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KINETICS OF MULTILAYER AMORPHISATION AND THE EFFECTS OF DEFORMATION AND
DISSOLVED OXYGEN
A. Yavari, P. Desre, F. Bordeaux
To cite this version:
A. Yavari, P. Desre, F. Bordeaux. KINETICS OF MULTILAYER AMORPHISATION AND THE
EFFECTS OF DEFORMATION AND DISSOLVED OXYGEN. Journal de Physique Colloques, 1990,
51 (C4), pp.C4-23-C4-36. �10.1051/jphyscol:1990403�. �jpa-00230763�
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Colloque C4, suppl6ment au 11-14, Tome 51, 15 juillet 1990
KINETICS OF MULTILAYER AMORPHISATION AND THE EFFECTS OF DEFORMATION AND DISSOLVED OXYGEN
A.R. YAVARI, P. DESRE and F. BORDEAUX
LTPCM-CNRS UA 29. Institut National Polytechnique de Grenoble, BP. 75, Domaine Universitaire, F-38402, Saint Martin dfH&res. France
RCsumB
-
Les conditions dkfinissant le rkgime de diffusion de Darken ne sont jamais satisfaites au debut d'amorphisation dans les multicouches B cause d'une forte assymetrie des mobilitks des constituants, ce qui creC des contraintes intemes et la loi en t pour les cinCtiques du dCbut de croissance de couches. Pour la suite, nous comparons les Ctudes cinitiques faites par calorimeme ?I balayage sur des couches de mgmes metaux obtenues par colaminage et par des techniques de dCp8t .Nous prksentons des mesures de % d'oxygkne en solution et discutons de son influence sur l'amorphisation de la matrice.Nous considCrons Cgalement les cinCtiques d'amorphisation lors d e recuits isothermes e t lors de traitements thkrmomkcaniques comme dans le broyage de multicouches et concluons que la viscositC des couches amorphes B la tempCrature effective de dCformation joue un role important dans le "mechanical alloying".Abstract
-
Because of the assymmetry of the mobilities of the constituent atoms,the conditions defining the Darken diffusion regime are never satisfied in the initial stage of amorphisation in multilayers and this results in the development of large internal stresses and the the t law for the mixing kinetics. For the subsequent diffusion-controlled regime, we compare calorimetric studies of amorphisation kinetics in multilayers of the same metals prepared by cold-rolling and by sputtering. We next study the effects on the amorphisation kinetics, of oxygen present in solid solution. Finally, we compare the kinetics of multilayer amorphisation during isothermal annealing and during thermomechanical treatments as in mechanical alloying. We conclude that the viscosity of the amorphous interlayers at the effective deformation temperatures is a key variable in amorphisation by mechanical alloying.Since the earlier studies/l,2/ of amorphous alloy formation by solid-state reaction in AB type multilayers during isothermal annealing$ has been shown that mechanical alloying of A-B mixtures of elemental powders can also result in the formation of amorphous alloys in many systems /3,4/. This symposium provides an opportunity for the simultaneous presentation of results obtained both techniques.Amorphisation of AB multilayers occurs by thermal diffusion during appropriate heat treatment in alloy systems where the heat of mixing AHmi, is strongly negative and one element diffuses much faster than the other or DB >> DA (for a review see Johnson 120.
It has also been shown that certain configurations of grain boundaries are required if formation of amorphous interlayers is to precede that of the intermetallics in the experimental time-temperature window.In particular in Ni-Zr multilayers, amorphous alloy nucleation and growth begin at triple boundaries where two Zr grains join a nickel interface/5/.Atomic configurations on grain boundaries can usually be modeled by an m a y of dislocations and many such configurations resemble motifs such as trigonal prisms/6land other polyhedra pre- dominant in amorphous alloys.For this reason,while there is little or no thermodynamic banier to the nucleation of alloys with AHmi, cc0 , growth of the amorphous version of such alloys is kineticly favored at certain grain boundaries. We suggest that the Zr-Zr grain boundaries contain a network of Zr mgonal prisms 161 with half of the Zr atoms belonging to each of the grains on the two sides.The fast diffusing nickel atoms which first penetrate along these grain boundaries will decorate these prisms' centers to generate a chemical short-range-order predominant both in amorphous and crystalline intermetallic structures such as that of NiZr which is isostructural with CrBl81without the long-range intermetallic crystalline order excluded by the grain boundary topology.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1990403
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In the early stage of amorphous alloy growth at the AB interface, the growing alloy layer thickness X may scale with annealing time t. This is the so-called interface reaction-banier-controlled regime(see for example/9/) where B atoms amving through the already formed alloy layer must await the advancement of the AB/A interface into the A layer thickness. As the diffusive flux of B atoms through the increasingly thick AB alloy layer drops off, the interfacial reaction for accomodation of arriving B atoms on an interfacial site is completed before the arrival of a subsequent B atom and the regime changes over to diffusion-controlled kinetics with X scaling with (t)'/2
.
Although large negative heats of mixing and fast diffusion of one of the constituents are accepted as independent criteria for amorphisation by solid-state reaction,the interdiffusion coefficient D is in fact dependent on AHmi,
.
For example in a regular solution, they are related via the Darken thermodynamic factor/lO/.
In addition to the atomic diffusion, the intense deformation occuring simultaneously with alloying during ball- milling and cold-rolling has been thaught to contribute to the amorphous AB layer growth kinetics. We will therefore discuss the different effects of such intense deformation on the atomic diffusion kinetics in relation to the Darken regime of interdiffusion.
Furthermore many metal matrices such as Zr, Ti and Hf which amorphise easily by solid-state reaction dissolve at ambiant temperature more than 30 at% of various gas atoms. We will follow the presence of such oxygen content from the as-prepared multilayers to the amorphous phase after the mixing reaction and through crystallisation at higher temperatures.
2
-
SOLID-STATE-REACTION IN THE DARKEN DIFFUSION-CONTROLLED REGIME;Consider the AB diffusion couple (2 semi-infinite rods) with atomic diffusive jumps occuring along the x- direction perpendicular to the AB interface as treated by Darken/lO/with the origin at x=O far from the AB interface where no diffusion occurs.
The total flux Ji of component i=l or 2 (for A and B) across the AB interface is given by :
where c i is the i-component atom fraction and C ni =nl +n2 is the total atom density(moles/cm~) or concentration and v is the velocity in the x-coordinate of any non-diffusing markers at the AB interface. If it is assumed that the molar volume V of the alloy is independent of composition (nl +n2 = const), which is equivalent to the statement, dntdt =0, it follows /l01 that
v=(D1 -D2)
.
dcl/dx andThe validity of the often used expression D =clD2 +c2D1 depends therefore on the assumption of constant atom density n.
Furthermore D1 and D2 themselves are not necessarily independent of composition. For example in regular solutions
Di = Di,id ' (1
-
2AHmiX(ci) / RT) andD = (clD2,id +
.
(1-
2AHmix(ci) l RT) (2)where Did is some dilute or ideal solution reference value and the heat of mixing AHmix scales with l/cl.c2.
Since the diffusion of the fast diffusing element D2 >> D1 , one can write approximately
D = clD2 (1
-
2AHmix/ RT) for an effective diffusion coefficient for multilayer amorphisation. Applied to amorphisation of systems such as NiZr where -Mmix >> RT, we can use D = -2cl.D2.
AHmix / RT andD = -2 cl.DZ0 exp(
-mdiff/
RT)-
AHmix / RT orln D = In (-2clDz0 AHmix/ RT)
-
AHdiff/ RT (3)where Mdiff is the activation energy for diffusive jumps of species 2=B. If D(T) can be measured, an Arhenius plot should yield AHdiff with some curvature intervening due to the temperature dependence of the pre- exponential.
In reality the Darken condition, dn/dt = 0 , is never satisfied during amorphisation by solid-state reaction as atomic volumes Vi of constituents of glass-forming systems are quite different. For example VNiNz, c 0.5.
For such situations, Stephenson / l l/, using a synthesis of the Darken analysis and the treatment of stress effects by Larch6 and Cahn/l2/, has recently shown in detail that large internal stresses develop during interdiffusion of A and B in AB multilayers in case of large differences in the products MA. VA and MB. VB where the mobilities Mi = Di /(RT- 2AHmix) in regular solutions. The modified Darken regime then corresponds to
MA'VA
-
MrVB = 0.In the case of the Ni-Zr couple, VNi = 0.5 Vzr and 106 > D N A > 104 (see/l3/), such that MNi.VNi /MZr.VZr
> 104. Stephenson demonstrates that the forced excess flux of for example nickel "volume" results in a stress gradient with stresses that can rise to :
For an order of magnitude, one can write
where we have used d2G/dc2 = (RT/cNi.(l-cNi)) (1
-
2AHmix /RT)and -AHmi, >> RT/V for strongly interacting AB systems.When MBVB/MAVA >> 1, diffusion and interpenetration are halted by such large internal pressures countering the thermodynamic driving force for mixing AHmix until such stresses are relaxed , unless the diffusion distance
X is already sufficient for such relaxation to occur in a time shorter than t = x2 /2DB. If not, the kinetics of further interdiffusion are controlled by the diffusion of the slow component atoms A or by any plastic deformation which can relax the internal stress P at a rate dP/dt = (-E/6q) P where E and q are the elastic modulus and the viscosity respectively.
The reader is referred to Stephenson's work for full details of which it is concluded that for given amorphous
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systems such as those studied here, the diffusion kinetics are initially plastic deformation-controlled and scale with t but as the diffusion distance increases, they switch over to the Darken diffusion-controlled regime and scale with t1f2
.
This is reminiscent of the switch from interfacial reaction barrier-controlled t o diffusion-controlled regimes in treatments such as that of Gosele and Tu/9/already discussed earlier for an amorphous layer growing between two crystals.The treatment of Stephenson as evoked so far is valid for diffusion into an existing amorphous phase but it is equally valid for fast diffusion of an interstitial component B into an A crystwl l/. If one supposes that such an A lattice becomes amorphous at a certain critical concentration of B atoms, then the Stephenson treatment can explain the kinetics of the early stage of amorphisation by solid-state reaction.
It is reasonable to suppose that B atoms must penetrate into the A crystal before amorphisation can occur so that it is difficult to imagine an atomic mechanism providing an interfacial attachment barrier at the amorphous ABIcrystalline A interface. We therefore conclude that as far as phenomenological treatments are concerned, a linear t law for the early stage of the amorphisation reaction, if observed, is more likely to be due to deformation rate-control than to interfacial attachment banier-control.
Amorohisation kinetics in multilavers with constant modulation lenethg:
The early growth kinetics scaling with t probably switch over to the Darken regime already at thicknesses of few atom layers. In most experiments, mixing to such an extent occurs during multilayer preparation such that usually only the t1I2 kinetics are observed.
Cotts et a1/14/ and Highmore et a11151 first studied such growth kinetics in sputter-deposited Ni-Zr multilayers using differential scanning calorimetry. These authors showed, assuming a constant heat of reaction AHmix per unit thickness W (dAHmix/dw = const ), dn/dt=O and the other assumptions implicit in the Darken analysis and the regular solution model, that the product of the total heat release as measured by the area of the D S c curve, A(T), and its rate of change, dA/dT in isochronal annealing should scale with the exponential exp(-AHdiff/kT), where
eiff
is the activation energy for diffusion-controlled amorphisation.TEMPERATURE (OC1
Figure 1: Plots of ln(A
.
dA/dt) vs ID' for Ni-Zr multilayers where A is the area under D S c exotherm corresponding to AHmix obtained at various heating rates11 51Figure 1 shows the results of Highmore et aV15/ presented as ln(A(T)-dA(Tf/dT) versus lfl
.
The constant slope yields AHdiff = 106 Wmole. At the same time the total area A corresponding to the heat of reaction occuring prior to the onset of crystallisation was reported to be 28kJig.at. compared to AHmi,= 50 kJ/g.at. /16/.This latter result indicates that the as-prepared samples were already partially amorphised (which also implies that only diffusion-controlled behavior is expected). Nevertheless the constant slope AHdiff/k observed over a broad T-range at various heating rates confirms the validity of their approximations. The deviation from linear behavior at high-T is a result of near completion of the reaction.
vers re pared hv CO-deformation:
Figure 2 Shows a SEM secondary electron image of an AI-Pt multilayer prepared by cold-rolling of AI and Pt ribbon spirals/l7,18/. A significant volume fraction of this multilayer is already amorphous/l9/ in the as- prepared state as witnessed by the amorphous halo visible in its x-ray diffraction pattem of figure 3.
2 0 (DEGREES)
Fimre 2 (tow lefo: SEM cross-sectional image of A1-Pt multilayer prepared by cold-rolling/l8/.
Firmre 3 (top right): x-ray diffraction pattem (Cu-Ka) for Al-Pt sample of figure 2.
Fimre 4 (ri~ht): TEM cross-sectional image of Ni-Zr multilayer prepared by cold-rolling/l9/.
Figure 4 shows a cross-sectional TEM image of a Ni-Zr multilayer prepared by the same technique. The grey teatureless areas are amorphous/l9/. The subsequent continuation of the amorphisation reaction can be followed by calorimetry. Figure 5 shows such data for Ni-Zr and AI-Pt multilayers plotted in the same fashion as those of Highmore et a1 /15/ of figure 1
.
Two major differences are evident. Firstly, the plots are non-linear indicating atCOLLOQUE DE PHYSIQUE
first cite, a temperature dependent activation energy. Secondly the slopes, AHdiff/k, are much lower than those reported for vapor-deposited or sputtered multilayers, yielding for example AHdiff < 70 Wmole for NiZrl201.
r 10 K / m i n
* 4 0 K l m i n 80 K l m i n
Ni-Zr
I t I I 1
1 . 5 2 2.5
1 0 3 F (K-l)
Fimre 5: Plot of ln(A
.
dA/dt ) vs l/T for multilayers of figures 2-5 prepared by cold-rolling, A is the area of DSc exotherm corresponding to amorphisationThe non-linearity of the plots can be attributed to a broad range of layer thicknesses in sampler, prepared by codeformation/21/ in the following manner: Figure 6 shows plots of ln(~,~.(dx,,/dT)) versus 1/T reported by Rubin and Schward221 for Ni-Zr multilayers prepared by sequential vapor-deposition were the amorphous layer thickness xarn(T) is obtained from isochronal resistivity measurements. Labels 1x,2x and 4x in this figure correspond to curves obtained at 10 Wmin for multilayers with increasing initial thickness n times X per layer and 2x-B corresponds to the 2x sample heated at 2 Wmin.It is seen that the deviation from linearity corresponding to the completion of the amorphisation reaction begins at lower temperatures for the thiner layers. This observation clearly shows that the non-linear behavior and the apparent variation of the activation energy in multilayers prepared by codeformation as observed in figure 5 are in fact due to a contineous shifting of ln(dA/dT) with the successive disappearance ,during isochronal heating ,of layers with various thicknesses starting with the thinest initially pure constituent layers
.
Figure 6 : Plot of In (X,,
.
dx,/dt ) vs l/r for Ni-Zr multilayers of different modulation lengths obtained from isochronal resistivity measurements.X, is the amorphous layer thickness at time t 1221.
The lower value of the activation energies(s1opes) is more difficult to explain. Furthermore, at higher temperatures, the appearance of a broad endothermic peak masked the details of the exothermic reaction kinetics in the case of Ni-Zr and Ni-Ti ,Ni-Nb and Ni-Mg multilayers prepared by codeformation but this phenomenon did not occur for the AI-Pt multilayers which do not dissolve oxygen. In order to better understand these anomalies we undertook a study of the oxygen content of the Ni-Zr multilayers.
3 - OXYGEN CONTENT IN Ni-Zr MULTILAYERS PREPARED BY COLD-ROLLING ND AFTER..AMORPHTSATION AND CRYSTALLISATION:
For many metal matrices with solid-state amorphisation capability, the binary metal-gas phase diagrams show solid solubilities in excess of 10 at% of gas atoms at room temperature.Examples are Ti-0,Ti-N,Nb-0,Zr- N and Zr-0. In particular in Zr, eventhough oxygen solubility drops with decreasing temperature, nearly 25 at%
oxygen and almost as much nitrogen 1231 are retained in solution at equilibrium at 300K.
The partial molar heat and entropy of dissolution of oxygen in Zr have been determined experimentally at high temperaturesJ24J. For Zr0.7500.25, AH(1/202) = -400 kJ1mole and AS(l/2O2)= -50 J/K.mole. Using these high-T values for a f i s t approximation of the free energy of oxygen dissolution at room temperature and the relation PO2 = exp(-2AG(l/2O2)JRT) for the oxygen partial pressure one obtains values below experimentally accessible vacuum 1evels.Although highly approximate, this result shows clearly that one cannot remove the dissolved oxygen by pumping alone.
We measured oxygen contents on cross-sections of multilayers of nominal composition Ni2Zr prepared by cold- rolling/l7,19/using wavelength dispersive x-ray microanalysis (WXDA) in a Carnebax apparatus under a vacuum of 10-10bars. As shown in the concentration profiles of figure 7, about 4 at% global oxygen content was detected in the as-prepared multilayers.
The thickness of the probed spot is more than the thickness per layer and some amorphisation has already occured during preparation by cold-rolling such that instead of pure Ni and Zr layers, we observe only fluctuations in Ni, Zr and 0 contents. However the correlation of the maxima of the 0 profile with those of Zr and the minima of the 0 profile(zer0 to the resolution of the probe) with the maxima of the Ni profile indicate that all of the oxygen is in the Zr layers thus corresponding to more than 10 at% dissolved oxygen in Zr under a vacuum of 10-lO bars at 300 K
.
This result is consistent with the very low expected oxygen partial pressures indicated by the very negative experimental values of AG(l/202).Figure.8 shows similar profiles for the Ni2Zr multilayer after amorphisation annealing at 28S°C(558 K). It indicates near complete smoothing of the concentration profiles after Ni diffusion into Zr. It also shows that the global oxygen content remains unchanged. Figure 9 shows another set of profiles for the amorphised multilayer after crystallisation at 600°C(873 K). The oxygen is still there but redistribution and segregation of the three elements have occured. The profiles present extrema consistent with Ni and Zr-rich intermetallic crystalline or amorphous zones but also regions of very high oxygen content which will be shown to correspond to the formation of Zr02 crytals. Finally figure 10 shows for comparison concentration profiles obtained on the cross- section of a Ni2Zr metallic glass tape prepared under pure argon gas showing near absence of oxygen and as expected, homogeneous distribution of Ni and Zr in the probed section.
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COflRECTED ATOMIC CONCENTRATION [XI c""'d' COMECIEO AIOttIC CONCEttTRATION l%) -I4
%NI /-
I\/
. - ,
20 20
10
O ' i i * i i i i i i i
Figures 7 and 8: Cross-sectional concentration profiles for Ni,Zr and 0 in cold-rolled Ni-Zr multilayers obtained by WDXA before(1eft) and after(right) amorphisation by solid-state-reaction.
CORHECrEII ATOI4IC COIIC~IITfIL.1 1011 (\I " L=- YI~, COdRiCTEn ATOMIC COElCiHTRAIION (I1 -'-U
Figure 9 (left): Same as figures 7 and 8 but after crystallisation at 600°C.
Figure 10 (righQ: WDXA concentration profiles for Ni2Zr metallic glass tape obtained by liquid quenching Figure 1 l(below): The onset of crystallisation in the Ni-Zr reacted multilayer of figure 8 as detected during in-situ
,
heating in the x-rav diffractorneter.T r:
o ZrOz cubic "
als.os8 ' NI 1
Figure 11 shows the x-ray diffraction pattern of the amorphised Ni2Zr multilayer at the onset of crystallisation during in situ annealing under argon gas(some pure nickel is still present). It is seen that apart from peaks due to unreacted Ni , Bragg peaks of cubic Zr02 with lattice parameter a0=0.509 nm appear first, indicating that it is the crystalline phase that nucleates first. Later on, most of this is transformed into another cubic Zr02 with a0=0.462.
Kang et al/25/ have shown that in the case of Ti-Si multilayers, Si atoms penetrate into Ti to form TiSi2 layers and in so doing, they push back the oxygen atoms in the titanium matrix into the depths of the Ti layers.
As Bordeaux has suggested/21/, Ni penetration into the Zr layers during amorphisation may cause a similar redistribution of dissolved oxygen resulting in strong oxygen enrichment in the inner Zr zones and the eventual nucleation of
m.
While oxygen presence even in small quantities has been shown to facilitate amorphisation by solid-state reactionl261, the mechanism that produces this phenomenon has not yet been determined.
We have shown recently that sharp concentration gradients VC occuring during multilayer amorphisation result in the suppression of the thermodynamic driving force for crystallisation of the amorphous interlayers. As mixing proceeds and these layers grow thicker, the concentration gradient flattens and the driving force for crystallisation is restored beyond a certain critical amorphous layer thickness/27,28/. Desr6 has now extended this treatment to ternary systems/29/. This more recent work indicates that due to the expected difficulty of dissolving oxygen in NiZr intemnetallic compounds, the presence of oxygen enhances amorphisation of Ni-Zr multilayers by increasing the critical thermodynamic thickness for the onset of crystallisation by about 50%.
There is also new evidence1301 that oxygen content influences the kinetics of amorphisation. Measuring the kinetics of the evolution of various x-ray Bragg peak intensities during in situ annealing, we found important variations of the kinetics with the degree of purity of the inert gas in the diffraction chamber. The kinetics were enhanced with oxygen contamination in the gas phase.The mechanism for such an effect is not clear. In particular the diffusivities of transition metals such as Ni in matrices such as Ti and Zr are more likely to be slowed than enhanced by the presence of dissolved oxygenBl1.
The following mechanism can be tentatively imagined: Even if no oxygen is present in the initial Zr , the Ni-Zr multilayers will take up oxygen during multilayer preparation in air.When they are subsequently heated under oxygen-free gas or high vacuum such that the partial pressure of oxygen is lower than the value in equilibrium with the oxygen concentration in solid solution, some of the up to 30 at% dissolved oxygen will leave the Zr layers via dislocation cores and grain boundaries. We saw that under 10-10 bars, the 0-content is reduced to about 10%. Thus oxygen will flow out of the Zr layers as the nickel atoms flow into those layers during the amorphisation annealing.While the system is reducing the dissolved 0 level towards the value in equilibrium with the ambiant gas, all the grain boundaries and dislocations which serve as diffusion paths to oxygen but are, as mentioned earlier, also geomemcally the preferred sites for amorphous phase nucleation and for nickel penetration will be saturated by oxygen atoms.The oxygen outward flow can thus slow down the reverse flow into the Zr layers, of nickel atoms which have little affinity for oxygen. The lower the partial pressure of oxygen during amorphisation annealing the stronger the driving force for oxygen flow towards grain boundaries and dislocations and the slower the kinetics of Ni penetration and amorphisation/30/ provided ofcourse the initial presence of dissolved oxygen.
We mentioned earlier that the calorimetric study of the amorphisation kinetics in Ni-Zr multilayers prepared by cold-rolling were hampered by the appearance of a broad and strong endothermic phenomenon (see figure 12) which distorts the details of the exothermic mixing reaction.Hollanders et a1 also reported this anomaly
COLLOQUE DE PHYSIQUE
during the mixing reaction in Ni-Ti multilayers 1321. Merk et a1 1331 attributed a similar observation of a broad endothermic peak in isochronal DSc thermograms of mechanically alloyed Ni-Zr to a complex redistribution of the constituents among the simultaneously present amorphous and intermetallic phases.
88 FILEIBCR?Z M TEMPERATURE <K> DSc
Figure 12: DSc thennogram for Ni-Zr multilayer as-prepared by cold-rolling (at 40 K/min). Dotted base line is trace of second heating cycle. The endothexmic reaction dominates the exotheric amorphisation signal at T > 700 K. Crystallisation begins with small exotherm at 830 K.
Consistent with the preceeding discussion of oxygen effects, a simpler explanation can be offered as follows: If some dissolved oxygen(and1or hydrogen) are present in the initial zirconium or titanium used in these experiments, they will be partially released during heating in an oxygen-free atmosphere and possibly replaced by nitrogen or other gases flowing in the calorimeter.
As noted earlier, the heat of dissolution AH(l/2O2) of oxygen in Zr is about 400 Wmole and the evacuation of for example 25 at.% 0 in the Zr layers will result in about 33 kJ/g.at. of Ni2Zr multilayer. In the calorimeter, this will produce a large endotherm which will be broadened for kinetic reasons. Since 0-Zr and 0-Ti interactions are more strongly,attractive than those of N-Zr and N-Ti , the replacement of the dissolved 0 by N will also produce a strong endothermic effect. We found that the endothermic phenomenon is less important when the Ni-Zr multilayers are stored under vacuum and more important when stored under pure oxygen before being transferred to the ca1orimeter.A more quantitative description requires treatment of the evolution of concentrations of all dissolved gases.Other investigations are currently underway by Saiter I341 using combined calorimetric and thermogravimemc measurements.
We were brought to study the role of oxygen in the amorphisation following the results presented in the previous section showing faster amorphisation kinetics in multilayers cold-rolled in air compared to those deposited in chambers under high vacuum.
The fast amorphisation kinetics mechanical alloying (cold-rollinglball-milling) will be discussed in the next section. As for the kinetics of continued amorphisation in such samples during subseauent heat treatment once the deformation is interrupted, the analysis of this section, while explaining most of the experimentally observed effects of oxygen presence, does not indicate any oxygen role in the obierved accelerated kinetics and in particular the lower activation energy AHdiff reported in the previous section. The accelerated kinetics during post- deformation annealing can therefore be attributed only to a higher density of defects especially grain boundaries as grain size decreases to a few nm before amorphisation in the highly deformed samples/4/.
4
-
m E T I C S OF MULTILAYER AMORPHISATTON BY ISOTHERMAL ANNEALING AND BY MECHANICAL ALLOYING:Various reports on Ni-Zr multilayers with layer thicknesses X I 100 nm indicate nearly complete amorphisation by solid-state reaction after 1 or 2 hours annealing time at temperatures in the range of 285 to 300°C( 558 to 573 R). On the other hand, depending on the experimental conditions, mechanical alloying of pure A and B elements (such as Zr and Ni ) often results in large amorphous volume fractions after milling times of the order of 5 hours (see for example/4/).
Since ball-milling initially produces particles constituted of AB multilayers/35,36/, one may suppose that during subsequent milling, solid-state reaction occurs in such multilayers in the same manner as in purely thermal treatments in which case the activation energy AHdiff may be the same.Under these assumptions, it remains only to determine the powder's effective temperature T knowing that the intense deformation of the powder particles hammered by energetic ball collisions results in significant local heating.If for Ni-Zr multilayers partial amorphisation(say 50%) occurs after time tl = 1 hour of isothermal annealing at T1 = 558 W20/, and after for example a time t2 = 3 hours during thermo-mechanical alloying, the temperature T2 during the latter process can be estimated by the relationt37k
In ( t l / t2) = (AHdiff/k).(l/T1 (6)
Using AHdiff=106 kJ/ g.at. for Ni-Zr derived from figure 1, we obtain T2 = 270°C(543 K) as the effective temperature of the NiZr multilayer particles during milling. It remains then only to show that the powders can indeed heat up to such temperatures by the deformation work.
For example Schulz et aV381, using Auger depth profiling, directly measured the extent of nickel penetration into Zr layers after various milling times and used these milling times and published values of Ni diffusivity to calculate the effective temperature (180°C). They then compared this temperature with estimates of the temperatures attained by deformation-induced adaibatic heating that occurs on the impact of two balls on powder particles.
Unfortunately, this procedure is inherently contradictory for a simple reason: each powder particle in fact spends a very small fraction of the total milling time being deformed in impact position between colliding balls or ball and vial. While its temperature does rise at such instances almost adiabatically, it will also cool down quickly because of its large surface to volume ratio such that estimates of "impact temperatue" have little to do with the powder's effective temperature during milling. Estimates of the "impact temperature" can only be used with the "integrated total impact time" which must be calculated from the number of impacts per unit milling time and corrected for the distibution of "impact temperatures" due to different impact geometries and consequent variations in the intensity of deformation per impact.
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A similar but simplified case is that of mechanical alloying by repeated cold-rolling. In this procedure, large regular shaped platelets of thick(200 pm) multilayer assemblies can be subjected to successive rolling passes with total deformation per pass fixed only by the distance separating the two rollers/l7/. On each pass, macroscopic volume elements, corresponding for example to various powder particles in ball-milling, will all experience the same deformation and rise in temperature. The sample can be examined after each pass or n number of passes.
We have seen earlier that in the case of several amorphisable AB multilayers and in particular for Ni-Zr, the experimental conditions resulted in the amorphisation of about one-half of the multilayer volume after about 50 rolling passes. Since the deformation time per pass for each volume element is less than 0.1 seconds, this represents a total thermomechanical processing time tz C 5 second. Applying eq.(6) as we did earlier using for comparison tl= 3600 S and T1 = 560 K for isothermal amorphisation by solid-state reaction, we find that the temperature must have attained T2 > 800 K during each cold-rolling cycle.
Since crystallisation of the amorphous product in the DSc occurs at T 2 800 W14,15/, this kineticly required T2 value is at the upper limit of the allowed T-range and to render the equivalency with amorphisation process during isothermal annealing at least plausible, we must show that the the heat released by the deformation is sufficient to heat the entire multilayer volume up to T2 > 800 K.
We have estimated1191 the near adiabatic self-heating generated by the plastic deformation during such cold- rolling. Using
AT
=l
ooY- Em. da / ( v m ) (7)where the yield stress ooy is derived from micro-hardness measurements, e and k are the strain and its rate, m is the strain-rate-hardening coefficient and
5
and V, are respectively the specific heat and volume. With such temperature increases,it was found that T2 < 450 K far below T2 > 800 K kineticly required by eq.(7) for the equivalence of the two amorphisation processes.It must therefore be tentatively concluded that somehow equivalent degrees of amorphisation during the thermomechanical treatment occur at significantly shorter times andlor lower temperatures than during isothermal annealing (without deformation) and that use of available atomic diffusion coefficients for estimating the kinetics of mechanical alloying leads to erroneous results.To explain these differences, several possibilities can be mentioned.
One can suppose, as we have previously/l9/, that effective diffusion during mechanical alloying is controlled by short-circuit paths such as grain-boundaries and dislocations/l0/with a significantly reduced activation energies AHdiff. However Frommeyer and Wassermann/39/ have shown that while dislocation densities up to 1014 cm-2 can be attained during heavy deformation of A-B metal composites, a large part of these dislocations seem to be released when the layer or fibre thickness drops below 60 nm. This still leaves the grain boundaries as short circuits and it has been shown that grain size decreases progressively to 10 nm or less prior to amorphisation during mechanical alloying/4/.
Contineous creation of fresh AA3 contact surfaces regenerating fast-diffusion conditions during mechanical alloying can also contribute to faster amorphisation.
A point which has received less attention is the role of the intense deformation on the relaxation rate of internal stresses in the diffusion layer. Using the conclusions of Stephenson/l l / we pointed out that in the early stage of amorphisation when the amorphous layer thicknesses are small, the asymmetry of the product of atomic mobility and volume, MiVi , for the constituent species results in large internal stresses that oppose the thermodynamic driving force for mixing (due to large negative AHmix) and that local deformation is required to relax such fast-
diffusion-generated pressures for further mixing to occur. Obviously externally imposed plastic deformation can help relax these microscopic interlayer stresses. This raises the interesting question of the deformation conditions in the amorphous interlayers.
Depending on the temperature attained during deformation, the amorphous layer can have viscosities of the order of c 1010 Poise such that it will deform as easily as the pure crystal layers under the prevailing stress ooy and strain-rate E following ooy = ve&/3. As such, the amorphous layer thickness will not only increase by deformation-heat-assisted atomic diffusion during each impact event(bal1-milling) or rolling pass(co1d-rolling), but will also decrease due to the deformation itself. Thus while the amorphous volume-fraction contineously increases as monitored for example by x-ray diffraction or calorimetry, the amorphous layer thickness or the diffusion distance X that controls the amorphisation rate can remain constant. This phenomenon ,which also allows the layer thickness to remain below the thermodynamic critical thickness for intermetallic phase nucleation/27,28/ is in our view essential to a better understanding of the kinetics of amorphisation by mechanical alloying and will be fully discussed in a future paperl401.
5 - CONCLUSIONS:
After nucleation at A-B-A triple grain boundaries, early amorphous layer growth does not obey the conditions for the Darken diffusion regime. Its rate is likely to scale with that of the relaxation of internal stresses generated by excess net flow of fast diffusing B atoms/ll/. However this growth regime which is expected to follow a linear t law, is not likely to be observed experimentally because as we showed in section 2, various experimental results indicate that both sputter-deposited multilayers/l5/ and those prepared by cold-rolling/l8,19/
are already partially amorphous in their as-prepared states. In such samples , the already formed amorphous layer thickness slows the kinetics down to the diffusion-controlled regime that is expected to scale with tlfl.We compare the kinetics of amorphous layer growth in this regime in multilayers prepared by sputtering and by cold- rolling and find that the latter are significantly more rapid. In particular the activation energy for atomic diffusion seems to be smaller in post deformation annealing. To explain this observation, in section 3 we have examined the different possible effects of a high oxygen content in the cold-rolled multilayers. The results indicate that although dissolved oxygen can stabilise certain amorphous compositions against compound nucleation,and that pumping on such dissolved oxygen by annealing under high vacuum can slow-down nickel diffusion and amorphisation, it cannot explain the faster kinetics of post-deformation amorphisation and this phenomenon is consequently attributed to a high density of grain boundaries and vacancy defects in cold-rolled multilayers. Finally in section 4 we consider the even faster kinetics of amorphisation during intense deformation
.
Considering meclianical alloying( cold-rolling / ball milling) as a thermomechanical treatment, we find it important to distinguish between the global multilayer deformation rate and that of any amorphous interlayers. We conclude that the amorphous phase viscosity at the deformation temperature is a key variable in amorphisation by mechanical alloying/40/.&owledzement:
Thanks are due to Niwle Valignat for the determination of cross-sectional wncentation profiles by WDXA.
COLLOQUE DE PHYSIQUE
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