Compressed correlation functions and fast aging dynamics in metallic glasses

0.52 MB·English

by  B. Ruta

\\
Compressed correlation functions and fast aging dynamics in metallic glasses
B. Ruta,1,a) G. Baldi,2 G. Monaco,1 and Y. Chushkin1
1)European Synchrotron Radiation Facility, BP220, F-38043 Grenoble, France.
2)IMEM-CNR Institute, Parco Area delle Scienze, I-43124 Parma, Italy
(Dated: 29 January 2013)
Wepresentx-rayphotoncorrelationspectroscopymeasurementsoftheatomicdynamicsinaZr Ni metallic
67 33
glass, well below its glass transition temperature. We find that the decay of the density fluctuations can be
welldescribedbycompressed,thusfasterthanexponential,correlationfunctionswhichcanbemodeledbythe
3
well-known Kohlrausch-Williams-Watts function with a shape exponent β larger than one. This parameter
1
is furthermore found to be independent of both waiting time and wave-vector, leading to the possibility to
0
rescaleallthe correlationfunctions to a single master curve. The dynamics in the glassystate is additionally
2
characterized by different aging regimes which persist in the deep glassy state. These features seem to be
n
universalinmetallicglassesandsuggestanondiffusivenatureofthedynamics. Thisuniversalityissupported
a
J by the possibility of describing the fast increase of the structural relaxation time with waiting time using a
unique model function, independently of the microscopic details of the system.
8
2
PACS numbers: 64.70.pe,65.60.+a,64.70.pv

]
t
f
o I. INTRODUCTION have been reported also in studies of aging effect on
s the intensity of the high frequency tail of the dielectric
.
at Understanding physical aging in glasses is essential spectra11–16. All these worksprovide information on the
m at a technological level, for controlling the material equilibration toward the supercooled liquid phase, but
properties and their temporal evolution, as well as at theydonotgiveanymicroscopicdetailsontheagingdy-
-
d a fundamental level, since glasses are often considered namics in the glassy state. This information can instead
n as archetypes for systems far from thermodynamical be obtained by the investigation,on a microscopic scale,
o equilibrium1,2. However, and despite the strong efforts of the temporal evolution of the structural relaxation
c done in the field, a complete picture of the dynamics in time, τ, which represents the time necessary for the
[
theglassystateisstillmissing. Themaindifficultyarises system to rearrange its structure toward a more stable

1 from the complexity of the glassy properties. When a configuration. Its value can be measured, for instance,
v supercooled liquid is cooled below its glass transition by monitoring the long time decay of the intermediate
0
temperature, T , the system falls out of equilibrium in a scattering function, f(q,t), on a length scale 2π/q,
1 g
6 metastable state which depends on the previous thermal with the wave-vector q corresponding to the mean inter
6 history, and which evolves, with waiting time, through particle distance. The intermediate scattering function
. different states toward the corresponding supercooled is related to the density-density correlation function
1
equilibriumliquidphase. Theexistenceofamultitudeof and contains all the information on the relaxation
0
3 different metastable glassy states which can be explored dynamics in the system on a length scale determined by
1 through different annealing procedures or cooling rates, q. While the dynamics in the supercooled liquid phase
: makes difficult the development of a universal theory hasbeen widely investigatedin the past,the difficulty of
v
for glasses or even a plain comparison between different probingthe particle-leveldynamicsinrealisticmolecular
i
X experimental results. glasses both with experiments and simulations has
r Physical aging in polymeric, metallic or more conven- instead strongly delayed progress in the field. In fact
a tional inorganic glasses, is commonly studied by looking only very few studies exist of the behavior of τ below
at the temporal evolution of a given observable, keeping Tg3,12,17–24. Numerical simulations on a Lennard Jones
fixedotherexternalparameters,suchasthetemperature glass show that for small quenching from an equilibrium
and the pressure of the system. Macroscopic quantities configuration, τ slows down linearly or sub linearly with
like viscosity, refractive index, volume or elastic con- waiting time18 in agreement with previous results on
stants,areusually the subjectofthis kindofstudies3–10. polymericglasses3,12,17. Inaddition,the longtime decay
In these works, the investigated quantities evolve with of the correlation functions can be rescaled into a single
waitingtime,t ,inawaywhichdependsontheprevious master curve, leading to the validity of a time-waiting
w
thermal history and which can be accurately described time superposition principle in the glassy state18,25.
by stretched exponential functions6. Similar results Recently, the aging of a Mg65Cu25Y10 metallic glass has
been studied in both the supercooled liquid phase and
the glassy state by looking directly at the evolution of
the dynamics at the interatomic length scale23. The
a)Electronicmail: [email protected] glass transition has been found to be accompanied by
2
i) a crossover of the intermediate scattering function pre-alloyed by arc-melting under Ti-gettered Ar atmo-
from the well characterized stretched exponential shape sphere. The melt was then fast-quenched with a cooling
- thus described by a stretching exponent β < 1 - in rate of 106 K/s by injecting it on a Cu wheel spinning
the supercooled liquid phase, to an unusual compressed with a 40m/s perimeter velocity. The resulting metallic
exponentialform- defined by a parameterβ >1 - in the ribbonshaveathicknessof22±4µm,closetotheoptimal
glassy state and ii) to the presence of two very distinct value requiredtomaximize the scatteredintensity inthe
agingregimesbelowT . Inparticular,afast,exponential experiments. The ribbons were then held in a resistively
g
growth of τ has been reported for short waiting times, heatedfurnacecoveringatemperaturerangebetween270
followed by an extremely slow aging regime at larger t . K and 1000 K with a thermal stability of less than 1 K.
w
While the latter slow regime has been already reported The temperature of the sample was held at T = 373 K,
both in numerical simulations18 and in experiments on reached by heating from room temperature with a fixed
polymeric glasses3,12,17, the compressed shape of the rate of 3 K/min.
correlation functions and the fast aging regime had not X-rayphotoncorrelationspectroscopy(XPCS)measure-
been reported before in structural glasses. Two similar ments were carried out at the beamline ID10 at the
agingregimeshavebeenrecentlyobservedinanumerical European Synchrotron Radiation Facility in Grenoble,
study of a concentratedsystemof nearly hardspheres20. France. An incident x-ray beam of 8.0 keV (λ = 1.55
In this case, however,the correlationfunctions display a ˚A) was selected by using a single bounce Si(1,1,1) crys-
more stretched exponential behavior, and no signature tal monochromator with a bandwidth of ∆λ/λ ≈ 10−4.
of a compressed shape was reported20. Hard X-rays originating from higher order monochro-
Compressed correlation functions and different aging mator reflections were suppressed by a Si mirror placed
regimeshaveinsteadbeenreportedforoutofequilibrium downstream of the monochromator. A partially coher-
soft materials, where the dynamics is controlled more ent beam with ∼ 1010 photons/s was then obtained by
by ballistic-like rather than by diffusive motions26,27. rollerbladeslitsopenedto10×10µm,placed∼0.18mup-
The previous work on the metallic glass thus suggests a stream of the sample. In order to enhance the scattered
common nature of the dynamics in metallic glasses and intensity, speckle patterns were collected in transmission
soft materials. A very similar faster than exponential geometrybytwoIkonMcharge-coupleddevicesfromAn-
decay and strong aging behavior for the intermediate dor Technology (1024× 1024 pixels, 13× 13 µm pixel
scattering function has been observed also in a Zr-based size each one) installed in the vertical scattering plane
metallic glass by Leitner and coworkers24. In this case, ∼70 cm downstreamof the sample. All pixels of the two
however, this unusual dynamics has been associated CCD detectors were considered to belong to the same q
with the onset of a crystallization process. There are with a resolution of ∆q =0.04 ˚A−1. The detectors were
consequently several questions to clarify: i) are the mountedonadiffractometerandcouldrotatearoundthe
results found in Mg Cu Y really a universal feature center of the sample position, covering a q range up to
65 25 10
of metallic glasses or do they depend on the microscopic several ˚A−1. XPCS measurements were performed for
details of the system? ii) is it possible to find a common different wave-vectorsat and around the first diffraction
description of physical aging for different glasses? iii) peak of the static structure factor which corresponds to
what is the effect played by the wave-vector, q, on the q =2.55˚A−1, therebyprobingdirectlythe temporalre-
p
dynamics? laxation of density fluctuations at the inter-particle dis-
Here, we answer to these questions by presenting a tance 2π/q ∼ 2 ˚A. Time series of up to ∼5000 images
p
detailed investigation on physical aging in a Zr Ni were taken with 7 s exposure time per frame and were
67 33
metallic glass at the atomic length scale. We find analyzedfollowingtheproceduredescribedinRef.29. No
that in this case the dynamics in the glassy state is beamdamagewasobservedandtheamorphousstructure
also characterized by compressed correlation functions of the sample was checked during the whole experiment
and different aging regimes, supporting the idea of bymeasuringthecorrespondingstaticstructurefactorof
a universal mechanism for physical aging in metallic the system.
glasses. This hypothesis is moreover strengthened by
the possibility of describing the aging dynamics using
the same phenomenological exponential growth and
rescaling the results obtained for different systems into
a single master curve. III. RESULTS AND DISCUSSION
As previously discussed, physical aging implies a re-
laxation dynamics which is not the same at all times,
II. EXPERIMENTAL DETAILS
but strongly depends on the sample age or waiting time.
Thetemporaldependenceofthedynamicscanbeentirely
The Zr Ni samples (T = 647 K28) were produced capturedbyXPCSthroughthedeterminationofthetwo-
67 33 g
asthin ribbons by melt-spinning atthe PolytechnicUni- time correlation function G(t ,t ) (TTCF) which repre-
1 2
versity of Catalonia. The Zr and Ni pure metals were sents the instantaneous correlation of the intensity I at
3
indicates the sample age. The width of this diagonal
contour is instead proportional to the relaxation time τ.
The steady slowing down of the dynamics, and thus the
increase in the relaxation time due to physical aging, is
illustrated by the broadening of the diagonalcontour on
increasing the sample age. This effect is clearly visible
in the top panel of Figure 1 where we report data taken
between ∼ 1000 and ∼ 5000 s after temperature equili-
bration. After almost13 hours ofannealing (lowerpanel
of Figure 1), the dynamics was so slow that the inten-
sity along the diagonal covered almost the whole image,
despite the time interval was almost the double with re-
spect to the one reported in the top panel. After this
very long annealing the width of the diagonal contour
seems to be constant with time, as it would be in the
case of stationary equilibrium dynamics. As discussed
later,heretheeffectofphysicalagingisprobablysoslow
that the dynamics appears as stationary at least on our
experimental time scale.
Althoughthedynamicsisnotstationary,theagingissuf-
ficientlyslowthatitispossibletofindtimeintervalsover
which the G(t ,t ) can be averaged and thus to get the
1 2
standard intensity autocorrelationfunction
hI(q,t )I(q,t +t)i
D 1 1 pE
g (q,t)= (2)
2
hI(q,t )i hI(q,t )i
D 1 p 1 pE
where h...i is the temporal average over all the possible
starting times t . The intensity autocorrelationfunction
1
isrelatedtotheintermediatescatteringfunctionthrough
the Siegert relation g (q,t) = 1 + B(q)|f(q,t)|2, with
2
B(q) a setup-dependent parameter31, and its determina-
tion allows capturing snapshots of the dynamics at dif-
ferent waiting times. The Siegert relation requires the
temporal average to be equal to the ensemble average.
FIG.1. Two-timecorrelationfunctionsmeasuredwithXPCS This condition is fulfilled for systems at thermodynamic
inZr Ni atT=373K.Dataacquisitionstartedatt =1400s equilibrium. The extensionto non-ergodicsystems, such
67 33 0
(toppanel)andt =49000s(bottompanel)fromtemperature as glasses,is possible thanks to the use of an area detec-
0
equilibration. TheageofthesampleatanypointintheFigure tor, like the CDD used during our experiments. In this
canbetakenastage=t0+(t1+t2)/2s. Thehugeslowdown case in fact, the intensity distribution is sampled cor-
ofthedynamicsatthedifferentsampleagesiswellillustrated rectly by the average over all the pixels, independently
by the clear broadening of the intensity around the diagonal of the nature of the dynamics32,33.
from the left bottom corner to the top right corner in the
The time interval for temporal averaging was chosen
bottom panel with respect to the case corresponding to a
smallenoughthattheshapeofg (q,t)wasnotnoticeably
much shorter tw (top panel). 2
affected by the evolution of the dynamics, while keeping
a good signal to noise ratio. For each set of images, the
two times t1 and t2, being: sampleagewasdefinedastw =t0+(tf−ti)/2,wheret0is
the delayofthe startingpointfor the measurementfrom
hI(t1)I(t2)ip temperatureequilibration,andtf andti arethefinaland
G(t ,t )= . (1)
1 2 hI(t )i hI(t )i starting times of the interval used for the average.
1 p 2 p
Theαrelaxationprocessinglass-formerscanbe wellde-
Here, the average is performed on all the pixels of the scribedbyusingtheempiricalKohlrauschWilliamsWatt
CCD, that correspond to the same wave-vector q29–31. (KWW) model function1
Figure 1 shows the TTCF measured in Zr Ni in the
67 33 f(q,t)=f (T)·exp[−(t/τ)β] (3)
glassy state at two different sample age times from tem- q
perature equilibration. The colors represent the values Inthisexpression,τ isthecharacteristicrelaxationtime,
of G. The diagonal from bottom left to top right cor- β is the stretching parameter which quantifies the de-
responds to the time line of the experiment and it thus viation from a simple exponential behavior, and f (T)
q
4
the liquid above the glass transition temperature, these
theories predict a stretched, thus with β ≤ 1, decay of

thedensityfluctuationsevenintheglassystate. Theidea
is that the dynamic heterogeneities present in the liquid
1.0 phase partially freeze below T , leading to a narrower
g
distribution of relaxation times, and thus to an increase
c 0.8 of the shape exponent, up to the limiting case of β = 1.
/
1) This explanationwell describes the correlationfunctions
)- calculated in numerical simulation18 and the increase of
q,tp 0.6 β measured in some polymeric glasses12,17, but cannot
(
2 take into account the behavior reported in Figure 2.
g
( 0.4 tw= 2300 From the comparison with other systems, it seems then
tw= 3700 clear that metallic glassesbehave in a different universal
0.2 tw= 5000 way,independently oftheiratomicstructure. Inthecase
tw= 54800 ofMg65Cu25Y10,theunusualfasterthanexponentialbe-
0.0 haviorhasbeenattributedtothestrainfieldgeneratedby
10 100 1000 10000
arandomdistributionofslowly-evolvingsourcesofinter-
t (s)
nal stresses stored in the system during the quench, and
FIG. 2. Selection of the intensity correlation functions mea- which can then be released upon annealing the system
sured with XPCS at T = 373 K for different waiting times close to T 23,26. This interpretation suggests the exis-
g
from temperature equilibration. On increasing the waiting tence of a different kind of dynamics, rather than pure
time, the decay clearly shifts toward longer time scales due diffusion,inmetallicglasses,whichdisplaymanysimilar-
to physical aging. The data are reported together with the
ities with that of out-of-equilibrium soft materials, such
resulting fit obtained using equation (4).
as concentrated colloidal suspensions and nanoparticle
is the nonergodicity factor. It represents the height of probes in a glass former matrix23,39–42.
the intermediate-time plateau before the final decay as- InthecaseofZr67Ni33 theshapeparameterisevenlarger
sociated to the α-relaxation and it slightly depends on than the one reported for Mg65Cu25Y10 (β ∼ 1.5 for
temperature in the glassy state. a similar thermal path). This may suggest the pres-
Following the Siegert relation, the intensity correlation ence of larger atomic mobility or more internal stresses
functionsmeasuredwithXPCScanthenbedescribedby in Zr67Ni33, a conclusionwhich however requires further
investigations. While the value β ∼ 1.5 has been often
g2(q,t)=1+c(q,T)·exp[−2(t/τ)β] (4) observedin numerous experimentalstudies of soft mate-
rials and corresponds to the early-time regime proposed
where c = B(q)f2, being B(q) the parameter entering
q in the model of Bouchaud and Pitard26, values of β as
the Siegert relation.
large as those here reported for Zr Ni have been ob-
A selection of normalized intensity autocorrelationfunc- 67 33
served only in another Zr-based metallic glass24 and in
tionsobtainedatT =373Kforafixedq =q anddiffer-
p fewothersoftsystems,andtheirinterpretationisstillfar
ent waiting times is reported in Figure 2. The data are
from being reached41,43.
shown together with the best-fit line shapes obtained by
The waiting time dependence of the structural relax-
using equation (4). The intensity correlation functions
ation times obtained from the analysis of the g (q ,t) is
decorrelate completely on the experimental time scale, 2 p
shown in Figure 3 a) (squares). Data corresponding to
implying that the system is able to rearrange its struc-
differentq valuesaroundthemainpeakofthediffraction
ture on the probed spatial length scale of few ˚A. The
patternarealsoreported. Asexplainedintheexperimen-
effect of aging is illustrated by the shift of the decay to-
taldetails,thelowscatteredsignalallowedustomeasure
ward longer time scales upon increasing the sample age,
justone q vectorfor eachdetectorsetting. Consequently
in agreement with the analysis of the two times correla-
thedifferentqsaretakenatdifferentt fromtemperature
w
tion functions reported in Figure 1. As shown in Figure
equilibration. At all the investigated qs, τ grows rapidly
2, aging is so important that the decay time increases of
withthesampleage,inagreementwiththeresultsfound
almost a factor 10 in less than 13 hours. This fast aging
in the Mg Cu Y glass23. Interestingly, the dynam-
is likelyto be the reasonofthe wellknownrapidembrit- 65 25 10
ics is characterized by structural rearrangements which
tlement of metallic glasses34,35.
require ∼ 103 −104 s thus, relatively short times with
Interestingly, the correlation functions display a com-
respect to the common idea of an almost frozen dynam-
pressed,thusfasterthanexponentialbehavior,whichcan
ics in the deep glassy state. These values are however in
be well described by equation (4) with a shape param-
perfect agreement with those reported for both the Mg-
eter β ∼ 1.8, independent of the sample age. Such a
based and Zr-based metallic glasses23,24 and suggest the
high value is in agreement with the results reported for
presence of a peculiar dynamical behavior at the atomic
other metallic glasses23,24, while it cannot be explained
lengthscale. Hence,itwouldbeinterestingtoinvestigate
withinthecurrenttheoriesforthedynamicsintheglassy
the nature of the atomic dynamics in the glassy state
state36–38. Basedonthe observationsof the dynamics in
5
single master curve and define a time-waiting time-wave
vector superposition principle in the glass. This scaling

is reported in 3 d) where a selection of intensity auto
10000
correlationfunctions corresponding to the data reported
8000 a)
s) b) in panel a) are plotted as a function of t/τ. In the case
(6000
of Mg65Cu25Y10, β was found to be temperature and tw
4000 independentin the fastagingregime23. Ourresultsindi-
)
s catethatthisparameterisalsonotaffectedbythechoice
(
30000 40000 50000 ofthewave-vector,atleastforvaluesofq closetothatof
tw (s) the maximum ofthe static structure factor (see Figure 3
1000 e)).
As shown in Figure 3 a) and b), for q = q and large
p
t , the fast aging regime seems to change to a more
w
c) stationary or very slow one, as also suggested by the
1.8 analysis of the two times correlation function reported
in the bottom panel of Figure 1. The presence of a com-
-1 plexhierarchyofagingregimeshasbeenobservedalsoin
1.4 Q=2.38 ¯
Q=2.47 ¯-1 Mg65Cu25Y10butfortemperaturesveryclosetotheglass
-1 transitionone(T/Tg =0.995). Theresultsherereported
1.0 Q=2.75 ¯-1 forT/Tg =0.577showthatthis secondagingregimecan
Q=2.55 ¯ be foundalsointhe deepglassystate,after asufficiently
-1
0.6 Q=2.65 ¯ long annealing time. In the case of Mg65Cu25Y10, the
1000 10000 second aging regime was accompanied by a decrease in
t (s) the shape parameter. As shown in Figure 3 c), in the
w
presentcase the lack of a full complete decay ofg (t) for
2
1.0 d) thehighestt leadstoalargererrorinthedetermination
w
c tw=1 h ofβ, whichcanbe determined only fortw ≥50000s and
1)/ 0.8 tw=3 h remains however similar to the value obtained at lower
g(t)-20.6 Q)/I(Q)0 e) ttww==58 hh Fttworo.manthaelmeonsetrgsettaitciopnoairnyt odfyvniaemwi,csthesuagbgreustpst tchroesseoxviesr-
( 0.4 I( tence of a deep energy minimum in the potential en-
t =10 h
w
ergy landscape, where the system remains trapped for
0.2
1.5 2.0 2-.15 3.0 tw=15 h a very long time before eventually jumping into a dif-
Q (¯ ) ferent configuration44,45. A similar plateau has been re-
0.0
0.01 0.1 1 cently observed in the enthalpy recovery of glassy poly-
t/ (Q,t ) mers and has been interpreted as a thermodynamically
w
stable state10. This explanation cannot be extended to
FIG. 3. a) Waiting time dependence of the structural relax-
the case of metallic glasses. In fact, the comparison be-
ation time measured at T=373 K for different wave-vectors
around the first sharp diffraction peak (qp =2.55 ˚A−1). The tdwateaenfoXrPMCSg aCnduloYw temsupgegreasttusreinesqteuaidlibariugmradvuisaclosaitpy-
inset b) reports a zoom of the data taken at large waiting 65 25 10
proach toward equilibrium23, in agreement with the sub
times. c) Corresponding shape parameter. d) Selection of
linear aging regime found in other polymeric glassesand
the correlation curves corresponding to the data reported in
a) as a function of the time rescaled by the structural relax- colloids3,12,46.
ation time obtained from the analysis of the curves with the Following the procedure reported in Ref.23, we can de-
KWW model function of Eq. (4). The inset e) indicates the scribe the short t behavior of τ (t ) using the phe-
w qp w
position of thedifferent investigated qs. nomenologicalexpression
through the q dependence of the structural relaxation τ(T,t )=τ (T)exp(t /τ∗) (5)
w 0 w
time. Unfortunately, this information would require at
each investigated q a good knowledge of the aging in a where τ (T) is the value of τ for t = 0 at the temper-
0 w
∗
wide t range, which can be gained only by measuring ature equilibration time, and τ is a fitting parameter
w
the dynamics simultaneously for different wave-vectors. which describes the rate growth and is independent of
A higher incident flux, as the one available at free elec- temperature23. A fast exponential growth with t is ev-
w
tronlasersources,willmakethiskindofstudiespossible. ident also at the other investigated qs. However, in that
Interestingly, the shape parameter does not display any cases the lack of information on the behavior at shorter
dependence on q or t , and remains constant with β ∼ t does not allow for a more quantitative description of
w w
1.8±0.08 for all the investigated qs (Figure 3 c)). This the aging dependence for τ.
∗
means that it is possible to rescale all the data sets to a For q = q we find τ = 407±6 s and τ = 6490±170
p 0
6
IV. CONCLUSIONS

In conclusion, we have studied the physical aging in
a Zr Ni metallic glass, by following the temporal
67 33
evolution of the structural relaxation process at the
interatomic length scale. We find that the decay
10
) of the density fluctuations can be well described by
T
( compressed, thus faster than exponential correlation
0

/ functions, suggesting a peculiar origin for the atomic
dynamics27,31. This behavior seems to be universal
Mg65Cu25Y10 in metallic glasses23,24, and cannot be explained by
Mg65Cu25Y10 the well-known theories for glasses dynamics, which
Zr67Ni33 predict a stretched exponential shape of the correlation
functions, even in the glassy state36–38. Model systems
1 such as hard spheres and Lennard-Jones are unable to
1 2 3 4 5 6 7 8 9 10
* reproduce these intriguing dynamic effects18,20. In these
t /
w model systems, indeed, the dynamics appears to be
alwayscharacterizedbyabroadspectrumofrelaxations.
FIG. 4. Structural relaxation times measured in two as
Conversely, very similar results have been previously
quenched glasses of Mg65Cu25Y10 at T/Tg = 0.995 with dif-
ferentthermalhistoriesandinZr67Ni33 atT/Tg =0.577. All reportedforoutofequilibriumsoftmaterials,suggesting
the data are normalized for the τ parameter obtained from a universalmicroscopicdynamics forthese verydifferent
0
the analysis of the fast aging with the empirical model func- systems23. In these systems, the compressed behavior
tion (5) and are reported as a function of the time rescaled arises from ballistic-like motion due to the presence
∗
by the τ parameter. The data for Mg65Cu25Y10 are taken of internal stresses in the out of equilibrium state27.
from Ref.23. It would be interesting to check whether this is also
the case for metallic glasses. However, a q dependence
study wouldrequire a muchstrongersignalthan the one
achievable evenat a third generationsynchrotronsource
as the one used for the present study. Notwithstanding,
indication of the presence of distinct processes of atomic
s. The latter value is quite close to the one reported motion in metallic glasses have been reported for differ-
in ref.23 for Mg Cu Y at T/T = 0.995 and it is ent Zr-based metallic glass-formers studied with nuclear
65 25 10 g
of the same order of magnitude of that previously re- magnetic resonance48. In these systems the diffusive,
portedinthecaseofcolloidalgelsandLaponite39,47,thus collectivemotionisfoundtobeaccompaniedbyhopping
strengthening the idea of a universal out-of-equilibrium which becomes dominant in the glassy state, and could
behavior. The comparison with the Mg-based metallic then be related to the observed compressed relaxation
glass suggests that the physical aging is very similar for process in our glass.
both systems and that it should be possible to rescale Albeitwecouldnotgetinformationontheq dependence
the rapid growth of τ(t ) to a unique curve, indepen- of the relaxation time due to the impossibility of mea-
w
dently on the microscopic details of the system. This suring simultaneously different qs, we have investigated
scaling is shown in Figure 4, where the structural relax- the nature ofthe dynamics at differentwave-vectorsand
ation times of Zr Ni at T/T = 0.577 are compared sample ages. We find that the shape of the correlation
67 33 g
to those measuredin Mg Cu Y atT/T =0.995and functions does not show any dependence neither on
65 25 10 g
fortwodifferentthermalpaths. Whilesquaresandcircles the sample age nor on the wave-vector, at least for qs
correspondto as-quenched samples heated up to a given aroundthemaximumofthestaticstructurefactorofthe
temperature, stars refer to a state reached after having system, which is at q = 2.55 ˚A−1. These findings allow
p
partiallyannealedtheglassathighertemperatureswith- then to rescale all the correlation curves on the top of
outequilibration23. Allthe dataarerescaledforthe cor- each other and define a time-waiting time-wave-vector
responding τ parameter obtained from the analysis of superposition principle in the fast aging regime.
0
the fast aging using equation (5) and are reported as a The value of β seems to depend on the details of the
∗
function of the time rescaled by the τ parameter. For system, being larger in Zr-based systems than in the
short t , all the data fall into a unique master curve, previously reported Mg Cu Y 23. As both these
w 65 25 10
suggesting a common origin of the fast aging regime in glasses were obtained with the same thermal protocol,
metallic glasses. Differently, the crossover to the subse- we speculate that the observed difference could be re-
quent almost stationary dynamics strongly depends on lated to a larger atomic mobility in the first system and
the temperature and thermal path, and is reached only to the consequent presence of larger internal stresses.
for very long annealing times (circles) or after particular Despite this small difference, the comparison between
thermal treatments (stars). the two metallic glasses suggests the existence of a
7
universal dynamical behavior, also indicated by the 23B. Ruta, Y. Chushkin, G. Monaco, L. Cipelletti, E. Pineda,
scalingofthefastagingregimefortherelaxationtime to P.Bruna,V.M.Giordano,andM.Gonzalez-Silveira,Phys.Rev.
a single curve, independently of the microscopic details Lett.109,165701 (2012).
24M.Leitner,B.Sepiol,L.M.Stadler,andB.Pfau,Phys.Rev.B
of the systems. Additional theoretical and experimental
86,064202 (2012).
works is clearly required to elucidate this remarkable 25T. Hecksher, N. B. Olsen, K. Niss, and J. C. Dyre, J. Chem.
dynamical behavior of metallic glasses. Phys.133,174514 (2010).
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