palladium sample has been directly measured using an RLC Meter at 1 kHz and the absolute error in every single measurement is R = ± 0.001 . This is the instrumental error that affects Ro and R(x), but small oscillations of resistance value due to the physical-chemical processes on
Fig. 7. Relative resistance of PdHx versus composition x for x > 0.78. In this plot more than 20 different experiments shown are (red cross) performed, using the same sample geometry and experimental set-up and the literature curve (black dot). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of the article.)
P. Tripodi et al. / Journal of Alloys and Compounds 486 (2009) 55–59
palladium surface of about R = ± 0.01 are present in all measurements. Hence the error in the calculated relative resistance is the same for all measurements in the time and equals to (R/Ro ) = ±0.02 . • To calculate the composition x the following relationships has been used:
Q (t) =
I(t) · dt
(3)
as the experimental data is acquired at constant frequency of 1 Hz (one measurement every second) and at constant electrolytic current of 5 mA, the relationship (3) can be written as follows: Q (t) =
N
I·t =N·I·t
4. Conclusions
where N represents the number of experimental data measurements. The absolute error on the electrical current measurement is dI = 0.1 A that corresponds to a relative error dI/I = 2 × 10−5 . The error in measured time is dt = 0.1 ms that corresponds to dt/t = 10−5 . Using these errors, the distributed error on the electric charge transferred through the electrodes results: (4)
this value corresponds to an absolute maximum error on the electric charge measurement of dQ = 0.15 C. This error occurs on the first measurement of Q at the highest composition achieved. Then the error increases due to the integral and so, for each term of the sum (formula 3), during the hydrogen adsorption while the composition decreases, the error on Q increases. To achieve the maximum value of R/Ro (point C) as shown in Fig. 5 for experiments with very high composition (point D), a maximum number of 80 measurements have been acquired and N = 80 for all the experiments have been considered. This leads us to regard the value dQ = 12 C as the absolute maximum error of the electric charge. To calculate the error on the efficiency, we have considered a ratio (1) between the experimentally measured electric charge and the well known composition value of x = 0.760. The error on this value is stated as dx = 0.001 or dx/x = 1.3 × 10−3 , hence the error on ε is: dε dQ dx = + = 1.3 × 10−3 ε Q x
But assuming that the error on the efficiency εH is ten times greater than the error on ε, the absolute maximum error on composition x is x = ± 0.02. In Fig. 7, a series of curves of PdHx relative resistance versus x at room temperature is presented. A spread of composition, especially at high x value is evident. This non-homogeneity of data is imputable to the non-homogeneity of the sample, in particular to the diverse surfaces that the samples have. Clearly a sample with a large number of grain borders show dynamics of hydrogen atoms adsorption and absorption completely different from sample that has bigger grain size and smaller quantity of grain borders. This is because in the electrolytic loading of hydrogen atoms, is on the grain border that the maximum of hydrogen activity is present.
(4)
1
dI dt dQ = + = 3 × 10−5 Q I t
59
(5)
practically the uncertainty on the electric charge does not affect the error on the efficiency ε. The error affecting the composition is due to the error induced by the efficiency that for the reached composition x = 1.2 is dx = 0.001.
The important results reported in this paper are the comparison of literature data [11,6,12] and our new experimental results on the relative resistance R/Ro versus x as shown in Fig. 7. This plot shows evident general underestimation of composition x at high hydrogen concentrations in the PdHx system. Results are based on an accurate analysis of the electrochemical process efficiencies ε for composition values x > 0.78. The underestimation of ε implies that the composition x calculated with this method represents the lower limit of composition in PdHx . Acknowledgements We would like to give a particular thank to Dr. Antonio Cellucci and Dr. Riccardo Romanato for their useful help. This work is supported by the PNRM (National Plan of Military Research) of the Italian Ministry of Defense under contract no. 9239. References [1] G. Alefeld, J. Völkl, Hydrogen in Metals I, Springer-Verlag, 1978. [2] G. Alefeld, J. Völkl, Hydrogen in Metals II, Springer-Verlag, 1978. [3] N.F. Mott, H. Jones, The Theory of the Properties of Metal and Alloys, 183, Dover Publications, Inc., 1936, p. 186. [4] F.A. Lewis, The Palladium Hydrogen, Academic Press, 1967. [5] M.H. Lee, Sep. Sci. Technol. 15 (1980) 457. [6] S. Crouch-Baker, M.C.H. McKubre, F.L. Tanzella, Z. Phys. Chem. 204 (1998) 247–254. [7] B. Baranowski, S. Majchrzak, T.B. Flanagan, J. Phys. F: Metal Phys. 1 (1971) 258. [8] J.C. Barton, F.A. Lewis, I. Woodward, Trans. Faraday Soc. 59 (1963) 1201. [9] P. Tripodi, M.C.H. McKubre, F.L. Tanzella, P.A. Honnor, D. Di Gioacchino, F. Celani, V. Violante, Phys. Lett. A 276 (2000) 122. [10] P. Tripodi, D. Di Gioacchino, J.D. Vinko, Braz. J. Phys. 34 (2004), no. 3B. [11] P. Tripodi, D. Di Gioacchino, J.D. Vinko, Physica C 408–410 (2004) 350–352. [12] J. Tóth, L. Péter, I. Bakonyi, K. Tompa, J. Alloys Compd. 387 (2005) 172–178.
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jallcom
AC electrical resistance measurements of PdHx samples versus composition x Paolo Tripodi a,∗ , Daniele Di Gioacchino b , Jenny Darja Vinko a a b
H.E.R.A. SRL - Hydrogen Energy Research Agency, Corso della Repubblica 448, 00049 Velletri, Italy INFN-LNF – National Institute of Nuclear Physics – National Laboratory of Frascati, Via Enrico Fermi 40, 00044 Frascati, Italy
a r t i c l e
i n f o
Article history: Received 29 December 2008 Received in revised form 7 July 2009 Accepted 8 July 2009 Available online 16 July 2009 Keywords: PdHx Four probe AC electrical resistance Phase transitions
a b s t r a c t A brief introduction on the transport properties of PdHx system will be presented. The resistance ratio method is the most frequent technique used to measure the interstitial loading of hydrogen atoms into palladium. Using this technique a series of AC electrical resistance measurements of PdHx , demonstrating a stoichiometric values x > 1 obtained by electrochemical method at room temperature and pressure is presented. A full description of the used electrochemical method for preparing the samples PdHx with composition x > 1 and the analysis to determine the achieved composition will be presented. Conclusions on the electrical resistance of PdHx versus composition x and correlated physical phenomena have been done. In particular, these studies show the importance of the electrochemical processes efficiency. In order to have an accurate calculation of x value, precise efficiency amplitude estimation is needed. Our analysis underline the systematic underestimation of the x value in the well known PdHx relative electrical resistance versus x at room temperature as reported in literature. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Hydrogen and its isotopes dissolve in many metals and occupy interstitial sites in the host lattice producing an expansion of the lattice. Each interstitial hydrogen atom causes displacement of the metal atoms from their original sites while its electrons fill the electronic band of the metal at the Fermi energy level EF . This gives rise to a series of changes in physical properties of the hosting metal [1,2]. In this framework palladium is an intensely studied metal, for much of its peculiarities [3,4] like the capacity to adsorb large amount of hydrogen and the superconducting transition temperature in function of hydrogen composition. Generally, for palladium, the 4d10 state should be completely filled but in reality the 10 electrons are shared between two zones and the EF intersects the 4d and the broad 5sp bands [3–5]. There are 0.36 electrons in the 5sp band [5] and equal number of positive holes of unfilled state in the d shell. For this reason palladium absorbs hydrogen very strongly. In particular, interstitial hydrogen atoms affect the electrical resistance of the host metal [6–8]. New electron scattering centers are produced in metallic hydrides when interstitial vacancies are occupied by H(D,T) producing a new optical phonon band. This leads to a change in the
∗ Corresponding author. Tel.: +39 39 27868142; fax: +39 06 97258656. E-mail address: [email protected] (P. Tripodi). 0925-8388/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2009.07.052
resistance which can manifest itself even at room temperature. In the case of palladium this is the most important contribution considered in the overall changes observed. The relative resistance R(x)/Ro versus composition x [4] is shown in Fig. 1 where Ro is the pure Pd resistance and x is the molar ratio H/Pd. At room temperature, changing the composition x, the PdHx system exhibits several phases. The ␣ phase is present for composition in the range 0 < x < 0.05, while a coexisting ␣ +  phases exist for composition in the range 0.05 < x < 0.7. Then the  phase between 0.7 < x < 0.9 of the composition range is produced until the ␥ phase starts producing a  + ␥ phase in the composition range of 0.9 < x < x␥ and finally for composition x > x␥ with x␥ > 1 only the ␥ phase exists [9,10]. As would be expected the temperature coefficient of resistivity, , changes with hydrogen composition x in palladium. Information regarding the values range of the coefficient for corresponding composition x is well known [7,8]. In Refs. [9,10] an indication of a new phase transition in PdH system loaded at very high H composition, x > 1, is shown and is here reported in Figs. 2 and 3. In fact, the steep variation of the resistivity temperature coefficient in a short range of composition x, characterizes a strong evidence for a phase transition in PdH. During the transition, the softening of the optical phonons lattice elastic constant (due to the movement of hydrogen in the sub-lattice) lowers the same optical phonon energy, so that, these optical phonons begin to give a contribution to the resistivity value.
56
P. Tripodi et al. / Journal of Alloys and Compounds 486 (2009) 55–59 2. Experimental method
Fig. 1. Relative resistance of PdHx versus composition x at constant temperature T = 300 K.
Fig. 2. The temperature coefficient of resistance for PdHx , in function of hydrogen composition x [9]. The horizontal axes x has been reverted for a better comparison with Fig. 2. In this measurement the temperature coefficient reached a maximum value of = 14.0 × 10−3 K−1 . For pure palladium at composition x = 0 the temperature coefficient is = 3.7 × 10−3 K−1 .
Hydrogen is loaded into the palladium lattice using an electrochemical cell. This electrochemical hydrogen absorption process is used preferentially over physical absorption (via H2 as pressure) for one primary reason: this method allows higher composition to be achieved at room temperature and atmospheric pressure in respect to the other processes. The cell geometry consists of two parallel platinum square plates (100 mm × 100 mm × 0.05 mm) as anode electrodes, separated by 10 cm of electrolyte. The cathode was palladium wires (50 m diameter, length in the range 4–6 cm), placed in the middle between the two anodes. This unusual geometry and a short loading time were adopted in order to maximize the hydrogen loading into palladium cathode and to minimize the transfer of anodically produced species to the cathode. The attainment of very high loading levels is found to be critically dependent on controlling the impurities in the electrolyte. In our case, this is done using standard microelectronic industry clean procedures in all steps of the processes in a clean class 100 environment. The electrolyte consisted of strontium sulfate (SrSO4 ) dissolved in 18 M cm water (10−5 M) giving a slightly acidic solution (5.0 < pH < 6.5). The electrolysis required a DC current from 5 mA up to 50 mA. During the electrolysis the four probe AC resistance measurements of the palladium cathode were taken using an RCL meter at 1 KHz sinusoidal current. Highly loaded PdHx samples were electrochemically stabilized by adding (10−5 M) mercurous sulfate (Hg2 SO4 ) to the electrolyte. With this procedure the coated cathodes are found to be resistant to hydrogen de-loading for periods of months at room temperature and room pressure. The Pd–Hg “alloy” forms an amalgam that covers the palladium surface and the depth of this “coating” is hundreds of nanometers, so that the effect of the resistance decrease, due to this coating, is negligible. The final purpose of the alloy layer is to inhibit the hydrogen diffusion inside the palladium surface and at the same time to avoid hydrogen recombination. Hence, the composition x of PdHx sample is stable in time. There is another important intermediate effect of the alloy during the loading process. At the beginning, the Pd–Hg amalgam, only partially covers the cathode surface and goes preferentially in the de-loading defect points. This avoids the recombination of the atomic hydrogen absorbed into palladium lattice that diffuses on the surface in those defects producing H2 hydrogen molecules escaping from the cathode. For this reason a basic effect of stoichiometric ratio increase is obtained. Important characterization of the sample is the measurement of the average final stoichiometric value x. In order to obtain the x value, it is necessary to know the value of hydrogen and palladium moles. Palladium moles are measurable with a sensitivity of about 1 mol, but due to the low weight of hydrogen moles inside the palladium sample these measurements for hydrogen are not simple. For this purpose we have defined an electrochemical method, destructive however, for the measurement of stoichiometric ratio x in PdHx sample, based on the relative resistance R(x)/Ro measurements. This technique can be used as a standard method for the measurement of R(x)/Ro versus x as described below.
3. Analysis In order to obtain the functional of the relative resistance R(x)/Ro versus composition x as shown in Fig. 1, the composition x must be calculated since it is a variable not directly measurable. In Fig. 1, the plot of relative resistance versus x is time independent, while during the hydrogenation or dehydrogenation electrochemical process the time is a fundamental variable to calculate the total electrical charge Q[C] passing through the electrode. The Q[C] value is connected to x value. The x calculation using time, electrochemical current and some experimental constrain of relative resistance is described below and consequently, also the desired functional of relative resistance versus composition. The experimental data used for the composition x calculation are:
1. The behavior of R(x)/Ro versus x of the PdHx (Fig. 1), where Ro represents the pure palladium electrical resistance, has three experimental constraints: Fig. 3. The temperature coefficient of resistance of PdHx in function of time during a slight hydrogen leakage (elapsed time) [10]. After the hydrogen loading, the sample was not perfectly stabilized in order to have a hydrogen leak and hence a change in composition x. Each experimental point represents a measurement of in the temperature range 273–373 K. In these measurements the exact composition x, is not known, but x > 1 is present at the beginning of the experiment, i.e. when the elapsed time () is in the range [0 s < < 9 × 104 s]. It is interesting to note that the temperature coefficient of resistance reaches a maximum value of = 30.4 × 10−3 K−1 .
R(x) =1 Ro
for x = 0;
R(x) = 1.07 Ro
for x = 0.05
(1a)
(1b)
P. Tripodi et al. / Journal of Alloys and Compounds 486 (2009) 55–59
Fig. 4. Relative resistance of PdHx sample versus electrical current during the absorption process. Three regions are defined: region III where the ␣ phase is present and the calculated efficiency of absorption is very high; region II where the ␣, ␣ +  and  phases are present and the efficiency assumes a very low value; the region I where there are the phases ,  + ␥ and ␥ with efficiency close to zero.
that represents the composition value at which the  phase starts, i.e. the transition composition between ␣ and ␣ +  phase; R(x) = 1.76 for x = 0.78 Ro
(1c)
that represents the composition value in  phase where the electrical resistance has the maximum value; 2. The electric charge Q passing through the electrodes during the hydrogenation or dehydrogenation of PdHx samples is proportional to the amount of H moles that enter or exit Pd lattice. For the composition calculation a variable ε measured in C−1 named efficiency has been defined as follows: ε=
x Q
(1)
57
as the ratio between the variation of composition x and the corresponding amount of electrical charge Q transferred through the electrodes. During the hydrogen loading, when the palladium is the cathode, two reactions take place on the cathode surface; the hydrogen absorption inside the lattice and the hydrogen recombination. The relative resistance of PdHx versus total electric charge passing through the electrodes is shown in Fig. 4. In the phase ␣, at the beginning of electrochemical hydrogen loading process, an efficiency ε = 0.893 is found, because the R(x)/Ro = 1.07 at x = 0.05 is reached for a corresponding total electrochemical current Q = 0.056 C. Consequently, introducing the parasitic efficiency εH representing the quantity of electrochemical charge producing molecular hydrogen H2 , the value εH = 0.107 has been calculated. In this region the ratio between the two efficiencies is ε/εH = 8.35. Thus, the electrochemical current contributes to the composition with efficiency almost 8 times greater than the efficiency of the parasitic reaction. Furthermore, repeating the calculation in the ␣ +  phase region starting at x = 0.05 and ending at the maximum value of relative resistance (experimental constrain with x = 0.78, Eq. (1c)) the values ε = 0.060 and εH = 0.940 are obtained. Here the efficiency ratio is completely reversed giving a value ε/εH = 0.063. Only a small fraction of the electrochemical current contributes to the composition x, almost the totality of electrochemical charge yields the parasitic effect of H2 gas formation, the parasitic efficiency is almost 15 times greater then the efficiency ε. The estimation of efficiency ε in the region at higher composition becomes very difficult because the parasitic efficiency is very high εH ≈ 1. Unfortunately, this is the region where the calculation of efficiency is most important in order to calculate the final composition x. On the other hand, at high composition, the anodic process involves mainly the hydrogen absorbed into palladium sample, so that a more accurate x value can be obtained. After the loading procedure reached the maximum composition in reason of the boundary condition settled, the stripping of hydrogen is obtained inverting the polarity of electrochemical cell using the palladium electrode as anode. During the hydrogen deloading three reactions take place on the anode surface: hydrogen adsorption and oxygen recombination related to the electrochem-
Fig. 5. Relative resistance of PdHx sample versus electrical current during the adsorption process. In the region I where the ␥,  + ␥ and  phases are present, the calculated total efficiency is very high; region II where the ␣, ␣ +  and  phases are present and the region III where there is the ␣ phase.
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P. Tripodi et al. / Journal of Alloys and Compounds 486 (2009) 55–59
ical current provided to the electrodes; hydrogen recombination producing H2 molecules independent from the electrochemical current. In this anodic process, the third parasitic effect plays an important role especially at high composition. Analyzing Fig. 5, three regions are evident: region I in the interval [D–C], where the ␥,  + ␥ and  phases are present; region II in the interval [C–B] where the present phases are ␣, ␣ +  and  and region III in the interval [B–A] where the phase ␣ is present. The measurement of ε in the region III gives ε = 0.05 which is way too low for calculation of the final x value. The oxygen recombination is the dominant process in this region, the parasitic process of hydrogen recombination is negligible and the adsorption of hydrogen is strongly dependent on the hydrogen diffusion coefficient in palladium lattice. The absorbed hydrogen must diffuse from the inner lattice up to the palladium surface. Then in this region, the efficiency for the oxygen recombination named εO yields εO = 0.95, whereas ε = 0.05 and εH ≈ 0. The region II must be considered for a more accurate evaluation of ε. In the interval [C–B] the electric charge is Q = 1.425 C and comparing this data with the experimental constrains (1b) and (1c), we find an efficiency value ε = 0.533 and consequently εO = 0.467. In this region the contribution of the parasitic efficiency is present but negligible (still modest εH > 0) because of the low value of composition x. On the contrary, this parasitic efficiency gives an important contribution to the calculation of composition x in the region I, where composition x is very high and εH » ε. Here, if no voltage is applied to the electrodes, spontaneous and fast hydrogen deloading always takes place. In this case having no electrochemical current passing through the electrode the parasitic efficiency is mathematically enormous εH → ∞ because the large quantity of hydrogen absorbed in the palladium recombines on the surface. Moreover, to consider the amount of hydrogen lost by the parasitic effect, the following consideration for the εT (total efficiency) calculation have been evaluated: the efficiency ε in the region I assumes higher values, almost close to the unit, where the efficiency of oxygen recombination is very low in respect to the values in the region II. From the previously calculated efficiency ratio the following relationship εH > 15ε has been found for composition x < 0.78 then assuming the value εH = ε in the region I and assuming a total efficiency εT for this region as εT = ε + εH . This is still a strongly conservative estimation since the hydrogen recombination in this region is very high due to the superficial diffusion of adsorbed hydrogen atoms. With this ε estimation, the following composition x calculation in the region I has been performed. It can be assumed, with an acceptable under-estimation error of the total efficiency, that the two efficiencies, ε and εH , have same constant value inside the region I, which is the initial value of ε = 0.53. Hence, the average total efficiency in the region I, analyzing Fig. 4 results εT = 1.06. In Fig. 6 the behavior of efficiencies ε, εH and εT versus composition in the region I are shown. The efficiency ε in this region I is ε = 0.53 for composition x = 0.78, being the average value calculated in the region II. At the maximum x value, ε reaches the unit (1 C−1 ), i.e. x = Q. A linear behavior has been considered as a first order approximation of an exponential behavior. Exponential behavior of εH starting from εH = 0 at composition x = 0.78 and becoming very high (εH → ∞) at the maximum x value has been considered. Using the definition εT = ε + εH with εH = ε, the under-estimation of εT is evident. From this calculated εT value, the final mean x value is obtained. The electric charge in the zone I, from the point (C) to the point (D), is Q = 0.281 C. Hence, the mole number of the hydrogen absorbed in the sample for the zone I gives x = 0.298. Now, as stated in item (1c), the composition of the sample is x = 0.78. Therefore the final composition is xf = 0.78 + 0.298 = 1.078.
Fig. 6. Indicative efficiencies behavior in the region I during the electrochemical stripping of hydrogen. ε is related to the measured electrochemical hydrogen adsorption process; εH is associated to the parasitic hydrogen loss by H2 gas recombination; εT represents the average total efficiency.
For the pointed composition calculation for each electric charge measurement in the region I, the following equation has been used xi = (ε + εH ) · qi = εT · qi
(2)
where the xi is the pointed composition, qi is the pointed electric charge transferred and εT is the total efficiency in the region I. Using this method, the curves of relative resistance R(x)/Ro versus composition x have been produced as shown in Fig. 7. In Fig. 7 only relative resistance corresponding to the composition ratio x > 0.78 are plotted, because for lower composition such behavior it is well known. The data plotted in Fig. 7 is calculated in the following way: • The AC electrical resistance of palladium sample has been directly measured using an RLC Meter at 1 kHz and the absolute error in every single measurement is R = ± 0.001 . This is the instrumental error that affects Ro and R(x), but small oscillations of resistance value due to the physical-chemical processes on
Fig. 7. Relative resistance of PdHx versus composition x for x > 0.78. In this plot more than 20 different experiments shown are (red cross) performed, using the same sample geometry and experimental set-up and the literature curve (black dot). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of the article.)
P. Tripodi et al. / Journal of Alloys and Compounds 486 (2009) 55–59
palladium surface of about R = ± 0.01 are present in all measurements. Hence the error in the calculated relative resistance is the same for all measurements in the time and equals to (R/Ro ) = ±0.02 . • To calculate the composition x the following relationships has been used:
Q (t) =
I(t) · dt
(3)
as the experimental data is acquired at constant frequency of 1 Hz (one measurement every second) and at constant electrolytic current of 5 mA, the relationship (3) can be written as follows: Q (t) =
N
I·t =N·I·t
4. Conclusions
where N represents the number of experimental data measurements. The absolute error on the electrical current measurement is dI = 0.1 A that corresponds to a relative error dI/I = 2 × 10−5 . The error in measured time is dt = 0.1 ms that corresponds to dt/t = 10−5 . Using these errors, the distributed error on the electric charge transferred through the electrodes results: (4)
this value corresponds to an absolute maximum error on the electric charge measurement of dQ = 0.15 C. This error occurs on the first measurement of Q at the highest composition achieved. Then the error increases due to the integral and so, for each term of the sum (formula 3), during the hydrogen adsorption while the composition decreases, the error on Q increases. To achieve the maximum value of R/Ro (point C) as shown in Fig. 5 for experiments with very high composition (point D), a maximum number of 80 measurements have been acquired and N = 80 for all the experiments have been considered. This leads us to regard the value dQ = 12 C as the absolute maximum error of the electric charge. To calculate the error on the efficiency, we have considered a ratio (1) between the experimentally measured electric charge and the well known composition value of x = 0.760. The error on this value is stated as dx = 0.001 or dx/x = 1.3 × 10−3 , hence the error on ε is: dε dQ dx = + = 1.3 × 10−3 ε Q x
But assuming that the error on the efficiency εH is ten times greater than the error on ε, the absolute maximum error on composition x is x = ± 0.02. In Fig. 7, a series of curves of PdHx relative resistance versus x at room temperature is presented. A spread of composition, especially at high x value is evident. This non-homogeneity of data is imputable to the non-homogeneity of the sample, in particular to the diverse surfaces that the samples have. Clearly a sample with a large number of grain borders show dynamics of hydrogen atoms adsorption and absorption completely different from sample that has bigger grain size and smaller quantity of grain borders. This is because in the electrolytic loading of hydrogen atoms, is on the grain border that the maximum of hydrogen activity is present.
(4)
1
dI dt dQ = + = 3 × 10−5 Q I t
59
(5)
practically the uncertainty on the electric charge does not affect the error on the efficiency ε. The error affecting the composition is due to the error induced by the efficiency that for the reached composition x = 1.2 is dx = 0.001.
The important results reported in this paper are the comparison of literature data [11,6,12] and our new experimental results on the relative resistance R/Ro versus x as shown in Fig. 7. This plot shows evident general underestimation of composition x at high hydrogen concentrations in the PdHx system. Results are based on an accurate analysis of the electrochemical process efficiencies ε for composition values x > 0.78. The underestimation of ε implies that the composition x calculated with this method represents the lower limit of composition in PdHx . Acknowledgements We would like to give a particular thank to Dr. Antonio Cellucci and Dr. Riccardo Romanato for their useful help. This work is supported by the PNRM (National Plan of Military Research) of the Italian Ministry of Defense under contract no. 9239. References [1] G. Alefeld, J. Völkl, Hydrogen in Metals I, Springer-Verlag, 1978. [2] G. Alefeld, J. Völkl, Hydrogen in Metals II, Springer-Verlag, 1978. [3] N.F. Mott, H. Jones, The Theory of the Properties of Metal and Alloys, 183, Dover Publications, Inc., 1936, p. 186. [4] F.A. Lewis, The Palladium Hydrogen, Academic Press, 1967. [5] M.H. Lee, Sep. Sci. Technol. 15 (1980) 457. [6] S. Crouch-Baker, M.C.H. McKubre, F.L. Tanzella, Z. Phys. Chem. 204 (1998) 247–254. [7] B. Baranowski, S. Majchrzak, T.B. Flanagan, J. Phys. F: Metal Phys. 1 (1971) 258. [8] J.C. Barton, F.A. Lewis, I. Woodward, Trans. Faraday Soc. 59 (1963) 1201. [9] P. Tripodi, M.C.H. McKubre, F.L. Tanzella, P.A. Honnor, D. Di Gioacchino, F. Celani, V. Violante, Phys. Lett. A 276 (2000) 122. [10] P. Tripodi, D. Di Gioacchino, J.D. Vinko, Braz. J. Phys. 34 (2004), no. 3B. [11] P. Tripodi, D. Di Gioacchino, J.D. Vinko, Physica C 408–410 (2004) 350–352. [12] J. Tóth, L. Péter, I. Bakonyi, K. Tompa, J. Alloys Compd. 387 (2005) 172–178.