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FURTHER SUPERCONDUCTING PROPERTIES OF
PdHx
≈ 1
D. Mclachlan, T. Doyle, J. Burger
To cite this version:
JOURNAL DE PHYSIQUE Colloque C6, supplément au n° 8, Tome. 39, août 1978, page C6-428
FURTHER SUPERCONDUCTING PROPERTIES OF P d Hx = 1
D.S. McLachlan, T.B. Doyle and J . P . Burger
University of the Witwatersrand., Johannesburg, South Africa
s Labovatoire de Physique des Solides, Orsay 91405, France
Résumé.- A partir des résultats précédents des auteurs cités, on obtient les valeurs de K(t) pour PdH s . En utilisant K ( 1 ) et H_(0) pour PdH, on estime la profondeur de pénétration et la longueur de cohérence.
Abstract.- From previous results of the above authors the values of K(t) for PdH are obtained. Using K ( 1 ) and H (0) for PdH the penetration depth and coherence length for PdH are estimated.
The purpose of this paper is to extract addi-tional information from recent critical magnetic field measurements /l/ in PdH < . This additional information confirms the tentative conclusion of re-ference /l/, namely that PdH is a type I supercon-ductor and enables a value of K = K,(T ) for PdH to
l c
be obtained for the first time. < (T) is given /2/
by Kj(T) = HC3(T)/(/2 C(T) HC(T))
where C(T) = H (T)/HC2(T) and C(Tc) = 1.695. As the
results of this paper will be compared with the K (T) values obtained from experiments /3/ on lead and mercury, where C(T) is assumed to be always equal to its value (1.695) at T , all computations done in this paper will also assume that C(T) = 1.695.
Figure 1 shows the critical magnetic field results obtained for sample 2 (x = .9957) of refe-rence /l/. The interpretation of this and similar
1600-u o o \
1200 - \ 1000 - \ -; 800 *^s.^ N,, X 6 0 0 " ^ ^ ^ N o . ^ V 400- ^^:°-3$fes. 2 0 0" ^°^^°^N<w 0 10 20 30 40 50 60 70 80 90 100 T2 (K2)Fig. 1 : Plots of HC L, HC D > and HR versus T2 for
sample 2 of reference 1. <HC LP ; HC U ° ! HRA )
results is that HC L (T)and Hc u (T) are the upper and
lower limits of the thermodynamic critical field curves of an inhomogeneous Type I superconductor, while IU(T) is H (T) determined from resistivity measurements. Therefore it is assumed that H is the surface nucleation field for the multiply con-nection region, on the specimen surface, with the highest H (and H ) . Therefore, if K ^ C T ) = 0.417 HC3(T)/HC(T) = 0.417 I ^ W / H ^ T ) is plotted as a function of T the characteristic temperature dependence of K (T) should be obtained in the region where K (T) >_ .417. Such plots have been made for
the two most stoichiometric specimens (Nos. 2 and 3) of reference /l/, which have the lowest residual resistivities (and K ' S ) , as it had been concluded that these were probably Type I superconductors. The results, as expected, levelled off at K (T) = .417 as T was approached. From this plot an approximate value of K ( T ) could be obtained by a straight line extrapolation of the temperature dependent region of the Kj(T) plot to T = T .
In order to show that the observed tempera-ture dependence of Kj(T) is similar to other Type I superconductors of similar K and to obtain more ac-curate values of K (T ) , the following procedure was used : The smooth curves through Smith and Cardona's results /3/ for Pb and Hg were normalized and plot-ted in figure 2. The present results for PdH were then similarly normalized, with K being chosen so that the points at the highest temperatures coinci-ded with the results for Pb. This choice was made because the extrapolated Kj(T ) values were closer to those of Pb ( K = .240 (spheres) and K = .255
Present Address : Department of Physics, Univer-sity of Natal, King George V Avenue, Durban, 4001
Fig. 2 : The results of K~(~)/K for samples Z(0)and
3(A) of reference 1 plotted as a function of t=T/T.
The lines represent the normalized best straight lis
nes of Smith and Cardona for K~(~)/K versus t. Hg
spheres (lower solid line) ; Pb spheres (upper solid
line) ; and Pb cylinders (dashed line)
(Cylinders) than that of Hg (K = .137). These re-
sults are also shown in figure 2 where it is appa-
rent that the agreement between the K~(~)/K results
for the PdH samples 2 and 3 and Pb is excellent.
X
Therefore, there can be little doubt that the pro-
cedure is a valid one. The values of K required for
the normalization are ; for sample no. 2 K = 0.32
and for sample no. 3 K = 0.34.
According to the Goodman /4/ relationship the
dependence of K on the normal state resistivity pof
a superconductor is
where K is the K value for an ideal material, y is
the electronic specific heat coefficient
(1.27 x
lo3
ergs/cm3~2 for PdH < )/I/ and p the re-sidual resistance is 0.85 pQ cm per % H vacancies.
From the above equation and results one finds
AK/Ax is
-
0.226 per % H vacancies /I/. The expec-ted difference in K between sample 2 (x = 9957) and
sample 3 (x = .9949) is 0.018, very close to the
observed value of 0.2. One can therefore with some confidence, use the Goodman formula to obtain
K = .223 from sample 2 and -225 from sample 3 ;
0
very close to what is observed for lead 131.
Now given K = .224, HC(0)
"
87010e, Tc" IOK',y = 1270 erg/cm3~l and the free electron parameters
of PdH, various other important superconducting pa- rameters for PdH can be estimated. As PdH and Ag are both s-type metals and their lattice constants are virtually identical, the free electron parame-
ters for Ag can be used, namely N = 5.76 x 1 0 ~ ~ / c m ~ ,
VF = 1.38 x 108cm/s and yo = 612 ergs/cm3 .'K In
table I these parameters are combined /5/ to calcu-
late the penetration and the coherence lengths as well as to check the internal self consistencies of the parameters obtained. It will be seen from Table1 that the results so obtained are reasonable and fol- low the patter observed for other type I superconduc- tors /7/,
Table I
Superconducting Properties of PdH
Y/Y, = 2
5
= 0.18 to Vp/kgTc = 1920;i
free electron theory
I
hL = (m c2/4n. ~e~)'~* = 220;i
from HC(0)
1
e0
= .96 h L / ~2Tc d HC(T)
2A(O) /kTc =
-
-
H,(O) dT
l6
-
3.3 from Hcu
'
S'The deviation [D(T/T~) = HC(T) /HC(0)
-
(1
-
(t)2)] of the thermodynamic critical field HC(T) from the parabolic temperature dependence has to be calculated for samples 2 and 3. The resulting deviation curves have the shape characteristic of a weak coupling superconductor with minima in the re-gion 0.4 ( t2 ( 0.5. However, the amplitudes, which
range between
-
0.062 and-
0.082 are extraordinari-ly large.
References
/I/ McLachlan, D.S., Doyle, T.B., and Burger, J.P.,
J. Low Temp. Phys.
2
(1977) 589/2/ Saint-James, D.,and De Gennes, P.G., Phys. Lett. 7 (1963) 306
-
131 Smith, F.W., and Cardona, M., Solid State Commm 6 (1968) 37
-
/4/ Goodman, B.B., Phys. Rev. Lett.
5
(1961) 597151 Most of these formula can be found in De Gennes
P.G., Superconductivity of Metals and Alloys (Benjamin, New York 1966)
161 Toxen, A.M., Phys. Rev. Lett.
15
(1965) 462/7/ See for instance Feder, J., and McLachlan, D.S.,
