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Physica C 408–410 (2004) 350–352

Superconductivity in PdH: phenomenological explanation

Paolo Tripodi a,b,*, Daniele Di Gioacchino b, Jenny Darja Vinko a

a H.E.R.A. S.r.l. Hydrogen Energy Research Agency, Corso della Repubblica 448, 00049 Velletri, Italyb I.N.F.N., Frascati National Laboratory, via Enrico Fermi 40, 00044 Frascati, Italy

Abstract

Experimental data on PdHx(D) at 300 K shows electrical resistivity q lower than that of the pure Pd for stoichi-

ometry x ¼ H=Pd close to the unit. At this stoichiometric value x ¼ 1 a Tc of 9 K and higher Tc for x > 1 have been

measured. In these systems Tc increases with stoichiometry x, hence a phenomenological description of the q for highly

loaded PdH(D) system at 300 K has been developed. This approach uses a parallel model of two concurrent electrical

transport processes: (i) q has a linear raise with the x, due to the increase of Pd lattice relative volume, (ii) q has an

exponential decrease versus x due to superconducting fluctuations at very high x in PdH(D). Under the assumption of

our model, PdHx could be considered as a possible room temperature superconductor. Inverse isotopic effect for

0:6 > x > 0:96 changes to normal isotopic effect at stoichiometry xW > 1.

� 2004 Elsevier B.V. All rights reserved.

Keywords: PdH superconductor; PdH resistivity

1. Introduction

Relative resistance R=R0 of the PdHx versus stoichi-

ometry x, where R0 is the resistance of pure Pd, is usually

interpreted with the Mott and the modified Mott model

for metals and metal-alloys [1]. This model considers

two phases: a-phase (0 < x < 0:02), b-phase (x > 0:6)and their coexistence [aþ b]-phase (0:02 < x < 0:6) in

Pd, so that the R� R0 variation in PdHx is proportional

to xð1� xÞ and ð0:6� xÞ2ð1� xÞx2 for s–s and s–d elec-

tron scattering respectively. The electronic configuration

changes with x, due to the filling up of the d-band

vacancies, hence a reduction of s–d scattering and the

consequent reduction of R=R0 would be expected [1,3,9].

The increasing of R is due to H vibration around their

Octahedral (O) sites at very high frequencies (optical

phonons) [10] together with the vibration of acoustic

phonons of the Pd lattice. Acoustic phonons are very

* Corresponding author. Address: Rua Bacaiuva no. 81,

Apartamento 104, Rio de Janeiro 21931340, Brazil. Tel.: +39-

333-9861039.

E-mail address: paolo.tripodi@lnf.infn.it (P. Tripodi).

0921-4534/$ - see front matter � 2004 Elsevier B.V. All rights reserv

doi:10.1016/j.physc.2004.02.099

sensitive to the Hþ fast hopping motion between O-sites

[8]. This approach, however, is not able to explain the

experimental R values with x � 1 lower than R0 at 300 K

[2,3] and at 100 K [4], therefore a new phenomenological

approach to explain the Pd-H(D) electrical resistance

behaviors for x > 1 at 300 K will be proposed. The Rfluctuation process used in our model considers a pos-

sible occurrence of new superconducting phases in stable

PdHx (x > 1) samples [5,6] at Tc much higher than 9 K,

previously measured [7].

2. Discussion: models and results

Our model of the Pd-H(D) resistance consists of two

different electric transport mechanisms. The first mech-

anism, for 0 < x < x0 where at x0 the R=R0 reaches the

maximum, correlates the raise of R=R0 with the lattice

expansion that occurs while the O sites are filling up. We

describe R=R0 linear change in the first Eq. (1a) where

the parameter m is directly correlated with the increase

of PdH relative volume. The second mechanism (Eq.

(1b)) of our approach describes the R decrease as a

fluctuation process of the superconducting state [12]

ed.

Fig. 1. R=R0 data fit for PdH and PdD vs x. Red and blue dots

are experimental data while the lines represent our model cal-

culation. (For interpretation of the references in colour in this

figure legend, the reader is referred to the web version of this

article.)

Fig. 2. Experimental data from literature are shown for the

known low Tc versus xc. Moreover two additional points at

Tc ¼ 300 K, calculated using our model, have been included.

(For interpretation of the references in colour in this figure

legend, the reader is referred to the web version of this article.)

P. Tripodi et al. / Physica C 408–410 (2004) 350–352 351

induced by H stoichiometry x at fixed T based on the

following experimental evidences:

(A) PdH superconducting state for x0 < x < 1 with Tc inthe range [2 K < Tc < 9 K] [11].

(B) Tc > 9 K for stable PdH samples at x > 1 [5,6].

At 300 K the following facts support our model:

(C) Magnetic susceptibility measurements show a para-

magnetic-diamagnetic transition above x ¼ 0:7[7,11].

(D) Hydrogen diffusion in Pd lattice produces local opti-

cal modes [8].

(E) It is well known that these optical modes are corre-

lated with the superconductivity in the Pd-H(D,T)

systems [10].

Increasing H stoichiometry x, the density of H in the

O-sites increases and these optical modes should become

non-local.

The two described mechanisms are:

R=R0j1 ¼ 1þ mx; R=R0j2 ¼ be�cðx�x0Þ ð1a;bÞ

In our model the two mechanisms are simultaneous and

mathematically the parallel between the two R=R0:

1=R=R0jp ¼ 1=R=R0j1 þ 1=R=R0j2 ð1cÞ

The pre-factor b [12] is correlated with the frequency

described in the fluctuation theory. At xc > x0 the con-

densation of Pd-H(D,T) system to macroscopic super-

conducting state is achieved. The xc value is extrapolatedat R6 10�6 X beyond the observable range of resistance

and represents the end of the thermodynamic fluctua-

tions. In Eqs. (2b) and (3b), the x value fixes, in our

opinion, the number n of fluctuating superconducting

domains for x0 < x < xc as follows [12]:

cðx� x0Þ ¼ U=KT ; U ¼ ½ðH 2c ðT Þn

3Þ=8p�n ð2a;bÞ

U is the free-energy increment [12], or the condensation

energy of the superconducting domains at x ¼ xc. Using

Eq. (2a,b) results the following:

cðT Þ ¼ U ½ðH 2c ðT Þn

3Þ=8p�KT ; n ¼ x� x0 ð3a;bÞ

The fit of the experimental R=R0 data at 300 K is shown

in Fig. 1. The values of xc for H and D are 1.6 and 1.7,

respectively.

The Tc versus xc for all isotopes are shown in Fig. 2

plotted with our calculated data at 300 K.

Some probable consequences of our proposed phe-

nomenological theory could be:

(i) Tc ¼ 300 K, the two fit of R=R0jp in Fig. 1 render val-

ues cðHÞ ¼ 12:4 and cðDÞ ¼ 11:2. Using Eq. (2a) the

condensation energy of the superconducting states

are UðHÞ ¼ 270 meV and UðDÞ ¼ 273 meV,

xcðHÞ ¼ 1:6, xcðDÞ ¼ 1:7.(ii) In Fig. 2, xcðDÞ > xcðHÞ for TcðDÞ ¼ TcðHÞ ¼ 300 K

shows a normal isotopic behavior TcðDÞ < TcðHÞ; xwwhere TcðDÞ ¼ TcðHÞ is the threshold from the in-

verse TcðDÞ > TcðHÞ to normal TcðDÞ < TcðHÞ isoto-pic behavior.

There also seems to be a correlation between our

calculated condensation energy and experimental data

[13] on potential barrier between O and T sites in PdH.

So, it would be expected that the occupation of T sites is

important to achieve high Tc in highly loaded PdH(D)

system.

352 P. Tripodi et al. / Physica C 408–410 (2004) 350–352

References

[1] N.F. Mott, H. Jones, The Theory and Properties of Metals

and Alloys, Dover Pub. Inc., NY, 1958, p. 296.

[2] S. Crouch-Baker et al., Z. fur Phys. Chemie. 204 (1998)

247.

[3] G. Bambakivis et al., Phys. Rev. 177 (1969) 1044.

[4] H. Hemmes et al., Phys. Rev. B 39 (1989) 4110.

[5] P. Tripodi patents: WO 0167525, EP1269550, AU7436301.

[6] P. Tripodi, D. Di Gioacchino, et al., Physica C 389 (2003)

571.

[7] T. Skoskiewicz et al., Solid State Phys. 7 (1974) 2670.

[8] M.H. Lee, Separ. Sci. Tech. 15 (1980) 457.

[9] B.M. Geerken et al., J. Phys. F: Met. Phys. 13 (1983)

963.

[10] D.S. MacLachlan et al., Solid State Commun. 17 (1975)

281.

[11] J.M.E. Harper, Phys. Lett. 47A (1974) 69.

[12] M. Tinkham, Introduction to Superconductivity,

McGraw-Hill, 1996, pp. 290–291.

[13] C. Elsasser, K.M. Ho, et al., Phys. Rev. B 44 (1991) 10377.