Nonisothermal viscous flow behaviour of Pd40Ni40P20 glassy alloy considered as a free volume related phenomenon

Nonisothermal viscous flow behaviour of Pd40Ni40P20 glassy alloy considered as a free volume related phenomenon

ScriptaMetahrgica et Materialia, Vol. 32, No. 2, pp. 271-276,1995 Copyright CI 1994 Elsevier Science Ltd Printed in the USA. All rights reserved 0956-...

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ScriptaMetahrgica et Materialia, Vol. 32, No. 2, pp. 271-276,1995 Copyright CI 1994 Elsevier Science Ltd Printed in the USA. All rights reserved 0956-716X/‘% $9.50 t .OO

Pergamon

NONISOTHERMAL ALLOY

VISCOUS

CONSIDERED

FLOW

BEHAVIOUR

AS A FREE

*, B.J.Zappel

K.Russew * Institut

for Metals

Max-Planck-Institut

VOLUME

Seestr.

1574 Sofia, Bulgaria Institut

92, D-70174

GLASSY

PHENOMENON

and F.Sommer

Science,

fur Metallforschung,

OF Pd4eNi4sPzs

RELATED

fiir Werkstoffwissenschaft,

Stuttgart,

FRG

(Received May 12, 1994) (Revised August 31, 1994) 1. Introduction The viscous

flow behaviour

years as it determines, a great

extent

fact that connected

time. with

structure. alloys.

the formation

metallic

for a given

This Under

with annealing

of amorphous

on one hand,

of their properties

subtle

is possible terms

during

changes

of the atomic

them

relaxation

structure

structural

relaxation

is reflected

isothermal

annealing,

most

time

reached

[l], PdNiPSi the isothermal

to produce

glasses are thermodynamically metastable, Before the crystallization occurs structural

[1,2]. It should

prior

the kinetics

of the free volume

theory

of viscosity

sensitively

the metastable a linear

the viscosity

et al. approach

equilibrium

increase

71 of glassy of viscosity value

of isothermal annealing. equilibrium viscosity has

studies

of AuGeSi shown

[3], PdCuSi that

studying

alloy near its quasiequilibrium,

towards

[9,10]. The basic equations

to

Due to the

will reach a constant

[6] h ave recently glassy

[l-5].

by the viscosity

exhibit

were the viscosity

P.Duine

for many

they crystallize upon annealing relaxation takes place which is

at the temperature glasses in which

of PddsNi4ePse

research

and, on the other hand, annealings

towards

alloys that

equilibrium of metallic

to crystallization

(5,6,8]. [4], and PdNiP viscous flow behaviour

to analyze

most

glassy

be expected

when the glass has reached metastable However, the only isothermal studies been clearly

alloys has been an area of intense

the possibility

its quasiequilibrium

of the kinetic

analysis

it

value in of Duine

et

al. [S] are as follows. The most generalized

temperature

dependence

of the viscosity

n can be represented

as [5,11]

Here Q,, is the activation energy for the viscous flow, 70 is a pre-exponential factor whose physical meaning is discussed in detail in [ll], and cf is the concentration of the so-called “flow-defects” responsible for viscous flow taking place under applied shear stress r. According to the free volume theory the amount of free volume in the quasiequilibrium state is given by

271

vrscous

212

Vf,eq = xeq(T)yv’

To are two model parameters

where

B and

(VFT)

constant

respectively,

necessary

“~/TV*. The relation

overlap

which

factor between

eqs.

to the Vogel-Fulcher-Tamman of the VFT

empirical

0.5 and 1, and u* the so-called

The reduced

1

free volume

equation, “critical

3: is defined

as z =

(> --

(I), (2) and (3), th e so-called viscosity qeq is obtained

quasiequilibrium

(2)

cf and z is given by [5] cf =exp

Combining

correspond

temperature

to form a flow defect.

between

(T -B To)yTJ*

=

and to the ideal glass transition

y is the geometrical

free volume”,

Vol.32,No. 2

FLOW

.

2

(3)

“hybride”

temperature

dependence

of the

(4 In the ca.ses when the glassy with increasing the most

annealing

suitable

time following

differential

time (due to defect qeq by sudden

alloy has not reached

changes

a bimolecular

equation,

annihilation

the quasiequilibrium

describing

kinetics

of the annealing

dcf

dt=

kinetics

which properly

temperature,

-

-bCj(Cj

Cf,e)

where

i(t)

is the rate

of annealing Text c(t) =

annealing.

for the viscous

eqs.

(l),

v, the jump

(2), (3) and

frequency,

concentration (5), together

Qr

at the with the

flow

of elongation time

Combining

of

(5) flow defect

of isothermal

with

the variation

. with

function

is the rate constant of relaxation -$$ ( > energy of relaxation, and cf,e the equilibrium

of Newton

[6] that

is

Here k, = v,exp

equation

along

of cf change

reflects

the activation temperature

cf changes

[1,5]. It has been shown

the bimolecular

or defect production),

state

of the sample,

one obtains

for the elongation

c(t) as a

[6]

(-0, > kT

cf,et

rloT

+

$, F

1 -

Cflo - Cf,e exp( -k,cf,et) Cf,O

-

LZns b

Cf,O

(7)

where cf,o is the concentration of flow defects at the beginning of an isothermal annealing. Duine et al. [6] have calculated the time dependence of the q approach towards equilibrium at two different temperatures

of isothermal

annealing

near equilibrium

from fits to the measured

elonga-

namely 70, Q,,, v,, Qr, B,Z’o, tion data according to eq.(7). Eq.(7) includes 7 fitting parameters, and cf,o. These fitting parameters have been successfully estimated by Duine et al. [6] and Koebrugge et al. [7] by using a nonlinear, multiparameter regression analysis. Taking into

Vol. 32, No. 2

VISCOUS FLOW

account

eq.(3)

studied,

as a function

it becomes

of free volume

possible

yields

release

tion [5], A. van den Beukel specific heat

cp measured

been experimentally

heating

and production

and JSietsma

free volume

rates.

of free volume

have proposed

[5,8] to be almost

a simple

quantitatively

gives an additional

as annealing

requires linear

energy

relation

alloy out

consump-

between

the

(dx/dT)q, which has

change

fulfilled.

confirmation

3: of the glassy

Furthermore,

with DSC, and the rate of free volume

proved

[6] obtained

The successful

the reduced

at different

of heat,

rate used in DSC. This result parameters

to calculate

of temperature

213

q is the constant

for the reliability

heating

of the fitting

with the aid of eq.(7).

application

of the approach

of P.Duine

et al. [6] is limited

to glassy alloys with

extremely high thermal stability. Most amorphous alloys with practical significance crystallize in the close proximity of their glass transition temperatures, thus making any study of their viscous

flow behaviour

under

isothermal

conditions

practically

impossible.

The experimental

difficulties imposed by crystallization can be overcome to a great extent ing q under continuous heating rather than under isothermal conditions. earlier

works

described

above,

we have undertaken

this

study

aiming

[12-14) by measurStimulated by the

to carry

out viscosity

measurements on PddsNitsPzs glassy alloy under constant heating rate conditions (heating 10 Km+-’ ). Special attention was given to the possibility for theoretical interpretation the experimental and Spaepen

results.

Thus,

we have further

[l], A. van den Beukel

nonisothermal viscosity measurements alloys including those with relatively

Under

constant with

heating

time

under

rate

conditions

isothermal

the change

of cf with temperature.

differential

equation

approach

et al.

for practically

of Tsao

[6] for the case of

all well known glassy

Considerations

conditions,

eq.(5),

the flow defect concentration d escribing has to be transformed in order to describe

Taking

account

into

that

(2)

= (g)

q, the following

is obtained g

with P(T)

the theoretical

[5], and P.Duine

making it applicable low thermal stability.

2. Theoretical

change

developed

and J.Sietsma

rate of

= -:exp

+ P(T)C~ = and Q(T)

$1 = -

J;

Q(+e-

[email protected](T)

= -Fexp

. Its analytical

solution

is

J:P(z)dz& $, J’(z)dz

-1 J; P(z)dz + cf,oe

with To used as the starting temperature of heating. By combining eq.(9) with es.(l) it is possible to represent the measured temperature dependence of 77at constant q in the temperature range around T,. The parameters could be obtained in a way quite similar to the nonlinear multiparameter least square regression analysis of Duine et al. [6]. However, in order to be able to prove the validity of eq.(9) we have simply performed nonisothermal viscous flow measurements

under

a constant

heating

rate

using

the Pd40Ni40Pze

glassy

alloy, which

has been

VISCOUS

214

well studied

under

isothermal

basis of the parameter

conditons

values

FLOW

Vol. 32, No. 2

[6], and have calculated

given by Duine

the q(T)

et al. [6], and Koebrugge

dependence

on the

et al. [7] using eqs.(9)

and (1).

3. Experimental The glassy PddsNidePzs of a narrow

ribbon

were carried described

out

in detail

Approach

alloy used in this study

with cross-section at q =

dimensions

lOKmin-’

elsewhere

using

[12].

The

was kindly of 1.45

a Heraeus

x

supplied

0.049 mm’.

TMA

temperature

Viscosity

500 silica

accuracy

glass

was f2K.

elongation measurements was better than flpm. The apparent as a function of temperature using a modified Newtonian equation viscosity measurements as described elsewhere [13]

TJm=

by J.Sietsma

in the form

measurements dilatometer

The

as

accuracy

of

viscosity 71,~~ was calculated for the case of nonisothermal

&

00)

where Ar is the shear stress difference of two successive elongation measurements performed under different loads, and Ai is the strain rate difference of the same creep experiments as a function

of temperature

(time).

More details

4. Experimental Figure cording tively.

1 shows to es.(l)

the calculated and

eq.(9)

In the calculations

the values

the two viscosity

, as obtained values

ity data

at temperatures between

higher

rates

as obtained

of the glassy

alloy ac-

100 Kmin-‘,

Qq = 1931cJmolC’,

respecv, = 3.4 .

by Duine

by Duine

than

dependencies

of 0.01, 0.1, 1, 10, and

by Koebrugge

determined

the calculated

and Discussion

of 70 = 3.26 . 10-23Pas,

representative points of our nonisothermal a good agreement between the calculated difference

Results

viscosity-temperature

for heating

1025s11, B = 6600K, Te = 355K, c~,~ = 2.135 . lo-l1

are given in [12-141.

et al. [6], and Q+ = 1581cJmoZ-‘, and purposes et al. [7], were used. For comparison

et al.

[6] at 553 and 563 K, as well as several

viscosity measurements qen values and the data

Tg exists.

At temperatures

and experimentally

obtained

are given. It is obvious that of Duine [6] and our viscosaround

Tg there is a slight

non-equilibrium

viscosity

data.

At temperatures

lower than 550K the experimental values are by a factor of approximately in Figure 2 that the viscosities 2 higher than the calculated ones. It is clearly demonstrated measured do not depend on the applied stress, thus confirming the fact that the stress level used is within the Newtonian viscous regime. It should be noted as well that small changes of the fitting parameters cause relatively great changes in the viscosity-temperature dependence. The proper way to obtain better agreement between q,,lC and qezp is to determine the whole set of fitting parameters from the set of experimental viscosity range Tg - 40K to To,, the onset temperature of crystallization.

values

within

the temperature

Vol. 32, No. 2

vK!ous

215

FLOW

‘I’, K 600

550

500 1014

0 - Duine et al. 30

0 - this work

10’2 F2

v) 2

25 10’0 I=-

20 106 1.7

1.8

1.9

T-l,

Fig.1.

Calculated

viscosity-temperature

6 - qe9 calculated

according

563 K are also given,

together

to eq.(4).

1O-3 K-’

dependencies

rates OE 1 - O.OlKmin-‘, 2 - O.lKmin-‘,

2.0

of PdJsNi4sPzs

3 - lKmin_‘,

The q,, -data

with nonisothermal

glassy

ahoy

at heating

4 - lOKmin_‘, 5 - lOOKmin_’

of Duine

qezr, -data

et al. (61, measured obtained

and

at 553 and

at q = lOKmin_‘.

T, K 600

550

500

1’

1o12

F

c 0 1.66 YPa

Duine et al.

-

109 20

1

I

,

I

1.7

1.8

1.9

T-l,

Fig.2. Calculated viscosity-temperature Duine et al. [6] and Koebrugge et al. stresses are also shown.

2.0

1O-3 K-r

dependencies

using

[7]. Experimental

the original values

fitting

measured

parameters

at different

of

shear

Vol. 32. No. 2

VISCOUS FLOW

276

5. Conclusions

Nonisothermal tions

provide

approach

viscosity

an attractive

of Tsao

measurements possibility

and Spaepen

alloys

viscosity

under

constant

the theoretical

[l], A. van den Beukel

[6] for the case of nonisothermal exhibiting

of glassy to extend

measurements

heating

and isothermal

and J.Sietsma

rate

condi-

experimental

[5], and P.Duine

on practically

alI known

et al.

glassy alloys

glass transition.

Acknowledgment The authors

are indebted

One of us (K. Russew)

to Dr.

gratefully

J. Sietsma

acknowledges

for providing a 3 month

the amorphous

EU PECO

research

ribbon grant

studied. NR.:1069.

References 1.

S.S.Tsao

2.

A.v.d.

and F.Spaepen,

3. 4.

H.S.Chen and D.TurnbuIl, J. Chem. Phys. 48, 2560 (1968). C.A.Volkert and F.Spaepen, Actu Metall. 37, 1355 (1989).

5.

A.v.d.

6. 7. 8.

P.A.Duine, J.Sietsma and A.v.d. Beukel, Acta Metal Muter. 40, 743 (1992). G.W.Koebrugge, J.Sietsma and A.v.d. Beukel, Actu Metall. Muter. 40, 753 (1992). P.Tuinstra, P.Duine and J.Sietsma, J. Non-Cry&. Solids, 156-158, 519 (1993).

9.

M.H.Cohen

Beukel,

Beukel

10.

D.TurnbuII

11.

F.Spaepen

12.

K.Russew, K.Russew K.Russew,

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and J.Sietsma,

33, 881 (1985).

and S.v.d.

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38, 383 (1990).

and D.TurnbuII,

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E.Huizer,

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F.Sommer,

P.Duhaj

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and L.Stojanova, Muter. Sci. Engng. A 123, 59 (1990). LStojanova and A.Lovas, Int.J.of Rapid Solidification, 8, 147 (1993).