Low-temperature thermodynamic properties of amorphous sputtered Zr 100-xCux alloys. Effect of structural relaxation

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Submitted on 1 Jan 1989

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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:

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₎

Résumé. 2014 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

thermodynami-ques 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.}

Abstract. 2014 We

report on

_{low-temperature specific}

heat measurements of

_{superconducting}

amorphous Zr100-xCux

(19 ~

x ~

₆₄₎

_{alloys prepared by sputtering}

that we _compare to

corre-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.

Classification

Physics

Abstracts 65.40 - 63.50 - 74.20F

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

vapor-quenching

(V.Q.)

or

_{liquid-quenching}

_(L.Q.)

_techniques.

_Moreover,

_{upon these}

_conditions,

they

are

differently

sensitive to structural relaxation

_[1].

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}

vapor-quenching

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

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 to the

_annealing

of the frozen-in free volume. Irreversible contraction

¥

of about 2 x

10- 4

has been measured

by

Hillairet et al. in a similar

_{sputtered Zr76Ni24 alloy,}

which

Table I. - Characterization data

of sputtered

ZrlOO-xCux

samples.

* _{See also reference}

[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

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

Qp = 4 sin

()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

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. -

D.S.C.

thermograms

of parts of

_{sputtered samples}

_(exact

_composition

_reported)

at a

_heating

rate T = 20 K

min- l.

The dashed line is the base-line

corresponding

to the

recrystallized

state. For

(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).

Fig.

3.

_{- Sputtered samples : crystallization}

_(T.,

_symbol

_D)

and

glass-transition

(TG,

symbol

0)

temperatures versus x. Below x = 28 at%, 8 and. represent the two

crystallization

_stages

(see

Fig.

2 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).

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

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.

Samples

have been measured

_firstly

in their «

_{as-prepared »}

_state, after

_being

removed from the

_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

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

four-wire

_{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 ;

Fig.

4.

_{- a)}

shows the _temperature

_decay

after a heat

pulse

and its

_{analysis by}

means of a

microcomputer

for 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

_R

_f

_{( 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

_Ci

_i 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

addenda,

is

_mC

= Tf - Ti

The

_specific

heat of the

_sample

is obtained after

_subtracting

the

3.

_Spécifie

heat data

_analysis

and results. 3.1 DATA ANALYSIS. - We

can

_distinguish

three

_temperature

_{ranges, characterized}

_by

different

_weights

for

_phonon,

electronic or T.L.S. contributions :

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 Zr-based

_{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

states at Fermi level :

_{N, (EF)}

=

3 y

(states.

e v- 1 .

atom- 1,

with _y in mJ.

mole - 1 .

K- 2) ;

,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.

ii)

the electronic

_specific

heat

_Ce,

obtained from

_Cp

after

_subtracting

the

_phonon

ceT

_Fi

_{12 . The}

contribution {3

T3,

can be

_plotted

as

T

versus T

(Fig. 6)

or

_log

Ce

versus

T

_{(Fig. 12).}

The

T

_{’Y Tc}

T

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

7"

20132).

This determination is also

_improved

if one subtracts the T.L.S

contribution,

as

T

)

p

discussed in section 5.

iii)

this T.L.S. contribution becomes

_predominant

for

_temperatures

below 0.5

K,

or more

7"

precisely

when

_Ces

has

vanished,

i.e.

for ) ±

6

_{(Fig. 12).}

h Y es

Fig. 6.

against

T. This

_diagram

allows the determination of

_{T, by}

the

_equalization

of entropy for both

_experimental

and idealized

_specific

heat

_jump

at

_T,.

It also allows a

_good

determination

of the electronic coefficient y above

Tc;

; here y = 11.7 ±

0.2 mJ.mole-l.K-2 for

ZrS1Cu19

(II)

and

7.45 ± 0.1

rnJ.mole-l.K-2

for

_{ZrCu32 (annealed).}

3.2 RESULTS FOR THE NORMAL STATE.

3.2.1 Electronic

_density

_of

states. - In table Il and

figure

7 are collected values of

N y(EF).

These values determined from yn above

T,,

have been submitted to the criterion of

equality

of

entropy

in

_{superconducting}

and normal states. If we assume the same lattice

/3 T3

term in the two states, one must have

Sn (Tc)

=

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> Yn),}

_except

for

_{Zrg1Cu19 (I)}

and

_(II)

where ys

exceeds

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.

For

_Zr52Cu48,

there is a

_{slight discontinuity}

at T = 1.9 K

(see

Fig.

5)

which can be

_analysed

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 :}

a)

the electronic D.O.S. is very sensitive to heat treatment or to

_ageing

effects.

Figure

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,.

Table II. -

Superconducting

and

_{thermodynamic}

_parameters

_{of sputtered Zr,oo - xcux}

samples.

(1)

From reference

_[5].

(2)

From reference

_[6].

It seems that there is a cross-over effect for

_Zrg1Cu19

_(I)

between two «

equilibrium

» values

(Fig. 8b) :

firstly,

on

_ageing

at room

_temperature

over

_period

of a few

_{months, y decreases}

toward a value rather similar to

L.Q.

alloys

(points

1,

2,

3),

and also close to heat-treated

Zr77CU23,

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

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

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

weak-coupling superconductors

in the

_dirty

_limit,

one can also determine the D.O.S. at the Fermi level from electrical

_resistivity

p and upper critical field

_Hc2

measurements

_[28]

_{by :}

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].

3.2.2

_Debye

_temperature.

- In table II and

figure

9 are also

_reported

the values of the lattice

coefficient

_/3

and

_OD.

However,

we have to take care in

_using

the

_Debye

model for the

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,,&

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

description

of vibrational

_spectra

at low

_frequencies

in disordered solids :

_despite

a

T3 specific

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

80

[by

-4 oc

(p,

the mass

density)].

_However,

we intend to define a calorimetric

(JD

PVD

OD

value that we can _compare to those of

L.Q.

alloys

determined in the same _way.

The main results 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

as-prepared

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.

Fig.

10. -

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

relative

decrease

à T,:

of about 0.1 K/at%.

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 in

_good

_agreement

with the electrical

_resistivity

transition which

_{naturally corresponds}

to 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).

b)

Electron-phonon coupling strength.

In absence of

_tunneling

measurements on these

alloys,

we use the

_general

McMillan numerical formula

[32]

for transition metallic

_alloys,

which determines the

_coupling

_{parameter À}

from

_{Te and OD :}

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 determine as indicated in

_figure

6 the

_specific

heat

_jump

AC and estimate the value

of T âC

=

Ces (Tc) - Cen(Tc)

which

are

_reported

in table II.

_They

Y TC

Tc C en (Tc)

are

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.}

4. Discussion of the normal state and

_T,.

4.1 CONCERNING

_{N (EF)}

AND

_OD-

- In a

general

way, it has been shown before that

sputtered alloys

are in a

_{higher degree}

of 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 connection appears the most obvious for the

_low-energy

excitations,

as discussed elsewhere

[7].

a)

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

tigth-binding

model

_{proposed by Cyrot-Lackmann}

_[33]

which

_explains

_{semi-quantitatively,}

for

the shear

_modulus,

which is related to the lattice sound

_{velocity by}

v,

= ( 2013 ) ,

p

being

the

P

mass

_density.

The

_{theory predicts}

a variation of

_OD

of the order of 10 %

betwèen

the

amorphous

and the

_crystalline

states. But

_experiments

in Zr-Cu

_{(Fig. 9)}

indicate that

indeed,

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

=

156 K

₍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.

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}

melt-spinning,

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

excess free-volume.

_Hence,

are understandable the

_general

_higher

values of

_N,(EF).

However,

the

_unexpectable

sense 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

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

melt-spinning

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