- Email: [email protected]
Phonon resistivity of implanted palladium deuteride
Solid Sta=e Communications, Vol.43,No.9, pp.659-661, Printed in Great Britain.
PHONON
RESISTIVITY
OF
IMPLANTED
]982.
PALLADIUM
0038-I098/82/330659-03503.00/0 Pergamon Press Ltd.
DEUTERIDE
L. M e n d o z a - Z e l i s : : , A. Traverse, H. Bernas, Centre de Spectrom~trie Nucl~aire et de Spectrom~trie de Masse, B.P. N ° I F. 91406 0rsay. and L. Dumoulin Laboratoire de Physique des Solides, Universit~ Paris XI F. 91405 0rsay. Received March 15, 1982 by A. Blandin, in revised form May 4, 1982) The temperature dependent resistivity of low-temperature implanted palladium deuteride was measured. A T 3 dependence was found for the low energy (acoustic) phonon contribution to the resistivity as in previous studies on implanted hydrides. Above ~ 45K, the results are analysed by assuming that the optic phonon contribution adds independently. The results (characteristic optic phonon temperature and acoustic-to-optic phonon-electron coupling ratio) agree with those obtained on alectrolytically prepared samples in spite of the four fold difference in residual resistivities.
The temperature dependence of the electrical resistivity in ordered metals and alloys provides information about their photon spectrum and the electron-phonon interaction I . By contrast, in highly disordered or amorphous alloys, the resistivity temperature dependence is usually very weak and depends Tostly on the lattice or electronic structure 2 .3~ns~reviou s work on ionimplanted metal hydrides - , we found a situation between theses two extrems. Ordering of hydrogen occurs in the sense that implanted protons were found to occupy octahedral interstitial sites of the metal lattice 4), as in electrolytically charged samples. However the residual resistivities of both systems differ by a factor between 4 and 10, due to implantation disorder in the metal lattice itself ~'. The H atoms and implantation-induced disorder contribute a temperature independent resistivity which is larger than the temperature dependent part. The purpose of this paper is to demonstrate that it is still possible to obtain reliable information on the phonon structure and electron-phonon interaction in such implanted systems from resistivity measurements. According to the Bloch-Gr~neisen law I) the phonon resistivity characterized by the integral le2(w)F(~)p(~)d~ where ~2 is an electronphonon interaction matrix element, F(~) the phonon spectrum and p(~) a thermal population term should display a TS-dependence. This was indeed the case for PdH(D)x, NiH x and (Pd.
In this letter we show that the phonon resistivity of D-implanted PdD also displays a T3-dependence, that it is st~ll possible to derive the influence of the optic phonon modes, and that the features of th~ latter are identical to those previously f o u n d S " in the corresponding electrolytically prepared samples. Experimental Deuterium ions of 3.25keY were implanted at 5K into palladium thin films (350A) prepared by evaporation on quartz substrates in a 5xi0 -s torr vacuum. At this incident energy the calcu-lated implanted ion profile is broad (FWHM~670 A), so that there should be less than 10% D inhomogeneity in the sample. Using a standard four-point probe technique we have measured the normal resistivity and the superconducting critical temperature against implanted dose. As in our previous work 4) on H-implanted Pd, a plateau was found in the normal resistivity, coinciding with the superconductivity onset. The highest critical temperature measured in our films under these conditions was 7.7K. The sample was then annealed up to 90K. The critical temperature rose to 8.3K (transition width 0.TK) presumably as a result of better D uniformity throughout the film. Its resistivity temperature dependence was then measured by thermal cycling between 4 and 85K.
Niy)H x produced by electrolytica! charging-6)_8 ) yl Analysis
Implantation disorder was found to prod~c~ a T3-dependence in the latter two cases 3;s; For (Pdl_yNiy)H x prepared electrolytically and
We analyse the temperature dependence of the resistivity in terms of two independent phonon branches, i.e. : p(T)=po+Pac(T)+Pop(T).
by implantation, the quantities ~2(~)F(~) obtained from a deconvolution of the phonon resistivity were found to be very similar)despite the differing temperature dependences 5 .
At low enough temperatures only acoustical thermal phonons are excited so that D(T)= o+Oac(T).
:: visitor from Universidad de La Plata under a fellowship of CONICET (Argentina). 659
Vol. 43, No. 9
PHONON RESISTIVITY OF IMPLANTED PALLADIUM DEUTERIDE
660
As in implanted NiHx and (Pd 1_y Niy)H x alloys 3)S) the experimental points agree well with a T 3 law, i.e. : 2A = ac T3j3 (@ac/r) Pac (T) 02
0.2
E
ac
where : X
% (X)
=~ e z z 3 (eZ-l)-2dz, J O Qac is the characteristic temperature of the acoustical phonon spectrum and Aac measures the electron-phonon interaction strength (note that Pac = AacT when T>>Gac ) . By fitting our data in this way between 30 and 45K. we obtain Sac = (315±20)K, A = 2.2 |0-1°[h~m/K with Po = 3.9 lO-T[~xm.a~t must be emphasized that
' '; ' ~; ' ';T(K)
.
i
50
a Ts (GrSneisen)-law does not fit the experimental points, even at low temperatures. Above 45-50K, the experimental resistivity increases faster than predicted for electronacoustic phonon scattering alone (Fig. I) indicating that another scattering mechanism sets in. Following Ref. 6 we assume that the optic phonon branch is thermally excited and analyse the resistivity excess in terms of : Pop(T). = Aop Pop f (@op/T) where : f(x) = xe x (eX-l) -2
60
I0
i
T (K)
80
Fig. l Inplanted PdD x optic phonon resistivity. small-angle scattering condition in the BlockGrSneisen analysis, a problem that warrants further theoretical work. Our analysis assumes that the lattice disorder affects the electron-acoustic phonon and electron optic phonon interactions independently. In fact, (i) the optic phonon modes essentially depend on near-neighbour interactions and (ii) local H or D ordering exists around metal atoms
Table 1
Implanted PdD
Electrolytically charged PdD X
R e s i s t i v i t y a) po(H~ x cm)
39
T max (K)
8.3
x
R e s i s t i v i t y b)
T u n n e l i n g c)
1 8.15
7.7
c
O @
ac op
(K) (K)
%op/%ac
d)
315(20)
210
550(50)
480
2.6
3.0
1.5-2.0
a) : This work ; b):Ref. 6 ; c) : Ref. 6 and P. Nedellec (private communication) ; d):thetunnelingmeasured(see text), ratio is Aop/Aac in the resistivity experiment and ~op/~ac in
The results in Fig. I then provide @op = (550± 50)K and A
op
= 5.8 lO-1°Qxm/K.
Discussion Our results show that, as in other implanted hydrides, the acoustic phonon term in the resistivity has a T3-dependence. This may be due ~) to the disorder-induced breakdown of the
even when the implanted metal lattice is significantly disordered 9). This accounts for the fact (Table I) that the characteristic parameter Q of ~he optic phonon term does not depend m u ~ on the degree of sample disorder, in spite of a fourty-fold difference in the disorderinduced residual resistivity and the different phonon resistivity temperature-dependences below 45K. Table I also shows that the ratios Aop/Aac
Vol. 43, No. 9
PHONON RESISTIVITY OF IMPLANTED PAJ~LADIUM DEUTERIDE
for the electrocharged and implanted deuterides are very similar, an important result since the superconducting electron-phonon coupling constant i is essentially proportional to A (note also that - in view of the uncertainties in the experimental analysis - satisfactory agreement is also obtained with the tunneling result on the electrocharged sample). Moreover (Table I) the superconducting critical temperatures, which depend on the sum hop + lac , are the same for both experiments. From the latter two results, we conclude that l and op l separately are very similar in the electroac
661
charged and implanted samples. A similar conclusion could be drawn from the analysis of Ref. 5 for the Pd-Ni hydride. We conclude that the disorder due to highfluence D implantation in Pd perturbs the resistivity temperature-dependence (viz, the scattering mechanism) ; it does not perturb the amplitude of the electron-phonon interaction for either optic or acoustic phonons in PdD . x Acknowledgements We are gra~eful to J. Chaumont and F. Lalu for their contribution to the experiments, and to J.P. Burger and P. Nedellec for discussions.
References
I. J.M. Ziman, Electrons and Phonons, Oxford University Press, 1979. 2. H.J. G~ntherodt and H.U. KHnzi, Metallic Glasses Eds. H.J. Leamy and J.J. Gilman (Metals Park, Ohio 1978). 3. L. Brossard, L. Thom~, A. Traverse, H. Bernas, J. Chaumont and F. Lalu, Physica Statu Solidi A 68 (1981) I19. 4. H. Bernas, A. Traverse, L. Brossard, J. Chaumont, F. Lalu and L. Dumoulin, Nuclear Instruments and Methods 182/183 (1981) I033. 5. A.J. Pindor, L. Sniadower, L. Dumoulin, P. Nedellec, H. Bernas and J.P. Burger, Physica
107B (1981) 143. 6. P. Nedellec, L. Dumoulin, C. Arzoumanian, J.P. Burger, Journal de Physiqe C6, Suppl~ment au N°8, Tome 39 (1978),C6-432. 7. D.S. McLachlan, I. Papadopoulos and T.B. Doyle, Journal de Physique C6, suppl~ment au N=8, Tome 39 (1978), C6 430. 8. L. Sniadower, L. Dumoulin, P. Nedellec, J.P. Burger, Journal de Physique Lettres 42 (1981) LI3. 9. H. Bernas and P. Nedellec, Nuclear Instruments and Methods 182/|83 (198|) 845.
PHONON
RESISTIVITY
OF
IMPLANTED
]982.
PALLADIUM
0038-I098/82/330659-03503.00/0 Pergamon Press Ltd.
DEUTERIDE
L. M e n d o z a - Z e l i s : : , A. Traverse, H. Bernas, Centre de Spectrom~trie Nucl~aire et de Spectrom~trie de Masse, B.P. N ° I F. 91406 0rsay. and L. Dumoulin Laboratoire de Physique des Solides, Universit~ Paris XI F. 91405 0rsay. Received March 15, 1982 by A. Blandin, in revised form May 4, 1982) The temperature dependent resistivity of low-temperature implanted palladium deuteride was measured. A T 3 dependence was found for the low energy (acoustic) phonon contribution to the resistivity as in previous studies on implanted hydrides. Above ~ 45K, the results are analysed by assuming that the optic phonon contribution adds independently. The results (characteristic optic phonon temperature and acoustic-to-optic phonon-electron coupling ratio) agree with those obtained on alectrolytically prepared samples in spite of the four fold difference in residual resistivities.
The temperature dependence of the electrical resistivity in ordered metals and alloys provides information about their photon spectrum and the electron-phonon interaction I . By contrast, in highly disordered or amorphous alloys, the resistivity temperature dependence is usually very weak and depends Tostly on the lattice or electronic structure 2 .3~ns~reviou s work on ionimplanted metal hydrides - , we found a situation between theses two extrems. Ordering of hydrogen occurs in the sense that implanted protons were found to occupy octahedral interstitial sites of the metal lattice 4), as in electrolytically charged samples. However the residual resistivities of both systems differ by a factor between 4 and 10, due to implantation disorder in the metal lattice itself ~'. The H atoms and implantation-induced disorder contribute a temperature independent resistivity which is larger than the temperature dependent part. The purpose of this paper is to demonstrate that it is still possible to obtain reliable information on the phonon structure and electron-phonon interaction in such implanted systems from resistivity measurements. According to the Bloch-Gr~neisen law I) the phonon resistivity characterized by the integral le2(w)F(~)p(~)d~ where ~2 is an electronphonon interaction matrix element, F(~) the phonon spectrum and p(~) a thermal population term should display a TS-dependence. This was indeed the case for PdH(D)x, NiH x and (Pd.
In this letter we show that the phonon resistivity of D-implanted PdD also displays a T3-dependence, that it is st~ll possible to derive the influence of the optic phonon modes, and that the features of th~ latter are identical to those previously f o u n d S " in the corresponding electrolytically prepared samples. Experimental Deuterium ions of 3.25keY were implanted at 5K into palladium thin films (350A) prepared by evaporation on quartz substrates in a 5xi0 -s torr vacuum. At this incident energy the calcu-lated implanted ion profile is broad (FWHM~670 A), so that there should be less than 10% D inhomogeneity in the sample. Using a standard four-point probe technique we have measured the normal resistivity and the superconducting critical temperature against implanted dose. As in our previous work 4) on H-implanted Pd, a plateau was found in the normal resistivity, coinciding with the superconductivity onset. The highest critical temperature measured in our films under these conditions was 7.7K. The sample was then annealed up to 90K. The critical temperature rose to 8.3K (transition width 0.TK) presumably as a result of better D uniformity throughout the film. Its resistivity temperature dependence was then measured by thermal cycling between 4 and 85K.
Niy)H x produced by electrolytica! charging-6)_8 ) yl Analysis
Implantation disorder was found to prod~c~ a T3-dependence in the latter two cases 3;s; For (Pdl_yNiy)H x prepared electrolytically and
We analyse the temperature dependence of the resistivity in terms of two independent phonon branches, i.e. : p(T)=po+Pac(T)+Pop(T).
by implantation, the quantities ~2(~)F(~) obtained from a deconvolution of the phonon resistivity were found to be very similar)despite the differing temperature dependences 5 .
At low enough temperatures only acoustical thermal phonons are excited so that D(T)= o+Oac(T).
:: visitor from Universidad de La Plata under a fellowship of CONICET (Argentina). 659
Vol. 43, No. 9
PHONON RESISTIVITY OF IMPLANTED PALLADIUM DEUTERIDE
660
As in implanted NiHx and (Pd 1_y Niy)H x alloys 3)S) the experimental points agree well with a T 3 law, i.e. : 2A = ac T3j3 (@ac/r) Pac (T) 02
0.2
E
ac
where : X
% (X)
=~ e z z 3 (eZ-l)-2dz, J O Qac is the characteristic temperature of the acoustical phonon spectrum and Aac measures the electron-phonon interaction strength (note that Pac = AacT when T>>Gac ) . By fitting our data in this way between 30 and 45K. we obtain Sac = (315±20)K, A = 2.2 |0-1°[h~m/K with Po = 3.9 lO-T[~xm.a~t must be emphasized that
' '; ' ~; ' ';T(K)
.
i
50
a Ts (GrSneisen)-law does not fit the experimental points, even at low temperatures. Above 45-50K, the experimental resistivity increases faster than predicted for electronacoustic phonon scattering alone (Fig. I) indicating that another scattering mechanism sets in. Following Ref. 6 we assume that the optic phonon branch is thermally excited and analyse the resistivity excess in terms of : Pop(T). = Aop Pop f (@op/T) where : f(x) = xe x (eX-l) -2
60
I0
i
T (K)
80
Fig. l Inplanted PdD x optic phonon resistivity. small-angle scattering condition in the BlockGrSneisen analysis, a problem that warrants further theoretical work. Our analysis assumes that the lattice disorder affects the electron-acoustic phonon and electron optic phonon interactions independently. In fact, (i) the optic phonon modes essentially depend on near-neighbour interactions and (ii) local H or D ordering exists around metal atoms
Table 1
Implanted PdD
Electrolytically charged PdD X
R e s i s t i v i t y a) po(H~ x cm)
39
T max (K)
8.3
x
R e s i s t i v i t y b)
T u n n e l i n g c)
1 8.15
7.7
c
O @
ac op
(K) (K)
%op/%ac
d)
315(20)
210
550(50)
480
2.6
3.0
1.5-2.0
a) : This work ; b):Ref. 6 ; c) : Ref. 6 and P. Nedellec (private communication) ; d):thetunnelingmeasured(see text), ratio is Aop/Aac in the resistivity experiment and ~op/~ac in
The results in Fig. I then provide @op = (550± 50)K and A
op
= 5.8 lO-1°Qxm/K.
Discussion Our results show that, as in other implanted hydrides, the acoustic phonon term in the resistivity has a T3-dependence. This may be due ~) to the disorder-induced breakdown of the
even when the implanted metal lattice is significantly disordered 9). This accounts for the fact (Table I) that the characteristic parameter Q of ~he optic phonon term does not depend m u ~ on the degree of sample disorder, in spite of a fourty-fold difference in the disorderinduced residual resistivity and the different phonon resistivity temperature-dependences below 45K. Table I also shows that the ratios Aop/Aac
Vol. 43, No. 9
PHONON RESISTIVITY OF IMPLANTED PAJ~LADIUM DEUTERIDE
for the electrocharged and implanted deuterides are very similar, an important result since the superconducting electron-phonon coupling constant i is essentially proportional to A (note also that - in view of the uncertainties in the experimental analysis - satisfactory agreement is also obtained with the tunneling result on the electrocharged sample). Moreover (Table I) the superconducting critical temperatures, which depend on the sum hop + lac , are the same for both experiments. From the latter two results, we conclude that l and op l separately are very similar in the electroac
661
charged and implanted samples. A similar conclusion could be drawn from the analysis of Ref. 5 for the Pd-Ni hydride. We conclude that the disorder due to highfluence D implantation in Pd perturbs the resistivity temperature-dependence (viz, the scattering mechanism) ; it does not perturb the amplitude of the electron-phonon interaction for either optic or acoustic phonons in PdD . x Acknowledgements We are gra~eful to J. Chaumont and F. Lalu for their contribution to the experiments, and to J.P. Burger and P. Nedellec for discussions.
References
I. J.M. Ziman, Electrons and Phonons, Oxford University Press, 1979. 2. H.J. G~ntherodt and H.U. KHnzi, Metallic Glasses Eds. H.J. Leamy and J.J. Gilman (Metals Park, Ohio 1978). 3. L. Brossard, L. Thom~, A. Traverse, H. Bernas, J. Chaumont and F. Lalu, Physica Statu Solidi A 68 (1981) I19. 4. H. Bernas, A. Traverse, L. Brossard, J. Chaumont, F. Lalu and L. Dumoulin, Nuclear Instruments and Methods 182/183 (1981) I033. 5. A.J. Pindor, L. Sniadower, L. Dumoulin, P. Nedellec, H. Bernas and J.P. Burger, Physica
107B (1981) 143. 6. P. Nedellec, L. Dumoulin, C. Arzoumanian, J.P. Burger, Journal de Physiqe C6, Suppl~ment au N°8, Tome 39 (1978),C6-432. 7. D.S. McLachlan, I. Papadopoulos and T.B. Doyle, Journal de Physique C6, suppl~ment au N=8, Tome 39 (1978), C6 430. 8. L. Sniadower, L. Dumoulin, P. Nedellec, J.P. Burger, Journal de Physique Lettres 42 (1981) LI3. 9. H. Bernas and P. Nedellec, Nuclear Instruments and Methods 182/|83 (198|) 845.