- Email: [email protected]
Early and late stages of solid state amorphization reactions
Journal of the Less-Common
EARLY AND LATE REACTIONS*
Metals, 140 (1988)
STAGES
25 - 31
OF SOLID
STATE
25
AMORPHIZATION
K. SAMWER
Keck Laboratory, California Institute of Technology, Pasadena, CA 91125 and I. Physikalisches Znstitut der Universitat Gottingen, Bunsenstrasse 9, D-3400 Gottingen (F.R.G.)
(U.S.A.)
Summary
The early and late stages of solid state amorphization are surveyed for the solid-gas and the solid-solid reaction. In the early stages both crystal-toglass transformations are limited by an interfacial barrier. Later the solidsolid reaction switches to a diffusion limited growth, which slows down the reaction rate with the growing product. Due to the different kinetics only the solid-gas reaction proceeds without forming an intermetallic compound.
1. Introduction
Metallic glasses (non-crystalline or amorphous metals) are distinguished by the lack of long-range order or periodicity in their microscopic structure. The name glass indicates the non-equilibrium state in which the melt solidifies by sufficient undercooling and configurational disorder is frozen-in. In the past, several different methods of rapid quenching from the melt or the vapour phase were mostly used to achieve the glassy state. To avoid crystallization, the quenching process has to be done on a timescale t, much shorter than the timescale t, for nucleation and growth of the competing crystalline phases. Several years ago it was found that amorphization in solid metallic systems can be obtained when certain kinetic constraints are involved in the production of crystalline alloys. An overview of this subject has been given recently in ref. 1. This paper deals with two different amorphization reactions and their kinetics: the solid-gas reaction and the solid-solid reaction. It will be argued that a kinetic constraint similar to that for rapid quenching allows, in the case of the solid-gas reaction, the formation of a continuous amorphization process. However, the interdiffusion of two crystalline layers changes its time dependence with increasing reaction time and following the formation of the amorphous alloy it will lead to the formation of a crystalline compound. *Paper Los Alamos,
presented at the Conference NM, August 10 - 13, 1987.
0022-5088/88/$3.50
on Solid
State
Amorphizing
@ Elsevier Sequoia/Printed
Transformations,
in The Netherlands
26
2. Crystal-to-glass
transition
by a diffusion
reaction
2.1. The solid-gas reaction Up to 1983 no systematic experiments had been done to demonstrate that the absorption of hydrogen in a metallic alloy can produce an amorphous phase. Figure 1 shows the X-ray diffraction pattern of a Zr3Rh sample before and after the reaction with hydrogen gas below a temperature of 225 “C! [2]. Transmission electron microscopy (TEM) pictures during [ 31 and after [4] the amorphization process demonstrate that the amorphous hydride phase forms at the grain boundaries of the original microcrystals and subsequently grows into the interior of the grain until the amorphization reaction is complete. The driving force for the amorphization is the chemical energy stored in the two reactants (crystalline ZrsRh alloy and the hydrogen gas). The observed reaction processes can be summarized as follows (c, crystalline; a, amorphous) [ 51:
T < 225 “C: c-Zr3Rh + 2.75 H, = a-Zr3RhHS.,
(1)
T > 230 “C: c-Zr3Rh + H, = c-Zr,Rh
(2)
+ c-ZrHa
T > 300 “C: c-ZrsRh + 3H, = 3 (c-ZrHJ
+ c-Rh
(3)
The crystal-to-glass transition is always achieved if the temperature is held below 225 “C. No other phases occur at this temperature. In an early work we assumed that the reaction kinetics for the solid-gas reaction were
28
30
46
56
( 2 8 1(degrees)
68
78
Depth
(pm)
Fig. 1. X-ray diffraction diagram (Cu Kcr radiation) for a crystalline ZrsRh sample with Cu& structure and for the same sample after hydriding (180 “C, 1 atm Hz), magnified 10x. Fig. 2. Hydrogen concentration sample was mechanically abraded
profiles in ZrsRhH, during hydriding before hydriding (taken from ref. 3).
at
180 “C. The
27
interface limited since the ~o~housph~e grew linearly with time [4]. This assumption was verified by Yeh [ 31 who used a nuclear depth-profiling technique to show that the rate of the hydrogen absorption is in fact limited by hydrogen transfer at the surface. Figure 2 (taken from ref. 3) shows the hydrogen concentration profile in Zr,RhH, us. sample depth. It is clearly seen that within the resolution of this technique the hydrogen concentration remains constant throughout the sample during the reaction as the total hydrogen content of the specimen increases. Since the activation energy for hydrogen diffusion is very small (0.3 - 0.5 eV) [6] compared with that of the metal species (1.2 - 2.7 eV) [?I, at T x 220 “C the hydrogen atoms are very mobile with respect to the metal atoms, which are nearly frozen-in. Therefore, by opening the surface of the specimen in a suitable way, the rate of the reaction at fixed temperature can be changed. At the same time these results indicate that the crystd-to-glass transition in the solid-gas reaction process is not limited by diffusion but by the gas-sample interface kinetics. This interface-limited reaction process will not change with time in contrast to the second example of a solid-solid reaction as we will see later. Therefore, even a bulk crystalline Zr,Rh sample can be transformed into amorphous Zr3RhH,., since the asymmetry in the atomic mobilities is constant for a fixed temperature. It is worthwhile to note that the temperature window in which these phase transitions can occur is defined by the mobilities of the slower atoms, here the metal atoms (e.g. rhodium). 2.2. The s&d-solid reaction The observation of Schwarz and Johnson ]S] that isothermal annealing of thin-film multilayers of two different crystalline metals (lanthanum and gold) can lead to the formation of an amorphous alloy followed the recognition that the asymmetry in the diffusion constants provides the key to the necessary kinetic constraint for a crystal-to-glass tr~sitio~ [9]. Again, the formation of the crystalline compound is restricted in the early stages of the reaction due to the limited mobility of the early transition metal species (e.g. lithium, zirconium, hafnium). The results of Rutherford backscattering measurements [lo], cross-sectional TEM [ 111 and resistance measurements [12] on the Zr-X diffusion couple can be summarized in a schematic diagram as shown in Fig. 3. In the early stages the reaction between crystalline zirconium and crystalline cobalt is limited by an interfacial reaction (I) as demonstrated by the observed linear time dependence of the growth of the amorphous interlayer 1121. The concentration of the moving species (here cobalt) drops across the interface. In the diffusion-limited regime (II) the concentration of cobalt in the amorphous layer varies linearly between approximately 40% and 70%. In order to grow the interlayer, the cobalt atoms have to diffuse through the amorphous phase and reset with the zirconium atoms at the amorphous-crystalline zirconium interface. The kinetics of this process can be described by a simple equation (for more details see ref. 12): x2+Ax=Bt
28
Zr
0 4 ---_-e-s
I I t
co 100 interface
limited regime
j -------
o__x’oo 8a) o~‘oo diffusion
limited regime
@
b,o-“‘oo Fig.
3.
Schenlatic
concentration
profile
for
compound
formation
low temperature
compound
formation
high temperature
a Zr-Co
diffusion
couple
at various
stages of the amorphization reaction.
where x is the thickness of the amorphous interlayer, B is proportional to the ~terdiffusion coefficient and B/A is the interface velocity of the growing amorphous layer. Measured interface limited growth velocities [12] are plotted in Fig. 4 us. reciprocal temperature. At a fixed temperature the reaction proceeds with an interface velocity u,, to form the amorphous phase. In regime II of Fig. 3, u,, slows down due to the increasing film thickness x 2x For longer reaction times, the interface velocity for formation rate) slows down so much because of the slow supply of cobalt atoms that a critical value is reached where the formation rate of the amorphous phase becomes equal to the formation rate of the competing crystalline compound. Then u,, = u, and the crystalline compound is formed. In this regime III, two different cases were recently observed (see Fig. 3) [ 131. At low temperatures, the crystalline compound grows only in the forward {z~conium) direction, whereas at higher temperatures the compound also consumes the already formed amorphous phase and grows in both directions. The latter observation is an indication that the compound formation is not only kinet-
29
10'
105
10'
f
-J >
lo3
10'
10
1
1
1.5
l/T
2.0
2.4
[1000/k]
Fig. 4. Interface velocity u us. reciprocal temperature T-l for the Zr-Co system. The us, line is the amorphous-crystalline interface velocity in the interface limited regime I of the solid-solid amorphization reaction. The ux line gives the upper bound for the crystallinecompound-crystalline-elemental-layer interface velocity. The crossover at 780 K marks the upper limit for amorphization in this system. The ~(540 A) and u (1000 8) lines give calculated interface velocities for the amorphous phase in the diffusion limited growth regime II for two specific thicknesses.
ically restricted but also includes a nucleation barrier. In Fig. 4 the u, line represents the growth velocities of the intermetallic compound ZrCo. If u,, reaches this critical value u, the intermetallic compound is formed. Therefore u, gives the lower limit of the amorphous phase. Since u,, and u, have different activation energies, no amorphous phase is expected to form in a solid-solid reaction above 780 K for the ZrCo system [ 141. According to Fig. 4, a relatively large amorphous interlayer should be able to grow at low temperature (see ~(540 A) and ~(1000 A), which are calculated interface velocities for amorphous interlayers 540 A and 1000 A in thickness). Unfortunately, an additional effects sets in during the growth of the amorphous phase, which slows down the interface velocities more rapidly than expected [ 151. Mechanical stresses are believed to build up during the interdiffusion
30
reaction, which make the diffusion coefficient timedependent. This can limit the maximum layer thickness of the amorphous phase to about 1000 A [13], and cause the compound formation. Therefore, the formation of a bulk amorphous phase in a single diffusion couple is limited and the need for multilayers with their problems of void formation due to the Kirkendall effect [ 111 is given. Before concluding, it should be noted that in a related area several authors [ 161 have used a high-energy ball mill to alloy mechanically physical mixtures of two metal powders to obtain finely dispersed mixtures and ultimately an amorphous alloy. The actual mechanism of this crystal-to-glass transformation is not yet fully understood. It seems likely that a combination of an interdiffusion reaction and a size effect might be responsible for the amorphization process. Since intermetallic compounds have also been mechanically ground and transformed into the glassy state, defects might play an important role for this process as in the irradiation of initially stable intermetallic compounds [ 161.
3. Conclusions Solid state amorphization by diffusion reaction is probably initiated by a process of nucleation and growth [17]. Evidence of this includes the need for polycrystalline zirconium in a diffusion couple experiment [ 18,191 and the observation that in the solid-gas reaction the transformation starts at grain boundaries. In contrast, recent experiments by Blatter and von AlImen [20] and several arguments concerning the symmetry of superheating and undercooling by Johnson [21] indicate that a crystal-to-glass transition is also possible in a massive transformation. For a crystalline state, the ultimate limit of its stability is then reached, when the shear modulus vanishes. This could happen by increasing the temperature, by alloying at very low temperatures or by introducing defects of several kinds. Massive transformations require no nucleation and melting might become a secondorder phase transition. In this limit, early and late stages of the amorphization reaction are no longer different. Acknowledgment The Johnson, Financial 126 at the
author kindly acknowledges valuable discussions with W. L. H. Schroder, M. Moske, K. Pampus, W. J. Meng and E. Cotts. support is given by the NSF-MRG at Caltech and the DFG-SFB University of Giittingen.
References 1 K. Samwer, Phys. l?ep., (1988) in the press. 2 X. L. Yeh, K. Samwer atid W. L. Johnson,Appl.
Phys. Left.,
42 (1983)
242.
31 3 X. L. Yeh, Ph. D. Thesis, California Institute of Technology, 1987. 4 K. Samwer, in R. C. Bowman, Jr. and G. Bambakides (eds.), Amorphous and Disordered Hydrides in NATO ASI Series B: Physics, Vol. 136, Plenum, New York, 1986, p. 173. 5 W. L. Johnson, M. Atzmon, M. van Rossum, B. P. Dolgin and X. L. Yeh, in S. Steeb and H. Warlimont (eds.), Rapidly Quenched Metals, North-Holland, Amsterdam, 1985, p. 1515. 6 R. C. Bowman, Jr., J. S. Cantrell, E. L. Venturi, R. Schulz, J. E. Wagner, A. Attalla and B. D. Draft, in S. Steeb and H. Warlimont (eds.), Rapidly Quenched Metals, North-Holland, Amsterdam, 1985, p. 1541. B. S. Berry and W. C. Pritchet, in S. Steeb and H. Warlimont (eds.), Rapidly Quenched Metals, North-Holland, Amsterdam, 1985, p. 1529. 7 B. Cantor and R. Cahn, in F. Luborsky (ed.) Amorphous Metallic Alloys, Butterworths, London 1983, p. 487. 8 R. B. Schwarz and W. L. Johnson, Phys. Rev. Left., 51 (1983) 415. 9 W. L. Johnson, Mater. Sci. Eng., 97 (1988) 1. 10 M. van Rossum, M.-A. Nicolet and W. L. Johnson, Phys. Rev. B, 29 (1984) 5498. Y. T. Cheng, W. L. Johnson and M.-A. Nicolet, Appl. Phys. Lett., 47 (1985) 800. 11 H. Schroder, K. Samwer and U. Koster, Phys. Rev. Lett., 54 (1985) 197. 12 H. Schroder and K. Samwer, J. Mater. Res., (1988) in the press. 13 W. J. Meng, S. C.-W. Nieh and W. L. Johnson, Mater. Sci. Eng., 97 (1988) 87. 14 K. Samwer, K. Pampus and H. Schroder, Mater. Sci. Eng., 97 (1988) 63. 15 H. U. Krebs and K. Samwer, Europhys. Lett., 2 (1986) 141. 16 J. Less-Common Met., 140 (1988). 17 R. W. Cahn and W. L. Johnson, J. Mater. Res., I (1986) 724. 18 J. F. M. Westendorp, Ph. D. Thesis, University of Utrecht, The Netherlands, 1986. 19 K. Pampus, K. Samwer and J. Bottiger, Europhys. Lett., 3 (1987) 581. 20 A. Blatter and M. von Allmen, Phys. Rev. Lett., 54 (1985) 2103; J. Less-Common Met., 140 (1988). 21 W. L. Johnson, Prog. Mater. Sci., 30 (1986) 81.
EARLY AND LATE REACTIONS*
Metals, 140 (1988)
STAGES
25 - 31
OF SOLID
STATE
25
AMORPHIZATION
K. SAMWER
Keck Laboratory, California Institute of Technology, Pasadena, CA 91125 and I. Physikalisches Znstitut der Universitat Gottingen, Bunsenstrasse 9, D-3400 Gottingen (F.R.G.)
(U.S.A.)
Summary
The early and late stages of solid state amorphization are surveyed for the solid-gas and the solid-solid reaction. In the early stages both crystal-toglass transformations are limited by an interfacial barrier. Later the solidsolid reaction switches to a diffusion limited growth, which slows down the reaction rate with the growing product. Due to the different kinetics only the solid-gas reaction proceeds without forming an intermetallic compound.
1. Introduction
Metallic glasses (non-crystalline or amorphous metals) are distinguished by the lack of long-range order or periodicity in their microscopic structure. The name glass indicates the non-equilibrium state in which the melt solidifies by sufficient undercooling and configurational disorder is frozen-in. In the past, several different methods of rapid quenching from the melt or the vapour phase were mostly used to achieve the glassy state. To avoid crystallization, the quenching process has to be done on a timescale t, much shorter than the timescale t, for nucleation and growth of the competing crystalline phases. Several years ago it was found that amorphization in solid metallic systems can be obtained when certain kinetic constraints are involved in the production of crystalline alloys. An overview of this subject has been given recently in ref. 1. This paper deals with two different amorphization reactions and their kinetics: the solid-gas reaction and the solid-solid reaction. It will be argued that a kinetic constraint similar to that for rapid quenching allows, in the case of the solid-gas reaction, the formation of a continuous amorphization process. However, the interdiffusion of two crystalline layers changes its time dependence with increasing reaction time and following the formation of the amorphous alloy it will lead to the formation of a crystalline compound. *Paper Los Alamos,
presented at the Conference NM, August 10 - 13, 1987.
0022-5088/88/$3.50
on Solid
State
Amorphizing
@ Elsevier Sequoia/Printed
Transformations,
in The Netherlands
26
2. Crystal-to-glass
transition
by a diffusion
reaction
2.1. The solid-gas reaction Up to 1983 no systematic experiments had been done to demonstrate that the absorption of hydrogen in a metallic alloy can produce an amorphous phase. Figure 1 shows the X-ray diffraction pattern of a Zr3Rh sample before and after the reaction with hydrogen gas below a temperature of 225 “C! [2]. Transmission electron microscopy (TEM) pictures during [ 31 and after [4] the amorphization process demonstrate that the amorphous hydride phase forms at the grain boundaries of the original microcrystals and subsequently grows into the interior of the grain until the amorphization reaction is complete. The driving force for the amorphization is the chemical energy stored in the two reactants (crystalline ZrsRh alloy and the hydrogen gas). The observed reaction processes can be summarized as follows (c, crystalline; a, amorphous) [ 51:
T < 225 “C: c-Zr3Rh + 2.75 H, = a-Zr3RhHS.,
(1)
T > 230 “C: c-Zr3Rh + H, = c-Zr,Rh
(2)
+ c-ZrHa
T > 300 “C: c-ZrsRh + 3H, = 3 (c-ZrHJ
+ c-Rh
(3)
The crystal-to-glass transition is always achieved if the temperature is held below 225 “C. No other phases occur at this temperature. In an early work we assumed that the reaction kinetics for the solid-gas reaction were
28
30
46
56
( 2 8 1(degrees)
68
78
Depth
(pm)
Fig. 1. X-ray diffraction diagram (Cu Kcr radiation) for a crystalline ZrsRh sample with Cu& structure and for the same sample after hydriding (180 “C, 1 atm Hz), magnified 10x. Fig. 2. Hydrogen concentration sample was mechanically abraded
profiles in ZrsRhH, during hydriding before hydriding (taken from ref. 3).
at
180 “C. The
27
interface limited since the ~o~housph~e grew linearly with time [4]. This assumption was verified by Yeh [ 31 who used a nuclear depth-profiling technique to show that the rate of the hydrogen absorption is in fact limited by hydrogen transfer at the surface. Figure 2 (taken from ref. 3) shows the hydrogen concentration profile in Zr,RhH, us. sample depth. It is clearly seen that within the resolution of this technique the hydrogen concentration remains constant throughout the sample during the reaction as the total hydrogen content of the specimen increases. Since the activation energy for hydrogen diffusion is very small (0.3 - 0.5 eV) [6] compared with that of the metal species (1.2 - 2.7 eV) [?I, at T x 220 “C the hydrogen atoms are very mobile with respect to the metal atoms, which are nearly frozen-in. Therefore, by opening the surface of the specimen in a suitable way, the rate of the reaction at fixed temperature can be changed. At the same time these results indicate that the crystd-to-glass transition in the solid-gas reaction process is not limited by diffusion but by the gas-sample interface kinetics. This interface-limited reaction process will not change with time in contrast to the second example of a solid-solid reaction as we will see later. Therefore, even a bulk crystalline Zr,Rh sample can be transformed into amorphous Zr3RhH,., since the asymmetry in the atomic mobilities is constant for a fixed temperature. It is worthwhile to note that the temperature window in which these phase transitions can occur is defined by the mobilities of the slower atoms, here the metal atoms (e.g. rhodium). 2.2. The s&d-solid reaction The observation of Schwarz and Johnson ]S] that isothermal annealing of thin-film multilayers of two different crystalline metals (lanthanum and gold) can lead to the formation of an amorphous alloy followed the recognition that the asymmetry in the diffusion constants provides the key to the necessary kinetic constraint for a crystal-to-glass tr~sitio~ [9]. Again, the formation of the crystalline compound is restricted in the early stages of the reaction due to the limited mobility of the early transition metal species (e.g. lithium, zirconium, hafnium). The results of Rutherford backscattering measurements [lo], cross-sectional TEM [ 111 and resistance measurements [12] on the Zr-X diffusion couple can be summarized in a schematic diagram as shown in Fig. 3. In the early stages the reaction between crystalline zirconium and crystalline cobalt is limited by an interfacial reaction (I) as demonstrated by the observed linear time dependence of the growth of the amorphous interlayer 1121. The concentration of the moving species (here cobalt) drops across the interface. In the diffusion-limited regime (II) the concentration of cobalt in the amorphous layer varies linearly between approximately 40% and 70%. In order to grow the interlayer, the cobalt atoms have to diffuse through the amorphous phase and reset with the zirconium atoms at the amorphous-crystalline zirconium interface. The kinetics of this process can be described by a simple equation (for more details see ref. 12): x2+Ax=Bt
28
Zr
0 4 ---_-e-s
I I t
co 100 interface
limited regime
j -------
o__x’oo 8a) o~‘oo diffusion
limited regime
@
b,o-“‘oo Fig.
3.
Schenlatic
concentration
profile
for
compound
formation
low temperature
compound
formation
high temperature
a Zr-Co
diffusion
couple
at various
stages of the amorphization reaction.
where x is the thickness of the amorphous interlayer, B is proportional to the ~terdiffusion coefficient and B/A is the interface velocity of the growing amorphous layer. Measured interface limited growth velocities [12] are plotted in Fig. 4 us. reciprocal temperature. At a fixed temperature the reaction proceeds with an interface velocity u,, to form the amorphous phase. In regime II of Fig. 3, u,, slows down due to the increasing film thickness x 2x For longer reaction times, the interface velocity for formation rate) slows down so much because of the slow supply of cobalt atoms that a critical value is reached where the formation rate of the amorphous phase becomes equal to the formation rate of the competing crystalline compound. Then u,, = u, and the crystalline compound is formed. In this regime III, two different cases were recently observed (see Fig. 3) [ 131. At low temperatures, the crystalline compound grows only in the forward {z~conium) direction, whereas at higher temperatures the compound also consumes the already formed amorphous phase and grows in both directions. The latter observation is an indication that the compound formation is not only kinet-
29
10'
105
10'
f
-J >
lo3
10'
10
1
1
1.5
l/T
2.0
2.4
[1000/k]
Fig. 4. Interface velocity u us. reciprocal temperature T-l for the Zr-Co system. The us, line is the amorphous-crystalline interface velocity in the interface limited regime I of the solid-solid amorphization reaction. The ux line gives the upper bound for the crystallinecompound-crystalline-elemental-layer interface velocity. The crossover at 780 K marks the upper limit for amorphization in this system. The ~(540 A) and u (1000 8) lines give calculated interface velocities for the amorphous phase in the diffusion limited growth regime II for two specific thicknesses.
ically restricted but also includes a nucleation barrier. In Fig. 4 the u, line represents the growth velocities of the intermetallic compound ZrCo. If u,, reaches this critical value u, the intermetallic compound is formed. Therefore u, gives the lower limit of the amorphous phase. Since u,, and u, have different activation energies, no amorphous phase is expected to form in a solid-solid reaction above 780 K for the ZrCo system [ 141. According to Fig. 4, a relatively large amorphous interlayer should be able to grow at low temperature (see ~(540 A) and ~(1000 A), which are calculated interface velocities for amorphous interlayers 540 A and 1000 A in thickness). Unfortunately, an additional effects sets in during the growth of the amorphous phase, which slows down the interface velocities more rapidly than expected [ 151. Mechanical stresses are believed to build up during the interdiffusion
30
reaction, which make the diffusion coefficient timedependent. This can limit the maximum layer thickness of the amorphous phase to about 1000 A [13], and cause the compound formation. Therefore, the formation of a bulk amorphous phase in a single diffusion couple is limited and the need for multilayers with their problems of void formation due to the Kirkendall effect [ 111 is given. Before concluding, it should be noted that in a related area several authors [ 161 have used a high-energy ball mill to alloy mechanically physical mixtures of two metal powders to obtain finely dispersed mixtures and ultimately an amorphous alloy. The actual mechanism of this crystal-to-glass transformation is not yet fully understood. It seems likely that a combination of an interdiffusion reaction and a size effect might be responsible for the amorphization process. Since intermetallic compounds have also been mechanically ground and transformed into the glassy state, defects might play an important role for this process as in the irradiation of initially stable intermetallic compounds [ 161.
3. Conclusions Solid state amorphization by diffusion reaction is probably initiated by a process of nucleation and growth [17]. Evidence of this includes the need for polycrystalline zirconium in a diffusion couple experiment [ 18,191 and the observation that in the solid-gas reaction the transformation starts at grain boundaries. In contrast, recent experiments by Blatter and von AlImen [20] and several arguments concerning the symmetry of superheating and undercooling by Johnson [21] indicate that a crystal-to-glass transition is also possible in a massive transformation. For a crystalline state, the ultimate limit of its stability is then reached, when the shear modulus vanishes. This could happen by increasing the temperature, by alloying at very low temperatures or by introducing defects of several kinds. Massive transformations require no nucleation and melting might become a secondorder phase transition. In this limit, early and late stages of the amorphization reaction are no longer different. Acknowledgment The Johnson, Financial 126 at the
author kindly acknowledges valuable discussions with W. L. H. Schroder, M. Moske, K. Pampus, W. J. Meng and E. Cotts. support is given by the NSF-MRG at Caltech and the DFG-SFB University of Giittingen.
References 1 K. Samwer, Phys. l?ep., (1988) in the press. 2 X. L. Yeh, K. Samwer atid W. L. Johnson,Appl.
Phys. Left.,
42 (1983)
242.
31 3 X. L. Yeh, Ph. D. Thesis, California Institute of Technology, 1987. 4 K. Samwer, in R. C. Bowman, Jr. and G. Bambakides (eds.), Amorphous and Disordered Hydrides in NATO ASI Series B: Physics, Vol. 136, Plenum, New York, 1986, p. 173. 5 W. L. Johnson, M. Atzmon, M. van Rossum, B. P. Dolgin and X. L. Yeh, in S. Steeb and H. Warlimont (eds.), Rapidly Quenched Metals, North-Holland, Amsterdam, 1985, p. 1515. 6 R. C. Bowman, Jr., J. S. Cantrell, E. L. Venturi, R. Schulz, J. E. Wagner, A. Attalla and B. D. Draft, in S. Steeb and H. Warlimont (eds.), Rapidly Quenched Metals, North-Holland, Amsterdam, 1985, p. 1541. B. S. Berry and W. C. Pritchet, in S. Steeb and H. Warlimont (eds.), Rapidly Quenched Metals, North-Holland, Amsterdam, 1985, p. 1529. 7 B. Cantor and R. Cahn, in F. Luborsky (ed.) Amorphous Metallic Alloys, Butterworths, London 1983, p. 487. 8 R. B. Schwarz and W. L. Johnson, Phys. Rev. Left., 51 (1983) 415. 9 W. L. Johnson, Mater. Sci. Eng., 97 (1988) 1. 10 M. van Rossum, M.-A. Nicolet and W. L. Johnson, Phys. Rev. B, 29 (1984) 5498. Y. T. Cheng, W. L. Johnson and M.-A. Nicolet, Appl. Phys. Lett., 47 (1985) 800. 11 H. Schroder, K. Samwer and U. Koster, Phys. Rev. Lett., 54 (1985) 197. 12 H. Schroder and K. Samwer, J. Mater. Res., (1988) in the press. 13 W. J. Meng, S. C.-W. Nieh and W. L. Johnson, Mater. Sci. Eng., 97 (1988) 87. 14 K. Samwer, K. Pampus and H. Schroder, Mater. Sci. Eng., 97 (1988) 63. 15 H. U. Krebs and K. Samwer, Europhys. Lett., 2 (1986) 141. 16 J. Less-Common Met., 140 (1988). 17 R. W. Cahn and W. L. Johnson, J. Mater. Res., I (1986) 724. 18 J. F. M. Westendorp, Ph. D. Thesis, University of Utrecht, The Netherlands, 1986. 19 K. Pampus, K. Samwer and J. Bottiger, Europhys. Lett., 3 (1987) 581. 20 A. Blatter and M. von Allmen, Phys. Rev. Lett., 54 (1985) 2103; J. Less-Common Met., 140 (1988). 21 W. L. Johnson, Prog. Mater. Sci., 30 (1986) 81.