Brazilian Journal of Physics, vol. 34, no. 3B, September, 2004 1177

Magnetic and Transport Properties of PdH:Intriguing Superconductive Observations∗

Paolo Tripodi1†, Daniele Di Gioacchino2, and Jenny Darja Vinko1

1H.E.R.A., Hydrogen Energy Research Agency, Corso della Repubblica 448, 00049 Velletri, Italy2INFN-LNF National Institute of Nuclear Physics - National Laboratory of Frascati, Via Enrico Fermi 40, 00044 Frascati, Italy

Received on May 21, 2003

Since the discovery of superconductivity in palladium-hydrogen (PdH) and its isotopes (D,T) at low tempera-ture, several efforts have been made to study the properties of this system. Superconductivity of PdH system hasbeen initially claimed by resistance drop versus temperature and then confirmed by dc magnetic susceptibilitymeasurements. These studies have shown that the critical transition temperature is a function of the hydrogenconcentration x in the PdHx system. In all these experiments, the highest concentration x of hydrogen in palla-dium was lower than the unit. In the last decade we defined a room temperature and room pressure technique toload hydrogen and its isotopes into palladium at levels higher than unit, using electrochemical set-up, followedby a stabilization process to maintain the hydrogen concentration in palladium lattice stable. In the meanwhile,several measurements of resistance versus temperature have been performed. These measurements have shownseveral resistive drops in the range of [18K< Tc < 273K] similar to the results presented in literature, when thesuperconducting phase has been discovered. Moreover, on PdH wires 6cm long the current-voltage characteris-tic with a current density greater than 6 ∗ 104 Acm−2 has been measured at liquid nitrogen temperature. Thesemeasurements have the same behavior as superconducting I-V characteristic with sample resistivity, at 77K, oftwo orders of magnitude lower than copper or silver at the same temperature. The measurements of first andthird harmonic of ac magnetic susceptibility in PdHx system have been performed. These represent a goodtool to understand the vortex dynamics, since the superconducting response is strongly non-linear. Clear acsusceptibility signals confirming the literature data at low temperature (9K) and new significant signals at hightemperature (263K) have been detected. A phenomenological approach to describe the resistance behaviour ofPdH versus stoichiometry x at room temperature has been developed. The value x=1.6 to achieve a macroscopicsuperconducting state in PdHx has been predicted.

1 Introduction

1.1 PdHx: overview

Hydrogen (H) and its isotopes dissolve in many metals andoccupy interstitial sites in the host lattice producing an ex-pansion of the lattice. Each interstitial H causes displace-ment of the metal atoms from their original sites while itselectrons fill the electronic band of the metal at the Fermienergy level EF . This gives rise to a series of changes inphysical properties of the hosting metal [1, 2]. In this frame-work Palladium (Pd) is a metal, intensely studied, for muchof its peculiarities [3]. Usually it is employed as catalystfor hydrogen reactions [4]. Generally, for Pd the 4d10 stateshould be completely filled but in reality the 10 electrons areshared between two zones and the EF intersects the 4d andthe broad 5sp bands [3, 5]. There are 0.36 electrons in the5sp band [5] and equal number of positive holes of unfilledstate in d shell. For this reason Pd absorbs H very strongly.The paramagnetic susceptibility of pure Pd decreases from550 − 600 ∗ 10−6 cgs units to diamagnetic behaviour ofPdHx for stoichiometry x =0.75, where x represents theratio between Pd and H moles [4]. These measurements lead

to deduction that the electron of the H goes into the d shell,thereby the number of positive holes decreases and hencethe paramagnetic behaviour diminishes. There is a relation-ship between the electrical resistance of PdHx and the Hstoichiometric value x (Fig. 1). Analysing the relative resis-tance R(x)/Ro, where R(x) is the PdHx electrical resis-tance versus x and Ro is the pure Pd electrical resistance, anexperimental pseudo-parabolic curve with negative concav-ity is observed. At room temperature, this curve has a max-imum at x≈0.75 and then it decreases almost to the initialvalue at x≈1. Considering that ideally in the fcc Pd latticeit should be possible to achieve a value x=3 when all theoctahedral and tetrahedral sites are occupied, immediatelyrises the question: what happens to the electrical resistivityof the PdH at room temperature for x>1? For low temper-atures, with x≤1 the answer is well known: PdHx systembecomes superconductor [7, 8] with Tc proportional to thex, namely, from x =0.75 with Tc=1K up to Tc=9K for xclose to 1. We will attempt a reply to our questions throughexperimental details.

∗Presented at the Workshop on Unconventional Superconductors (U-Super), Campinas May 20-24, 2003.†Also at INFN-LNF National Institute of Nuclear Physics National Laboratory of Frascati, Via Enrico Fermi 40, 00044 Frascati, Italy;

paolo.tripodi@heraphysics.it

1178 Paolo Tripodi et al.

1.0

1.2

1.4

1.6

1.8

2.0

0 0.2 0.4 0.6 0.8 1

DeuteriumHydrogen

R/R

0

x=H(D)/Pd

β phaseα phase α +β phase

A B C

Figure 1. Relative resistance R/Ro versus H stoichiometryx =H/Pd (D/Pd) for PdHx sample (full line) and for PdDx (dot-ted line). Ro is the resistance of pure Pd sample at stoichiometryx =0.

1.2 PdHx: thermal coefficient of resistance λ

We have studied the thermal coefficient of resistance λ forPdHx system. It is well known that the resistance of metal-lic compounds depends on temperature. For a narrow tem-perature range, the resistance is described by equation (1):

R (T ) = R (To) (1 + λ∆T ) (1)

where R(To) is the resistance of the sample at 0oC. ∆T =T -To is the change in temperature and λ represents the tem-perature coefficient of resistance. From the equation (1) theλ equation (2) is calculated:

λ =(

R (T )R (To) − 1

)∗ ∆T−1 (2)

where λ expresses the sensitivity of the resistive elementversus temperature.

103

104

105

00.20.40.60.81

λ 10

-6[K

-1]

x

α ph

ase

α+β phaseβ phaseγ phase

Figure 2. Thermal coefficient λ of PdHx, in function of hydrogenstoichiometry x [6]. The horizontal axes has been reverted for abetter comparison with Fig. 3.

103

104

105

0 100 3 104 6 104 9 104 1,2 105 1,5 105

λ 10

-6[K

-1]

Elapsed time [s]

λMAX

previously measured [6]

λMIN

previously measured

λ of pure Pd

x<1x>1

Figure 3. Thermal coefficient λ of PdHx, in function of time dur-ing a slight H deloading (Elapsed time). Each experimental pointrepresents a measurement of λ in the temperature range 273-373K.In these measurements the exact stoichiometry x, is not known, butx >1 is present at the beginning of the experiment, i.e. when theelapsed time (τ ) is in the range [0s < τ < 9 ∗ 104s]. After the Hloading the sample was stabilized and measured in temperature asto define λ versus elapsed time while the sample slightly leaks H.

There are contributions to the resistivity other than thosedue to lattice vibrations. For example, if a second elementis present in a metal either as an impurity or as an alloy-ing element, this destroys the periodicity in the electricalpotential and gives rise to elastic scattering, hence the re-sistivity increases. On the other hand, if a short or longrange order is present then the resistivity decreases. Clearlythe resistivity and in particular λ, are rather sensitive tothe order/disorder states [9]. It is well known that λ isalso dependent on the variation of stoichiometry x. PurePd (Fig. 2) has λ =4000ppm then it increases to a maxi-mum of λ=4200ppm at x≈0.05 corresponding to the phasetransition between the α and the α+β phase. Increasingthe H stoichiometry x, λ decreases reaching a minimum ofλ=1800ppm at x≈0.75 corresponding to the phase transi-tion between the α+β and the β phase where λ remains con-stant [4]. Then a steep increase of λ=15000ppm (Fig. 2)has been measured at about x≈1 [6]. This quasi-asymptoticbehaviour shown in Fig. 2 would indicate a possible newphase transition between the β phase and the new γ phase atx=0.95 [6].

In Fig. 3 we show further new experimental data demon-strating that with x >1 the coefficient λ decreases to lowervalues, that confirm the presence of the phase transition be-tween the β and the new γ phase [6]. Experimental methodto obtain these results is as follows: in the temperature rangebetween the ice melting temperature T0 and the water boil-ing temperature TB , for fixed stoichiometry x, the temper-ature coefficient of resistance λ can be considered constant,i.e. we assume that in the temperature range ∆T=TB-T0 theslope of resistance versus temperature is constant as claimedin the formula (1). After the loading procedure the samplewas cooled to T0 and the resistance was measured. Afterthat, the sample was warmed to TB and again the resistancewas measured. Using the measured resistance and tempera-ture values, λ has been calculated with equation (2). In or-der to change the stoichiometry x the sample was immersed

Brazilian Journal of Physics, vol. 34, no. 3B, September, 2004 1179

again in the electrolitycal cell in floating configuration toobtain a slight H deloading. This procedure was repeatedseveral times and in Fig. 3 every experimental point rep-resents a measurement of λ in function of the elapsed timeduring slow H deloading. During these measurements it wasimpossible to measure the H stoichiometry x in the sample.The only available indication on x is that the stoichiometryis decreasing in time, i.e at elapsed time zero, x is maximumand then it decreases with time. The last three λ points, inFig. 3, are coherent with λ values for x <1 shown in Fig. 2[6]. This indicates that the other points in Fig. 3 show λ atvery high stoichiometry x >1. In conclusion, in the new γphase (x >1) the λ value is extremely low, in some caseswe have measured a λ as low as 1ppm, whereas close to thetransition stoichiometry (x≈1) λ achieves very high values,up to 66000ppm.

1.3 PdHx: electrical transport measurements

A series of electrical transport measurements on PdHx

wires, with 50µm diameter, will be presented. Experimentaldata on the PdHx behaviour at very high, unexplored, stableH concentration x versus temperature (Fig. 4) shows a resis-tance drop at Tc=51.6K. Applying 1T dc magnetic field, theresistive drop splits to two lower temperatures of 31.3K and18.8K [10, 11]. This data renders more consistent, but notdefinitive reply to our question, on the presence of a pos-sible superconducting phase. In the light of this data, weprepared several PdHx samples with very high stoichiome-try x and hence several resistive drops have been measuredfrom 80K up to 273K as shown in Fig. 4. These measuredresistance drops, from 5% to 10% of the offset resistancevalues, have already been published [10, 11]. The presenceof these resistance drops for different temperatures Tc in-dicates different x concentrations in the samples and thatonly a small fractions of the sample have the x value suchas to cause the decreases of the resistance at given temper-ature. In order to calculate the corresponding xc values weused the equation presented in Fig. 13. This equation corre-lates xc with Tc. Another interesting measurement is the I-Vcharacteristic for a PdHx sample at LN2 temperature thatshows superconducting critical current greater than 6 ∗ 104

Acm−2 (Fig. 5) [10]. The I-V value threshold is by 2 or-ders of magnitude higher, as we have already underlined inthe reference [10]. However, our evaluation is based on thefact that the voltage drop on the PdHx wire at 77K is aconstant value with a variable current I. This cannot be a be-havior of a normal resistance since there is no slope of theI-V characteristic. Moreover, the rapid increase of the volt-age drop V around the current value of 1A indicates a rapidresistance increase. As shown in Fig. 5, the effective PdHx

sample resistivity at 77K is 5nΩcm which is lower than cop-per and silver resistivity at 77K respectively of 300nΩcmand 200nΩcm.

20 40 600

1

2

3

4

5

Nor

mal

ized

Res

ista

nce

80 90 100

TEMPERATURE (K)265 275

Figure 4. A series of superconducting transitions for PdHx. Thenormalized resistance versus temperature is shown, as reported inliterature [8].

0

1

2

3

4

5

6

7

0.0 0.2 0.4 0.6 0.8 1.0 1.2

V(m

V)

I(A)

lenght=6cm ; diameter=50 micron

Jc = 6*104 [A/cm2]

Ec=3x10-4 V/cm

T=77K

Figure 5. Critical current in PdHx wire at T=77K [10].

1.4 PdHx: sample preparation

H was loaded into the Pd lattice using an electrochemi-cal cell. This chemical absorption process of H was usedpreferentially over physical absorption ( via H2 gas pres-sure) for one primary reason. This method allows higherH/Pd concentrations to be achieved at room temperatureand atmospheric pressure in respect to other processes.The cell geometry consists of two parallel Pt square plates(100x100x0.05 mm3) as anode electrodes, separated by15cm of electrolyte. The cathode was a Pd sample, placedin the middle between the two anodes. The used Pd sam-ples were thin wires (50µm diameter, lenght in the range 6-30cm) or tapes (50µm thickness, lenght in the range 2-4cm,width 0.4cm). This unusual geometry and a short loadingtime were adopted to maximize the H loading in Pd cathodeand to minimize the transfer of anodically produced species

1180 Paolo Tripodi et al.

to the cathode. The attainment of very high loading levelswas found to be critically dependent on controlling the im-purities in the electrolyte. The electrolyte consisted of stron-tium sulfate (SrSO4) dissolved in 18MΩcm water (10−5 M)giving a slightly acidic solution (5.0≤pH≤6.5). The elec-trolysis required a dc current from 5mA up to 200mA. Dur-ing electrolysis the four probe ac resistance measurementsof the Pd cathode were taken using an RCL meter at 1mA,1KHz sinusoidal current. Highly loaded PdHx samples,were electrochemically stabilised by adding (10−5 M) mer-curous sulfate (Hg2SO4) to the electrolyte. With this pro-cedure the coated cathodes are found to be resistant to Hdeloading for periods of months at room temperature andpressure. The Pd-Hg “ alloy” forms an amalgam that coversthe Pd surface and the depth of this “ coating” is hundreds ofnanometers, so that the effect of the resistance decrease, dueto this coating, is negligible.

1.5 PdHx: mean stoichiometry measurement

Important characterization of the sample is the measurementof the average final stoichiometric value x. In order to ob-tain the x value, it is necessary to know the value of Hand Pd moles. Pd moles are measurable with a sensitiv-ity of about 1µmol, but due to the low weight of H molesinside the Pd sample these measurements for hydrogen arenot simple. For this purpose we have defined an electro-chemical method, destructive however, for the PdHx sam-ple. Therefore it can only be used as a standard method forthe measurement of relative resistance R(x)/Ro versus x asdescribed below. To calculate x we need to evaluate the effi-ciency ε during the electrochemical H deloading process toavoid the undesired overestimation of x. ε is defined as ratiobetween the variation of stoichiometry ∆x correlated withdeloaded H from the sample and the corresponding amountof electrical charge ∆Q transferred through the electrodes:

ε =∆x

∆Q(3)

For the ε calculation the following experimental evi-dences are used:

1. the behavior of R(x)/Ro versus x of the PdHx (fig.1)has 3 experimental constraints:

(a) point (A) where R(x)/Ro=1 for x=0;

(b) point (B) that is the separation point betweenα and α + β phase where R(x)/Ro=1.07 forx≈0.05;

(c) point (C) the maximum of the curve whereR(x)/Ro=1.76 for x=0.75;

2. The electric charge Q passed through the electrodesduring the deloading of PdHx samples, proportionalto the amount of H moles that exit Pd lattice.

For the average final value x, the following is used:

1. The final value R(x)/Ro achieved during the H load-ing in Pd (point D Fig. 6);

2. The estimated efficiency ε value.

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

0 1 2 3 4

R/R

0

Total electrical charge [C]

H/Pd<0.05α

x = 0.78x = 0.76

ε =

26%

QC= 0.7363 Q

A = 4.60Q

B = 3.6454

ε =

2%

I IIIII

AD C B

ε= 5

2%

Figure 6. R(x)/Ro during H deloading versus electric chargepassed trough the electrodes.

During the H loading, electrochemical concurrent pro-cesses and long loading time affect the efficiency calcula-tion ε (overestimation) particularly in the zone I (Fig. 6), sothat it is necessary to calculate ε during the H deloading.This way ε is underestimated and hence renders acceptablex value. In Fig. 6 the R(x)/Ro during the H anodic deload-ing in PdHx wire sample is plotted in function of the totalelectric charge transferred through the electrodes. The be-havior is divided in 3 regions: I in the interval [D-C], II inthe interval [C-B] and III in the interval [B-A]. To estimatethe ε value we start evaluating the separation point betweenthe zone II and the zone III (point B) which fits the transitionpoint between the α and α + β phase. The electric chargenecessary to change the R(x)/Ro from the value 1 (point A)to 1.07 (point B) is ∆Q=1 Coulomb. Comparing this ex-perimental data with the data in item 1(b) we find that theefficiency is ε=5%, which is way too low. The H strippingdynamics is dominated by two processes: the superficial re-combination and the H diffusion from the inside to the sur-face of the Pd. Since the ε is determined only by the superfi-cial recombination and in the zone III the diffusion effect isdominant, the underestimation of the ε occurs in this zone.Therefore the zone II must be considered for a more accu-rate evaluation of ε. In the interval [C-B] the electric chargeis ∆Q=2.8 Coulomb and comparing this data with the items1(b) and 1(c), we find an efficiency of ε=26%. In the zone Ithe sample is overloaded with H. Initially, around the point(D) the deloading efficiency is ε=100% until the change ofthe slope (Fig. 6), to arrive to ε=26% at the point (C). Wepresume that the average efficiency is 52% in this zone (dou-bled efficiency of the zone II) which is still strongly con-servative estimation in respect to the arithmetic mean value(ε=63%).

Brazilian Journal of Physics, vol. 34, no. 3B, September, 2004 1181

6.1

6.2

6.3

0.0

2.5

5.0

7.5

10.0

4 6 8 10 12 14 16

χ'1

χ"1

χ '1 (

arb.

unit

x 10

-3) χ "

1 (arb.unit x 10-5)

Temperature (K)

Figure 7. Real (triangles) and imaginary (circles) part of first har-monic (Hac=6G f=1KHz) of PdHx slab (x≈1).

1.10

1.12

1.14

2.20

2.24

2.28

2.32

2.36

2.40

4 6 8 10 12 14

χ'3 χ"

3

χ '3(a

rb.u

nit x

10-4

) χ "3 (arb.unit x 10

-5)

Temperature (K)

Figure 8. Real (triangles) and imaginary (circles) part of third har-monic (Hac=6G f=1KHz) of PdHx slab (x≈1).

From this definitive ε value we obtain the final mean xvalue. The electric charge in the zone I, from the point (C)to the point (D), is ∆Q=0.8 Coulomb. Hence the mole num-ber of the H entered in the sample for the zone I, consid-ering ε=52%, gives ∆x=0.4. Now, as stated in item 1(c),the stoichiometry of the sample is ∆x=0.75. Therefore thefinal stoichiometry is xf ≥ 0.75 + 0.4 = 1.15. Resumingthis procedure, there are two important implications. Firstof all, this method is general and valid for any sample ge-ometry. Secondly, it is independent from any concurrentelectrochemical processes and from Pd sample moles.

2 Results and Discussion

To further define the possible superconducting properties ofPdHx at high temperatures, we have performed and arepresenting in this paper, the measurements of ac magneticsusceptibility and its higher harmonics. It is extremely im-portant to check the presence of high harmonics since thesuperconducting response is strongly non-linear. In fact inthe following section 2.1, we will discuss the first and thirdharmonic of the ac magnetic susceptibility measurements,moreover in section 2.2 a possible simple phenomenologi-cal approach that explains the PdHx relative resistance infunction of x at fixed temperature (300K) will be presented.

-2

0

2

4

6

8

10

12

14

258 260 262 264 266

1 measure2 measure

χ "1 (

arb.

units

x 1

0-5)

Temperature (K)

Figure 9. Imaginary parts of first harmonic of PdHx slab, firstmeasure (full circles), second measure after 1 week (empty circles)(x >1).

2.1 ac susceptibility measurements

The ac magnetic susceptibility (χn = χ′n + i χ”

n : n=1,3)measurements were performed with the European Facility8T flow cryostat [12]. This cryostat has a susceptometerwith an in-line double pick-up coil (Helmotz like) bridgewith an exciting external ac magnetic field up to 6G at fre-quency in the range [31Hz<f<2kHz], able to acquire witha lock-in amplifier the first seven harmonics of ac magneticsusceptibility, with the possibility to use a dc magnetic fieldup to 8T. The sample was cooled down to LHe temperaturein ZFC (Zero Field Cooling) then the temperature has beenslowly increased up to 300K. The data file collects the exper-imental value of ac susceptibility as the average value of 5points while the temperature is not varied more than 0.01K.The subtraction of the null file due to the measurement sys-tem has been performed.

Some consideration on the phase measurement of thesample must be done for clarity. Usually in the ac mag-netic susceptibility measurements the phase of the signal isimposed in order to maximize the in-phase (χ

′1) component

and minimize the out-phase (χ”1) component when the sam-

ple is in superconducting or normal state (zero-phase pro-cedure). In this case we minimized the imaginary part atLHe temperature. In Fig. 7, the real χ

′1 and the imaginary

χ”1 components of the first harmonic are plotted at low tem-

perature and a Tc of 9K [7] is shown. In Fig. 8, the thirdharmonic χ

′3 and χ”

3 shows similar behavior of the sam-ple. This indicates the presence of the well-known super-conducting phase at low temperature. This superconduct-ing phase, in accordance with literature data, is achieved fora stoichiometry x≈1 [7]. In Fig. 9 (first measurement) avery significant signal of the imaginary component χ

′′1 is

shown at 263.5K, corresponding to zones of PdHx withstoichiometry x>1. A week later, the same measurementswere repeated on this PdHx sample (second measurement),shown in Fig. 9, and the critical temperature shifted down

1182 Paolo Tripodi et al.

to lower temperature Tc=261.5K (slight deloading, proba-bly due to thermal cycles). A clear diamagnetic signal of thereal component χ

′1 is shown in Fig. 10, overlapped with an

extensive paramagnetic signal due to the PdHx zones withstoichiometry in the range [0 ≤ x < 0.75] [4, 13]. This in-dicates that only a small fraction of the PdHx sample hasthe appropriate stoichiometry x >1 corresponding to the su-perconducting phase at this critical temperature Tc=263.5K.This slope recalls the magnetic susceptibility behavior ofthe RBa2Cu3O7−x with paramagnetic ordered rare earths(R=Sa,Eu,etc.) where, decreasing the temperature well be-low Tc, the behavior changes from diamagnetism to param-agnetism [14].

6,95

7,00

7,05

7,10

258 260 262 264

1 measure2 measure

χ'1 (

arb.

units

x 1

0-3)

Temperature (K)

Figure 10. Real parts of first harmonic of PdHx slab, first mea-sure (full squares), second measure after 1 week (empty triangles)(x >1).

-10

-5

0

5

10

-1

-0,5

0

0,5

1

240 245 250 255 260 265

χ'3

χ' '3χ '

3(arb

. uni

t x10

-6)

χ''3 (arb. unit x10-6)

Temperature (K)

Figure 11. Real and imaginary parts of third harmonic of PdHx

slab (first measure).

The fact that χ′1 signal has a value lower than expected

(about 1/6 less) in comparison with the imaginary compo-nent χ

′′1 , can be imputed to the non-appropriate zero-phase

procedure, in fact, the imaginary component has been min-imized at 4.2K and this procedure is strongly dependent onthe temperature. We checked the presence of the third har-monic and in Fig. 11 the third harmonic real and imaginarypart of first measure show a clear oscillation with an onset

temperature of 264K. These results have been obtained af-ter two months (room temperature and pressure) storage ofthese highly H loaded PdHx samples and the same samplerendered nearly the same Tc in three consequent measure-ments.

2.2 R/Ro H loading at 300K: a phenomeno-logical approach

The behaviour interpretation of the relative resistance R/Ro

at 300K in function of x content, uses the concept of the twophases (α,β) and their coexistence (α+β) in the PdHx sys-tem [3] but since H is not a parent metal of Pd, this approachis not applicable. As shown in Fig. 12, a phenomenologicalmodel has been developed. The model predicts that R/Ro

of the PdHx systems at room temperature will exponen-tially decrease with the increasing of H loading x for x>1.Moreover, it predicts that R/Ro will decrease to zero resis-tance at xc=1.6, so that the PdHx will be in a room temper-ature superconducting state. The PdHx system is modelledas having two electron transport mechanisms available inparallel: one superconducting fluctuation transport and theother normal transport. In other words, their correspondingresistances are in parallel to obtain the overall resistance.

0.0

0.5

1.0

1.5

2.0

0 0.5 1 1.5 2

R/R

0

X

X0

Xc

T=300K

Figure 12. The best fit of experimental data for PdHx sampleusing the parallel model of the relative resistance. A critical tem-perature Tc =300K is achieved at xc=1.6. The xo represents theH stoichiometry where the relative resistance is at maximum value.

The normal electron transport mechanism is modelled todescribe a relative resistance that linearly increases with thestoichiometry x. This linear dependence is believed to resultfrom the linear increase in the number of scattering centresin the system with the increase of x. Thus, the relative resis-tance is written as:

(R

Ro

)l

= 1 + Λx (4)

where R is the resistance at stoichiometry x, Ro is the resis-tance of a pure palladium and Λ is a constant of proportion-ality. The superconducting fluctuation transport mechanism

Brazilian Journal of Physics, vol. 34, no. 3B, September, 2004 1183

is modelled to describe a relative resistance that exponen-tially decreases with x. This exponential dependence forx>1 is written as:(

R

Ro

)e

= βe−γ(x−xo) (5)

where R and Ro are as defined in Eq. 4, β is correlated withthe frequency described in the superconducting fluctuationtheory [15]. γ is the ratio between the free energy increment[15] or the condensation energy of the superconducting do-mains and the Boltzmann factor kT at 300K. (x- xo) rep-resents the number of fluctuating superconductive domainsfor x in the range [0.75<x<xc][16].

This superconducting fluctuation process can be ex-plained as follows: During the H loading, the H electronfills the unfilled 4d state easily without affecting much theEF level due to the high electron state density in 4d shell.Increasing H stoichiometry, the electrons fill the unfilled 5spbands above the 4d bands. Due to the low electron statedensity of 5sp band, the EF must be raised. This leads usto deduce that the dissolved H atoms in Pd are completelyionised (H+) in interstitial position without being specifi-cally bound to a particular Pd atom. The dissolved H+ ions[5] are also extremely mobile. The transition rate is 1012

s−1 and the self-diffusion coefficient is 10−6 cm2s−1. H+

ions localized in a cluster, in average remain about their sitesfor 10 oscillations before moving to nearest-neighbour sites.Meanwhile, the sub-lattice vibrates with very high localizedoptical frequencies at about 1013Hz, due to the lightness ofthe H mass. In this context a local fluctuation of supercon-ductivity in PdHx can occur with a rather unusual couplingbetween localised optical phonons and the EF electrons thatspent considerable time around H+ ions. This combinationallows the electrons at EF level to experience the attractionthrough H-sub-lattice (BCS like approach). Increasing Hcontent, the number of clusters and local superconductingfluctuations increases achieving the complete superconduct-ing phase.

0

1

2

3

4

5

6

-0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

ln(T

c)

ln(x)

Tc

= n Xn

Figure 13. Experimental stoichiometry x data for PdHx sampleswith low Tc [7] (empty circles) together with our phenomenologi-cal approach datum (gray square). In accordance with this model,x values for a series of experimental Tc shown in Fig. 4, have beenprinted as full circles.

Adding the relative resistances from Eq. 4 and Eq. 5in parallel, one obtains a phenomenological expression forR/Ro at room temperature as a function of x:

(R

Ro

)p

=(1 + Λx)βe−γ(x−xo)

1 + Λx + βe−γ(x−xo)(6)

Using the fitted free parameters, the resulting curve is shownin Fig. 12. The best fit of equation (6) produces the finalequations (7,8):

(R

Ro

)l

= 1 + 1.16x (7)

(R

Ro

)e

= 40e−12.4(x−0.76) (8)

In equation (7), the parameter Λ=1.16 is strictly corre-lated with the linear lattice expansion during H loading [1].From equation (8) the condensation energy of 270meV forthe superconducting phase can be calculated at x=xc. Thisvalue is in the expected range for the formation energy ofcoherent systems. The equations 6-8 render the value R=0for xc=1.6. This indicates a possible superconducting stateat 300K for xc=1.6. This datum (gray square in Fig. 13)together with the experimental data at low Tc (empty cir-cles in Fig. 13) reported in literature, are used to extrapolatethe relationship in Fig. 13: Tc=nxn. For PdHx system re-sults n=7.86. Using this relationship we added the resistancedrops data (Fig. 4) to the plot in Fig. 13 (full circles) to ob-tain a quantification of the mean stoichiometry x that resultsin the range [1.27 < xc < 1.57].

3 Summary and conclusions

This letter presents first and third harmonics of ac suscep-tibility data together with our previous variety of experi-mental data [10] on electrical transport. These measure-ments together with several resistive drops in the temper-ature range [51.6K < Tc < 273K] give some further indica-tion to answer the question: what happens at room temper-ature for x>1 in PdHx system? Should the PdHx systemwith x>1 be a HTSC, the presented data must be confirmedwith a clear Meissner effect measurement. Nevertheless, asmall diamagnetic signal of χ

′1 at 263K in coincidence with

imaginary part of χ′′1 and real and imaginary part of third

harmonics have been measured. A simple phenomenologi-cal approach based on the parallel of two electric transportmechanisms in order to explain the R/Ro behaviour at roomtemperature in the PdHx system as a function of the H con-centration x has been developed. The first mechanism ex-plains the experimental increases of the relative resistance inthe PdHx system due to the lattice expansion in the range[0<x<xo=0.75]. The second mechanism explains the de-creases of the PdHx relative resistance at x>xo, as a typicalexpression of the superconducting fluctuations of resistance.The superconducting state at room temperature Tc=300K forconcentration xc=1.6 has been predicted.

1184 Paolo Tripodi et al.

Acknowledgements

We wish to thank our collaborators Antonio Celluci andRiccardo Romanato for their valuable collaboration.

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