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Interdiffusion studies in metallic glasses using compositionally modulated thin films
Journal of Non-CrystallineSolids 61 & 62 (1984) 889-894 North-Holland, Amsterdam
889
INTERDIFFUSION STUDIES IN METALLIC GLASSES USING COMPOSITIONALLY MODULATED THIN FILMS
R.C. CAMMARATAand A.L. GREER Division of Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, U.S.A. I n t e r d i f f u s i v i t i e s are measured in compositionally modulated amorphous thin films as a function of modulation wavelength. The sensitivity of this method is demonstrated by the measurement of very low i n t e r d i f f u s i v i t i e s , and permits the observation of structural relaxation effects. From these results we are able to determine the general thermodynamicbehavior of the alloy system, and to derive the bulk i n t e r d i f f u s i v i t y . Our data suggest that, contrary to earlier reports, the Stokes-Einstein equation (relating d i f f u s i v i t y and viscosity) is not valid in metallic glasses. I. INTRODUCTION Two major d i f f i c u l t i e s arise when making diffusion measurements in metallic glasses.
The f i r s t is that the experiments must be performed below the glass
transition temperature Tg in order to avoid crystallization. d i f f u s i v i t i e s tend to be rather low (
Consequently, the
The second d i f f i c u l t y is
that structural relaxation may occur, and this should be taken into account. In order to derive a physically meaningful activation energy for diffusion, i t is necessary to make measurements on samples with the same degree of relaxation. In this work i n t e r d i f f u s i v i t i e s were obtained from X-ray measurements of the decay in amplitude of a composition modulation in a thin film.
Time-resolved
measurements of very low d i f f u s i v i t i e s are possible with this technique. allows the monitoring of structural relaxation.
This
In addition, i t is possible to
determine an activation energy for diffusion from isoconfigurational measurements in one sample at different temperatures. In this paper, which extends the earlier work of Greer, et al. l we have investigated the dependenceof the i n t e r d i f f u s i v i t y in compositionally modulated amorphous thin films on the modulation wavelength. Somefeatures of atomic transport in metallic glasses, inferred from these results, necessitate a revision of the conclusions presented in the previous work. 2. EXPERIMENTAL METHODS The measurement of i n t e r d i f f u s i v i t i e s through the use of compositionally modulated thin films was f i r s t suggested by Dumondand Youtz, 2 and developed 0022-3093[84/$03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
R. C, Cammarata, A.L. Greer / In terdiffusion studies in metallic glosses
890
for e p i t a x i a l c r y s t a l l i n e films by Cook and H i l l i a r d . 3 This technique
~6
was f i r s t applied to amorphous systems by Rosenblum, et al. 4 .,
J4 <~
'.~
[
".~
In this study, compositionally
z
modulated amorphous films of
O3
,,=,z (.9
0
I
]lll~L
2
4 8 SPUTTER TIME(mini
(Pd85Si15)50/(Fe85B15)50 were produced by DC sputtering. Figure 1 ~".., ,,_ shows the composition v a r i a t i o n of an as-deposited f i l m of modulation I o ~0 wavelength ~ = 68.8A. This p r o f i l e was obtained by Auger electron spec-
FIGURE 1 Composition variation in an as-produced compositionally modulated thin film (~ = 68.8~), measured by Auger spectroscopy,
troscopy, which continuously measured the composition of the f i l m surface as i t was being ion milled. The figure shows that the f i l m con-
tains a d e f i n i t e p e r i o d i c i t y in composition v a r i a t i o n . (Determination of the modulation wavelength, by X-ray measurements, can be used to c a l i b r a t e the ion m i l l i n g rate.)
Since ion m i l l i n g rates and the Auger electron escape depths
can vary for each element, and since the bottom of the milled area may not be p a r a l l e l with the layers, any detailed conclusions drawn from the figure are unreliable. In an amorphous f i l m , the composition modulation gives rise to X-ray satell i t e s about the (000) r e f l e c t i o n , which correspond to the Fourier modes of the modulation.
When the composition amplitudes are small, the various modes
behave independently during annealing.
The e f f e c t i v e i n t e r d i f f u s i v i t y D~, as a
function of ~, is obtainable from the rate of decay of the i n t e n s i t y l ( t ) of the f i r s t - o r d e r s a t e l l i t e 2 D~ : - ( X 2 1 n [ l ( t 2 ) / l ( t l ) ] ) / B ~ 2 ( t 2 - t l )
(I)
The complete experimental details of the preparation, annealing, and X-ray measurements of the modulated thin films can be found elsewhere. 1'4
3. THEORY According to the Cahn-Hilliard theory of compositionally inhomogeneous systems,5 DX, for binary alloys, is related to the bulk interdiffusivity D by DX = D[I + 8~2K/f~ 2] where f"o is the second derivative, with respect to composition, of the Helmholtz free energy of a homogeneous phase per unit volume and K is a
(2)
891
R.C, Cammarata, A.L. Greer / lnterdiffusion studies in metallic glasses
gradient energy coefficient.
These
can be evaluated f o r a regular solu5 tion model : f" = 4[RT- 2iIU]/V o K = 2/xUr2/3V.
(3)
K:+ $i
&U is the energy of mixing per mole
fo: --
,J
of equiatomic s o l u t i o n , V is the
>:
molar volume, R is the gas constant,
I.-
~ , ,
0'} h h
w I-z
T is the absolute temperature, and r K:+ IS':+
is the nearest neighbor distance. Since, from Equations (3), f " and
5®(*)
0
K can be e i t h e r p o s i t i v e or negative, a v a r i e t y of possible behavior
W
>_ I..-
of DI
with respect to ~ can be conceived,
o. . . . . . . . . . . . . . . . . . .
as shown schematically in Figure 2.
0
The f i r s t
curve represents the case
when K is p o s i t i v e and foiI is nega-
I
fo':+
t i v e , conditions under which an
)
unstable homogeneous system can spinodally decompose.
When K and f " o
are both p o s i t i v e , the behavior of BX is shown by the second curve. MODULATION
WAVELENGTH,
),,
For
a homogeneous a l l o y , these conditions describe a stable or metastable phase
FIGURE 2 Schematic behavior of the effective interdiffusivity D~ as a function of the modulation wavelength h for the three possible thermodynamic conditions.
separating system.
The behavior
exhibited by the t h i r d curve is expected when K is negative and fo is p o s i t i v e , conditions which describe
ordering systems.
As can be seen from Equations (3), in the regular solution
model, K and f " cannot be negative simultaneously. 0
According to the above discussion, by measuring the dependence of D~ on ~ in compositionally modulated thin f i l m s , the general thermodynamic behavior of the bulk system can be ascertained.
Since thermodynamic information on glass
forming compositions is scarce and d i f f i c u l t
to determine by conventional means
at high undercooling, the modulated thin f i l m technique is expected to be quite useful in characterizing the thermodynamic behavior of amorphous a l l o y s . As was mentioned, the above analysis is v a l i d f o r binary a l l o y s . paper, we w i l l consider our films to be binary Pd-Fe systems.
In this
I t is hoped that
892
R.C. Cammarata, A.L. Greer / In terdiffi~sion studies in metallic glasses
this has some v a l i d i t y , since they are the predominant species, and would account for almost a l l the measured X-ray scattering. 4. RESULTSAND DISCUSSION I n t e r d i f f u s i v i t i e s were obtained for four films with modulation wavelengths between 20.6 and 39.4X.
During the early stages of the anneals (at 250°C) a l l
films displayed a nonlinear decrease of I n l ( t ) with respect to time. this i n i t i a l
Most of
nonlinearity can be a t t r i b u t e d to structural relaxation. 6 Eventu-
a l l y , a l l films exhibited l i n e a r behavior, and DX for each f i l m was calculated using Equation ( I ) .
This l i n e a r behavior (constant D~) implies that each of
the films were, during this part of t h e i r anneals, in an isoconfigurational state. Presumably, since a l l the films were produced in the same way and exhibited linear behavior a f t e r approximately the same amount of annealing (~15 hours), they a l l had about the same degree of relaxation.
~_~_i___i_i_'~.
The values of D~, are plotted in
"m ~;~ 2=_ .
.
.
.
Figure 3.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
-~
Comparison with Figure 2
shows that amorphous PdSi/FeB
behaves as an ordering system.
'~~,~~>
In
the c r y s t a l l i n e state, there are
"
ordering reactions in the Pd-Fe system. 7 In the present case, however, the unknown effects of the
metalloids preclude any d e f i n i t i v e 20 40 60 80 MODULATION WAVELENGTH, X {~)
100
FIGURE 3 The measured interdiffusivity Dh at 250°C as a function of the modulation
w~pelen£/th ~.
conclusions about the thermodynamic behavior of an amorphous Pd-Fe system. A l i n e a r regression f i t of D~ versus I/~ 2 was made using Equation (2), and the bulk (~ ÷ oo) i n t e r d i f -
f u s i v i t y at 250°C was determined to be 1.94 x lO'24m2s - I .
The value of the
pre-exponential factor (which was determined using the reported I activation energy of 195kJ/mole), 5.6 x lO-5m2s" I , appears reasonable. As a comparison, for c r y s t a l l i n e systems, the pre-exponential factor is 4.9 x lO'5m2s "I for Fe diffusion in T-Fe and is 2.1 x lO'5m2s -I for Pd s e l f diffusion. 8 I t has been reported 9 that in metallic glasses, D is
dependent on the
atomic radius, a, of the diffusing metal only, and independent of the r a d i i of the atoms comprising the glass. Assuming that D is j u s t a function of this p a r t i c u l a r atomic radius, the viscosity n, and the temperature, dimensional analysis (see, for example, I0) leads to the following expression:
R. C. Cammarata, A.L. Greer / lnterdiffusion studies in metallic glasses
D = ~T/qa
893
(4)
where ~ is a p r o p o r t i o n a l i t y constant.
When ~ is equal to k/6~, where k is
Boltzmann's constant, Equation (4) becomes the Stokes-Einstein equation, which has been shown to be v a l i d to w i t h i n 50% in some l i q u i d metals when a is taken to be an average ionic radius. I I I t had been reported I that the Stokes162o
~
Einstein equation may also be v a l i d •
o*
f o r Pd d i f f u s i o n in PdSi/FeB m e t a l l i c
m • + o+ ld22
glasses.
v
o
However, an e f f e c t i v e
interdiffusivity
was used, uncor-
rected f o r the wavelength dependence. Using the value f o r D determined in
id 24
this work, and taking I a = 0.721, leads to an ~ in Equation (4) equal 09
10
1.1
1J2
113
Tg,'T
14
to about 31k which means that the Stokes-Einstein equation is not
FIGURE 4 Compilation of data on metal diffusion in metal-metalloid glasses. [] Pd-Fe interdiffusion in PdSi/FeB, isoconfigurational measurements, this and previous work. 1 • Au in relaxed Pd77" 5Cu~i16.5 (I~)
valid.
This has important implica-
tions regarding the nature of atomic transport mechanisms in amorphous metals. 12
o Au in relaxed Pd77" 5Cu~i16.5 (14) + Au in relaxed Fe4~i4oB20 (14) V Au in Pd8Si20(15) 5. COMPARISONWITH OTHER DIFFUSION MEASUREMENTS In Figure 4, the
diffusivity
of Au in Pd- and Fe-based m e t a l l i c glasses
measured by various p r o f i l i n g techniques 13-15 has been p l o t t e d along with the d i f f u s i o n measurements made in this and previous work I by the modulated thin f i l m method f o r the PdSi/FeB system.
The temperature axis has been normalized
with respect to the glass t r a n s i t i o n temperature.
As can be seen, when plotted
in t h i s way, the measurements made by the thin f i l m method are in good agreement with the other data, in both absolute value and a c t i v a t i o n energy. With the exception of Chen et a i . , 1 3 in the other work on Au d i f f u s i o n , 14'15 no effects of s t r u c t u r a l r e l a x a t i o n were observed.
This is probably due to the
lack of s e n s i t i v i t y , r e l a t i v e to the modulated f i l m technique, of the p r o f i l i n g methods used. 12
894
R. C. Cammarata, A.L. Greer / Interdiffusion studies in metallic glasses
6. CONCLUSIONS We have measured i n t e r d i f f u s i v i t i e s in metallic glasses through the use of compositionally modulated thin films.
This method is very sensitive, allowing
the detection of structural relaxation effects and the measurement of low d i f f u s i v i t i e s (~10-27m2s-l).
The i n t e r d i f f u s i v i t i e s were found to be dependent
on the modulation wavelength.
From these measurements we were able to c l a s s i f y
the PdSi/FeB amorphous a l l o y as an ordering system, which may have implications concerning compositional short range ordering 12'16 in metallic glasses. Also a bulk i n t e r d i f f u s i v i t y was determined to be 5.6x lO-5exp(-195kJmol-I/RT)m2s - I . Based on this value, we have shown that the Stokes-Einstein equation, r e l a t i n g d i f f u s i v i t y to viscosity, is not v a l i d in m e t a l l i c glasses as has been previously reported. ACKNOWLEDGEMENTS The authors thank Prof. F. Spaepen and Mr. C.-J. Lin for many useful discussions, and Mr. F.N. Molea, Mr. J.L. Bell, and Mr. K. Campbell for t h e i r technical assistance.
This work was supported by the Office of Naval Research
under contract N00014-77-C-0002 and by the National Science Foundation under contract DMR80-20247. REFERENCES I) A.L. Greer, C.-J. Lin, and F. Spaepen, in: Proc. 4th Int. Conf. on Rapidly Quenched Metals, eds. T. Masumoto and K. Susuki (japan Inst. of Metals, 1982) pp. 567-572. 2) J. Dumond and J.P. Youtz, J. Appl. Phys. I I (1940) 357. 3) H.E. Cook and J.E. H i l l i a r d , J. Appl. Phys. 40 (1969) 2191. 4) M.P. Rosenblum, F. Spaepen, and D. Turnbull, Appl. Phys. Lett. 37 (1980) 184. 5) J.W. Cahn and J.E. H i l l i a r d , J. Chem. Phys. 28 (1958) 258. 6) A.L. Greer, in: Modulated Structure Materials, NATO ASI Series, Applied Sciences, ed. T. Tsakalakos (Martinus N i j o f f , The Hague, 1983) in press. 7) M. Hansen, Constitution of Binary Alloys (McGraw-Hill, New York, 1958). 8) J. A s k i l l , Tracer Diffusion Data for Metals, Alloys, and Simple Oxides (Plenum Press, New York, 1970). g) B. Cantor and R.W. Cahn, in: Amorphous Metallic Alloys, ed. F.E. Luborsky (Butterworths, London, 1983) pp. 487-505. I0) A.H. C o t t r e l l , Mechanical Properties of Matter (John Wiley and Sons, New York, 1964). I I ) N.H. Nachtrieb, in: Liquid Metals and S o l i d i f i c a t i o n (ASM, Cleveland, Ohio, 1958) p. 49. 12) A.L. Greer, this volume. 13) H.S. Chen, L.C. Kimerling, J.P. Poate, and W.L. Brown, Appl. Phys. Lett. 32 (1978) 461. 14) D. Akhtar, B. Cantor, and R.W. Cahn, Acta Metall. 30 (1982) 1571. 15) P. Gupta, K.N. Tu, and K.W. Asai, Thin Solid Films 90 (1982) 131. 16) T. Egami, Mater. Res. Bull. 13 (1978) 557.
889
INTERDIFFUSION STUDIES IN METALLIC GLASSES USING COMPOSITIONALLY MODULATED THIN FILMS
R.C. CAMMARATAand A.L. GREER Division of Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, U.S.A. I n t e r d i f f u s i v i t i e s are measured in compositionally modulated amorphous thin films as a function of modulation wavelength. The sensitivity of this method is demonstrated by the measurement of very low i n t e r d i f f u s i v i t i e s , and permits the observation of structural relaxation effects. From these results we are able to determine the general thermodynamicbehavior of the alloy system, and to derive the bulk i n t e r d i f f u s i v i t y . Our data suggest that, contrary to earlier reports, the Stokes-Einstein equation (relating d i f f u s i v i t y and viscosity) is not valid in metallic glasses. I. INTRODUCTION Two major d i f f i c u l t i e s arise when making diffusion measurements in metallic glasses.
The f i r s t is that the experiments must be performed below the glass
transition temperature Tg in order to avoid crystallization. d i f f u s i v i t i e s tend to be rather low (
Consequently, the
The second d i f f i c u l t y is
that structural relaxation may occur, and this should be taken into account. In order to derive a physically meaningful activation energy for diffusion, i t is necessary to make measurements on samples with the same degree of relaxation. In this work i n t e r d i f f u s i v i t i e s were obtained from X-ray measurements of the decay in amplitude of a composition modulation in a thin film.
Time-resolved
measurements of very low d i f f u s i v i t i e s are possible with this technique. allows the monitoring of structural relaxation.
This
In addition, i t is possible to
determine an activation energy for diffusion from isoconfigurational measurements in one sample at different temperatures. In this paper, which extends the earlier work of Greer, et al. l we have investigated the dependenceof the i n t e r d i f f u s i v i t y in compositionally modulated amorphous thin films on the modulation wavelength. Somefeatures of atomic transport in metallic glasses, inferred from these results, necessitate a revision of the conclusions presented in the previous work. 2. EXPERIMENTAL METHODS The measurement of i n t e r d i f f u s i v i t i e s through the use of compositionally modulated thin films was f i r s t suggested by Dumondand Youtz, 2 and developed 0022-3093[84/$03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
R. C, Cammarata, A.L. Greer / In terdiffusion studies in metallic glosses
890
for e p i t a x i a l c r y s t a l l i n e films by Cook and H i l l i a r d . 3 This technique
~6
was f i r s t applied to amorphous systems by Rosenblum, et al. 4 .,
J4 <~
'.~
[
".~
In this study, compositionally
z
modulated amorphous films of
O3
,,=,z (.9
0
I
]lll~L
2
4 8 SPUTTER TIME(mini
(Pd85Si15)50/(Fe85B15)50 were produced by DC sputtering. Figure 1 ~".., ,,_ shows the composition v a r i a t i o n of an as-deposited f i l m of modulation I o ~0 wavelength ~ = 68.8A. This p r o f i l e was obtained by Auger electron spec-
FIGURE 1 Composition variation in an as-produced compositionally modulated thin film (~ = 68.8~), measured by Auger spectroscopy,
troscopy, which continuously measured the composition of the f i l m surface as i t was being ion milled. The figure shows that the f i l m con-
tains a d e f i n i t e p e r i o d i c i t y in composition v a r i a t i o n . (Determination of the modulation wavelength, by X-ray measurements, can be used to c a l i b r a t e the ion m i l l i n g rate.)
Since ion m i l l i n g rates and the Auger electron escape depths
can vary for each element, and since the bottom of the milled area may not be p a r a l l e l with the layers, any detailed conclusions drawn from the figure are unreliable. In an amorphous f i l m , the composition modulation gives rise to X-ray satell i t e s about the (000) r e f l e c t i o n , which correspond to the Fourier modes of the modulation.
When the composition amplitudes are small, the various modes
behave independently during annealing.
The e f f e c t i v e i n t e r d i f f u s i v i t y D~, as a
function of ~, is obtainable from the rate of decay of the i n t e n s i t y l ( t ) of the f i r s t - o r d e r s a t e l l i t e 2 D~ : - ( X 2 1 n [ l ( t 2 ) / l ( t l ) ] ) / B ~ 2 ( t 2 - t l )
(I)
The complete experimental details of the preparation, annealing, and X-ray measurements of the modulated thin films can be found elsewhere. 1'4
3. THEORY According to the Cahn-Hilliard theory of compositionally inhomogeneous systems,5 DX, for binary alloys, is related to the bulk interdiffusivity D by DX = D[I + 8~2K/f~ 2] where f"o is the second derivative, with respect to composition, of the Helmholtz free energy of a homogeneous phase per unit volume and K is a
(2)
891
R.C, Cammarata, A.L. Greer / lnterdiffusion studies in metallic glasses
gradient energy coefficient.
These
can be evaluated f o r a regular solu5 tion model : f" = 4[RT- 2iIU]/V o K = 2/xUr2/3V.
(3)
K:+ $i
&U is the energy of mixing per mole
fo: --
,J
of equiatomic s o l u t i o n , V is the
>:
molar volume, R is the gas constant,
I.-
~ , ,
0'} h h
w I-z
T is the absolute temperature, and r K:+ IS':+
is the nearest neighbor distance. Since, from Equations (3), f " and
5®(*)
0
K can be e i t h e r p o s i t i v e or negative, a v a r i e t y of possible behavior
W
>_ I..-
of DI
with respect to ~ can be conceived,
o. . . . . . . . . . . . . . . . . . .
as shown schematically in Figure 2.
0
The f i r s t
curve represents the case
when K is p o s i t i v e and foiI is nega-
I
fo':+
t i v e , conditions under which an
)
unstable homogeneous system can spinodally decompose.
When K and f " o
are both p o s i t i v e , the behavior of BX is shown by the second curve. MODULATION
WAVELENGTH,
),,
For
a homogeneous a l l o y , these conditions describe a stable or metastable phase
FIGURE 2 Schematic behavior of the effective interdiffusivity D~ as a function of the modulation wavelength h for the three possible thermodynamic conditions.
separating system.
The behavior
exhibited by the t h i r d curve is expected when K is negative and fo is p o s i t i v e , conditions which describe
ordering systems.
As can be seen from Equations (3), in the regular solution
model, K and f " cannot be negative simultaneously. 0
According to the above discussion, by measuring the dependence of D~ on ~ in compositionally modulated thin f i l m s , the general thermodynamic behavior of the bulk system can be ascertained.
Since thermodynamic information on glass
forming compositions is scarce and d i f f i c u l t
to determine by conventional means
at high undercooling, the modulated thin f i l m technique is expected to be quite useful in characterizing the thermodynamic behavior of amorphous a l l o y s . As was mentioned, the above analysis is v a l i d f o r binary a l l o y s . paper, we w i l l consider our films to be binary Pd-Fe systems.
In this
I t is hoped that
892
R.C. Cammarata, A.L. Greer / In terdiffi~sion studies in metallic glasses
this has some v a l i d i t y , since they are the predominant species, and would account for almost a l l the measured X-ray scattering. 4. RESULTSAND DISCUSSION I n t e r d i f f u s i v i t i e s were obtained for four films with modulation wavelengths between 20.6 and 39.4X.
During the early stages of the anneals (at 250°C) a l l
films displayed a nonlinear decrease of I n l ( t ) with respect to time. this i n i t i a l
Most of
nonlinearity can be a t t r i b u t e d to structural relaxation. 6 Eventu-
a l l y , a l l films exhibited l i n e a r behavior, and DX for each f i l m was calculated using Equation ( I ) .
This l i n e a r behavior (constant D~) implies that each of
the films were, during this part of t h e i r anneals, in an isoconfigurational state. Presumably, since a l l the films were produced in the same way and exhibited linear behavior a f t e r approximately the same amount of annealing (~15 hours), they a l l had about the same degree of relaxation.
~_~_i___i_i_'~.
The values of D~, are plotted in
"m ~;~ 2=_ .
.
.
.
Figure 3.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
-~
Comparison with Figure 2
shows that amorphous PdSi/FeB
behaves as an ordering system.
'~~,~~>
In
the c r y s t a l l i n e state, there are
"
ordering reactions in the Pd-Fe system. 7 In the present case, however, the unknown effects of the
metalloids preclude any d e f i n i t i v e 20 40 60 80 MODULATION WAVELENGTH, X {~)
100
FIGURE 3 The measured interdiffusivity Dh at 250°C as a function of the modulation
w~pelen£/th ~.
conclusions about the thermodynamic behavior of an amorphous Pd-Fe system. A l i n e a r regression f i t of D~ versus I/~ 2 was made using Equation (2), and the bulk (~ ÷ oo) i n t e r d i f -
f u s i v i t y at 250°C was determined to be 1.94 x lO'24m2s - I .
The value of the
pre-exponential factor (which was determined using the reported I activation energy of 195kJ/mole), 5.6 x lO-5m2s" I , appears reasonable. As a comparison, for c r y s t a l l i n e systems, the pre-exponential factor is 4.9 x lO'5m2s "I for Fe diffusion in T-Fe and is 2.1 x lO'5m2s -I for Pd s e l f diffusion. 8 I t has been reported 9 that in metallic glasses, D is
dependent on the
atomic radius, a, of the diffusing metal only, and independent of the r a d i i of the atoms comprising the glass. Assuming that D is j u s t a function of this p a r t i c u l a r atomic radius, the viscosity n, and the temperature, dimensional analysis (see, for example, I0) leads to the following expression:
R. C. Cammarata, A.L. Greer / lnterdiffusion studies in metallic glasses
D = ~T/qa
893
(4)
where ~ is a p r o p o r t i o n a l i t y constant.
When ~ is equal to k/6~, where k is
Boltzmann's constant, Equation (4) becomes the Stokes-Einstein equation, which has been shown to be v a l i d to w i t h i n 50% in some l i q u i d metals when a is taken to be an average ionic radius. I I I t had been reported I that the Stokes162o
~
Einstein equation may also be v a l i d •
o*
f o r Pd d i f f u s i o n in PdSi/FeB m e t a l l i c
m • + o+ ld22
glasses.
v
o
However, an e f f e c t i v e
interdiffusivity
was used, uncor-
rected f o r the wavelength dependence. Using the value f o r D determined in
id 24
this work, and taking I a = 0.721, leads to an ~ in Equation (4) equal 09
10
1.1
1J2
113
Tg,'T
14
to about 31k which means that the Stokes-Einstein equation is not
FIGURE 4 Compilation of data on metal diffusion in metal-metalloid glasses. [] Pd-Fe interdiffusion in PdSi/FeB, isoconfigurational measurements, this and previous work. 1 • Au in relaxed Pd77" 5Cu~i16.5 (I~)
valid.
This has important implica-
tions regarding the nature of atomic transport mechanisms in amorphous metals. 12
o Au in relaxed Pd77" 5Cu~i16.5 (14) + Au in relaxed Fe4~i4oB20 (14) V Au in Pd8Si20(15) 5. COMPARISONWITH OTHER DIFFUSION MEASUREMENTS In Figure 4, the
diffusivity
of Au in Pd- and Fe-based m e t a l l i c glasses
measured by various p r o f i l i n g techniques 13-15 has been p l o t t e d along with the d i f f u s i o n measurements made in this and previous work I by the modulated thin f i l m method f o r the PdSi/FeB system.
The temperature axis has been normalized
with respect to the glass t r a n s i t i o n temperature.
As can be seen, when plotted
in t h i s way, the measurements made by the thin f i l m method are in good agreement with the other data, in both absolute value and a c t i v a t i o n energy. With the exception of Chen et a i . , 1 3 in the other work on Au d i f f u s i o n , 14'15 no effects of s t r u c t u r a l r e l a x a t i o n were observed.
This is probably due to the
lack of s e n s i t i v i t y , r e l a t i v e to the modulated f i l m technique, of the p r o f i l i n g methods used. 12
894
R. C. Cammarata, A.L. Greer / Interdiffusion studies in metallic glasses
6. CONCLUSIONS We have measured i n t e r d i f f u s i v i t i e s in metallic glasses through the use of compositionally modulated thin films.
This method is very sensitive, allowing
the detection of structural relaxation effects and the measurement of low d i f f u s i v i t i e s (~10-27m2s-l).
The i n t e r d i f f u s i v i t i e s were found to be dependent
on the modulation wavelength.
From these measurements we were able to c l a s s i f y
the PdSi/FeB amorphous a l l o y as an ordering system, which may have implications concerning compositional short range ordering 12'16 in metallic glasses. Also a bulk i n t e r d i f f u s i v i t y was determined to be 5.6x lO-5exp(-195kJmol-I/RT)m2s - I . Based on this value, we have shown that the Stokes-Einstein equation, r e l a t i n g d i f f u s i v i t y to viscosity, is not v a l i d in m e t a l l i c glasses as has been previously reported. ACKNOWLEDGEMENTS The authors thank Prof. F. Spaepen and Mr. C.-J. Lin for many useful discussions, and Mr. F.N. Molea, Mr. J.L. Bell, and Mr. K. Campbell for t h e i r technical assistance.
This work was supported by the Office of Naval Research
under contract N00014-77-C-0002 and by the National Science Foundation under contract DMR80-20247. REFERENCES I) A.L. Greer, C.-J. Lin, and F. Spaepen, in: Proc. 4th Int. Conf. on Rapidly Quenched Metals, eds. T. Masumoto and K. Susuki (japan Inst. of Metals, 1982) pp. 567-572. 2) J. Dumond and J.P. Youtz, J. Appl. Phys. I I (1940) 357. 3) H.E. Cook and J.E. H i l l i a r d , J. Appl. Phys. 40 (1969) 2191. 4) M.P. Rosenblum, F. Spaepen, and D. Turnbull, Appl. Phys. Lett. 37 (1980) 184. 5) J.W. Cahn and J.E. H i l l i a r d , J. Chem. Phys. 28 (1958) 258. 6) A.L. Greer, in: Modulated Structure Materials, NATO ASI Series, Applied Sciences, ed. T. Tsakalakos (Martinus N i j o f f , The Hague, 1983) in press. 7) M. Hansen, Constitution of Binary Alloys (McGraw-Hill, New York, 1958). 8) J. A s k i l l , Tracer Diffusion Data for Metals, Alloys, and Simple Oxides (Plenum Press, New York, 1970). g) B. Cantor and R.W. Cahn, in: Amorphous Metallic Alloys, ed. F.E. Luborsky (Butterworths, London, 1983) pp. 487-505. I0) A.H. C o t t r e l l , Mechanical Properties of Matter (John Wiley and Sons, New York, 1964). I I ) N.H. Nachtrieb, in: Liquid Metals and S o l i d i f i c a t i o n (ASM, Cleveland, Ohio, 1958) p. 49. 12) A.L. Greer, this volume. 13) H.S. Chen, L.C. Kimerling, J.P. Poate, and W.L. Brown, Appl. Phys. Lett. 32 (1978) 461. 14) D. Akhtar, B. Cantor, and R.W. Cahn, Acta Metall. 30 (1982) 1571. 15) P. Gupta, K.N. Tu, and K.W. Asai, Thin Solid Films 90 (1982) 131. 16) T. Egami, Mater. Res. Bull. 13 (1978) 557.