Low-temperature thermodynamic properties of
amorphous sputtered Zr 100-xCux alloys. Effect of
structural relaxation
F. Zougmoré, J.C. Lasjaunias, O. Béthoux
To cite this version:
F. Zougmoré, J.C. Lasjaunias, O. Béthoux. Low-temperature thermodynamic properties of
amorphous sputtered Zr 100-xCux alloys. Effect of structural relaxation. Journal de Physique,
1989, 50 (10), pp.1241-1265. <10.1051/jphys:0198900500100124100>. <jpa-00210992>
HAL Id: jpa-00210992
https://hal.archives-ouvertes.fr/jpa-00210992
Submitted on 1 Jan 1989
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J.
Phys.
France 50
(1989)
15
1241-1265
MAI
1989,
1241
Classification
Physics Abstracts
65.40
-
63.50
-
74.20F
Low-temperature thermodynamic properties of amorphous
sputtered Zr100-xCux alloys. Effect of structural relaxation
F.
Zougmoré, J. C. Lasjaunias and O. Béthoux
Centre de Recherches
sur
les Très Basses
Températures, C.N.R.S.,
B.P. 166 X, 38042 Grenoble
Cedex, France
(Reçu
le 10 octobre 1988, révisé le 3
janvier 1989, accepté
le 9
janvier 1989)
Nous rapportons sur des mesures de chaleur spécifique à basse température d’alliages
Zr100-xCux (19~ x~ 64) préparés par pulvérisation cathodique, que nous comparons aux alliages
correspondants obtenus par la technique d’ultra-trempe de l’état liquide. Alors que la
température de transition supraconductrice Tc est très voisine pour les deux types d’alliages
amorphes, indication qu’elle est pratiquement insensible au degré de désordre structural plus
élevé induit par la technique de pulvérisation, par contre à la fois le coefficient électronique y et la
contribution de réseau 03B2 T3 sont plus élevés pour les alliages « pulvérisés ». Le caractère commun
aux deux alliages d’une croissance de 03B3 avec la concentration en Zr est considérablement accentué
dans le cas des alliages « pulvérisés ». Cependant, ces fortes valeurs de 03B3 assez surprenantes ne
conduisent pas à un comportement anormal pour le processus supraconducteur, ainsi que le
prouve la condensation électronique totale en dessous de Tc. Tous les paramètres thermodynamiques sont sensibles à la relaxation structurale, au contraire des alliages trempés du liquide, tandis
que la diminution de la Tc est similaire dans les deux types d’alliages.
Résumé.
2014
low-temperature specific heat measurements of superconducting
64) alloys prepared by sputtering that we compare to correamorphous Zr100-xCux (19 ~
sponding alloys obtained by fast liquid-quenching technique. Whereas the superconducting
transition temperature Tc is very close for these two kinds of amorphous alloys, indicating that it is
almost insensitive to the higher degree of structural disorder inherent to sputtering, both the
electronic coefficient 03B3 and the lattice 03B2T3 contribution are larger for the sputtered alloys. The
common character of an increasing value of 03B3 with the Zr content is considerably enhanced for the
sputtered alloys. However, such surprisingly high y values do not lead to any anomalous
behaviour for the superconductivity process, as proved by the complete electronic condensation
below Tc. All thermodynamic parameters are sensitive to structural relaxation, at variance with
the liquid-quenched alloys, whereas the Tc depression is of the same magnitude in both kinds of
alloys.
Abstract.
2014
We report
on
x ~
1. Introduction.
There is a growing experimental evidence for a dependence of numerous physical properties
of amorphous metallic alloys upon their conditions of preparation, e.g. either by vaporquenching (V.Q.) or liquid-quenching (L.Q.) techniques. Moreover, upon these conditions,
they are differently sensitive to structural relaxation [1].
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198900500100124100
1242
It is now demonstrated by X-ray measurements, differential scanning calorimetry (DSC)
[2], extended X-ray absorption fine structure (EXAFS) [3] and small angle X-ray scattering
[4] that sputtered samples exhibit a more disordered structure than liquid-quenched ones with
a degree of disorder probably intermediate between thin films vapor-quenched onto a cold
substrate and melt-spun ribbons. Furthermore, properties of materials prepared by vaporquenching onto a cold substrate can be significantly modified by a subsequent thermal
treatment, contrary to the case of the L.Q. ones which have been already stabilized during
quenching from the melt. We had previously studied the effect of structural relaxation on the
low-temperature thermal properties of Zr-based sputtered alloys, at Zr composition close to
75 at% : nominal Zr76Ni24, Zr76CU24, Zr80CU20 [5, 6]. In that case, thermodynamic properties
such as the electronic coefficient y, the Debye temperature BD, the density of low-energy
excitations (or two-level systems, T.L.S.) tend toward the values of the corresponding L.Q.
materials with initial densities for every kind of excitations (electron, phonon, and T.L.S.)
which largely exceed those of L.Q. alloys ; in the same time, the superconducting transition
temperature T, decreases in a similar way as in L.Q. alloys.
We have used the possibility by varying continuously the concentration and by relaxing the
structure to extend a similar thermodynamic study to a large concentration range
(19 -- x , 64 at%) of the Zr,oo - xcux system, that we report here. Most of the previous
conclusions are confirmed, concerning the Debye temperature, the superconducting transition
and the low-energy T.L.S. excitations. However, the behaviour of the electronic y coefficient
is quite unexpected. Its magnitude remains always larger than for L.Q. Zr-Cu alloys,
especially at high Zr content where the structural stability of the alloy decreases. Moreover, y
is very sensitive to thermal treatments, even to ageing at room temperature, with senses of
variation which depend on the concentration range of the alloy.
The paper is subdivised as following : in section 2 we describe samples preparation and
characterization, and the acquisition of specific heat data technique, i.e. the analysis of the
transient responses to an heat pulse ; in section 3, we describe results and analysis in the
whole temperature range, including the determination of 7c and the electronic contribution
Ce in both normal and superconducting states ; in section 4, we discuss the normal state
properties and the relation of Tc with the electronic and phonon densities of states. In a final
section 5, we discuss the superconducting state, with the electronic condensation process, the
phonon contribution at very low temperature and the onset on the T.L.S contribution.
Elsewhere is reported [7] the analysis of the TLS excitations, which are known to be a
characteristic of these amorphous materials.
«
2.
»
Experimental.
2.1 SAMPLES PREPARATION AND CHARACTERIZATION. - The amorphous samples of
nominal concentration varying between 20 -- x -- 65 were prepared by a high-rate (10 jim/h)
D.C. magnetron sputtering technique [6] at a deposition temperature of 77 K, in the form of
foils about 2 x 4 cm2, 80 to 100 m in thickness, about 0.5 g weight. In all the series,
hydrogen which could be present at rather large concentration in sputtered films [8], is not
detected by chemical analysis [9] within the limit of detection, i.e. 10-2 weight % or about
1 at%. The absence of hydrogen in these bulk samples is confirmed by the excellent
agreement of 7c with L.Q. ZrCu, since 7c is known to be very sensitive to the presence of
hydrogen in Zr-based alloys [ZrPd, Zr-Ni, ...] [10].
The exact composition, obtained by absorption chemical analysis, indicates that in
comparison to the nominal concentration of the target, there is a depletion in Cu which
increases from about 1 at% for ZrSOCu20 to about 2 at% for Zr5oCu5o and Zr3SCu6S. In the
following, only
exact
compositions
are
reported.
1243
Characterization results.
1) The homogeneity of the samples is proved by the mass density measurements
systematically performed [by Archimede method with toluene as acting fluid] on each of the
five or six foils of a same deposition batch, and which generally differ by less than
0.03 g.cm- 3. These fluctuations of mass density, between different foils, can be accounted for
by those of concentrations, of the order or less than 1 at%. We verify the very good
agreement between our values (Tab. 1 and Fig. 1) and those for L. Q. alloys from two groups
[11, 12], which differ between them by about 2 %. The effect of densification (- 0.25 %) on
thermal annealing, previously pointed out on a same foil of Zr77CU23 [6] could not be detected
for other compositions, being within the uncertainty of the measurements (about
0.01 g.cm- 3). As well as for densification effects, a decrease of length could be expected due
of about
to the annealing of the frozen-in free volume. Irreversible contraction
2 x 10- 4 has been measured by Hillairet et al. in a similar sputtered Zr76Ni24 alloy, which
¥
Table I.
*
-
Characterization data
See also reference
of sputtered ZrlOO-xCux samples.
[6].
Fig. 1. - Mass density versus the copper concentration x of sputtered samples (symbol 0) and two
series of liquid-quenched from reference [11] (Symbol e) and reference [12] (symbol Âà, ). Data of
sputtered lie between those of L.Q. which differ between them by 2 %.
1244
corresponds to an (almost undetectable) densification effect of the order or less than
10- 3 [13].
2) Similar good agreement with L.Q. ZrCu alloys [11, 12] is obtained for the position
(2 () m) of the main X-ray di f fraction halo (Tab. 1 with the corresponding transfert momentum
()m (À- with À 1.542 À for Cu-Ka). These 6max values are not notably
affected by heat treatment either for L.Q. or sputtered alloys. But one observes, for the
sputtered ones, a narrowing (-10%) of the width of the halo which indicates a
reorganisation of the short-range structural order [4b]. When comparison is made (e.g.
Zr6Ni24 prepared in the same way [4c]), the first halo is a little bit broader (- 10 %) for the
sputtered samples.
In a general way, these results for () m (Q p) and density confirm the similarity of the average
Qp = 4 sin
=
structural parameters for both kinds of materials.
3) Differential thermal analysis data, generally obtained at a heating rate of 20 K/min, are
shown on figures 2 and 3. At high Zr content i.e. x -- 28 at% (Fig. 2), recrystallization occurs
in two stages, as already discussed [7] : the first broad exothermic peak (symbol A in Fig. 3) is
the formation of metastable co-Zr, which thereafter transforms in equilibrium cy-Zr above
400 °C [4b]. We note that this w crystallization occurs at a rapidly decreasing temperature for
an increasing Zr content. The second sharp peak (symbol e in Fig. 3) is the formation of
Zr2Cu at a rather constant temperature of 340 °C. For copper content larger than 28 at%, the
w-Zr crystallization stage is no more detected. Instead, the unique crystallization peak
Fig.
2.
rate
T
D.S.C. thermograms of parts of sputtered samples (exact composition reported) at a heating
20 K min- l. The dashed line is the base-line corresponding to the recrystallized state. For
x -- 28 at% one observes a broad endothermic signal characteristic of a TG, immediately followed by a
sharp unique crystallization peak. For x : 28 at% a TG is no longer apparent.
-
=
1245
(T., symbol 0 in Fig. 3) is preceeded by a broad endothermic signal characteristic of a glass
transition ( TG, symbol 0 for x
32, 38, 48 at%) defined as the beginning of the endothermic
effect.’ Also in that case a very good agreement for both TG and T. is obtained between these
sputtered alloys and the L.Q. ones (Fig. 3).
=
- Sputtered samples : crystallization (T., symbol D) and glass-transition (TG, symbol 0)
28 at%, 8 and. represent the two crystallization stages (see Fig. 2
versus x. Below x
and text) ; symbols (D and M represent TG and Tx of sputtered Zr40Cu60 from Walmsley et al. [16]
(T = 20 K min-l) ; the dashed-lines for melt-spun from reference [12] ( T 10 K min- 1).
Fig.
3.
temperatures
=
=
A characteristic difference between both kinds of alloys lies in the larger irreversible
exothermic effect for the sputtered alloys, measured by sensitive differential scanning
calorimetry (DSC) on the first heating above room temperature [2]. For Zrg1Cu19 and
Zr77CU23, the heat release is of the order of 1 kJ/mole [14]. This effect has been ascribed to a
decrease of the configurational enthalpy, which is larger in the initial state of sputtered alloys,
due to higher disorder [15].
4) Sensitive structural investigations such as extended X-ray absorption fine structure
(EXAFS) and small-angle X-ray scattering (SAXS) were performed on some samples. Both
techniques confirm the higher degree of structural disorder in comparison to L.Q. alloys. In
SAXS, the flat Laue scattering of the « as-sputtered » samples is the indication of an
homogeneous medium [4b].
Thermal treatments cause tiny, but still detectable, variations of the structural parameters.
There is a trend for clustering of the Zr atoms in Zr77Cu23 as shown by EXAFS [3].
5) Another characteristic difference between the two kinds of alloys is the irreversible
decrease of the electrical resistivity on first heating (by about 1 %) in sputtered alloys
(Zr76Ni24, [13]), whereas it is almost absent ($ lo- 4) in L. Q. This relaxation effect is ascribed
to a topological reorganization on a local scale [13].
In conclusion, sputtered alloys are in a higher degree o f structural disorder than L.0. on the
different scales of the structure : short range order (X-ray scattering and EXAFS results),
medium and long range order (SAXS results). This is also in agreement with higher densities
of two-level systems [7], which are very sensitive to the degree of disorder, as proved by a
1246
recent study of their dependence upon the conditions of low-temperature deposition for
amorphous H20 or D20 films [17]. The effects of structural relaxation are consequently larger
in sputtered alloys than in L.Q. However, no structural inhomogeneities such as phases
separation have been detected in these samples, either by X-ray investigations [4, 18] or from
their superconducting properties by the unicity of the transition.
At last, EXAFS investigations [3, 19] do not point out chemical short range order
(C.S.R.O.) in the Zr-Cu system, either for sputtered (Zr77CU23, Zr8lCU19-II) or L. Q. , except
at high Cu content (Zr40CU60-L.O.). This is at variance with the Zr-Ni system.
Thermal Treatments.
have been measured firstly in their « as-prepared » state, after being removed
the
from
deposition apparatus at room temperature, and secondly generally after an
isothermal annealing of one hour, under an atmosphere of ultra-pure argon, at temperature
Ta well blow the crystallization temperature ( Ta 200 °C for 19 -- x -- 38, Ta 250 °C for
x
48), or ageing at room temperature. Between the measurements, samples are stored in
Samples
=
=
=
liquid nitrogen.
2.2 SPECIFIC HEAT TECHNIQUE. - The specific heat of about 1 to 1.5 g of material (two or
three foils) was measured on a He3-He4 dilution refrigerator by means of a transient heat
pulse technique. The temperature varies step by step, over a range (0.08 K to 7.5 K) which
includes the superconducting transition T,. The validity of the transient technique is based on
the condition that the internal time constant due to the thermal coupling between the sample
foils must remain small compared to T which characterizes the exponential temperature decay
back to thermal equilibrium, and which is equal to the product of the total heat capacity times
the thermal resistance Re of the link to the cold sink [20a]. In the present case, this is obtained
by a sample holder arrangement well adapted to the sample geometry and which ensures a
good thermal diffusivity, especially at very low temperatures (T« Tc) where no more
electronic diffusivity is present : the sample foils are pressed between two silicon plates of
similar surface, one of those is equipped with the heater, and the opposite with the
thermometer and the thermal link, with an adapted value of Rp . Such an arrangement has
been tested and used in numerous samples of bad thermal diffusivity [6, 20a-b, 21].
The accuracy of determination of C p has been improved by an automatic data acquisition
and analysis of the exponential transients (Figs. 4a and b). During a set of acquisition, the
reference temperature of the copper screen around the sample holder is regulated by a fourwire probe bridge within 10- 4 of the fixed temperature. The signal of the measurement
resistance is also amplified by an a.c. ( f
90 Hz) bridge. The procedure is the following :
=
a) for the definition of the base line, corresponding to the reference temperature, 10 data
points are taken. Each of them is the average of 4 points taken at microcomputer clock pace
(every 10 ms). So they give a well-defined base line, parallel to the x axis (time) ;
b) at the 10th point, a heat pulse of energy R 2 t is automatically sent on the sample during a
laps of time t. Throughout the 40th data point after the maximum (kl on Fig. 4a), data points
are taken without averaging, at a pace which is generally 10 times greater than for the
averaged points. So one gets experimental data (S,,,,p) very close to the real signal in the
critical region for the specific heat calculation : heating up, decay of the signal down to or
beyond the inflexion point (k2 in Fig. 4a), which corresponds to the onset of the exponential
decay regime of the temperature, when thermal equilibrium is established within the whole
sample and also between the sample and the different addenda ;
c) thereafter, as the rate signal/noise grows fading, data points are taken anew at lower
pace, and averaged over 4 points, like in stage (a) ;
1247
Fig. 4. - a) shows
microcomputer for
the temperature decay after a heat pulse and its analysis by means of a
determination of the exponential variation : + for experimental decay (Se.,P) ;
dashed-line for theoretical one (Sth). K2 and K3 can be moved for fitting as close as possible the
experimental data ; b) is a plot of AS Sth - S,,,p versus times (arbitrary units). It shows that the fit of
figure 4a is within about 1 % of the signal.
=
d) between k2 and k3, the point at which the signal equals 20 % of the maximum deflection,
the exponential decay is fitted to exp (- ak + b ), called Sthe,,, ; a and b being determined by a
linear regression ;
e) thereafter, we determine kI, point of the idealized instantaneous heat jump of the
sample, by equalization of areas A and B of figure 4a, corresponding to the conservation of
energy sent into the sample :
or
where the integration of Sexp is performed by a trapezoidal approximation method in this
region with large density of data points.
Then, from abscissa kI, one gets the final Rf ( oc Sf = exp ak, + b ]) and initial
R; ( oc S; of Fig. 4a) resistance values of the thermometer, and from the calibration law the
initial and final temperatures (Ti, T f) . The three coefficients Ai, Bi and Cii of the
standardization law of the thermometer [Log Ri = Ai (Log. T)2 + Bi (Log., T) + Ci] are
determined for each value of the resistance Ri by fitting the calibration curve to a parabola
throughout the i - 3, i - 2, i - 1, i, i + 1, i + 2, i + 3, points of calibration [20a]. This
determination of 3 parameters Ai, Bi and Ci, well adapted to the Si-doped thermometers, is
more precise and continuous than the usual method of approximation by polynomials of
higher degree over a larger number of calibration points.
The thermometers presently used are Si sheets doped with P or B by ionic implantation.
They show a remarkable stability against the thermal cycles. In the present case, along this
series of experiments (about 20), the resistance varied by less than 0.05 Q over 80 at 4.2 K,
corresponding to a variation in temperature less than 10 mK.
At last, if W is the electrical power (Rf t) used for heating, the total heat capacity, including
W
The specific heat of the sample is obtained after subtracting the
addenda, is
mC
heat
capacity
of
= Tf - Ti
addenda, previously measured by blank experiments.
1248
3.
Spécifie
heat data
analysis
and results.
We can distinguish three temperature ranges, characterized
3.1 DATA ANALYSIS.
different weights for phonon, electronic or T.L.S. contributions :
-
by
i) between T, and 7 K, there is a good agreement of C p with the usual y T +
,8 T3 law, as shown by the plot C/T versus T 2in figure 5 for some samples of the series. Such a
variation, including sometimes higher power terms (oc T5), is generally also obeyed for Zrbased melt-spun alloys in similar T-range [22-24], and more generally for numerous
amorphous metallic alloys [25]. From the electronic coefficient y one obtains the density of
3 y (states. e v- 1 . atom- 1, with y in mJ. mole - 1 . K- 2) ;
states at Fermi level : N, (EF)
,7r 2 k2
=
.- .-lu
and from the lattice
T3 term, the Debye temperature :
Fig. 5. Cp/T versus T2 for sputtered amorphous samples. All data, but for x = 19 at% (sample II),
correspond to annealed samples. The continuous lines represent the fit to the l’ T + f3 T3 law above
Tc.
-
specific heat Ce, obtained from Cp after subtracting the phonon
ceT
versus
12).. The
(Fig. 12
contribution {3 T3, can be plotted as T versus T (Fig. 6) or log
T
’Y Tc
first diagram enables the determination of 7c by the criterion of equalization of entropy for
the experimental transition and for the idealized specific heat jump at T
Tc ; it also enables
an improved determination of y in comparison to figure 5. The second diagram allows one to
verify the exponential decay of the electronic contribution C es below 7c (starting at
ii)
the electronic
TFi
Ce
T
=
7"
20132).
)
T
This determination is also
improved
p
if
one
subtracts the T.L.S contribution,
as
discussed in section 5.
iii) this T.L.S. contribution becomes predominant for temperatures
7"
g 12).
)
preciselyY when Ces has vanished, i.e. for T) ± 6 ((Fig.
h
es
below 0.5 K,
or more
1249
Fig. 6.
against
T. This
diagram allows the determination of T, by the equalization of
a good determination
0.2 mJ.mole-l.K-2 for ZrS1Cu19 (II) and
entropy for both experimental and idealized specific heat jump at T,. It also allows
of the electronic coefficient y above Tc;; here y
7.45 ± 0.1 rnJ.mole-l.K-2 for ZrCu32 (annealed).
3.2 RESULTS
=
11.7 ±
FOR THE NORMAL STATE.
In table Il and figure 7 are collected values of
3.2.1 Electronic density of states.
from
values
determined
These
yn above T,, have been submitted to the criterion of
N y(EF).
in
of
superconducting and normal states. If we assume the same lattice
entropy
equality
term
in
the
two
states, one must have Sn (Tc)
/3 T3
Ss(Tc), and therefore :
-
=
There is a good agreement for the whole series : calculated ys agrees with the measured
Yn above Tc within 1 to 6 % (with Ys&#x3E; Yn), except for Zrg1Cu19 (I) and (II) where
ysexceeds yn by 11-14 %. But we note that at this high Zr content, there is an uncertainty
concerning the lattice contribution in the superconducting state which is very probably smaller
than above Tc [Ref. [6] and Sect. 5] and which could parly explain the discrepancy.
1.9 K (see Fig. 5) which can be analysed
For Zr52Cu48, there is a slight discontinuity at T
as an increase in y by about 5 % below this temperature, feature which is not modified by
subsequent annealing. A similar feature has been observed in Zr60Cu40 [23] and in
Zr62.9Ni37.1 [29], which, for the second case, has been ascribed to the presence of a second
amorphous phase, but undetectable by X-rays.
The main results for N y (EF) are the following :
=
electronic D.O.S. is very sensitive to heat treatment or to ageing effects.
8a shows the effect of a stay of a few days at room temperature, between two
successive experiments. One observes a variation of 10 % of the electronic y T term, without
any change either for 0 D or for T,.
Senses of variation upon heat treatment or ageing are not systematic as seen in figure 7 :
whereas y decreases for Zrrcun and Zr73CU27, it increases for all other concentrations.
a) the
Figure
1250
Table II.
-
Superconducting
and
thermodynamic parameters of sputtered Zr,oo - xcux
samples.
(1)
(2)
From reference
From reference
It
seems
that there is
(Fig. 8b) : firstly,
toward
[5].
[6].
on
a cross-over
ageing
effect for
Zrg1Cu19 (I) between two equilibrium
«
»
values
temperature over period of a few months, y decreases
L.Q. alloys (points 1, 2, 3), and also close to heat-treated
at room
value rather similar to
about 5 mJ/mole.K2. After a thermal treatment at 200 °C and during subsequent
storage at - 20 °C, y tends toward a much higher value of about 11 mJ/mole.K2 (points 4, 5,
6). Note also in figure 8b that in the same time there is a small variation of Tc, following the
initial decrease which appears as a general consequence of structural relaxation (see below).
This strong sensitivity to thermal treatments is at variance to L.Q. Zr-Cu alloys, where no
systematic and much smaller variations (increase) can be detected (in Zr54Cu46 [26] and
a
Zr77CU23,
Zr72CU28 [27]) ;
b) values of Ny (EF) considerably exceed those of L.Q. alloys, obtained by melt-spinning
[22, 23]. There is an overall trend of Ny (EF) to increase at high Zr content. For L. Q . alloys,
the variation is almost linear with concentration. It is also the case for the extreme maximum
values of the sputtered alloys, which concern the concentrations x = 19 (1), 38, 48 at%
(relaxed state) and x 19 (II), 27, 63.5 at% (as-prepared state). The differences of amplitude
between these linear variations decrease when x increases, as does the difference between the
values of crystalline and amorphous phases, with a trend to a common value at large Cu
content. This confirms the predominant role of Zr in the electronic D.O.S. of these
amorphous alloys, and especially in the sputtered samples ;
=
1251
Fig. 7. Electronic coefficient y and corresponding D.O.S. versus the concentration for : sputtered
samples : ZrSlCu19 (I), see figure 8b ; for other samples : (0) as-prepared, (A) annealed state. Upper
dashed line is drawn through the high y values for both annealed (Zr81Cu19 (I), Zr62Cu3g,
Zr,2CU48) and as-prepared state (Zrg1Cu19 (II), Zr73CuZ7, Zr36.5Cu63.5)· Melt spun : (x ) from reference
[23] ; (0) from reference [22]. Dashed line : mean value of electronic D.O.S. from Hc2 and p
measurement of both sputtered samples (either as-prepared or annealed state) and L. Q. samples
(Refs. [11, 23, 28]). The effect of annealing on Zr54Cu46 (Ref. [26]) is indicated. Crystalline : (8.) from
-
reference
[22].
c) within the G.L.A.G. (Ginzburg, Landau, Abrikosov, Gor’kov) theory for
coupling superconductors in the dirty limit, one can also determine the D.O.S. at the
level from electrical resistivity p and upper critical field Hc2 measurements [28] by :
weakFermi
with
These determinations show that there is no effect of thermal treatment on ’Y He2 and that the
D.O.S. determined in that way decreases linearly with x as NH (EF)= 2.5 (1 - x)
[states.eV-1, atom -1], in good agreement with the values of L.Q. alloys (shown by the lower
dashed line in Fig. 7). Therefore, there is a discrepancy between N ’B1 1 (EF) and N H e2 (EF) for the
sputtered alloys, which is much larger than that previously reported for L.Q. Zr-Cu or Zr-Ni
[23, 29].
In table II and figure 9
3.2.2 Debye temperature.
coefficient /3 and OD. However, we have to take
-
JOURNAL DE PHYSIQUE. - T. 50, N° 10, 15 MAI 1989
also
care in
are
reported the values of the lattice
using the Debye model for the
1252
Fig. 8a.
Fig. 8b.
Fig. 8. Sensitivity of the electronic coefficient y on thermal treatments : a) a subsequent experiment
following a stay of a few days at room temperature indicates an increase of y without any change either
for 0 D or 7c ; b) a cross-over effect of y is observed for Zr81Cu19 (I) with the thermal history : points (1),
(2), (3) : as-prepared state then ageing of 45 days and 4 months at room temperature, point (4) : effect
of annealing (200 °C-1 h) ; points (5) and (6) : ageing at around - 20 °C after heat treatment. On the
right side the corresponding superconducting transition temperature Tc (0 and A,,&#x26; respectively aged,
annealed and highly-relaxed states). Note the quasi-invariance of 7c for the annealed state while y had
largely increased.
-
Fig. 9. - Debye temperature 0 D (calculated from the cubic term of the specific heat) versus x.
Sputtered samples : (0) as-prepared, (A) annealed, (À) highly-relaxed : ZrSlCu19 (I). Melt-spun :
(x) from reference [23], (0) from reference [22] ; the effect of thermal annealing on Zr54CU4 [26] is
indicated. Crystalline (0) from reference [22] ; the drop of 6D for Zr40Cu60 has been ascribed to the
complexity of the crystalline phase CUlOZr7.
1253
of vibrational spectra at low frequencies in disordered solids : despite a
heat contribution in these amorphous alloys, there is some experimental evidence
of additional excitations to the actual ùj 2 phonon contribution. Hitherto, published acoustic
data are only available in L.Q. Zr4oCu6o [30] which indicate an acoustic determination
Oacoustic 272 K higher than the calorimetric one : (Jcalor. 230 K [22]. We did not presently
get systematic experimental values of sound velocities which allow us to determine exactly
description
T3 specific
=
=
80 [by
-4 oc (p,
(JD
OD value that
the
mass
density)]. However,
we
intend to define
a
calorimetric
PVD
we can
The main results
compare to those of L.Q.
alloys determined
in the
same
way.
are :
a) OD of sputtered samples are lower than for L. Q. , even after structural relaxation by
subsequent heat treatment ;
b) like for y, at variance to L. Q. alloys, OD iS sensitive to structural relaxation. One
observes a systematic increase, whereas such variations are not systematic in melt-spun
samples : e.g. only in Zr60Cu40 (increase of 10 % [27]) and in ZrS4Cu46 (surprisingly a decrease
of 2 % [26]).
3.2.3 Superconducting transition.
a) The superconducting transition tempe rature Tc (Tab. Il and Fig. 10) exhibits universal
properties for the different kinds of Zr-Cu amorphous alloys. Firstly, similar values in the asprepared state, despite the different degree of structural disorder. The calorimetric transition
width is somewhat larger for the sputtered samples (0.30 to 0.45 K) than for L.Q. (0.1 to
0.4 K). Notice that this rather large width cannot be entirely accounted for by the chemical
concentration fluctuations which are of about 1 at% between the mean values of different
foils, or up to 2 at% within a same foil of a sputtered sample, and which would correspond to
widths of 0.1 to 0.2 K.
Superconducting transition temperature versus x. Sputtered : same symbols as in figure 9 ;
melt spun (as-prepared state) : (e) from reference [11] [resistive measurement] ; (x) from reference
[23]. The effect of thermal annealing is indicated for melt-spun Zr54CU46 [0, Ref. [26]]. Despite the very
different numerical values and behaviour of the electronic D.O.S., the Tc seems to be universal with a
dT
Fig.
10.
-
relative decrease àAXT,:
of about 0.1 K/at%.
1254
Secondly,
after heat treatment,
Tc drops by
about 0.3-0.4 K
independently
of the
alloy
concentration, but the width remains almost unchanged. Again this behaviour is universal for
the different kinds of alloys, despite the different behaviour on relaxation of the physical
parameters which are supposed to govern Tc, mainly (JD and N (EF). For example, the
increase of 0 D on annealing, which could explain the 7c depression, is not systematic for L.Q.
alloys.
As previously reported [28, 31], this calorimetric determination is
the electrical resistivity transition which naturally corresponds to
in good agreement with
the higher side of the
calorimetric one, and with a width of the order of 100 mK, in better agreement with the
concentration fluctuations for a much smaller piece of sample used in the resistivity
experiments (about 1 mm x 15 mm).
In absence of tunneling measurements on these
the
McMillan
numerical
formula [32] for transition metallic alloys,
alloys,
general
from
which determines the coupling parameter À
Te and OD :
b) Electron-phonon coupling strength.
we use
with * = 0.13 for transition metals .
(1)
Values of À [Tab. II] indicate that the coupling strength deviates progressively from weak to
intermediate when the Zr concentration increases from 35 to 80 at%. This progressive and
very continuous behaviour has also been pointed out by the precise analysis of the
thermodynamic critical field Hc(T) determined from Ces (T) below Tc, and estimation of the
B.C.S. parameters such as the condensation energy, or the deviation function of
H (T) [31]. After heat treatment, À decreases by 0.03-0.04.
For the « as-prepared » alloys, À for the sputtered is higher than for L. Q. by about 0.05 in
the whole concentration range. Since their Tc’s are similar (cf. Fig. 10), we suppose that the
use of McMillan formula implies that the increase of À is compensated by the decrease of
0 D. However, in absence of tunneling measurements which would give directly the value of À,
this hypothesis remains to be confirmed.
c)
At the
transition,
one can
AC and estimate the value
determine
as
indicated in
of TY âCTC Ces Tc(Tc)C en-(Tc)Cen(Tc)
=
figure
which
are
6 the
specific
heat
reported in table
II.
jump
They
systematically somewhat larger (for x -- 50 at%) than the B.C.S. value of 1.43 for weak
coupling superconductors, and almost similar to L.Q. alloys, without a clear trend to increase
with the Zr content, as one could expect for an increasing coupling strength.
are
4. Discussion of the normal state and
T,.
In a general way, it has been shown before that
N (EF) AND ODin
a
of
sputtered alloys
higher degree structural disorder than L. Q. ones on every scale of
the structure : short, medium and long-range order. We intend to try to connect this
specificity to the different contributions, mainly those of phonons and electrons, whereas this
4.1 CONCERNING
-
are
connection appears the most obvious for the
[7].
a)
low-energy excitations,
as
discussed elsewhere
With this property, are consistent the Debye temperature (OD) values, which are lower
than in L.Q. alloys, due to a more loosely connected lattice. This is supported by a tigthbinding model proposed by Cyrot-Lackmann [33] which explains semi-quantitatively, for
transition-metals, the decrease of OD in the amorphous state. The decrease is due to that of IL,
1255
the shear modulus, which is related to the lattice sound
velocity by v,
being
= ( 2013 ) ,betwèen
P
p
the
the
density. The theory predicts a variation of OD of the order of 10 %
and
the
But
in
that
states.
indicate
Zr-Cu
indeed,
amorphous
crystalline
experiments
(Fig. 9)
it can be more higher ; the drop of OD increases with an increasing structural disorder of the
amorphous state as shown by the following results for Zr68Cu32 :
crystalline state : 0 D 315 K ; liquid quenched (amorphous) : 189 K (40 % of relative
variation) ; sputtered : annealed (amorphous) (JD 163 K (48 %) and as-prepared, OD
mass
=
=
=
(50 % of relative variation).
Annealing induces in the sputtered alloys a systematic increase of 6D, due to an increase of
stiffness of the material. A rather similar behaviour occurs for the low-energy (TLS)
excitations [7] : a much larger density of states comparatively to L.Q. alloys and its systematic
reduction on annealing. Both correspond to a much higher overall D.O.S. of the low-energy
vibrational spectrum (including the TLS, defined as configurational localized excitations)
which is depressed by the structural relaxation.
156 K
b) The consequence of a less stable structure is particularly striking in the case of the
electronic D.O. S. at the Fermi level : N y(Ep) values are much larger than for L.O. alloys,
especially at high Zr content. For ZrSlCu19, a composition which cannot be prepared by meltspinning, the variation of N,(EF) between two different samples (I and II) or for a same
sample (I) upon the thermal history, reaches a factor of two ! As reported previously, there is
a cross-over effect of NY(EF) at this high Zr content. Note that larger effective
Ny values reflect very probably higher D.O.S. of the band structure at Ep, N(0), since
renormalization effects, supposed here to be limited to electron-phonon interactions, are
similar for both kinds of materials, sputtered and L.Q.
A first explanation for these differences could be in differences in the chemical short-range
order [C.S.R.O.]. For example, studying the Zr-Ni system, Kroeger et al. [29] found a
peculiar behaviour of NY(EF). They observed rapid variations of NY(EF) between 60 and
65 at% Zr. These values exceeded by 20-25 % those observed by Altounian and Strom-Olsen
[11], obtained from H,2 and resistive measurements, at about the same concentrations. These
features have been ascribed to rapid changes of the C.S.R.O. due to a competition of two
amorphous phases Zr3Ni2 and Zr2Ni. But in our case, this interpretation is not expectable :
EXAFS measurements show that C.S.R.O. is absent in the sputtered Zr77Cu23 and
Zrg1Cu19 ; instead, there is a slight tendency to clustering for Zr atoms [3]. More generally, it
seems that chemical short-range order does not characterize the ZrCu system when Zr
content is higher than 50 at% [19], at variance with ZrNi. It is therefore difficult to test the
role of C.S.R.O. in the ZrCu alloys, which has been suggested [34] to lead to a decrease of
N (EF).
On the other hand, our data agree with the general ideas of Morruzi et al. [35] about the
relationship between the electronic d-band properties and the stability of transition-metal
glasses. They argue that high D.O.S. at Fermi level are characteristic of the relative instability
of their short-range atomic arrangements. At variance, energetically favorable atomic
arrangements will lead to small N (EF). That is to say that a high N (EF ) implies a high free
energy, less-stable configuration. These arguments were tested on the y values of crystalline
and amorphous Zr-Ni alloys by Kuentzler [36].
Characterization data, particularly the irreversible decay on annealing of the enthalpy and
of the electrical resistivity (Zr77CU23), much higher in sputtered than in L.O. alloys, are
consistent with this less stable configuration in sputtered alloys. This hypothesis is also
consistent with both the smaller Debye temperature, indicative of less cohesive local
arrangements, and the higher density of TLS, originating in structural defects related to some
1256
free-volume. Hence,
However, the unexpectable
understandable the general higher values of N,(EF).
of variation of y on annealing cannot agree with a
systematic trend toward a more « stabilized » state.
According to these ideas, one can also account for the differences in NY(EF) between
different series of L.Q. alloys and the sensitivity of some of them to thermal treatment,
features which have still not been matter of discussion. Since L.Q. alloys, due to their much
lower effective quenching rate than for sputtering, have already reached a more « stabilized »
state, one could expect almost similar values of N,(EF). However, experimental data show
that, even among L. Q. , there exist differences which exceed largely the uncertainties of the
excess
are
sense
experiments.
For example,
in the ZrNi system, values of N y from references [29] and [24] exceed largely
those of Onn et al. [37] ; and the striking behaviour of N y at Zr content around 60-65 at%
described by Kroeger et al. [29] has not been seen by other groups [11, 37]. In the case of
reference [29], samples were prepared by arc-hammer technique in comparison to meltspinning for two other groups. For ZrCu, results of Garoche et al. [22] indicate higher values
than Samwer and Lôhneysen [23], both groups using the melt-spinning technique. Within the
scheme of Moruzzi et al., one could explain these differences by differences in the cooling
rates during the glass-forming process, which lead to more or less « stabilized » structures,
and therefore to different electronic D.O.S. ; and some of them will be significantly sensitive
to thermal treatment. This is supported, firstly, by the results of Kroeger et al. on ZrNi, and
secondly for ZrCu, by the observable effects (increase by 5-10 %) of structural relaxation on
ZrS4Cu46 [26], Zr72Cu28 and Zr6gCu32 [27] whereas no effect was reported in Zr6oCu4o [27] and
Zr70CU30 [38].
c) An unexpected feature is the discrepancy which exists between the values of
N y (EF) and N H,:2 (EF), the electronic D.a.S. determined within the GLAG theory, by the
resistivity p and the slope of Hc2 at T,, with N y always exceeding N H,:2* This disagreement
could result from these two different ways (local electronic transport property or global
thermodynamic property) used to study the superconductivity, as already discussed by
Laborde et al. [31] and in reference [29]. But, it is striking that the amplitude of this
discrepancy varies accordingly to the technique of preparation of the amorphous state :
for the series ZrCu obtained by melt-spinning, this amplitude varies between 6 % and
17% [11, 22, 23] ;
- for ZrNi obtained by the arc-hammer technique, it is about 20 % [11, 29] ;
for sputtered ZrNi [31] or ZrCu [28], it varies between 20 % [Zr77CU23 ] and 100 %
[Zr8lCU19]. Note that for Zr-Cu, NH "2(EF) is similar for both kinds of alloys.
-
-
An extended discussion [40] about the determination of y from p and the slope of
Hc2 at Tc, shows that one must be careful when using this method for calculation of the D.O.S.
at EF. Indeed, experimental uncertainties are typically of about 10 %, mainly due to the
resistivity measurements.
But, in the case of Zr-based alloys, the discrepancy exceeds the uncertainties. It can no
more be due to inhomogeneity of the sputtered samples, because all characterization
measurements indicate that the whole series is homogeneous [41]. It appears that the
discrepancy is actual and probably related to the degree of structural disorder of the material.
In the case of the sputtered ZrCu (or ZrNi) alloys, one can assume that the electronic
D.O.S. thermodynamically determined, largely in excess to that of L.Q. alloys, and which
does not intervene in the superconducting properties, is of localized nature. A structural
origin, which is now being tested by transmission electron microscopy, could be in clusters of
Zr atoms of size less than the coherence length )(0), sufficiently disconnected from the
1257
remaining Zr-Cu matrix. The part of the electronic D.O.S., almost similar to that of L.Q.
alloys, of delocalized nature (itinerent electrons) is that one which determiqes the
superconducting properties, including Tc. It corresponds to the electronic diffusivity,
which is inversely proportional to the slope of the upper critical field
D = 1 VF f,
Hc2
at
T2 :
(kB : Boltzman’s constant, J.Lo = 4 7T X 10-7 and e the electronic electrical charge), and which
is almost insensitive to the structural relaxation, either for L.Q. [39] or sputtered [28] alloys.
becomes more complicated in
This problem of discrepancy between Ny(Ep) et
view of the recent results of magnetoresistance measurements on Zr43CuS7, Zr40Cu60 and
Zr61Cu39 [42-44] which indicate the existence of weak localization in these materials.
N H e2 (EF)
4.2 CONCERNING
Tc.
a) Below the superconducting transition temperature, Tc, the condensation of quasiparticles
into Cooper pairs is complete, with evidence given by the exponential decay over several
orders of magnitude of the electronic specific heat Ces (see Sect. 5). Therefore, it appears that
the high N (EF ) values of sputtered alloys does not lead to an abnormal superconducting
behaviour.
On the other hand, Tc does not depend essentially on N y (EF ), since its value is universal
for the different ZrCu alloys, either sputtered or L.Q. The overall insensitivity of
7c to either N (EF ) or 0 D (respectively higher and lower in sputtered than in L.Q.) can be
viewed as a confirmation of the Anderson’s theorem which predicts no significant effects of
disorder on the value of Tc ; here the amount of disorder is not modified by external means
(irradiation, impurities) as in the case of « high T, » A-15 superconductors [45], but is entirely
intrinsic. An alternative explanation of the insensitivity of Tc to N y(EF) is based on our
precedent argument of existence of localized electrons which do not intervene in the
superconducting properties. In the following, we test the usual B.C.S. and McMillan
formalism with the electronic D.O.S. N He2(EF).
b)
The B.C.S. relation which relates
together Tc, OD
and the electronic D.O.S. :
or :
[V being the net attractive electron-phonon interaction potential ; N (0)
in states of
frequency], is
for A(0) thé
one
spin. eV-’. atom-’ ;
very well
obeyed
A
either for
ocOD
BD
as-prepared
D.O. S. calculated from p and
where ( w )
or
is
32 ir2ky2 expressed
averaged phonon
an
annealed series
(Fig. 11),
HZ L (+dT ) JJ
oc -
p . y
if
we use
which détermines
superconducting behaviour, and which varies linearly with the concentration : N (0)
1.25 (1 - x) states of one spin.ev- latom- 1. We find values of V close to 0.4 eV
(V 0.40 eV for as-prepared and 0.34 for annealed), in good agreement with other transition
the
=
1258
11.
Fig.
( (Jo versus 1
for sputtered samples (0.81, [Zr] , 0.52). Same symbols as on
0,
[Zr]
exponential variation is found either for as-prepared (0) or annealed (A), with a higher
- Log
figure 9. An
slope for the annealed
(see
state
text for
details).
metal alloys (crystalline) calculated in the
than in literature where A
0.85.
same
way
[46].
But the values of A
are
twice lower
=
of "k ú) &#x3E;
However, in equation (2), A is calculated with the approximation
34 ,
which is valid for
crystalline
materials
[47].
But for
to
kB OD
amorphous samples
this numerical
approximation is no more correct,
frequency modes in the
because one must take into account the increasing weight
vibrational spectrum of the amorphous phase, which leads
to a lower ú) &#x3E; /OD ratio. We suppose that this is accentuated when 0 D decreases, and we
remember the large variation, by about a factor of two in the present case, of
8 D between crystalline and amorphous phases. Indeed, the value of A is reduced according to
increasing structural disorder : Aannealed 0.415 ; Aas-prepared 0.303.
of the low
=
c)
[N cff
The definition of the
=
coupling strength parameter
À is
[32] :
is the effective density of states, ([2) is the average over the Fermi surface of the
matrix element and M is the atomic mass].
electron-phonon
If we still
use
for each series
for Neff
(0.745
prediction of Varma
the D.O.S.
for
and
as-prepared,
Dynes [48]
on
and 0.710 for
the constancy of the rate
transition metal alloys. This result is also
V of the B.C.S. formula.
potential
He2 data, then À is almost constant
Neff
annealed). This is consistent with the
obtained form p and
a
12&#x3E;2
for
a same
series of
M w
confirmation of the constancy of the attractive
1259
Indeed, if we compare the McMillan’s relation (1) which can, in that case, be approximated
TC-6 D - exp - 1 +,k ,
to
À
,
to the B.C.S. formula where
therefore V is the
N(O)
is
the bare D.O.S.
strictly
qualitative equivalent of
.
We note that the
decrease of V on annealing is consistent with the increase of the Debye temperature, which is
generally the approximation used for the mean phonon frequency ( w) . Hence, we get a
coherent interpretation of the behaviour of Tc and OD for both the as-prepared and annealed
series, if one uses the electronic D.O.S. which governs the superconductivity, and which
varies proportionally to the Zr concentration. A same structural state (as-prepared or
annealed) corresponds to a unique value of the net attractive electron-phonon interaction
potential V for the whole series.
d) We finish this
physical parameter :
discussion about Tc by outlining the absence of relation with another
the tunneling TLS states [49, 50], which also behave very differently in
these different kinds of alloys. Once more, we emphasize the universal properties of
7c among different Zr-Cu amorphous alloys.
5.
Superconducting
state.
We discuss now for the concentration range 19 , x , 48 the specific heat in the superconducting state, which is determined by the condensation process of the electronic contribution and
at very low temperature, i.e. for T:5 0.5 K, by the presence of the low-energy excitations
(tunneling states or two-level systems : TLS). An analysis of the TLS contribution and its
comparison to values for corresponding liquid-quenched alloys is discussed elsewhere [7].
Concerning the electronic (Ces) and lattice contributions, our main results are : (1) the
electronic condensation is a complete process following the classic B.C.S. theory of the
superconductivity, despite the unusual behaviour in the normal state. (2) With increasing Zr
concentration, there is a very continuous and progressive deviation from the B.C.S. weakcoupling limit for the coefficient b of the exponential regime (Ces - a e-
bTc/T).
_
The analysis of the specific heat is almost similar to that previously
5.1 DATA ANALYSIS.
described in reference [6] for Zr77CU23 ; below Tc, Cp is the sum of three contributions : the
lattice one, that we will firstly suppose to be similar as in the normal state above
7c (= 8 T 3)@ the electronic one that we show here it exactly obeys an exponential decay
/
with y the electronic coefficient defined above Tc) in the T-range
-
CesTca e - bTcIT
TC
reported figure
,
7"
T
Tc
predominant for T 7. Typical examples are
in
12 for four different samples with increasing Tc values. After subtraction of
the phonon /3 T3 contribution (see values in Tab. II) specific heat is plotted in the usual semilogarithmic diagram for the determination of exponential variations : log Tc versus
1.5--
T
7, and the TLS
one
which becomes
c
r
TT .
The
exponential decay
temperatures decreasing down
the TLS contribution.
of
to a
Ces
is
T
valu-obeyed
TC 5-6,
T
over
about 3 orders of
where the
rapid
magnitude
for
deviation is then due to
1260
Fig. 12a.
Fig.
12c.
Fig. 12b.
Fig.
12d.
Fig. 12. Specific heat of four different samples (with increasing Tc) in the superconducting state after
subtraction of the phonon contribution, plotted in a semi-logarithmic diagram. For a, b and c,
both obeying exponential
Cp is analysed as the sum of the electronic Ces and the TLS contributions,
T
variations (dashed lines). For (d) a deviation to this analysis occurs at
to 8.
T
-
--6
1261
One
can
7"
T 15-20,
verify that
in the intermediate T range
the TLS contribution
can
T
from Tl,
-8
T
also be fitted in this
and
extending
diagram by
a
down to
(very smooth)
exponential variation. We don’t ascribe a peculiar physical meaning to this law, but when
reported in a direct C p versus T diagram, it indicates a progressive deviation to the limit
Ta regime observed below 0.15-0.20 K (see the fits in Fig. 3 in [7]), that we interpret as an
interaction effect between quasiparticles and TLS and will be discussed separately [51].
Therefore, within the assumption that such a variation can be extrapolated up to
T
the subtraction of the TLS contribution leads to a well defined exponential decay for
T
TICCes,-3-4,
than 4 orders of magnitude, for Zr concentration up to around 70 at% (curves
an extent of this regime is similar to the best samples of crystalline
Such
a, b, c).
metals
(see, e.g. Refs. [52] and [53]).
superconducting
For Zr concentration higher than 70 at%, a typical feature appears in the data for
over more
TCTT -
sharp break for Zr73CU27 (curve d), which
a local minimum at still higher Zr content, instead of the smooth
becomes
curvature due to the transition between the two exponential contributions, from Ces(T) to
CvLs(r). We have already pointed out this feature for Zrrcun [6] which corresponds to an
unphysical local maximum around 0.3-0.4 K for the TLS specific heat if we maintain for /3 the
value determined in the normal state above T,,. So we interpret it as being due to an overestimated value of the phonon contribution f3 T3 in view of the value determined above
T,. Indeed at high Zr content, there is a temperature window (0.3,-5 T:5 0.6 K) where the
relative contribution of the phonon term becomes large in comparison to either Ces or
CTLS, so that the residual specific heat studied here becomes very sensitive to the exact /3
T
value in this T-range. Anyway, down to ; = 5 the exponential variation of Ces remains well
T
established over three orders of magnitude.
The value of the exponential coefficient b is reported for the whole series of samples in
figure 13, versus the superconducting coupling strength parameter À defined from the
6-10
Fig. 13.
(corresponding
in this diagram
-
Exponential
to T - 0.4-0.6
K)
as a
factor b of the electronic
specific
parameter A. Symbols 0 and A correspond respectively
temperature)
and annealed
samples.
heat
Ces
to unannealed
coupling McMillan
(as-prepared or aged at room
versus
the
1262
II). There is a progressive and continuous deviation when À
increasing Zr concentration, from the B.C.S. weak-coupling limit
b
1.44 [54]. This B.C.S. variation is very well obeyed for Zr52Cu48 (as-prepared) and
Zr62Cu38 (annealed at 200 °C).
McMillan’s formalism
increases, that is
(see
Tab.
to say for
=
5.2 DISCUSSION OF THE SUPERCONDUCTING STATE.
Firstly, our data as presented in
are
reminiscent
of
some
results
in
figure 12,
previous
crystalline superconducting metals
which exhibit a sudden deviation from the expected exponential decay of C es for
T
as an effect of
7-8, e.g.
[ ] These results have been interpreted
g in Nb [53],
[ ] V [55],
[ ] Ta [53].
p
T
gap-anisotropy or existence of two gaps, inducing for Ces two successive exponential regimes.
In particular, the data of Nb look very similar to ours. However, in our case firstly the slope of
the second exponential is still about 3 times smaller than for Nb, and secondly for the Zrbased amorphous alloys, this anomaly correlated to the thermal conductivity has been
unambiguously related to the presence of TLS [56, 5]. Moreover, one can presently wonder
whether in some cases of crystalline materials the deviation from the exponential behaviour of
Ces could not be a manifestation of low-energy excitations, ignored at that time, and which
have been revealed for example in crystalline niobium when doped at very small amount (less
than 1 at%) by 0 and H or D [57].
Secondly, amorphous Zr-based alloys such as ZryoPd3o [56] and Zr-Cu [23] have already
been found to behave as weak or intermediate coupled superconductors ; but in addition we
show here the very continuous evolution of the coupling strength from weak (and in that case
in excellent agreement with the B.C.S. prediction) to intermediate when the Zr content
increases along this series, which is a typical property of these amorphous metallic alloys.
Moreover, this continuity does not depend on the structural state (annealed or unannealed) of
each sample. The same evolution has been established for the different thermodynamic
parameters deduced from the variation of the thermodynamic critical field Hc(T) and is
discussed in reference [31b] together with a discussion about the Ginzburg-Landau parameter
-
TC
-
K.
6. Conclusion.
In conclusion, we have shown that the high degree of structural disorder which characterize
the sputtered ZrCu alloys in comparison to the melt-spun, influencates quite differently the
superconducting and thermodynamic parameters presently investigated. The behaviour of the
transition Tc, identical in both kinds of alloys, can be understood as following the Anderson’s
theorem [58], that is the weak dependence of 7c on the structural disorder. On the contrary,
the low-frequency phonon contribution and, at more extent, the electronic D.O.S. at
EF are sensitive to this type of structural disorder. The lower Debye temperature, in
comparison to melt-spun alloys, increases by about 10 % on subsequent annealing. This
behaviour is quite similar to that of the low-energy excitations (TLS), with a large initial
contribution which is reduced by a subsequent structural relaxation. Both evolutions are
compatible with a reorganization toward a more « stabilized » structure, but which still
remains for from the liquid-quenched state.
The electronic D.O.S. at EF appears to be the most sensitive parameter to the structural
disorder. A large part of the D.O.S., which increases with the Zr content, seems to do not
intervene on the superconducting properties such as the coupling strength À and
Tc, and on the upper critical field Hc2- We suggest that this contribution, in excess to that of
the melt-spun alloys, could originate in more localized d states related to the Zr atoms
environment. In a general way, these results are in agreement with the arguments of Moruzzi
1263
al. which relate large electronic D.O.S. at EF to unstable short-range atomic arrangements
in transition-metal amorphous alloys.
The precise analysis of the specific heat in the superconducting state indicate a complete
electronic condensation mechanism in good agreement with the usual gap interpretation of
the B.C.S. theory. The progressive deviation from the B.C.S. limit of the exponential
coefficient of the electronic specific heat indicates an evolution from weak to intermediate
coupling when the Zr concentration increases from 50 to 80 at%. This very continuous
evolution upon the chemical composition appears as a typical behaviour for this amorphous
alloys series, mainly determined by the Zr element.
et
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The B.C.S.
a
prediction is
= 8.5
e-1.44 Tc/T for 2.5
zero-temperature energy gap 2
DEEN
0394(0)
=
3.52
~ T ~ 6, the value b
kB Tc,
and 26
$$
Progress in Low Temp. Physics,
between 6 and 8, both expressions
J. and SCHRIEFFER J. R.,
chap. VI].
[55]
Ces/03B3Tc
In fact, for
Tc/T
RADEBAUGH R. and KEESOM P. H.,
Phys.
Rev. 149
(1966)
209.
=
1.44
for
Ed. C. J.
are
corresponding to
7 ~ Tc/T ~ 11
[BAR-
Gorter, 1961 Vol. 3,
almost
undistinguishable.
1265
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