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  • Iron self-diffusion in amorphous FeZr/ 57FeZr multilayers measured by neutron reflectometry

    Mukul Gupta,1,* Ajay Gupta,2 J. Stahn,1 M. Horisberger,1 T. Gutberlet,1 and P. Allenspach11Laboratory for Neutron Scattering, ETHZ and PSI, Paul Scherrer Institute, Villigen CH-5232, Switzerland

    2Inter-University Consortium for DAE Facilities, Khandwa Road, Indore IN-452017, India(Received 19 May 2004; revised manuscript received 7 September 2004; published 18 November 2004)

    Self-diffusion of iron innaturalFe67Zr33/57Fe67Zr33 multilayers has been investigated by neutron reflectometry.

    The as-deposited multilayer is amorphous in nature. It remains amorphous up to a temperature of 573 K andthereafter nanocrystallizes with an average grain size of 6 nm. The self-diffusion in the multilayers has beenmeasured after isothermal vacuum annealing below the nanocrystallization temperature by monitoring thedecay of the intensity of the first order Bragg peak, arising due to the isotopic periodicity. It has been found thatthe diffusivity at different temperatures follows an Arrhenius-type behavior with the preexponential factorD0=5310

    181 m2 s1 and the activation energyE=0.380.05 eV, respectively. These values ofE and D0follow the well-knownED0 correlation and on the basis of this correlation it is suggested that diffusionmechanism in the present case is not highly collective but involves a rather small group of atoms.

    DOI: 10.1103/PhysRevB.70.184206 PACS number(s): 66.30.Fq

    I. INTRODUCTION

    Amorphous metallic alloys also known as metallicglasses, are important from the point of their applications inindustry for computers, information technology, recordingmedia, etc.1 They differ from their crystalline counterparts bya nearly random arrangement of atoms and are an example ofthe paradigm of dense random packing which leads to a greatfundamental interest in these alloys.2 Generally, these alloysare metastable, and at elevated temperatures various atomicrearrangements take place above their crystallization tem-peratureTx, the atomic mobility increases drastically causinga rapid crystallization, and even belowTx the amorphousmatrix is internally unstable and transforms continuously toamorphous states of lower free energy. Transformation of astructure towards lower free energy is well-known as struc-tural relaxation of amorphous structure and leads to changesin most of the physical properties. Atomic transport proper-ties, such as diffusion are among the most affected duringstructural relaxation process and may change by several or-ders of magnitude.3 This leads to a strong need for an under-standing of the diffusion behavior in amorphous alloys. Be-cause of their limited thermal stability it was not possible tostudy long range atomic transport in these alloys.

    Various attempts have been made to increase the thermalstability of these alloys using a multicomponent matrix inbulk metallic glasses and melt spun ribbons. Self-diffusionmeasurements have been performed in a series of alloys, e.g.,ZrCuNiTiBe,4 CoFeNbB,5 ZrCuNiAl6 (and Ref. 2 and refer-ences therein). Some studies have also been done in binaryamorphous alloys, e.g., NiZr,7 CoZr,8 TiZr,9 etc. at tempera-tures.470 K. Most of these studies have been done usingprofiling and sectioning techniques such as radiotracer tech-niques, secondary ion mass spectroscopy(SIMS), Rutherfordbackscattering(RBS), Auger electron spectroscopy(AES),etc. Since the depth resolution available with these tech-niques is of the order of a few nm, diffusion length less thanthat could not be probed. Generally, the crystallization tem-perature in amorphous alloys is around 700 K which gives

    an upper limit for the diffusion annealing. Typical diffusionlengths at low temperaturess,400 Kd in a reasonable timewould be much shorter than the detection limit of cross-sectioning or depth-profiling techniques. In addition, forstudying diffusion in amorphous ultrathin filmssthickness, few nmd a technique with greater sensitivity is required asthe crystallization temperature in such layers is significantlylower as compared to bulk metallic glasses or melt-spun rib-bons.

    Measurement of interdiffusion in compositionally modu-lated multilayer structures using x-ray scattering is one tech-nique to study diffusion lengths much shorter than the detec-tion limit of sectioning and profiling techniques.1013Severalattempts have been made to study interdiffusion in chemi-cally inhomogeneous multilayers. In a study by Mizoguchiet al.,14 interdiffusion and structural relaxation have beenstudied in 3d transition metal(TM)/Zr multilayers in thecomposition range of TM67Zr33 using x-ray diffraction(XRD) technique. Amorphization in these multilayers hasbeen achieved with a solid state reaction and diffusion mea-surements were performed at temperatures as low as 393 K.In another study Wanget al.15 have studied interdiffusion innanometer-scale multilayers using low-angle x-ray diffrac-tion in a series of polycrystalline binary alloys. While x-raydiffraction/reflection techniques can be successfully used forinterdiffusion studies in chemical-composition modulatedmultilayers, they cannot be used for studying self-diffusionin a chemically homogeneous structure because of electronicinteraction with x-rays.

    Neutron reflectivity is a nondestructive technique, whichcan be used for studying self-diffusion in a chemically ho-mogeneous multilayer with a resolution as small as 0.1 nm,by taking advantage of isotopic labeling. Greeret al.10,16,17

    have demonstrated the application of neutron reflectivity,measuring self-diffusion in amorphous NiZr multilayers. Inanother study by Bakeret al.18 self-diffusion of amorphous11B on 10B in isotopically enriched thin films of11B/10B onSi was investigated. It is rather surprising that since thenpractically no studies on self-diffusion measurements in me-

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  • tallic multilayers using the neutron reflectivity techniquewere performed in spite of its unique potential. Another tech-nique through which scattering contrast between two differ-ent isotopes of an element can be obtained is nuclear reso-nance reflectivity (NRR) of synchrotron radiation.19,20

    Possibility of using this technique for self-diffusion measure-ments of a Mssbauer active isotope was pointed out.20 In arecent study this technique has been used to study self-diffusion of 57Fe in some amorphous and nanocrystallinealloys.21

    In the present study we have measured self-diffusion ofiron in an isotopic multilayer of FeZr/57FeZr in the amor-phous state. The self-diffusion measurements have been car-ried out measuring the neutron reflectivity of the multilayerafter isothermal vacuum annealing below the crystallizationtemperature. The height of the Bragg peak arising due toisotopic periodicity decays with annealing temperature andtime and depicts the self-diffusion and the activation energyfor a chemically homogeneous structure. In addition, a de-tailed fitting of the neutron reflectivity profile measured atroom temperature yields interdiffusion at ambient conditions.The results of the obtained diffusion behavior are presentedand discussed in this article.

    II. EXPERIMENT

    Amorphous FeZr isotopic multilayers have been preparedusing a magnetron sputtering system. Natural Fe and57Feenriched targets were sputtered alternatively to deposit themultilayer structure. The57Fe target was prepared by pastinga 57Fe foil (57Fe enrichment,95%) onto a natural iron tar-get. Small circular pieces of Zr(12 pieces) were pasted onthe natural Fe as well as57Fe in an area ratio of Fe to Zrabout 1:0.3. The multilayer with a nominal layer structureglass ssubstrated / fnaturalFeZrs9 nmd / 57FeZrs5 nmdg20 wasprepared. The composition of the film has been measuredusing x-ray photoelectron spectroscopy(XPS). The structuralcharacterizations of the film have been carried out usingx-ray reflectometry(XRR) and XRD techniques using a stan-dard x-ray diffractometer and CuKa radiation. Since theoverall thickness of the film is relatively small, the XRDpattern of the film has been measured in the asymmetricBraggBrentano geometry at grazing incidence so that thebackground from the glass substrate can be minimized(keeping the incident angle just above the critical edge).Prior to diffusion measurements the crystallization behaviorof the amorphous film has been studied using XRD afterannealing the film isochronally in a vacuum furnace with abase vacuum of the order of 106 mbar.

    The self-diffusion measurements have been carried outusing neutron reflectivity after annealing the samples isother-mally at four different temperatures. The neutron reflectivitymeasurements have been carried out in the time-of-flightmode on the AMOR reflectometer and in theu-2u mode onthe MORPHEUS reflectometer both at SINQ/PSI.22 With anincoming wavelength band of 0.20.9 nm the reflectivitypattern was measured using two different angular settings inthe time of flight mode and on MORPHEUS using a mono-chromatic neutron beam with a wavelength of 0.474 nm.

    III. RESULTS AND DISCUSSION

    The composition of the cosputtered film was determinedusing XPS depth profiling. The average composition of thefilm was found to be Fe673Zr333 consistent with the arearatio of the targets used for sputtering. Figure 1 shows thex-ray diffraction pattern of the multilayer in the as-depositedstate and after isochronal annealing in the temperature rangeof 373673 K in a step of 100 K. The GIXRD pattern of theas-deposited film shows a broad hump centered around 2u=44 which is typical for the iron based amorphous alloys.1

    The average interatomic distance can be estimated using therelationa=1.23l /2 sinu, whereu is taken to be the angle atthe center of the amorphous hump, and the factor 1.23 is ageometric factor which rationalizes the nearest neighbor dis-tance with the spacing between pseudo-close packedplanes.23 The calculation gives an average interatomic dis-tance in the present case equal to 0.2550.001 nm for theas-deposited sample. The inset in Fig. 1 shows the variationin the interatomic distance as a function of annealing tem-perature. As can be seen the interatomic distance shows adecrease with an increase of annealing temperature. Such adecrease indicates densification in the layer and is a directconsequence of structural relaxation which occurs due to an-nihilation of free volume during annealing. After annealingat 673 K, the amorphous hump converts into a relativelysharp peak indicating crystallization of the amorphous film.A detailed investigation of the peak shows that it is not pos-sible to fit the peak using a single function, instead the bestfit has been obtained using two Gaussian line shapesonecorresponding to the amorphous phase and the other to thecrystalline bcc-Fe phase. This indicates that the film has notbeen crystallized completely and represents a mixture ofamorphous and partially crystalline states. The width of thecrystalline peak has been used to calculate the average grain

    FIG. 1. X-ray diffraction pattern of the glass(substrate)/fFeZr s9 nmd / 57FeZr s5 nmdg20 isotopic multilayer in the as-deposited state and after annealing at various temperatures as indi-cated in the figure. The measurements were carried out in the graz-ing incidence geometry using CuKa x-rays. The inset in the figureshows the change in interatomic distance as a function of annealingtemperature. The point corresponding to annealing at 673 K is afternanocrystallization.

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  • size using the Scherrer formula yielding a value of about6 nm. The area ratio of the two components can be used toestimate the amount of crystallization which indicates thatabout 50% of the film has converted into the nanocrystallinephase.

    Neutron reflectivity, in combination with x-ray reflectivitycan be used to extract more information about the crystalli-zation process of the amorphous multilayer. Figure 2 showsthe neutron and the x-ray reflectivity pattern of the as-deposited multilayer. While a Bragg peak arising due to iso-topic periodicity can be seen clearly in the neutron reflectiv-ity pattern, no such structure can be seen in the x-rayreflectivity pattern. This shows that there is no chemical con-trast betweennaturalFeZr and57FeZr, as expected. In fact, thisis a prerequisite for studying self-diffusion in a chemicallyhomogeneous multilayer as any chemical contrast would af-fect the diffusion process significantly and the measured dif-fusivity would no longer be self-diffusion but mediated bychemical inhomogeneity. The fitting of the neutron reflectiv-ity data of the multilayer yields the following structure:Glass ssubstrated / fnaturalFeZrs9.1 nmd / 57FeZrs5.3 nmdg20,which is close to the designed nominal structure. The neutronreflectivity pattern was fitted using a computer program

    based on Parratts formalism24 and it was found that the pat-tern could not be fitted assuming sharp interfaces; instead athin interlayer of thicknesss0.80.4d nm with the mean scat-tering length density of the two layers had to be introducedas interdiffused layer. This means that at room temperaturethere is some amount of interdiffusion in the multilayer. Thex-ray reflectivity pattern was fitted assuming a single layerwith a thin layer of scattering length density 50% of bulklayer, on the top of the film because of a possible oxidationof the film when exposed to the atmosphere.

    Figure 3 shows the x-ray reflectivity pattern of themultilayer after annealing at 523, 573, and 673 K. It wasobserved that up to an annealing temperature of 523 K, thex-ray reflectivity pattern of the isotopic multilayer does notchange significantly; only the thickness corresponding to theoxide layer is found to increase with annealing temperature.Whereas, after annealing at 573 K, a small Bragg peak ap-pears indicating an evolution of chemical contrast betweenthe natural and57Fe layers. Further annealing at 673 Ksharpens this peak. As it is evident from the x-ray diffractionpattern of the multilayer that nanocrystalline Fe precipitatesout from the amorphous phase after annealing at 673 K andthe volume fraction of this nanocrystalline phase is about50%. This information was taken as an input parameter whilefitting the x-ray reflectivity pattern of the multilayer afterannealing at 673 K. Two thin layers of pure iron(density9095% of bulk iron) were introduced on both sides of natu-ral and57Fe layers with total thickness of this interlayer ap-proximately equal to half of the bilayer thickness and thissimple model, as shown in Fig. 4, gives a reasonably goodfitting of the x-ray reflectivity pattern. Figure 5 shows theneutron reflectivity pattern of the multilayer after annealingat 573 and 673 K and for comparison in the as-depositedstate (measured again inu-2u mode). Exactly the samemodel, as discussed above was applied for fitting the 673 Kannealed neutron reflectivity pattern. Since neutrons have asignificant contrast betweennaturalFe and57Fe layers, the re-flectivity at the Bragg peak should be more intense withneutrons as compared to x-rays. In the present case neutron

    FIG. 2. Neutron(upper) and x-ray(below) reflectivity pattern ofthe fFeZr s9 nmd / 57FeZrs5 nmdg20 isotopic multilayer. The neutronreflectivity pattern was measured in the time-of-flight mode on theAMOR reflectometer using an incoming wavelength band of0.20.9 nm and using two angular settings. A Bragg peak corre-sponding to isotopic periodicity appears in the neutron reflectivitypattern while no such structure is visible for the x-rays. The x-rayreflectivity pattern was measured using CuKa x-rays and standardu-2u geometry.

    FIG. 3. X-ray reflectivity pattern of the isotopic multilayer afterannealing at different temperatures. For 573 and 673 K patterns theintensity has been multiplied by a factor of 100 and 10 000, respec-tively, for clarity.

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  • reflectivity was found to be more than 10 times in intensitywith neutrons as compared with x-rays after annealing tem-perature of 673 K. In fact the neutron reflectivity for 673 Kannealed sample is about 3 times higher in intensity as com-pared with that of the as-deposited sample. This indicatesthat upon nanocrystallization iron has precipitated out fromthe amorphous FeZr at the interfaces. The used model givesa reasonable fitting of both x-ray and neutron reflectivity dataand is consistent with the XRD data. Therefore the crystalli-zation process of the amorphous layers can be understood asa phase separation of iron from the amorphous phase at theinterfaces. Due to the fact that the iron diffusivity is about105 times higher25 compared to that of zirconium, iron atomswould move much faster and precipitate out at the surface orinterfaces upon crystallization. Using a model as discussedabove, the x-ray reflectivity pattern of the multilayer an-nealed at 573 K can be fitted. It can be seen from the XRDdata that the overall structure at 573 K is still amorphous; thevolume fraction of the iron layer which would precipitate outat the interfaces should be very small. A thin layer of ironwith a thicknesss0.40.2d nm gives a reasonably good fit-ting of the x-ray reflectivity pattern after annealing tempera-ture of 573 K.

    Comparing the observed crystallization behavior with thatreported in the literature, it can be seen that typical amor-phous binary alloys that form a nanocrystalline microstruc-ture have been found to crystallize in two steps. The primarycrystallization reaction of amorphous alloys often leads tothe evolution of nanocrystalline microstructures whereas thephase formed after the second stage results in an intermetal-lic compound along with nanocrystalline phase. The nominalreaction for such crystallization process had been given as:amorphousa+amorphousa+b; wherea is the primaryphase that precipitates out from the amorphous matrix andbis an intermetallic compound.26,27 In the present case phaseseparation of iron from the amorphous layers could be de-scribed as the first stage of crystallization. However, no at-tempt has been made to study the second step of crystalliza-tion primarily because the aim of the present work is to studydiffusion in the amorphous state only and second the samplesin the present case were prepared on float glass substratesand for an annealing temperature higher than 700 K the glasssubstrate would melt.

    Keeping in mind the above discussed crystallization be-havior, the self-diffusion measurements have been performedat annealing temperatures of 523 K and below, so as to avoidcrystallization of the amorphous layers during diffusion mea-surements. The diffusivity has been obtained after annealingthe multilayer at 373, 423, 473, and 523 K for various peri-ods of time. Figure 6 shows a typical decay of the Braggpeak intensity as a function of annealing time at 373 K. Ascan be seen, after an annealing time of 22 h the Bragg peakhas completely vanished indicating that the whole layer hasbeen diffused, while at initial times a shift of Bragg peaktowards higherq values has been observed. This shift of theBragg peak towards higherq would mean a reduction in thebilayer period and can be related to annihilation of free vol-ume as a result of structural relaxation during annealing. Asimilar decay of the Bragg peak has been observed at above-mentioned temperatures. The decay of the Bragg peak inten-sity can be used to calculate the diffusion coefficient usingthe expression:28

    FIG. 4. Schematic diagram of the model used for fitting thex-ray and neutron reflectivity data:(a) represents the situation in theamorphous phase with a small interdiffusion but no chemical phaseseparation and(b) depicts the situation after nanocrystallizationwhere Fe has precipitated out of the interfaces.

    FIG. 5. Neutron reflectivity pattern of the isotopic multilayerafter annealing at different temperatures. For the 573 and 673 Kpatterns the intensity has been multiplied by a factor of 102 and 104,respectively, for clarity.

    FIG. 6. Decay of Bragg peak intensity in the neutron reflectivitypattern of thefFeZrs9 nmd / 57FeZrs5 nmdg20 isotopic multilayer af-ter annealing at 373 K for different period of time.

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  • d

    dtFlnS Istd

    I0DG = 8p2n2

    d2DsTd, s1d

    whereI0 is the intensity of thenth order Bragg peak at timet=0; D is the diffusivity at the annealing temperatureT, andd is the bilayer periodicity. The diffusion lengthLd is relatedto the diffusivity DsTd, through the relationLd=4DsTdt; tbeing the annealing time.

    The height of the Bragg peak was determined after sub-tracting the background due to Fresnel reflectivity by multi-plying the data by a factor ofq4 (see Fig. 6), whereq is themomentum transfer. Figure 7 shows the evolution of the dif-fusion length as a function of annealing time at 473 K. Ascan be seen, the diffusion length at longer annealing timedoes not increase linearly as compared to the diffusion lengthobtained at room temperature. A nonlinear increase in thediffusion length is not unexpected and essentially shows thatthe diffusion length increases much faster at a lower anneal-ing time. Such an annealing time dependence of the diffusiv-ity is attributed to structural relaxation in amorphousstructures.29,30 It may be noted that the maximum diffusionlength that can be measured in the present case is limited bythe thickness of the57FeZr layer. On achieving diffusionlength of about 80% of the total layer thickness the diffusionlength becomes almost constant. Therefore, at each tempera-ture the annealing time was varied in order to achieve adiffusion length of 40.2 nm. It is interesting to see that inorder to achieve a constant diffusion length of 40.2 nm, therequired time decreases exponentially. A plot of the anneal-ing temperature versus the annealing time is shown in Fig. 8,which has been used to obtain the average value of diffusiv-ity over the annealing time. The values for the diffusivityobtained at four abovementioned temperatures were used tocalculate the activation energy and the preexponential factorusing the relationD=D0 expsE/kBTd, whereD0, E, andTare the preexponential factor, the activation energy and the

    annealing temperature respectively andkB is the Boltzmannconstant. Figure 9 shows a plot of the diffusion coefficientversus the inverse of temperature, which follows the Arrhen-ius type behavior. The calculated values ofD0 and the acti-vation energyE are 5310181 m2 s1 and 0.380.05 eV,respectively. It may be noted that the values of both thepreexponential factor and the activation energy are signifi-cantly smaller in the present case as compared with that ofiron based amorphous alloys, e.g., for Fe diffusion ina-Fe91Zr9D0=3.1310

    7 m2 s1 and E=1.45 eV.31,32 On theother hand, the values obtained in the present case follow thewell-known correlation betweenD0 andE for self and impu-rity diffusion in conventional and bulk amorphousalloys.2,15,33,34This relationship seems to have a universalcharacter as it has been observed not only for self and impu-rity diffusion in amorphous alloys but also in nanocrystallineand crystalline alloys.34

    FIG. 7. Evolution of the diffusion length as a function of an-nealing time at 473 K. The diffusion length at room temperature hasbeen obtained by fitting the neutron reflectivity data and at highertemperatures using Eq.(1). The dotted line is a guide to the eye.

    FIG. 8. Annealing time required to achieve a constant diffusionlength of 40.2 nm at different annealing temperatures. The solidline is a guide to the eye.

    FIG. 9. Arrhenius behavior of the diffusivity. The solid circlesrepresent the average diffusivity at a given temperature obtainedusing the data of Fig. 8. Solid line has been obtained using theequation:D=D0 expsE/kBTd.

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  • The data point corresponding to the present study isshown in Fig. 10 along with the values obtained in theliterature.2 The relationship betweenD0 and E is known asisokinetic relation and is given by:35

    ln D0 = ln A +E

    B, s2d

    where A and B are constants. Taking our data point intoaccount(as shown in Fig. 10) we find the values forA andBequal to 231020 and 0.056, respectively, which are veryclose to the values obtained for diffusion in amorphousalloys2 and interdiffusion in chemically inhomogeneous me-tallic multilayers.15 Following the approach as discussed byShewmon36 the preexponential factorD0 can be expressedas:

    ln D0 = lnsga2fy0d + SDSkB D , s3dwhereg is a geometry factor,a the effective jump distance,y0 the effective jump attempt frequency,f the correlationfactor, andDS the entropy for diffusion. Using Eqs.(2) and(3) the values for the constantsA andB can be written as:

    A = ga2fy0, B = kBE/DS. s4d

    With the calculated values ofB andE the entropy termDSfor the present sample would be about 7kB, which is muchsmaller as compared to 19kB56kB observed for amorphousalloys and close to the value of 8kB15kB obtained for inter-diffusion in chemically inhomogeneous multilayers. Thevalue of 7kB would roughly correspond to a cluster of sevenatoms15 that may move through the defects. This wouldmean that diffusion in the chemically homogeneousmultilayer would not be highly collective but would involve

    a relatively small group of atoms, indicating a much fasterdiffusion as compared with that of bulk amorphous alloys.The values obtained in the present case can be comparedwith the values obtained for iron self-diffusion in amorphous57Fe70Zr30 s3 nmd /Fe70Zr30 s4 nmd isotopic multilayer, pre-pared by ion beam sputtering and measured by nuclear reso-nance reflectivity of synchrotron radiation.21 The obtainedvalues of the activation energy and the preexponential factorwere,E=0.42 eV andD0=1310

    17 m2 s1 which are withinexperimental errors comparable to the values obtained in thepresent case.

    There has been much discussion in the literature regardingthe effect of preparation techniques on the diffusivity. Forexample, in a number of studies37,38 diffusivity of a numberof impurities like Au, Cu, Fe, and Ti has been measured foramorphous films of NiZr produced by coevaporation. Inthese films no variation of the diffusivity was observed withstructural relaxation. The authors attributed this to the factthat the evaporation produced well relaxed samples. Further-more, Faupelet al.,39,40 found a significant isotope effect inthe diffusivity of Co in melt-spun amorphousCo76.7Fe2Nb14.3B7 while in sputter deposited amorphousCo51Zr49 no isotope effect was observed. This difference wasagain attributed to a difference in the structure of as preparedmelt-spun and sputter deposited amorphous alloy. In thiscontext it is interesting to observe that in the present case,the films produced by two different techniques, namely mag-netron sputtering and ion beam sputtering have similar dif-fusivity, suggesting that they are similar in structure.

    IV. CONCLUSIONS

    In the present work self-diffusion of iron in chemicallyhomogeneous amorphous Fe67Zr33 isotopic multilayers hasbeen measured by neutron reflectivity. Careful examinationof the isotopic multilayer structure with neutron and x-rayreflectivity reveals that even after the longest annealing timesno chemical inhomogeneity develops in the multilayer belowan annealing temperature of 523 K. Above this temperaturethe phase separation of Fe starts at 573 K and at 673 K abouthalf of the amorphous structure precipitates out in nanocrys-talline grains of iron at the interfaces. The activation energysEd, and the prefactor for diffusionsD0d in the system sup-ports the universal typeED0 correlation. This correlationalong with the observed value of the activation energy sug-gests that the diffusion mechanism in the present case is nothighly collective in contrast to melt spun metallic glasses;instead it involves only a small group of atoms.

    ACKNOWLEDGMENTS

    Thanks are due to Dr. Fabio Raimondi, General EnergyResearch, Paul Scherrer Institute, for providing help in x-rayphotoelectron spectroscopy measurements.

    FIG. 10. Correlation between the preexponential factorD0 andthe activation energyE for amorphous and crystalline alloys(takenfrom Ref. 2); (h) corresponds to the present study.

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