This paper provides evidence that the physical aging of deeply and rapidly quenched metallic glasses is promoted by the Johari–Goldstein slow beta relaxation, resulting in a significant irreversible increase in the mechanical modulus on initial heating. Dynamic mechanical analysis has been used to characterize relaxation phenomena of a strong and a fragile metallic glass. In addition, we can extrapolate the temperature dependence of beta- and alpha-relaxation peaks to higher temperatures and calculate the merging temperature for both types of glasses

Bedorf, Dennis

Demetriou, Marios D.

Hachenberg, Jörg

Johnson, William L.

Kahl, Annelen

Richert, Ranko

Samwer, Konrad

English

Caltech Authors - Main

Merging of the  and  relaxations and aging via the Johari–Goldstein
modes in rapidly quenched metallic glasses
Jörg Hachenberg,1 Dennis Bedorf,1 Konrad Samwer,1,a Ranko Richert,1,b Annelen Kahl,2
Marios D. Demetriou,2 and William L. Johnson2
1I. Physikalisches Institut, Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
2Keck Engineering Laboratories, California Institute of Technology, Pasadena, California 91125, USA
Received 7 February 2008; accepted 7 March 2008; published online 4 April 2008
This paper provides evidence that the physical aging of deeply and rapidly quenched metallic
glasses is promoted by the Johari–Goldstein slow  relaxation, resulting in a significant irreversible
increase in the mechanical modulus on initial heating. Dynamic mechanical analysis has been used
to characterize relaxation phenomena of a strong and a fragile metallic glass. In addition, we can
extrapolate the temperature dependence of - and -relaxation peaks to higher temperatures and
calculate the merging temperature for both types of glasses. © 2008 American Institute of Physics.
DOI: 10.1063/1.2903697
The kinetic feature of a liquid and a glass including the
glass transition is of fundamental interest as well as essential
for industrial applications, but not yet completely
understood.1,2 Regarding metallic glass-forming alloys, a
quantitative description of how elasticity and viscosity cor-
relate with the shear modulus of a glass or a liquid can now
be quantitatively described.3 It is now also understood that a
single process, termed  relaxation or primary relaxation, is
not sufficient to describe in general glassy dynamics.4
Metallic glasses are typically regarded as nearly ideal
because their structure is thought to represent a mixture of
hard spheres. A slow  relaxation, also termed Johari–
Goldstein process,5 has been identified in metallic glasses in
experiments as well as simulations.6–10 Consequently, the
slow  relaxation is regarded as a universal feature of the
glassy dynamics.10 Recent evidence suggests that this
-relaxation or, more precisely, the local cooperate dynamics
of several  relaxations, give rise to one shear transformation
event, or one  relaxation,11,12 and is thought to be the driv-
ing process for enhanced diffusion.13
In the literature, there is often an additional relaxational
process discussed that occurs during the heating of an unan-
nealed, as-quenched glass. This effect has been repeatedly
observed as an increase in Young’s modulus14,15 or decrease
of the free volume,16 at temperatures at which irreversible
aging of the macroscropic structure, the partial restoration of
equilibrium structure below Tg, where complete equilibration
is significantly longer than the experimental time window, is
negligible on experimental timescales.17 Already at tempera-
tures of 100 K or more below the glass transition tempera-
ture, a change of the elastic constant indicates local relax-
ation events,18 which are incompatible with the typical
picture of physical aging regarding the structure of the glass.
Depending on whether the material hardens or softens, the
terms physical aging or rejuvenation are used.19
In this paper, evidence is provided that this aging process
observed well below Tg can be associated with the slow
Johari–Goldstein type  relaxation, in the following denoted
as  relaxation. Furthermore, a Kissinger analysis20 provides
an estimate for the activation energy of this  relaxations. If
the measured data are extrapolated to higher temperatures, a
merging temperature of  and  relaxations can be assessed.
That merging temperature is in close vicinity to the mode-
coupling theory MCT temperature Tc.27
Pd77Cu6Si17 fragile, m=52.8–77.0 and Zr65Al7.5Cu27.5
strong, m=36.4–38.47,10,21,22 have been prealloyed by arc
melting the pure elements in argon atmosphere. The crushed
lumps have been inductively molten and melt spun onto a
rotating copper wheel in argon atmosphere, quenching the
sample at approximately 105 K /s.23 The resulting metallic
glass bands are 20–30 m thick and have been cut into
strips, 10–15 mm long, and 1–2 mm wide. Composition
and amorphicity have been verified using energy-dispersive
x-ray spectroscopy, wide angle x-ray scattering, and differ-
ential scanning calorimetry.
Mechanical spectroscopy has been performed using a
Perkin Elmer dynamic mechanical analyzer DMA 7. All
experiments are carried out in the extensional mode at a con-
stant frequency of =5 Hz and at constant heating rates of
0.5–20 K /min in nitrogen atmosphere. The data shown in
Fig. 1 has been measured using a liquid nitrogen cooling and
initial stresses of 7.5 MPa of static stress, onto which a dy-
namic stress of 4.6 MPa is superimposed. All following mea-
surements have been carried out with a constant glycol cool-
ing, providing more stable conditions at higher temperatures
and less disturbing mechanical vibrations. The initial values
have been increased to typically 11 MPa of static stress plus
9 MPa of dynamic stress. All samples except the one of Fig.
1 are from the same melt-spinning run. More experimental
details are found in Ref. 10.
Figure 1 shows a typical curve of a PdCuSi sample re-
peatedly heated at 10 K /min. The real part of the Young’s
modulus, also called storage modulus E, shows a nearly
constant regime below 400 K with a shallow minimum
around 26020 K. Toward higher temperatures, a strong in-
crease in storage modulus is observed with an onset at
46020 K and a turning point at 51510 K. The heating
was stopped at 609 K at the first indications of a decrease of
E. The storage modulus at this maximum is about 40 GPa.
The sample is then cooled down, starting with a cooling rate
aElectronic mail: ksamwer@gwde.de.
bOn leave from Department of Chemistry and Biochemistry, Arizona State
University, Tempe, Arizona 85287, USA.
APPLIED PHYSICS LETTERS 92, 131911 2008
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of 30 K /min not shown. The storage modulus during the
second run shows the behavior expected from aging well
below Tg behavior. A linear decrease of initially 48 GPa with
a small slope of 0.0045 GPa /K is followed by a strong de-
crease of tens of gigapascal above 550 K.
The changes in tan  between first and second heating
are less pronounced than the changes in storage modulus E.
Below 500 K, the average slope during the second run is
smaller. Above 500 K, tan  bends over in a steeper increase
and the values of the second run are decreased compared to
the first heating scan.
To determine the heating-rate dependence, as-quenched
PdCuSi and ZrAlCu samples have been investigated by
DMA above room temperature. Figure 2 only shows the re-
sults of the smallest 0.5 K /min and highest 20 K /min
heating rates used. In both types of glasses, a clear tempera-
ture shift of the onset of the increase and the final decrease in
storage modulus E is observed. On the other hand, the onset
of the bending over of tan  is only weakly affected by a
change in heating rate.
The determined positions of the onset and turning points
of E are plotted in Fig. 3 using a Kissinger-type plot20 and
fitted with a straight line. In addition, the onset points of the
change in sample length l, which is measured in the DMA
Ref. 10 and is an indication for viscous flow or irreversible
configurational changes termed -relaxation of the sample,
are plotted and fitted linearly.
As shown in Fig. 1 the as-quenched sample shows a
change in slope and a clear increase in storage modulus that
is missing during the second run. It is a result of a pro-
nounced physical aging, relaxing internal stresses that origi-
nate from the rapid quench at a rate of 105 K /s. The onset
temperature the resulting increase in the instantaneous modu-
lus E0 appears at around 450 K. The total irreversible change
in E0 between the initial and subsequent runs is considerable
and exceeds 60%. At higher temperatures 550 K the E0
values reach the values of the second run equivalent to that
temperature and heating rate before the strong drop of both
curves occur due to viscous-plastic flow. As in molecular
glasses,24 the amplitude of this  process itself is consider-
ably decreased by aging. This feature is seen here for PdCuSi
in Fig. 1 as change of tan  between first and second heating
run in the temperature range between 500 and 600 K.
Both types of metallic glasses strong and fragile clearly
show that the onset of physical aging is highly dependent
upon heating rate see Fig. 2. Observing a high heating-rate
dependence at temperatures far below the -relaxation activ-
ity indicates that this aging is governed by relatively fast
modes compared with the so called primary structural relax-
ation. The increase in E is consequently attributed to
-relaxation steps within a megabasin of the potential energy
landscape.2 Such an assignment is consistent with the sub-
stantial increase in E because the curvature of the potential
energy increases when the system moves toward a local
minimum of the metabasin.3 It is also supported by the low
stretching exponents observed for isothermal aging of alloys
well below Tg,16 with values around =0.3 being typical for
FIG. 1. Color online Storage modulus E and tangents of phase angle tan 
vs temperature for an as-quenched 1 and an annealed 2 PdCuSi sample,
measured by DMA in extensional spectroscopy mode.
FIG. 2. Color online Storage modulus E and tangents of phase angle tan 
vs temperature at heating rates of 0.5 K /min 0.5 and 20 K /min 20 for
as-quenched samples of PdCuSi and ZrAlCu as labeled.
FIG. 3. Color online Kissinger-type plots, summarizing the temperatures
of the discussed events at all investigated heating rates for PdCuSi and
ZrAlCu, including linear fits of the data. The quantities considered are the
onset of length change l—onset, the onset E—onset and turning
point E—turn.pt. of the change in storage modulus E.
131911-2 Hachenberg et al. Appl. Phys. Lett. 92, 131911 2008
Downloaded 04 Apr 2008 to 131.215.225.137. Redistribution subject to AIP license or copyright; see http://apl.aip.org/apl/copyright.jsp
slow  processes. In terms of energy landscape and activa-
tion pictures, the current aging process that starts from a
highly excited potential energy state is compared with regu-
lar aging of the -dynamics in Fig. 4.
Figure 3 summarizes the results of all measured heating
rates in terms of a Kissinger-type plot.20 The onset points of
viscous flow are interpreted as the start of the -relaxation
on timescales corresponding to the heating rate. In this ex-
perimentally limited regime of accessible heating rates, the
data points are linearly fitted instead of using a curved
Vogel–Fulcher–Tammann fit.25 For high temperatures, all
curves tend to merge together, consistent with the  relax-
ation no longer distinguishable from the  relaxation at very
short timescales in the TTc regime see also Fig. 4.
13,26 If
linearly extrapolated, the fitted lines of the onsets of  and 
relaxations intersect at 720110 K for the fragile PdCuSi
system and at 870290 K for the strong ZrAlCu system.
These values are close by the reported values for the critical
temperatures Tc 710 K for PdNiCuP and 875 K for ZrTiCu-
NiBe of the idealized MCT.13,27 This is due to the fact that
the curve of the  relaxation is bent more strongly than those
of the  relaxation, as already established for organic glass
formers.26 An activation energy of the  relaxation can be
estimated from the slope of the turning points, plotted in the
Kissinger plots. The values are 0.670.11 eV for PdCuSi
and 0.590.39 eV for ZrAlCu. These energies are quite
similar for the two glasses and much bigger than kBT, which
can be attributed to the cooperative nature of the 
relaxation.9,13,27
In summary, the present aging and the excess wing can
be attributed to common degrees of freedom: the slow
-relaxation process. This can be regarded as a universal
feature of glass dynamics, because it occurs for both, strong
and fragile, metallic glasses. Furthermore, the estimated ac-
tivation energy is calculated within a Kissinger analysis.20
Recalling the conjecture that several  relaxations give rise
to an  relaxation and that the  relaxation might be the
driving process of diffusion, the fundamental character of the
 relaxation becomes apparent. The phenomenon of physical
aging at very high levels of the energy landscape and the
slow  relaxation can be interpreted as a  process alone
while several of them cause an  relaxation, which eventu-
ally leads to viscous flow. In addition we can also determine
the merging temperature of both processes which is close to
the Tc of the MCT. This temperature is seen as critical for the
entire low-frequency relaxation spectrum of a simple,
quenched-in system of hard spheres.
The authors are very grateful for stimulating discussions
with C. A. Angell and for experimental support by U.
Bete. Financial support from the following programs are ac-
knowledged: Deutsche Forschungsgemeinschaft through
SFB 602 TP B8, Graduiertenkolleg 782, and Leibniz pro-
gram. This work was also supported in part by the MRSEC
Program of the National Science Foundation under Award
No. DMR-0520565.
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131911-3 Hachenberg et al. Appl. Phys. Lett. 92, 131911 2008
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Merging of the alpha and beta relaxations and aging via the Johari–Goldstein modes in rapidly quenched metallic glasses

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Merging of the alpha and beta relaxations and aging via the Johari–Goldstein modes in rapidly quenched metallic glasses

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