Criticality in Bulk Metallic Glass Constituent Elements
Criticality in Bulk Metallic Glass Constituent Elements
RODRIGO MIGUEL OJEDA MOTA 0
T.E. GRAEDEL 0
EVGENIA PEKARSKAYA 0
JAN SCHROERS 0
0 1.-Department of Mechanical Engineering, Yale University , New Haven, CT 06510, USA 2. -School of Forestry and Environmental Studies, Yale University , New Haven, CT, USA 3.-Supercool Metals, New Haven, CT 06511, USA. 4.- , USA
Bulk metallic glasses (BMGs), which readily form amorphous phases during solidification, are increasingly being used in first applications of watch components, electronic casings, and sporting goods. The compositions of BMGs typically include four to six elements. Various political and geological factors have recently led to supply disruptions for several metals, including some present in BMG compositions. In this work, we assess the ''criticality'' of 22 technologically interesting BMG compositions, compare the results with those for three common engineering alloy groups, and derive recommendations for BMG composition choices from a criticality perspective. The criticality of BMGs is found to be generally much higher compared with those for the established engineering alloys. Therefore, criticality concerns should also be considered in the choice between existing and developing novel BMGs.
Bulk metallic glasses (BMGs) are alloys that
readily form an amorphous phase during
solidification.1,2 The adjective ‘‘readily’’ indicates
solidification of an alloy in amorphous form with at least
1 mm thickness, which approximately corresponds
to cooling rates for vitrification below 1000 K/s.2
BMGs comprise transition metals that are often
combined with metalloids, which are then combined
in a multicomponent alloy.3,4 The amorphous
structure results in very high strength and elasticity,
properties that are often paired with toughness,5
flaw tolerance,6 high corrosion resistance,7–10
biocompatibility,11–13 and favorable electrochemical
behavior.14 These properties have triggered wide
commercial exploration of BMGs.15–17 One of the
most unusual and useful attributes of BMGs are that
they escape the typical materials trade-off of
processibility versus properties.18 The high stability
against crystallization results in a supercooled
liquid region that enables thermoplastic forming (TPF)
similar to the processing of thermoplastics.18 Thus,
BMGs can be considered high-strength metals that
can be processed like plastics.18,19 TPF-based
processes for BMGs like blow-molding,18 extrusion,20,21
compression molding,22,23 micro- and
nano-molding,17,24 and hot-rolling25 permit BMGs to be formed
into many complex shapes on various length scales.
It has been estimated that more than 10 million
alloys form BMGs.26 The selection criteria for
BMGforming elements include their relative size,2,4,27,28
their thermodynamic attraction quantified in the
pairwise heat of mixing,2,29,30 and the stability of
the liquid compared with the crystal.31–33 The latter
is quantified by the suppression of the liquidus
temperature compared with the weighted rule of
mixing of the melting temperature of the
constituents. These complex selection rules for BMG
constituents do not a priori identify or disqualify
elements. Rather, their suitability is primarily
determined by the interplay of the constituents
rather than their inherent properties.4 Overall,
more than 30 elements have been reported to be
present in BMGs.26
GROWTH OF BMG COMMERCIAL USAGE
The combination of BMG properties with
thermoplastic formability has led to rapidly growing
commercial interest. Early adaptation includes the use
of BMGs in sporting goods, watch components, and
electronic casings.16,19,34,35 The focus of the early
applications has been on the small scale, typically
below 10 cm. This length scale has its origin in
limited supply chains, high materials costs for most
advanced BMGs, and a limited processing
infrastructure.15,36 In principle, considering BMG
constituent selection criteria and the wide range of
potential BMGs, the BMG application range is
limited in thickness but not in size. Current
understanding suggests that it may be most promising to
use BMGs in applications where at least one
dimension is smaller than 1 mm.37 In such
dimensions, BMGs offer significant ductility in addition to
the earlier discussed property advantages.37 Such
geometries are typical in aerospace, automotive,
and space applications, as well as in a wide range of
To provide perspective on possible increasing
metal demand for constitutive BMG elements, we
address growth trends in current activities in the
commercial and academic arena. As an example, we
consider electronic casings for mobile phones, where
because of current size limitations in fabricating
BMGs, most near-term commercial activities have
occurred. One could argue that BMGs could
constitute some 20% of the mobile casing market based on
current metal usage and the trend to higher
performance materials. With the annual global sales of
cell phones at 1.5 billion, and 50 g per phone for
the casing fabrication, the material demand is of the
order of 75,000 metric tons (75 Gg) of BMG
constituents annually. Other electronic casings and
larger size applications in aerospace and automotive
sectors are less quantifiable and likely will not be
widely employed within the next 3 years. When
they are, however, these applications will consume
dramatically larger quantities of materials than
BMGs do at present. Because some BMG
formulations contain elements with tiny annual productions
(e.g., Be38 and Er39), it behooves materials scientists
to be aware of the potential supply limitations of
candidate BMG constituents.
One attribute of BMG-forming mixtures that has
not heretofore been considered in assessing BMG
commercial viability and suitability is elemental
criticality. Criticality is defined as ‘‘essential to
economic development but having limited supplies
and being subject to supply–demand imbalances’’.40
Thus, in theory, an element may be ideal for glass
formation or a BMGs’ property or application, but if
that application becomes robustly deployed,
limitations may be imposed by factors such as geological
availability or toxicological attributes that could
constrain use in BMG applications.
Despite one’s intuition that it should be
straightforward to designate one element as critical and
another as not, determining criticality turns out to
be very challenging indeed.41 This is because
criticality depends not only on geological abundance
but also on a host of other factors such as the
potential for substitution, the degree to which ore
deposits are geopolitically concentrated, the state of
mining technology, the amount of regulatory
oversight, geopolitical initiatives, and degree of
governmental instability.40 As various
organizations (e.g., Refs. 41–43) have attempted to
determine resource criticality in recent years, various
metrics and methodological approaches have been
chosen. The predictable result has been that
criticality designations have differed widely.44
The criticality methodology that we employ in the
present work45 was designed to be applicable to
users of different organizational types (e.g.,
corporations, national governments, and global-level
analysts), and it is purposely flexible to allow user
control over aspects of the methodology such as the
relative weighting of variables. As with any
evaluation employing an aggregation of indicators, the
choice of those indicators is, in part, an exercise in
judgment,46 but alternative choices have been
evaluated over several years and we believe all of our
final choices to be defendable in detail. The
methodology locates individual metals in a
three-dimensional ‘‘criticality space,’’ the axes being supply risk,
Environmental Implications, and Vulnerability to
Supply Restriction (Fig. 1). Evaluations of each axis
involve numerous criticality-related indicators, each
measured on a 0–100 scale and weighted equally.
For the evaluation of the criticality of BMG
constituents, we regard medium-term supply risk as
the most important characteristic to be assessed. Its
assessment involves three components and six
indicators, as shown in Fig. 1. (Each of the
indicators is discussed in detail in Ref. 45).
The methodology has been applied to 62 metals
and metalloids (hereafter termed ‘‘elements’’ for
simplicity of exposition)—essentially all elements
except highly soluble alkalis and halogens, the noble
gases, nature’s ‘‘grand nutrients’’ (carbon, nitrogen,
oxygen, phosphorus, sulfur), and radioactive
elements such as radium and francium that are of little
technological use. Detailed results for individual
groups of elements have been published
separately.47–53 In general, the elements with the
highest crustal abundances (iron, aluminum, copper,
etc.) are of little concern from a criticality
perspective. Those that are rare, especially if they are only
available as by-products of the major metals, rank
higher in the criticality evaluation.
To apply the concept of criticality to BMGs, we
identified 32 elements as potential constituents in
BMG alloys. Figure 2 depicts their supply risk and
their most significant supply range matrix.
APPLICATION OF THE CRITICALITY
CONCEPT TO BULK METALLIC GLASSES
How can metal criticality information be useful
in the selection of constituents for BMGs? We
propose that a promising approach is to plot data
from criticality assessments of metals against
some suitable characteristic parameter for a
BMG composition (or perhaps a BMG family).
The concept is illustrated in Fig. 3. In general, one
would like to choose a BMG composition with a
low supply risk (SR) and a high performance
parameter, so that the composition would fall in
the upper lift quadrant of Fig. 3. A composition
with a low performance parameter (thus, falling in
the lower left and lower right quadrants) would
obviously be not suitable as a BMG. A composition
with both a high performance parameter and a
Some suitable performance parameter for a BMG family
Low risk, Low performance
High risk, Low performance
Supply risk (individual metals) (from criticality assessment)
Fig. 3. Speculative diagram to identify BMG groups that combine
varying degrees of criticality and performance.
high supply risk (upper right quadrant) might
perform well but could perhaps come under supply
constraints if employed extensively.
An evaluation of the type suggested in Fig. 3
could be done in several ways. As an example for
discussion, we suggest plotting for a given BMG
composition the highest constituent SR value on the
abscissa and a function of one or more
characteristics of the composition on the ordinate. A simple
example, but a useful one, is that of selected
physical properties of BMG compositions. We choose
to express the performance of an individual BMG as
the product of yield strength, ry, and fracture
toughness, Ki. To make such data more meaningful
for a relative comparison, we normalize values by
their median value, which we determine from a
broad selection of BMGs; i.e.,
Pi ¼ ðKiðBMGiÞ =KiðBMGmÞÞ
where Pi is the performance of composition i, and
subscript m refers to the median of the values in
Table I. In this formulation, a BMG composition
that has the fracture toughness and yield strength
of the average BMG composition would thus have a
performance rating of unity.
To represent the material class of BMGs broadly,
we considered overall 22 different alloys (Table I).
As a comparison, we chose a representative common
steel, stainless steel, titanium, and aluminum alloy.
Criticality information for considered alloys are
listed in Table I and organized by their performance
in Fig. 3. There is a significant performance range
among the considered alloys. Ni62Pd19Si2P17
performs more than 100% better than the median
BMG, whereas Mg65Cu25Y10 exhibits only 2% of
the performance of the median BMG. For the
established conventional alloys, Ti6V4Al performs
comparable to the median BMG, whereas the steels
perform 50% and aluminum alloys 10% of that of
the median BMG.
The information from Table I can now be used to
generate a performance-criticality matrix of the
type indicated in Fig. 3. The results are shown in
Fig. 4. The technique populates all four regions of
the diagram. From the perspective of this analysis,
the most desirable BMG compositions are
Ni62Pd19Si2P17, Cu49Hf42Al9, Cu60Zr20Hf10Ti10, and
Pt57.5Cu14.7Ni5.3P22.5, which are in the upper left
quadrant. These alloys are limited by copper and
palladium as their highest criticality value. In
contrast, the least desirable compositions are those
that populate the lower right quadrant:
Fe48Cr15Mo14Er2C15B6, and Ni40Cu5Ti17Zr28Al10.
These less desirable alloys are limited by zirconium,
silver, and erbium.
It is important to understand why some elements
in Table I (e.g., silver) have higher SR values when
compared with those of other elements in the BMG
compositions. As it happens, the Yale methodology45
evaluates SR based on six indicators (Fig. 1). In the
case of silver, for example, the depletion time is
short (currently 20 years), and the companion
fraction is high.52 Most silver is produced as a
byproduct of lead–zinc and copper ores. Other
indicators are high for other metals. In Table I, column 7,
we indicate the expanded SR metric most
responsible for the SR rating of the different BMG
compositions. It is clear that because compositions such as
BMGs generally use one or more of the less
abundant materials, their criticality could prove to be
much more significant than is the case for common
Overall, because criticality depends on the most
critical element in an alloy (at least under the
methodology employed herein), simpler alloys
generally tend to be less critical than those that are
more compositionally diverse. This suggests that as
a result of their multicomponent nature, generally
BMG alloys are more critical than simple alloys.
Nevertheless, BMGs are less critical than, for
example, high-entropy alloys, which constitute
more than five elements,86 or superalloys, which
often contain more than ten elements.39 We do not
imply that criticality should be the dominant factor
in making compositional choices for any of these
types of alloys. Yet, we believe that criticality
should be a factor that enters into considerations
of compositional choice. In this article, we present
one possible approach to taking criticality into
In the development of an alloy, a broad range of
requirements are considered that at least to some
extent are controlled by its constituent elements.
Specifically, for metallic glasses, element selection
is often considered through their collaborative
behavior to result in deep eutectics,2,33 large
negative heat of mixings,2 and size difference.2,4,28,87
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Individual constituent element properties can be
used to estimate material cost and, to some extent,
strength and plasticity.88 Acknowledging the
development status of BMG technology as being on the
threshold of wider commercial adaptation,15
criticality is another important aspect to be considered
when considering BMGs for applications or in the
development process of BMGs.
An important aspect of our analysis is that we
have chosen to select for the figures the element in a
BMG composition that has the highest criticality
value; that is, what is plotted on the abscissa of
those figures is not an average value for the
elements in a BMG composition. The criticality of
a BMG alloy, measured in this way, might thus
refer to an element present in tiny amounts.
Nonetheless, it could be essential to creating the
performance desired, so its unavailability would
essentially remove the entire BMG alloy from
It is shown elsewhere47,51 that the elements that
have high criticalities tend to be ‘‘companion
metals’’ (those only available as by-products of host
metals in ore deposits), and only those companion
metals that have no suitable substitutes for most or
all of their uses. It would be preferable to avoid
those elements in BMG compositions, if possible.
Alternatively, it would be advisable to use
highcriticality metals only for small, high-value-added
applications, and not in essential technologies
where the unavailability of a crucial BMG element
could have major consequences.
Elements that have been used in BMGs with
highest criticality are Zr (
), Ag (
), Mo (
), La (
), and Er (
). These elements have been
essential in warranting a high glass-forming ability
in the corresponding BMG alloy. Nonetheless, the
importance of these elements varies considerably.
Whereas La, Er, Mo, and Cr might be replaceable
and only affect a few alloys, specifically Zr is the
base element for many BMGs. This is because Zr
exhibits deep eutectics with Be and Ni, as well as
exhibits drastic reduction in liquidus temperature
with Cu and Al. Such destabilization of the
competing crystalline phase leads generally to an increase
in Tg/Tl, which indicates an enhanced glass-forming
ability (GFA; ease of glass formation).32
Furthermore, it has favorable phase diagrams with limited
high-temperature intermetallic phases, again
avoiding stable competing crystalline phases.
Furthermore, Zr also exhibits often large solubility with
many practical elements, most prominent with Ti.
This allows for substitution of Zr with these
elements that might yield other benefits such as
improved glass-forming ability or enhancement in
properties. A possible substitution for Zr is Hf. Yet,
SR for Hf of 53 is still high and would not generally
reduce criticality of such alloys. Furthermore, direct
substitution of Zr with Hf increases density and
reduces GFA and general processability.
In general, it is difficult to modify already
developed BMG alloys for specific needs (e.g., low
criticality). Often, BMG alloys have been developed for
GFA, and as a consequence, most modifications to
optimize for specific properties have resulted in a
reduction of GFA. Instead of modifying existing
BMGs, a more promising strategy might be to
consider criticality early on in the alloy development
process by restricting the pool of considered
elements to those with low criticality.
This work was supported by the Department of
Energy through the Office of Basic Energy Sciences
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