Existence of multiple critical cooling rates which generate different types of monolithic metallic glass
Existence of multiple critical cooling rates which generate different types of monolithic metallic glass
Via fast differential scanning calorimetry using an Au-based glass as an example, we show that metallic glasses should be classified into two types of amorphous/monolithic glass. The first type, termed self-doped glass (SDG), forms quenched-in nuclei or nucleation precursors upon cooling, whereas in the so-called chemically homogeneous glass (CHG) no quenched-in structures are found. For the Au-based glass investigated, the critical cooling and heating rates for the SDG are 500 K s?1 and 20,000 K s?1, respectively; for the CHG they are 4000 K s?1 and 6000 K s?1. The similarity in the critical rates for CHG, so far not reported in literature, and CHG's tendency towards stochastic nucleation underline the novelty of this glass state. Identifying different types of metallic glass, as is possible by advanced chip calorimetry, and comparing them with molecular and polymeric systems may help to elaborate a more generalized glass theory and improve metallic glass processing.
J?rgen E.K. Schawe1 & J?rg F. L?ffler
T Gustav Tammann1 85 years ago. According to his
he kinetic concept of glass formation was developed by
assumption, a glass can be formed by cooling if the curves
of the temperature dependency of nucleation and growth are
significantly separated. The tendency of a metallic alloy to form a
glass is usually characterized by the glass-forming ability (GFA),
which corresponds to a critical cooling rate, ?c,cr, at which no
crystallization occurs during cooling from the melt2-6. After
cooling at ?c,cr to temperatures below the glass transition region
the material is expected to form a monolithic glass, i.e., a glass
whose atomic structure is completely amorphous. The structure
of the glass can be changed by annealing it in the glassy state7?12
or by varying the cooling rate during glass formation13?16.
Another kinetic phenomenon is the critical heating rate, ?h,cr,
at which a glass does not crystallize upon heating14,15,17. It may
be expected that ?h,cr ? - ?c,cr, because nucleation is much more
dominant at deep undercooling, i.e., the maximum of the
nucleation rate is at lower temperatures than the maximum of the
growth rate14,15, and the critical size of nuclei may decrease at
The competition between glass formation and nucleation is a
general phenomenon and occurs not only in rapidly quenched
metallic alloys, but in various classes of metastable materials with
different types of bonding. While glass formation is relatively rare
in metallic alloys, polymers usually form a semicrystalline
structure where the macromolecule is part of the crystalline and
amorphous phase. Complete crystallization from the melt is thus
basically impossible in such systems, so that glass formation in
polymers can be considered a universal phenomenon. In
polymeric materials the terms amorphous glass and semicrystalline
glass are commonly used and distinguished from one another.
For metals, a somewhat different terminology is used and the
equivalent terms are monolithic glass and metallic glass
Since the introduction of non-adiabatic chip calorimetry18,19
and its commercialization20,21, calorimetric measurements at
defined cooling and heating conditions have been possible using
fast differential scanning calorimetry (FDSC). This technique is
frequently used to study glass transition phenomena and
nanostructure formation in polymers22?24, molecular glass
formers25, and chalcogenides26?29. However, recently FDSC has also
been identified by the metals community as a suitable method for
studying glass formation, nucleation, and phase transitions in
metastable metallic alloys14,30?36. In14, one of the authors of this
paper reported on the crystallization kinetics of an Au-based bulk
metallic glass (Au49Ag5.5Pd2.3Cu26.9Si16.337), and constructed, via
isothermal measurements in the millisecond range, complete
time?temperature?transformation (TTT) diagrams of
crystallization in the undercooled/supercooled liquid range upon
cooling and heating.
In this study we use a newly developed Flash DSC2+
instrument (see Methods) which allows us to perform calorimetric
experiments at ultrafast cooling rates of 40,000 Ks?1 and heating
rates greater than 60,000 Ks?1. The latter also allows us to
upquench a certain phase, where up-quenching denotes a heating
process that is so rapid that no structural changes occur before
melting of the previously frozen phase36.
In this work we performed FDSC investigations on the bulk
metallic glass (BMG) Au49Ag5.5Pd2.3Cu26.9Si16.3 at ultrafast rates
with linear heating and cooling. We illustrate here that in the case
of metals, amorphous (monolithic) glasses need to be classified
into two categories. We term these self-doped glass (SDG) and
chemically homogeneous glass (CHG). We show that
quenchedin nuclei or nucleation precursors form in the SDG upon cooling
at medium rates, which generates significant differences in the
critical cooling and heating rates (?c,SDG ? 500 K s?1 ? ?h,SDG ?
500 K s?1
1000 K s?1
20,000 K s?1). In contrast, such nuclei no longer form upon rapid
cooling, which leads to the fact that the rates of critical cooling
(?c,CHG ? 4000 K s?1) and critical heating (?h,CHG = 6000 K s?1)
are very similar for the CHG. This similarity has not been
reported before because the critical cooling rate measured has
always been that of an SDG38,39. The ramifications for the
understanding of metallic glass processing are, however,
significant because the conjectured and/or measured great
differences between critical cooling and heating rates have often been
explained by a pronounced asymmetry in crystallization
behavior14,15,17. By analyzing the FDSC results and discussing the
commonalities and differences involved in nucleation and glass
formation for metallic and polymeric glass formers, we also
intend to contribute to the development of a more generalized
Critical cooling rates and formation of different glasses.
Figure 1a reveals FDSC cooling curves measured at different
rates. Crystallization peaks are detected for cooling rates below
500 K s?1, and the temperature of the crystallization process
increases with decreasing cooling rate. The rate of 500 K s?1,
where crystallization is no longer evident, is the critical cooling
rate, i.e. the minimum cooling rate at which the liquid can form a
Figure 1b shows heating curves at 1000 K s?1 measured after
cooling at various rates (between 0.1 and 40,000 K s?1). The glass
transition takes place at about 160 ?C, and the exothermic
crystallization peak accrues in the temperature range between 260
and 315 ?C followed by an endothermic melting peak. The
crystallization shows a strong dependence on the previous cooling
conditions, an effect that has been seen frequently in various
materials14,32,40. The temperature of the crystallization peak,
TPeak, the intensity of the glass transition (step height ?cp), and
the total enthalpy, ?H, (containing crystallization and melting)
are evaluated from these curves.
The total enthalpy ?H reflects the crystallinity of the sample
after the cooling process41,42. In a first approximation the
crystallinity is ? = ?H/?Hm, where ?Hm is the equilibrium
melting enthalpy measured using a completely crystallized
material which was previously cooled at 1 K s?1. The actual
melting enthalpy measured, ?Hmelt, is usually smaller than the
equilibrium melting enthalpy, ?Hm. This is because the phase
which eventually melts is not necessarily the stable phase, and/or
the material has not completely crystallized before melting. In the
case of an amorphous specimen, ?H = ?Hcryst + ?Hmelt is
practically zero, i.e., ? = 0, because the enthalpy of possible
exothermic crystallization processes during heating is the same as
the enthalpy of melting of these crystals. Small differences are
generated by the heat capacity contribution43. On the other hand,
? = 1 for a fully crystallized sample.
The increase in the heat capacity at the glass transition, ?cp, is
the intensity of the glass transition, which also depends
on crystallinity. The relative intensity of the glass transition,
?cp/?cp,a, has been found to depend linearly on the crystallinity ?
(see Supplementary Note 1 and Supplementary Fig. 1), where for
the completely amorphous phase the intensity of the glass
transition is ?cp,a = 0.14 J g?1 K?1 (see Fig. 2b). Such a linear
dependence is expected for semi-crystalline materials with a
single type of amorphous phase and has also been observed for
molecular glasses, in contrast to macromolecular glasses44. Thus,
the relative glass transition intensity, ?cp/?cp,a, can be used as a
measure for the content of amorphous phase in semi-crystalline
glasses (SCGs). This is important because for small crystallinities
the change in ?cp is often more sensitive than the variation in
Measurements similar to those in Fig. 1 were recently
performed on a Ce-based BMG30, where the authors evaluated
the crystallization and melting events of the heating curves
obtained by nanocalorimetry. They interpreted the data by
introducing two critical cooling rates, and found that during slow
cooling only the crystalline phase occurred. After cooling at
medium rates, i.e., at those between the two critical cooling rates
identified, they observed a mixed glassy-crystalline structure,
while very rapid cooling above the second critical cooling rate
suppressed crystallization30. In our work, we performed
experiments with a sample mass on the order of micrograms to avoid
critical size effects14,45 and also evaluated the glass transition in
detail. We avoided potential oxidation effects by investigating a
precious-metal-based BMG. By significantly refining the
measurements we were thus able to distinguish between two different
types of amorphous glasses, as discussed in the following.
Figure 2a plots the temperature of the crystallization peaks
observed during heating at a rate of 1000 K s?1 vs. the cooling
rate at which the glass was formed (Fig. 1b). At slow cooling rates
(<200 K s?1) no crystallization is observed in the heating curves
because the sample completely crystallized during cooling. After
fast cooling (?4000 K s?1) the temperature of the crystallization
peak is constant and amounts to 314 ?C, i.e., in this range the
crystallization is invariant with respect to the previous cooling
rate or, in other words, the cooling condition required to form a
glass has no influence on the crystallization process during
heating. We assume that here no nuclei have formed during
cooling, so all nucleation must occur during heating.
After cooling at rates between 200 and 4000 K s?1 the
crystallization temperature, TPeak, is significantly lower than that
after fast cooling, and in this range TPeak increases with increasing
cooling rate. In these more slowly cooled glasses, the
crystallization is accelerated and may be interpreted by the formation of
(nano)structures during cooling such as quenched-in nuclei46 or
precursors of nucleation.
If a glass contains a sufficiently high number of quenched-in
nuclei, heterogeneously nucleated crystallization occurs during
heating. Based on the Kolmogorov?Johnson?Mehl?Avrami
(KJMA) equation47?49 for isothermal crystallization we can show
that the cooling rate dependence of the peak temperature follows
a power law (see Supplementary Discussion), i.e.,
TPeak ? T1 ? C ?c
where C and ? are empirical constants, T1 is the minimum
crystallization temperature during heating, ?0 is the minimum
cooling rate for crystallization during heating, and ?c is the
By fitting of the data in Fig. 2a, the parameters are determined
as C = 34.2 K, ? = 0.1, T1 = 224.9 ?C, and ?0 = 190.7 K s?1. The
resulting curve fits the experimental data well. This indicates that
the nucleation density is, in a first approximation, proportional to
the previous cooling rate. This agrees with investigations on a
Zrbased BMG, where model calculations indicate that the
crystallization kinetics during heating can be described by a number
density of pre-existing nuclei rather than by a nucleation rate50.
Figure 2b shows the intensity of the glass transition as a
function of the previous cooling rate. Below a cooling rate of
approximately 200 K s?1 no glass transition occurs, and the
material is completely crystalline. After cooling at a rate of more
than 500 K s?1 the glass transition intensity is constant (?cp =
0.14 J g?1 K?1) and the sample is completely amorphous. At
cooling rates between these limits, crystals have formed but the
crystallization time is too short for complete crystallization of the
sample. The reaming glassy phase generates a reduced glass
transition with ?cp < 0.14 J g?1 K?1. The intensity of the glass
transition vs. the previous cooling rate to form a glass in Fig. 2b,
and the shift of the crystallization temperature in Fig. 2a, indicate
the existence of three critical cooling rates.
The lowest critical cooling rate, ?c,SCG ? 200 K s?1, is the upper
cooling rate limit at which the material completely crystallizes
during cooling. Above this rate (and below 500 K s?1) crystals
and glassy regions coexist, and a semi-crystalline glass (SCG) or
glass composite (using metallurgy terminology) forms. Such a
glass often has the structure of a dispersion of nanoparticles in the
The second critical cooling rate, ?c,SDG ? 500 K s?1, is the lower
cooling rate limit at which an amorphous glass can be formed.
Above this rate (and below 4000 K s?1), the glass contains regions
with an increased local order, which comprises quenched-in
nuclei or precursors for nucleation (embryos). These metastable
structures accelerate nucleation or act directly as nuclei during
subsequent heating. We call such a glass self-doped glass (SDG).
The mass content of the quenched-in nuclei or precursors is so
small that it has no influence on the glass transition intensity
(Fig. 2b). The increase in the crystallization temperature with
increasing cooling rate, however, indicates a reduced number of
quenched-in nuclei or precursors after faster cooling (Fig. 2a).
The SDG contains nanostructures which may be
noncrystalline metastable clusters in the glass resulting from spatial
heterogeneities11,52,53 or quenched-in nuclei, as frequently noted
in Al-based BMGs54?59. Such nuclei form during quenching, but
their growth is limited due to the reduced temperature and solute
rejection55. Transmission electron microscopy (TEM) and X-ray
diffraction (XRD) measurements have shown that a BMG appears
completely amorphous even if it contains quenched-in nuclei56.
The number density of such structures in an Al-based BMG is on
the order of 1021 m?3 (ref. 60).
Above the highest critical cooling rate of ?c,CHG ? 4000 K s?1, a
chemically homogeneous glass (CHG) forms. Such a glass
contains no quenched-in nuclei or precursors which accelerate
nucleation during heating.
A comparison of the crystallization kinetics of the SCG and the
SDG in Fig. 2a shows no abrupt variations in the cooling-rate
dependence. In fact, for both glasses the cooling rate dependence
of the crystallization peak follows Eq. (
) with the same parameter
set, i.e., the nucleation kinetics in the SCG and the SDG are
comparable. This indicates that the crystals and the quenched-in
clusters act similarly in the crystallization process, which leads us
to conclude that the quenched-in clusters are nuclei rather than
precursors of nucleation at low temperatures.
In contrast to the above, a comparison of the crystallization
kinetics of SDG and CHG in Fig. 2a clearly shows a cooling-rate
dependence of the crystallization peak during heating for these
two types of amorphous glasses. Whereas in the CHG
crystallization is independent of cooling-rate variation, in the SDG a
lower previous cooling rate results in accelerated crystallization.
The influence of processing and cooling conditions on
crystallization of glasses during heating has been reported for
many different families of BMGs14,40,50,61,62. This leads us to
conclude that the formation of SDGs is a common occurrence in
BMG alloy processing.
To study the generality of this phenomenon, we also performed
similar measurements on the Pt-based BMG
Pt57.3Cu14.6Ni5.3P22.8, as described in Supplementary Note 2. Here we can
also distinguish between SCG, SDG, and CHG and obtain critical
cooling rates of ?c,SCG ? 2 K s?1, ?c,SDG ? 20 K s?1, and ?c,CHG ?
150 K s?1, respectively, as seen in Supplementary Fig. 2. The
occurrence of SDG and CHG thus appears to be a general
phenomenon in BMG processing.
Critical heating rates. If a glass is heated at sufficiently high rates,
no crystallization occurs. The critical heating rate is the lower
heating rate limit for avoiding crystallization, and it has been
frequently reported that it is substantially higher (in orders of
magnitude) than the critical cooling rate14,15,45,63,64. The
existence of differently structured glasses (SDG and CHG), however,
leads us to expect that each type of glass has its characteristic
critical heating rate.
To determine the critical heating rate of the CHG, the
Aubased liquid was cooled at 20,000 K s?1 and the resulting glass
reheated at various rates. Selected curves are shown in Fig. 3a. At
low heating rates crystallization occurs after the glass transition,
followed by melting. The crystallization peak shifts to higher
Cooling at 20,000 K s?1
Heating rate (K s?1)
Cooling at 600 K s?1
Heating rate (K s?1)
temperatures when the heating rate is increased, and at a heating
rate between 1000 and 5000 K s?1 crystallization is not finished
when melting starts. The material cannot crystallize completely,
i.e., the crystallization rate is thermodynamically limited.
Nevertheless, for all crystallization and melting processes the total
transformation enthalpy (containing crystallization and melting)
becomes zero within the error of the experimental detection limit.
Above the critical heating rate of ?h,CHG ? 6000 K s?1 no
crystallization can be observed. In that case, also no melting
To determine the critical heating rate, ?h,SDG, of an SDG the
liquid was cooled at 600 K s?1 to RT before heating the glass at
various rates (Fig. 3b). The curves appear similar to those in Fig. 3a,
but the effect of neither crystallization nor melting appears at a
much higher critical heating rate of ?h,SDG ? 20,000 K s?1.
The assumption that in metallic glasses the critical heating rate is
orders of magnitude higher than the critical cooling rate15,63,64 is
thus only valid for the nanostructured SDG (?c,SDG ? 500 K s?1,
?h,SDG ? 20,000 K s?1), where quenched-in nuclei or precursors
already exist. Here, to completely melt the glassy phase the heating
process has to be fast enough so that existing nuclei stay at
subcritical size. This happens when the heating rate is so high that
the increase in the critical size of a nucleus due to temperature
increase is faster than the actual nucleation, i.e.,
where ?h is the heating rate, V is the volume, v* is the volume of a
critical nucleus, and N is the number of nuclei. The second
possible mechanism for avoiding crystallization of a glass with
existing nuclei is to bypass the growth region during heating. In
the framework of a TTT diagram this means that the curve of the
total temperature program does not touch the growth region.
For CHGs the critical cooling and heating rates only differ by a
factor of 1.5 (?c,CHG ? 4000 K s?1, ?h,CHG ? 6000 K s?1). This
relatively small difference can be explained by an asymmetric
curve shape of the nucleation rate vs. temperature, or by a very
small number of remaining quenched-in nuclei or precursors.
In the next step the crystallization and melting behavior of
samples cooled at different rates between 10 and 40,0000 K s?1
was investigated upon heating at the two critical heating rates of
?h,SDG = 20,000 K s?1 and ?h,CHG = 6000 K s?1 (Fig. 4). The
heating curves at 20,000 K s?1 (Fig. 4a) are arranged in two
groups. After fast cooling (?c ? ?c,SDG ? 500 K s?1) no
crystallization occurs and only the glass transition is measured. For slow
cooling at rates ?c < ?c,SDG the formed glass contains crystals,
which reduces the intensity of the glass transition and causes a
melting peak. No crystallization is observed here because of the
high heating rate of 20,000 K s?1, which is fast enough to prevent
not only the crystallization of quenched-in structures, but also the
further growth of existing crystals. At this high heating rate it is
only possible to distinguish between amorphous glasses (CHG
and SDG) on the one hand and semicrystalline glasses (SCGs) or
fully crystalline material on the other. This information can also
be derived from the cooling curves in Fig. 1a and the intensity of
the glass transition in Fig. 2b.
Figure 4b shows heating curves of differently cooled samples
measured at a heating rate of 6000 K s?1. Here the curves can be
separated into four groups.
In the first group, where ?c ? ?c,CHG ? 4000 K s?1, no
crystallization and melting events occur in the heating curve. The
heating rate is fast enough to up-quench the chemically
homogeneous glass. Here, the term up-quenching refers to a
heating process at which the heating is so rapid that no structural
changes occur before melting of the previously frozen phase36.
At ?c,SDG ? 500 K s?1 ? ?c < ?c,CHG, the heat flow around the
glass transition region is independent of the previous cooling rate.
This means that the glass transition intensity does not vary with
the cooling rate (although changes are seen in the glass transition
region due to a variation in the enthalpy recovery peak, resulting
from the different cooling histories of the SDG). Furthermore,
crystallization and melting events can be detected in the
supercooled melt above the glass transition, but the total
transition enthalpy remains zero. The quenched-in clusters act
during heating as nuclei or precursors for nucleation, which
For ?c,SCG ? 200 K s?1 ? ?c < ?c,SDG, the glass transition
intensity reduces with decreased cooling rate. Here, crystallization also
occurs during heating but the melting peak is significantly higher
than the crystallization peak because the SCG already contains
crystals which melt, but no longer contribute to the crystallization
event upon heating.
Finally, after slow cooling at ?c < ?c,SCG, no glass transition and
crystallization are observed upon heating because the material
already crystallized completely during cooling. A slight decrease
in the melting peak temperature at faster cooling rates reveals the
reduced stability of the crystals formed. This indicates that the
Crystals SCG SDG CHG
crystals have sizes in the nanometer range, and that the melting
temperature of the nanocrystals decreases with a decrease in
particle size due to their surface enthalpy (Gibbs?Thomson
effect). A melting point depression has, for example, been
experimentally verified for nanosized indium particles65.
The intensity of the glass transition, ?cp, the total
transformation enthalpy, ?H, and the enthalpy of the exothermic
crystallization peak, ?Hcryst, were evaluated from the curves in Fig. 4b.
The 6000 K s?1 heating rate data regarding ?cp and ?H were also
added to Supplementary Fig. 1 to further verify the linear
correlation between the relative intensity of the glass transition
and the crystallinity. Figure 5 shows all data (?H, ?Hcryst, ?cp) as
a function of the cooling rate at which the glass was formed, and
clearly links the four different regimes with the cooling process.
In the CHG no crystallization and melting occur and the intensity
of the glass transition is maximal. The latter is also true for the
SDG, but here a small crystallization event is observed, and the
modulus of the crystallization enthalpy |?Hcryst| slightly increases
with a decrease in cooling rate. However, because the total
enthalpy of transformation is zero, all crystals must have formed
upon heating (whereas no crystals had formed upon cooling). The
crystallization process is accelerated (see Fig. 2a) due to the
existence of quenched-in nuclei, which, however, do not influence
the intensity of the glass transition.
In the SCG the crystallinity increases with a decrease in cooling
rate, which is reflected in the related increase in the total
transformation enthalpy and the decrease in the glass transition
intensity. During heating the remaining amorphous fraction
tends to crystallize, which generates a finite crystallization
enthalpy. Finally, in the crystalline material created after slow
cooling, only melting can be measured in the subsequent heating
curve, so that ?cp = 0 and ?H = ?Hmelt ? ?Hm reaches a
These results agree nicely with the findings in Fig. 2, so that
recommendations regarding the experimental parameters for a
detailed analysis of glass behavior can be derived: In cooling
experiments it is only possible to determine the critical cooling
rate for SDGs (see Fig. 2b), while more information on glass
properties can only be obtained from heating measurements.
Here, the heating rate selected is essential for the resolution of the
measurement, and the rate must be adapted to the kinetics of the
nucleation and growth processes. If the heating rate is ??h,SDG =
20,000 K s?1 (Fig. 4a), the results will only duplicate the
conclusions of the cooling measurements. If the heating rate is
too slow, nucleation will always occur during heating and the
resolution in the kinetic analysis will not be sufficient to
differentiate the various initial conditions in the glass. At heating
rates ?h,CHG ? ?h < ?h,SDG (Fig. 4b), the enthalpy determination by
peak integration (see Fig. 5) can be used. This is more sensitive
and robust than the evaluation of the peak temperature (Fig. 2a),
because it is an integral method without any curve shape
Isothermal crystallization. The non-isothermal measurements
indicate that two different kinds of completely amorphous glass
can be formed during cooling. The different nucleation densities
in the glasses also influence the isothermal crystallization kinetics.
To demonstrate this, CHG and SDG were formed upon cooling at
20,000 K s?1 and 500 K s?1, respectively, and heated at a rate of
30,000 K s?1 to a crystallization temperature between 179 and
349 ?C (see Supplementary Note 3). The heat-flow curves of
isothermal crystallization measured within a timeframe of 5 s are
shown in Supplementary Fig. 3. Most curves show multiple
crystallization events, which are possibly induced by the
formation of different phases. Multiple peaks during isothermal
crystallization are frequently reported for BMGs51,66. Here we
concentrate on the first event.
In the isothermal crystallization curves of the CHG
(Supplementary Fig. 3a) the shape of the crystallization peaks and their
positions fluctuate significantly. This can be explained by a lack of
nuclei in the supercooled melt, with the heat-flow curves
reflecting the statistics of spontaneous nuclei formation. This
causes the stochastic and non-predictable appearance of the
crystallization peaks seen in Supplementary Fig. 3a.
In contrast to the above, the crystallization curves of the SDG
(Supplementary Fig. 3b) show smoothed crystallization peaks, as
expected for nucleated material or materials with a high
nucleation rate. This means that the glass already contains
(quenched-in) nuclei, or at least precursors which require only a
small amount of free enthalpy to reach the critical size.
Time?temperature?transformation diagram. To characterize
the crystallization process, from the heat-flow curves in
Supplementary Fig. 3 we evaluated the onset times (beginning of
crystallization) and peak times of the crystallization (maximum
crystallization rate) as a function of temperature. The endset was
not selected due to the potential influences of subsequent
crystallization processes. Using these data, we can construct
time?temperature?transformation (TTT) diagrams (see Fig. 6)
for the SDG, obtained by cooling at a rate of 500 K s?1, and the
CHG, obtained by cooling at a rate of 20,000 K s?1. While the
TTT diagrams of the SDG and CHG are close at low
temperatures, which is the region of high nucleation rate and
growthcontrolled crystallization, they are significantly different at
medium and high temperatures, where the nucleation rate is low.
There the SDG crystallizes significantly faster than the CHG.
Furthermore, crystallization of the CHG becomes stochastic near
and above the nose of the TTT diagram (see region marked in
yellow) as the result of a stochastic nucleation process, and at
high temperatures the supercooled melt from the CHG does not
even crystallize in the timeframe of the investigation (see region
marked in light blue) due to a lack of nuclei. A TTT diagram on
heating was also measured in ref. 14 using a comparable Au-based
glass cooled at a rate of ?5000 K s?1. There, however, the TTT
diagram of an SDG was determined without detecting stochastic
No nuclei formation CHG
Stochastic nucleation 350 ) 300
Visualization of the critical scanning rates for the different
types of glasses. If the melt of a BMG alloy is quenched into the
glassy state, nanostructured heterogeneities may form in the glass
and influence the glass properties and crystallization kinetics
above the glass transition. These are metastable (nano)structures,
such as nanocrystals, nuclei, or precursors for nucleation, which
significantly influence the crystallization during reheating from
the glassy state. The nature of these heterogeneities is different to
that of dynamic heterogeneities discussed in the context of
cooperative motions in supercooled liquids67.
Based on TTT diagrams, Fig. 7 provides a schematic
visualization of the cooling conditions (solid lines) which
generate the different types of glasses. This figure also shows
the heating conditions needed to avoid crystallization (dashed
lines). The start and end temperatures of the heating and cooling
lines in Fig. 7 are always at a temperature slightly above the
equilibrium melting temperature and at a temperature in the
glassy state, respectively. In this model we assume a
thermodynamically equilibrated homogeneous (unstructured) melt
above the melting point. This means that the cooling process
starts without any heterogeneous nuclei. We also assume a
sufficiently large temperature distance between the maxima in
growth and nucleation rate.
Upon slow cooling, the melt completely crystallizes and no
glass is formed. Upon an increase in the cooling rate, a critical
rate, ?c,SCG, is reached, which is the minimum cooling rate at
which the material does not completely crystallize. Such an SCG
contains both crystalline and amorphous regions. The primary
crystallization occurs in the range between the onset and end of
the growth curve, but not above the nucleation curve. Figure 7a
demonstrates that the critical cooling rate ?c,SCG is obtained from
the intersection of the endset of the growth curve with the (onset
of the) nucleation curve. The high-temperature limit for
crystallization is the nucleation curve and the low-temperature limit is
the curve of growth onset. The shorter the time the material stays
in this region, the less is the crystallinity. The heating rate needed
to up-quench an SCG (i.e., to melt it without further
crystallization) must bypass the growth region; this heating rate is
illustrated as dashed line in Fig. 7a. Such a strategy of
upquenching a previously frozen metastable structure with the help
of advanced chip calorimetry may lead to the discovery of various
metastable phases (including their melting enthalpy and
temperature)36, and thus contribute to the understanding of
crystallization pathways not only in metallic systems, but also in
polymers, pharmaceuticals and biological systems.
Figure 7b shows the critical conditions for an SDG. The critical
cooling rate, ?c,SDG, at which the melt no longer crystallizes is
characterized by the intersection point of the growth and nucleation
curve. At such cooling the material remains in the nucleation region
for a certain time and, consequently, nuclei are formed during
cooling. The number of (quenched-in) nuclei in such SDGs
depends on the time during cooling in the nucleation region. The
critical heating rate, ?h,SDG, has to bypass the growth region. It is the
same as the up-quench rate for generating an SCG, and is
significantly greater than the critical cooling rate ?c,SDG.
Figure 7c illustrates the critical cooling and heating conditions
for a CHG. At the critical rates ?c,CHG and ?h,CHG the nucleation
region is bypassed and, thus, quenched-in nuclei do not form in
CHGs. Because of the lack of nuclei, the material can pass
through the growth region during heating without any
crystallization. To consider the dwell time of the supercooled liquid in
the temperature range of the maximum nucleation rate, the
heating line in Fig. 7c does not start at the origin of the
coordinates. Consequently, the critical heating and cooling rates
for a CHG differ somewhat (in our case by a factor of 1.5), but
not by orders of magnitude as reported frequently in literature by
determining the thermodynamics of an SDG14,15,63,64.
While scanning electron microscopy, X-ray diffraction or
conventional high-resolution TEM can detect metastable
microstructures and nano-scale precipitates in an SCG68, these
techniques may not be able to resolve structural inhomogeneities
in an SDG. Here electron correlation microscopy, as recently
applied to BMGs69, may resolve the nuclei in SDGs that clearly
influence the crystallization kinetics, as observed by FDSC.
Revealing atomic/nano-scale differences between SDGs and
CHGs via imaging techniques may be the focus of future work.
An Au49Ag5.5Pd2.3Cu26.9Si16.3 metallic glass quenched from the
melt into the glassy state under controlled linear cooling was
measured over a wide range of cooling rates by fast differential
scanning calorimetry (FDSC). The critical cooling rate at which
the sample does not crystallize can be directly determined from
the cooling curves measured. More information, however, was
obtained by analyzing the subsequent heating scans. This study
shows that different kinds of glass can be formed via cooling from
the melt, and that three different critical cooling rates for metallic
glass formation exist: ?c,SCG ? 200 K s?1, ?c,SDG ? 500 K s?1, and
?c,CHG ? 4000 K s?1. The crystallization behavior of these glasses
Cooling between ?c,SCG and ?c,SDG produces a semi-crystalline
glass (SCG) or glass composite, respectively. The crystalline phase
content increases with a decrease in the cooling rate. This is
measured using FDSC by the change in the intensity of the glass
transition, ?cp, or in the total enthalpy of phase transformation, ?H.
A self-doped glass (SDG) is formed at cooling rates between
?c,SDG and ?c,CHG. Such a glass appears completely amorphous, but
it contains nanoclusters which act as quenched-in nuclei or
precursors (embryos) and accelerate crystallization during reheating,
even though the glass transition intensity is maximal. Here, the
critical heating rate ?h,SDG = 20,000 K s?1 (which is the minimum
rate to melt the SDG without crystallization) is 40 times greater
than the critical cooling rate ?c,SDG. It seems that most of the
technically cooled bulk metallic glasses are SDGs, and that the
critical cooling and heating rates reported so far always relate to
Cooling at rates higher than ?c,CHG produces a chemically
homogeneous glass (CHG) without such quenched-in nuclei, and
thus crystallization ability is significantly reduced. For such a
CHG the critical heating rate ?h,CHG = 6000 K s?1 is much lower
than that of an SDG, and is comparable to the critical cooling rate
In conclusion, we emphasize that such detailed distinctions
between different types of glasses upon cooling have never been
made so far. In fact, they are only now possible because of newly
developed chip calorimetry which allows cooling rate variations
of up to 40,000 K s?1. The occurrence of SDG and CHG appears
to be a general phenomenon in metallic glass formation, as also
revealed by additional measurements on a Pt-based BMG (see
Supplementary Figure 2). The distinction between SDGs and
CHGs has important consequences for metallic glass processing,
and for glass theory in particular, in view of the fact that many
publications have reported on various glass-forming criteria
without drawing on detailed experimental knowledge of the glass
nanostructure or medium-range order. The concept of differently
structured glasses presented here is based on fundamental models
of glass formation and nucleation, and may also hold for other
kinds of thermal treatment (e.g., short annealing above the glass
transition). We therefore assume that SCG, SDG and CHG can
also form in molecular glasses in dependence on their preparation
condition. We thus also expect this phenomenon to be highly
relevant to the physical stability of molecular glasses, which are
used in many areas such as pharmaceuticals and biology.
Sample preparation. The elements Au (99.95%), Cu (99.9%), Ag (99.5%), Si
(99.95%), and Pd (99.95%) were pre-alloyed to a sample with nominal composition
Au49Ag5.5Pd2.3Cu26.9Si16.3 (in at.%) via repeated induction melting in a quartz tube
that was sealed under 99.999% pure Ar atmosphere14. The mass loss during
alloying was negligible, so that the real composition equaled the nominal one.
Chemically homogenous glassy ribbons of approximately 30 ?m thickness were
then produced by melt spinning under 5N+ pure He atmosphere.
Fast differential scanning calorimetry. FDSC measurements were performed
using a prototype of a Mettler-Toledo Flash DSC 2+. This instrument is an
advanced version based upon Flash DSC technology, with a sealed measurement
cell for reduced oxygen content. The Flash DSC 2+ can be operated with a UFS
1 sensor70 or a new UFH 1 sensor (see insert to Supplementary Fig. 4), which can
be operated to about 1000 ?C. The active area of the latter sensor is reduced by 1/3
and the membrane thickness is reduced compared to the UFS 1 sensor. The
diameter of the active zone is approximately 100 ?m, which increases the applicable
cooling rate to approximately 40,000 K s?1.
The sample support temperature of the FDSC was set to ?30 ?C using a Huber
intracooler TC45, and the furnace was purged with nitrogen at a flow rate of 60 ml
min?1. The melt-spun ribbons were cut under a stereomicroscope into small pieces
with a surface of approximately 104 ?m2. Their mass was estimated using the
melting enthalpy of ?Hm = 40.4 J g?1 (ref. 14) to be on the order of 1 ?g, for which
no size-dependent nucleation and crystallization effects are expected45. Details
regarding temperature calibration, thermal lag (Supplementary Fig. 4), and
enthalpy resolution (Supplementary Fig. 5) are given in the Supplementary
The datasets generated during and/or analysed during the current study are
available from the corresponding author on reasonable request.
This work was created because a person in industry and another in academia shared the
same enthusiasm for science. We thank ETH Zurich and Mettler-Toledo for supporting
this type of collaboration without the need of external funding.
J.E.K.S and J.F.L. conceived the study. J.F.L. provided the material and J.E.K.S conducted
the measurements. Both authors evaluated and discussed the data extensively and jointly
wrote the manuscript.
Journal peer review information: Nature Communications thanks the anonymous
reviewers for their contribution to the peer review of this work. Peer reviewer reports are
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Additional information Supplementary Information accompanies this paper at https://doi.org/10.1038/s41467- 018-07930-3.