Viscosity and enthalpy relaxation from the amorphous state into the supercooled liquid state was investigated in the bulk metallic glass forming Zr46.75Ti8.25Cu7.5Ni10Be27.5 alloy below the calorimetric glass transition. At different temperatures, the viscosities relax into states that obey the same Vogel–Fulcher–Tammann relation as the data obtained at higher temperatures in the supercooled liquid. Enthalpy recovery experiments after relaxation in the same temperature range show that the enthalpy of the material reaches values that also corresponds to the supercooled liquid state. The glass relaxes into a metastable supercooled liquid state, if it is observed on a long time scale. Equilibration is possible far below the calorimetric glass transition and very likely even below the isentropic temperature

Busch, R.

Johnson, W. L.

English

Caltech Authors - Main

APPLIED PHYSICS LETTERS VOLUME 72, NUMBER 21 25 MAY 1998The kinetic glass transition of the Zr46.75Ti8.25Cu7.5Ni10Be27.5 bulk metallic
glass former-supercooled liquids on a long time scale
R. Buscha) and W. L. Johnson
W. M. Keck Laboratory of Engineering Materials, California Institute of Technology, Pasadena,
California 91125
~Received 28 January 1998; accepted for publication 25 March 1998!
Viscosity and enthalpy relaxation from the amorphous state into the supercooled liquid state was
investigated in the bulk metallic glass forming Zr46.75Ti8.25Cu7.5Ni10Be27.5 alloy below the
calorimetric glass transition. At different temperatures, the viscosities relax into states that obey the
same Vogel–Fulcher–Tammann relation as the data obtained at higher temperatures in the
supercooled liquid. Enthalpy recovery experiments after relaxation in the same temperature range
show that the enthalpy of the material reaches values that also corresponds to the supercooled liquid
state. The glass relaxes into a metastable supercooled liquid state, if it is observed on a long time
scale. Equilibration is possible far below the calorimetric glass transition and very likely even below
the isentropic temperature. © 1998 American Institute of Physics. @S0003-6951~98!03221-5#Undercooling ~supercooling! of a liquid below the melt-
ing point is associated with a large increase of the viscosity
that represents the slowdown of the kinetics in the liquid.
When the viscosity reaches a value of the order of 1012 Pa s,
structural arrest occurs on the time scale of the cooling pro-
cess. This kinetic glass transition involves sudden changes of
the specific heat capacity and the expansion coefficient. Free
volume, enthalpy, and entropy are frozen in. A lot of re-
search has been devoted to understand the glass transition1,2
in terms of thermodynamics and kinetics.
Up to recently, in metallic systems cooling rates of the
order of 104 – 106 K/s were necessary to form a glass by
rapidly quenching the melt.3,4 The resulting thin ribbons
showed a low thermal stability with respect to crystallization
when heated into the glass transition region where the struc-
tural relaxation time reaches a value of about 102 s. In many
of these materials the glass transition cannot even be ob-
served since crystallization sets in at lower temperatures.
Novel multicomponent bulk metallic glass formers5–7
exhibit a high resistance with respect to crystallization in
their supercooled liquid region and at the glass transition.8 In
the present study the Zr46.75Ti8.25Cu7.5Ni10Be27.5 alloy serves
as a model system to investigate the relaxation from the
amorphous state into the supercooled liquid state. This alloy
has one major advantage compared to other bulk metallic
glass formers, like the Zr41.2Ti13.8Cu12.5Ni10.0Be22.5 alloy. It
does not show phase separation in the supercooled liquid that
leads to a destabilization of the noncrystalline state with re-
spect to primary crystallization of nanocrystals.9,10 We will
show in this letter that the amorphous alloy relaxes isother-
mally into a metastable state, in which it behaves thermody-
namically and kinetically like a supercooled liquid when ob-
served on a long time scale.
Bulk metallic glasses with a composition of
Zr46.75Ti8.25Cu7.5Ni10Be27.5 were prepared by cooling the
melt with a rate of approximately 10 K/s. The viscosity was
measured by three-point beam bending with constant heating
a!Electronic mail: busch@hyperfine.caltech.edu2690003-6951/98/72(21)/2695/3/$15.00
Downloaded 12 Jan 2006 to 131.215.240.9. Redistribution subject torate as well as isothermally.11 Calorimetric measurements
were performed in a Perkin Elmer DSC7 and a
Seteram DSC 2000 K. In order to calculate the thermody-
namic functions in the supercooled liquid, heats of fusion,
heats of crystallization, and specific heat capacities, cp , were
determined experimentally, as shown in Ref. 12 for the
Zr41.2Ti13.8Cu12.5Ni10.0Be22.5 alloy. The enthalpy recovery af-
ter isothermal annealing below the calorimetrically observed
glass transition was measured in experiments with constant
heating rate in the DSC.
In Fig. 1 viscosity data on the alloy in a range between
106 and 1013 Pa s are depicted. This region corresponds to an
interval of structural relaxation times between about 1022
and 105 s. Beam bending data measured with a constant
heating rate of 0.833 K/s ~L! and viscosity values after
FIG. 1. Viscosity in the glass transition region, measured by beam bending
with a constant heating rate ~L! and viscosity values after equilibrating the
material isothermally ~d!. The equilibrium data measured by parallel plate
rheometry are also shown ~s!.13 The solid line corresponds to a Vogel–
Fulcher–Tammann fit. The insert shows isothermal relaxation measure-
ments of the viscosity. The data are fitted with a stretched exponential func-
tion.5 © 1998 American Institute of Physics
 AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp
2696 Appl. Phys. Lett., Vol. 72, No. 21, 25 May 1998 R. Busch and W. L. Johnsonequilibrating the material in isothermal experiments ~d! are
plotted. Furthermore, equilibrium viscosity data obtained by
parallel plate rheometry ~s!13 are included. If a sample is
heated with a constant rate of 0.833 K/s, the viscosity relaxes
into the equilibrium value between 623 and 673 K. This is
the same temperature range where the calorimetric glass
transition is observed at the same heating rate. Above 673 K
the measured viscosity reaches the equilibrium value as mea-
sured by parallel plate rheometry ~s!. For lower tempera-
tures isothermal experiments are used to reach equilibrium.
Three examples of the viscosity relaxing into the equilibrium
state are shown in the insert in Fig. 1. The pathways of the
relaxation are indicated in Fig. 1 by arrows. The solid sym-
bols in Fig. 1 represent the equilibrium viscosities obtained
from fitting the relaxation curves with a stretched exponen-
tial relaxation function.14–16 The viscosities reach values that
are an extension of the viscosity data of the supercooled
liquid measured at higher temperatures. All equilibrium data
can be fitted well with one Vogel–Fulcher–Tammann ~VFT!
relation
h5h0 exp@DT0 /~T2T0!# , ~1!
with a fragility parameter D522.7 and a VFT temperature
T05372 K. The pre-exponential factor, h0 , was set as 4
31025 Pa s ~see Refs. 14 and 15!. The good agreement of
all equilibrium viscosity data indicates that the amorphous
alloys relax isothermally into the supercooled liquid state
with relaxation times that become increasingly longer at
lower temperatures. In this sense the measurements shown in
the insert in Fig. 1 represent the isothermal glass transition
for three different temperatures. The average relaxation time
is proportional to the equilibrium viscosity with a propor-
tional constant of 6.83108 Pa.
To investigate the thermodynamics of the alloy on a long
time scale, the specimens were first equilibrated above the
calorimetric glass transition and cooled with 0.083 K/s in
order to assure the same thermal history for all samples. The
alloys were then heat treated isothermally at different tem-
peratures. The annealing times were chosen to be ten times
the relaxation time that was determined during viscosity re-
laxation ~e.g., 1.23105 s at 583 K!. This guarantees that the
samples reach states that are very close to metastable equi-
librium. After the heat treatment the specimens were first
cooled to room temperature with a rate of 3.33 K/s. Subse-
quently a DSC experiment with a constant heating rate of
0.083 K/s was performed.
Figure 2 shows the results of these enthalpy recovery
experiments after annealing at four different temperatures as
well as for an unrelaxed sample that was heated above the
glass transition and cooled at the same rate ~0.083 K/s! prior
to the experiment. The annealed samples show a large endo-
thermic heat recovery in the calorimetric glass transition re-
gion, whereas the unrelaxed reference sample does not ex-
hibit this effect.
Van den Beukel and co-workers17 observed enthalpy re-
covery in metallic glasses previously in the Ni–Pd–P sys-
tem. They developed a model that describes the functional
form of the DSC curves based on free-volume theory. In the
present study we use the enthalpy recovery to determine theDownloaded 12 Jan 2006 to 131.215.240.9. Redistribution subject tochange of the enthalpic state of the sample that occurred
during the preceding relaxation.
Enthalpy recovery increases with decreasing annealing
temperature. The amount of enthalpy that was released dur-
ing the isothermal heat treatment and that was recovered dur-
ing reheating the sample, is the area between the curve of the
relaxed sample and the unrelaxed material. In Fig. 3 the mea-
sured recovered heats are plotted into an enthalpy diagram.
The enthalpy, DH , of the supercooled liquid in reference to
the crystalline state ~solid line! was determined indepen-
dently by DSC measurements.12
The enthalpy differences measured during enthalpy re-
covery are plotted, starting from the enthalpy of the super-
cooled liquid state in positive DH direction. The result is the
enthalpy curve ~solid circles! of the frozen-in amorphous al-
loy that was initially formed by cooling all samples with
0.083 K/s. We observe that the enthalpy of the amorphous
alloy only increases slightly with temperature. This is due to
the small specific heat capacity difference between the crys-
tal and the amorphous alloy ~see Fig. 4!.
The measured enthalpy change with temperature can be
attributed to a finite specific heat capacity difference between
FIG. 2. Enthalpy recovery measurements in the glass transition region after
isothermal relaxation from the amorphous into the supercooled liquid state
at different temperatures. In addition the measurement for an unrelaxed
sample is shown.
FIG. 3. Enthalpy difference, DH , with respect to the crystalline mixture for
the supercooled liquid. The enthalpy changes from the frozen-in amorphous
state ~d! into the supercooled liquid state ~s! as recovered with a rate of
0.083 K/s, are added in the diagram. The isentropic temperature, TK , is
marked by an arrow.
 AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp
2697Appl. Phys. Lett., Vol. 72, No. 21, 25 May 1998 R. Busch and W. L. Johnsonthe amorphous alloy and the supercooled liquid. This specific
heat capacity difference between supercooled liquid ~sl! and
amorphous ~am! state at a temperature T11(T22T1)/2 is
calculated as
Dcp
sl-am5@DHsl-am~T1!2DHsl-am~T2!#/~T22T1!, ~2!
where DHsl-am(Ti) are the recovered enthalpies after anneal-
ing at the temperatures T1 and T2 , respectively. The absolute
specific heat capacity cp
sl5cp
am1Dcp
sl-am of the supercooled
liquid on a long time scale ~L! is shown in Fig. 4 in com-
parison with other cp data of the crystal ~h!, the amorphous
state ~n!, and the supercooled liquid at higher temperatures
~s!. The data for the supercooled liquid on a long time scale
are in good agreement with the extrapolation of the specific
heat capacity data of the supercooled liquid obtained at
higher temperatures.
It is important to note that the high cp in the supercooled
liquid at low temperatures cannot be measured in the labo-
ratory directly. A cp measurement always involves a tem-
perature change. The time to perform this temperature
change ~seconds! is always much shorter than the enthalpy
relaxation time ~days! in the studied temperature range.
Therefore, the enthalpic state of the alloy will only change
by a fraction of what is expected after full relaxation. Thus,
the measured cp only accounts for the amount of enthalpy
that relaxed during this time period. In fact, when measured
on laboratory time scale, the supercooled liquid exhibits an
apparent cp equal to that of the amorphous alloy ~see Fig. 4!.
If cp experiments could be performed on a much longer time
scale ~e.g., geological time scale! the cp of the supercooled
liquid could be measured at lower temperatures directly. In
this sense, the observed location of the calorimetric glass
transition on the temperature axis is merely a result of our
very subjective feeling for time.
It is an interesting question whether one would observe a
thermodynamic glass transition at the isentropic ~Kauzmann!
temperature, TK , after proper equilibration or whether the
amorphous alloy would keep on relaxing into the super-
FIG. 4. Specific heat capacity of the supercooled liquid ~s! measured with
constant heating rate. The specific heats of the crystal ~h! the amorphous
state ~n! where measured in steps in reference to sapphire. The specific heat
capacity of the supercooled liquid on a long time scale was obtained from
the enthalpy recovery experiments ~L!. On a short time scale ~l! the
measured value for the relaxed sample corresponds to that of the amorphous
alloy.Downloaded 12 Jan 2006 to 131.215.240.9. Redistribution subject tocooled liquid below the isentropic temperature. The latter
case implies that the entropy of the supercooled liquid can
become smaller than that of the crystal. This was observed
during ‘‘inverse melting’’ in Ti–Cr and related alloys.18 It
was also proposed for the Mg65Cu25Y10 bulk glass former.
For this alloy it was shown that thermodynamics and kinetics
of the supercooled liquid are only in good agreement if it is
assumed that the configurational entropy of the liquid van-
ishes close to T0 but not at TK .16 It is most likely that this
condition also applies to the Zr46.75Ti8.25Cu7.5Ni10Be27.5 al-
loy. It is, in principle, possible to investigate if there is a
physical meaning to the isentropic temperature, because the
relaxation at that temperature would take about 108 s ~three
years!, whereas crystallization would take ten times as long
according to estimations from the heating rate dependence of
the primary crystallization.
In this letter, the relaxation from the amorphous state
into the supercooled liquid state was studied below the tem-
peratures where the calorimetric glass transition is observed
in a DSC experiment ~laboratory time scale!. The relaxation
of the viscosity and the enthalpy was measured in isothermal
experiments and compared with data obtained at higher tem-
peratures where the existence of a metastable supercooled
liquid state is out of the question. The comparison suggests
that at low temperatures there exists a metastable super-
cooled liquid on a long time scale. It is most likely that the
configurational entropy of the supercooled liquid does not
vanish at the isentropic temperature but at a far lower tem-
perature close to the VFT temperature. This means that a
metastable equilibrium supercooled liquid can exist even be-
low the isentropic temperature.
The authors thank A. Masuhr and E. Bakke for their
support and fruitful discussions. This work was supported by
the U.S. Department of Energy ~Grant No. DEFG-03-
86ER45242!.
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The kinetic glass transition of the Zr46.75Ti8.25Cu7.5Ni10Be27.5 bulk metallic glass former-supercooled liquids on a long time scale

https://authors.library.caltech.edu/1914/1/BUSapl98.pdf

The kinetic glass transition of the Zr46.75Ti8.25Cu7.5Ni10Be27.5 bulk metallic glass former-supercooled liquids on a long time scale

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