The viscosity of amorphous metallic thin films

The viscosity of amorphous metallic thin films

1274 Materials Science and Engineering, A 134 ( 1991 ) 1274-1277 The viscosity of amorphous metallic thin films A. Witvrouw, C. A. Volkert* and F. S...

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Materials Science and Engineering, A 134 ( 1991 ) 1274-1277

The viscosity of amorphous metallic thin films A. Witvrouw, C. A. Volkert* and F. Spaepen Division of Applied Sciences, Harvard University, Cambridge, MA 02138 (U.S.A.)

Abstract Creep and stress relaxation measurements on sputtered amorphous Pd-Si films show that the viscosity in these materials is similar to that of melt-quenched ribbons of similar composition: it increases linearly with time during isothermal structural relaxation, and the rate of increase as well as the isothermal activation enthalpy are similar over a wide range of temperatures and viscosities. This validates the earlier assumption that sample preparation is not a factor in the comparison of the viscosity of meltquenched ribbons and the diffusivity in sputtered multilayers.

1. Introduction The viscosity ~/ and the diffusivity D of an amorphous metal are related by a Stokes-Einstein-type expression [1]

kT r/D=-L


where k is Boltzmann's constant, T the temperature, and L a length that incorporates the geometry and kinetics of the atomic rearrangements governing flow and diffusion. In metallic liquids above the melting temperature, L is close to 2n2, where 2 is the interatomic distance [2]. Below the glass transition temperature, however, its value has not been unambiguously determined. The main problem is structural relaxation of the amorphous metal, which causes a continuous change of all physical properties, in particular atomic transport. It is therefore difficult to make use of measurements of ~/and D obtained from different samples, especially if those have been prepared by different methods. Until recently it was only possible to compare the results of diffusion studies on sputterdeposited artificial multilayers [3-6] with viscosity data from creep tests on melt-spun ribbons [7-12]. Several similarities were noted: the isoconfigurational activation enthalpies for r/and D *Present address: A.T.&T. Bell Laboratories, 600 Mountain Avenue, Murray Hill, NJ, U.S.A. 0921-5093/91/$3.50

were similar, both r/and (l/D) increased linearly with time as a result of structural relaxation, and the activation enthalpies of the (constant) rates of increase of these quantities were similar. It seems plausible, therefore, that the two phenomena are governed by related mechanisms, such as density fluctuations [6]. If the length L in eqn. (1) is assumed constant during structural relaxation, its value can be derived from the relaxation rates of r/and (l/D) by differentiating eqn. (1) dt

L dt


Only a few such determinations have been made, and they indicate that L is about two orders of magnitude smaller than the Stokes-Einstein value 2Jr;t [4-6]. The validity of the above comparison depends on the extent to which the atomic transport coefficients, which are known to be sensitive to small structural differences, depend on the method of preparation. To check this, the viscosity of amorphous sputtered Pd-Si thin films was measured and compared with the extensive literature data on melt-spun ribbons of the same composition [6-12]. 2. Experimental procedure

Z1. Creep experiments Free-standing sputtered films, about 1/~m thick, were clamped in the grips of a vertical © Elsevier Sequoia/Printed in The Netherlands


creep apparatus [13-15] operating in an argon atmosphere. The length change of the sample was measured by a linear differential voltage transformer (LVDT), and the shear viscosity obtained from the corresponding plastic strain rate g as o


where o is the uniaxial tensile stress. All tests were performed with o = 91 MPa, which is well within the Newtonian viscous regime for meltquenched Pd-Si glasses [16]. 2.2. Stress relaxation experiments The films, about 2.5 # m thick, were sputtered onto fused silica substrates, 1 in. x I in. x 530 # m in size. The curvature 1/R of the coated substrate was determined by measuring the displacement of a reflected laser spot upon translation of the sample [17[, using a high-precision apparatus with a computer-controlled nulldetector [18]. The biaxial stress in the film o is then [17, 19, 20] 1



-~ x 1




where E~ and v~ are Young's modulus and Poisson's ratio of the substrate, respectively, and d, and dr are the thickness of the substrate and film, respectively. The curvature of the film on its substrate was measured continuously during isothermal annealing in a chamber filled with an overpressure of flowing titanium-gettered helium. Most of the stress in these experiments arose from the difference in thermal expansion between substrate and film, and is compressive. Relaxation of the stress by viscous flow under biaxial loading occurs according to the differential equation O


6r1 E/1 - v


experiments, respectively. They were prepared by ion beam sputtering [23] from an alloy target. The flee-standing films for the creep experiments were deposited on a photoresist-covered glass slide, and were removed by dissolving the resist in acetone. The composition was checked with the electron microprobe, and X-ray diffraction was used to verify the absence of crystallinity before and after the tests. That no reaction of the film with the fused silica had occurred was verified with X-ray diffraction and Rutherford backscattering.

3. Results

3.1. Rate of structural relaxation During isothermal annealing the viscosity of metallic glasses increases with time as a result of structural relaxation. In creep experiments on melt-spun Pd-Si ribbons, it was observed that this increase is linear in time [7, 24]:

,7(t) =,7(0)+ 0t

where 0 is a constant (see Fig. 1). Microscopically, this corresponds to bimolecular annihilation of the defects governing flow [8, 9, 12]. The same linear increase was observed in the creep experiments on thin films, and the corresponding values of 0(T) are also plotted on Fig. 1. The change in the stress relaxing by flow with this time-dependent viscosity is found by solving


2.3. Sample preparation The films were composed of Pd798i21 and Pdv~Si22, for the creep and stress relaxation

,300 ' [


200 I

. . . .

1 O0 i



where ~/is the instantaneous shear viscosity, and E and v are the elastic constants of the film. They had been measured in an earlier set of experiments on films deposited on substrates with different pre-set curvatures [18] to be E = 100 GPa and v = 0.43, in good agreement with literature data on melt-spun glasses of similar composition [2l, 22].


E z


lo ~° ~

]~ i

1 6



I O4/T(K)

Fig. 1. Rate of increase of the viscosity as a result of structural relaxation during isothermal annealing of amorphous Pd-Si. Diamonds and triangles: creep experiments on meltquenched ribbons [12]; open circles: creep experiments on thin films [15]; full circles: stress relaxation measurements on thin films on fused silica substrates [18],


the differential equation formed by combining eqns. (5) and (6), which gives In a(t)=In a(0)

6(12 v) 0




where o(0) is the initial stress. Taub and Luborsky [24] used the uniaxial form of this expression in their analysis of tensile stress relaxation experiments on melt-quenched ribbons. The stress relaxation measurements of Fig. 2 clearly show that the viscosity varies with time: a constant r/ (i.e. 0 = 0 ) in eqn. (7) gives a simple exponentially decaying stress, and hence a straight line in Fig. 2. In its bimolecular form, eqn. (7) fits the data very well, consistently better than its unimolecular (exponentially increasing) alternative [18]. The values of fI(T) obtained from these fits are also shown on Fig. 1. The activation enthalpy is 0.14 eV, compared with 0.32 eV for the melt-quenched material [7]. 3.2. Isoconfigurational measurements

Isoconfigurational measurements are made to determine the temperature dependence of a glass in a particular state of structural relaxation. Over a large range of temperatures, sufficiently below the glass transition temperature, the isoconfigurational viscosity can be described by a simple Arrhenius-type equation r/(T) =r/0 exp ( Qr] \KI/

where r/0 depends on the state of relaxation. Since the rate of increase of the viscosity during isothermal annealing is constant, the relative rate of increase steadily slows down. At sufficiently high viscosities, therefore, creep data can be taken at several temperatures before appreciable structural relaxation has occurred. That the data are truly isoconfigurational is checked by reproducing the viscosity upon cycling of the temperature. After further isothermal annealing, a new set of isoconfigurational data can be taken. Figure 3 shows the results of isoconfigurational creep measurements on both ribbons [7] and films [15]. The average activation enthalpies are 2.0 eV and 1.8 eV, respectively. The isoconfigurational activation enthalpy could also be determined by stress relaxation measurements. After an isothermal anneal of about several hours, the temperature was raised by 50 K or 100 K, and again held isothermally. The temperature change during the heat-up, which usually took about 10 min, was recorded. Since the kinetics of the viscosity change are known (eqn. (6) and data from Fig. 1 ), assuming a value of Q in eqn. (8) allows the viscosity change during heat-up to be computed. With only a few trials, the viscosity change between the end of the first isothermal and the beginning of the last one could be matched with 1% precision for Q. It turned out, however, that the same values, within this precision, were obtained from the instantaneous viscosity change computed by extrapolating


T(oc) 1018

400 ~1 . . . .

300 I

200 I 2.0±0.2

. . . .

26 / bimeleculcr









3.0 ¸


Jnimolecu!or ( ,




~o k

= =




± ±












1 843E÷11









.02E+15 5





/ /


/ /


// / / /






/ /


1 O0 I

' eV / /

2,~1 eV 1.73 e

v 1.o2 ev

2.93 2.

Pos /sec

c 1012



, , .4 -3.6

I , ,


, I , ,


, I ,

2.0::=0.6 eV ~ , I , , ~ I




, , ~ I , , ,








O. 6


O. 8

1 ,'0


Fig. 2. Logarithmic plot of the evolution of the curvature of a Pd78Si22 amorphous thin film on a fused silica substrate as a function of isothermal annealing time at 100 °C. T h e fit with bimolecular relaxation of the viscosity is better than that with the unimolecular one (see ref. 18).


Fig. 3. lsoconfigurational viscosity of amorphous Pd-Si. Full line: stress relaxation measurements on thin films on fused silica substrates [18]; dashed line: creep experiments on thin films [15]; dot-dashed line: creep experiments on meltquenched ribbons [7]. T h e numbers in large type refer to the average activation enthalpy for each set of experiments.


the two isothermal viscosities to the same time at the middle of the heat-up stage, which is how the data are plotted on Fig. 3. Although there is considerably more scatter than in the creep data, the average value for Q, 2.0 eV, is remarkably similar. Isoconfigurational measurements are more difficult to make with the stress relaxation apparatus because it is impossible to avoid considerable structural relaxation over the accessible ranges of viscosity and heat-up time. 4. Conclusion Creep and stress relaxation are complementary experiments in the study of the viscosity of amorphous thin films: isoconfigurational measurements are best obtained with the former, whereas the latter is preferable for determining the absolute viscosity and the effects of structural relaxation. The sputtered and melt-quenched materials are similar in most respects: their viscosities increase linearly during isothermal structural relaxation, and the rates of increase O as well as the isoconfigurational activation enthalpies Q have similar values over a wide range of temperatures and viscosities. The few apparent differences (the differences in the, quite small, activation enthalpy of r), and the values of r) at high temperature in the two creep experiments) may be the result of the slight composition difference between the samples. These experiments therefore validate the earlier assumption that the sample preparation method does not affect the comparison of the viscosity of melt-quenched samples to the diffusivity in sputtered multilayers. At this point, however, the implications for the Stokes-Einstein relation are still subject to the assumption of a constant L in eqns. (1) and (2). This assumption awaits a direct test in simultaneous diffusion and viscosity measurements on the same sample. Acknowledgments This work has been supported by the Office of Naval Research under Contract number

N00014-85-K-0023. CAV acknowledges support by a pre-doctoral fellowship from the AlliedSignal Corporation.

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