Assignment in Physical Metallurgy
Theme : Metallic Glasses
Department of Mechanical Engineering
University of Thessaly
January 2016
Professor : Gregory Haidemenopoulos
Student : Kleanthis-Konstantinos Karagiannis
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ABSTRACT
The recent research in the field of materials science aims in discovery of new “hyper-
materials”. This kind of materials would combine various desirable properties like
toughness, high yield stress, corrosion and wear resistance and others. One
quintessential material is the metallic glass, which can be stronger and harder than
conventional metals and this is the reason why so much research is transacted
nowadays throughout the modern built world. So the purpose of this study is to
show the unique properties of metallic glasses and by the same time to clarify how
diffusion and other significant metallurgical characteristics are responsible for these.
Specifically, the aspects explored are the processes for producing metallic glasses,
their microstructure and thermodynamics and kinetics behind one major
transformation, crystal to glass. In contrast with the various advantages mentioned
two factors limitate the “glory” of metallic glasses, the great precised-techniques
needed for their production and brittleness which makes them vulnerable towards
cyclic fatigue.
keywords
Bulk metallic glass I diffusion І amorphous І glass transition temperature Tg
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CONTENTS
Introduction
Literature review
Discussion
Conclusions
References
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INTRODUCTION
Since 1960, when metallic glasses were first established by Caltech University, many scientists have tried to explain their unique mechanical properties. So far research was mainly focused on crystalline metals, but now this material displays an amorphous microstructure. This characteristic adds two additional factors that have to be seriously concerned, absence of long-range order and grain boundaries. Such specifics were only encountered in liquids and gasses, so scientists first looked for similarities with metallic glasses. For example diffusion in metallic glasses has to do with thermally activated, highly collective atomic processes and this has to be taken into concern before producing or using such materials. As far as the production many processes have been tried such as quenching from the liquid state, e.g., by melt spinning or splat quenching, or being produced by vapor condensation and sputter deposition. Other techniques for production of amorphous solids are solid-state reaction, ion implantation, neutron irradiation, ball milling and high-pressure application. The success of these preparation methods depends on the thermodynamic and kinetic aspects of the crystal to glass transformation, and the investigation of these aspects is the main concern of this study.
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LITERATURE REVIEW
Duwez and co-workers (Clement et al., 1960) were the first to produce a metallic
glass. They reported glass formation by rapid cooling of an Au-Si alloy melt. Duwez’s
group proved that the process of nucleation and growth of crystalline phases could
be kinetically bypassed in certain alloy melts, so a frozen liquid was produced. The
history of bulk metallic glasses probably started with the work of Chen (1974), at Bell
Laboratories, who succeeded in forming millimeter-diameter rods of ternary Pd-Cu-
Si alloys by suction casting methods at cooling rates of about 103 K/s. In the early
1980s, Turnbull and co-workers (Drehmann et al., 1982; Kui et al., 1984) carried out
experiments on Pd-Ni-P alloy melts and were able to demonstrate that these alloys
form bulk-metallic-glass ingots of centimeter size at cooling rates of only 10 K/s.
Around 1990 the field of bulk metallic glasses developed rapidly when Inoue and co-
workers in Sendai succeeded in producing amorphous aluminum alloys. They found
exceptional glass-forming ability in rare-earth-rich alloys such as La-Al-Ni and La-Al-
Cu (Inoue et al., 1990). Glassy rods and bars with casting thicknesses of several
millimeters were obtained. Studying similar quaternary and quinary alloys, the Inoue
group developed alloys (e.g., La-Al-Cu-Ni) that form glasses at cooling rates lower
than 100 K/s and critical casting thicknesses up to 1 cm (Inoue et al., 1992). A similar
family of Mgbased alloys (e.g., Mg-Y-Cu, Mg-Y-Ni; Inoue, 1995) and a family of Zr
based alloys (e.g., Zr-Cu-Ni-Al; Inoue et al., 1990b) were also developed.
Before procceding to the main part of the study it is crucial to define two
characteristic temperatures. The first is the fictive temperature, which is the
temperature where the extrapolations of the supercooled melt and glass lines
intersect in a diagram of volume or enthalpy-versus-temperature for a glass forming
alloy. The second is the glass transition temperature, in which a supercooled melt
transforms to glass.
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DISCUSSION
A first glance of some thermodynamic and kinetic aspects of crystal to glass
transformation would be very useful. Whenever the glass-forming conditions come
into consideration two diagrams can provide a clear view of the phenomenon,
enthalpy and volume-versus-temperature. In this study an enthalpy-versus-
temperature is used as showed in Fig. 1. At first we point out the melting
temperature Tm above of which the whole material is melt. By decrease of
temperature the crystal line begins and that means the onset of nucleation of the
crystalline phase.
Fig. 1. Enthalpy-versus-temperature diagram of a glass-forming material.
Exactly below the Tm one envisage a sudden decrease of enthalpy to a typical value
for crystals and by further cooling enthalpy takes an even smaller value. By
increasing the cooling rate the nucleus formation is avoided and the melted
structure remains. Further increase does not affect the value of enthalpy, while the
material is in metastable configurational equilibrium, until the deviation of the
current condition and onset of a line of gradually decreasing slope. By the same time
a massive increase of viscosity of about 15 orders of magnitude occurs until a critical
point is reached where viscosity no longer depends on temperature. At this point the
previous melted material transforms to a rigid glass. According to Fig. 1 the
temperature region which matches between the enthalpies of the equilibrated liquid
and the glass is called glass transformation region.
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Both metallic glasses and their supercooled melts are metastable and this is proved
by two factors, they can attain crystal structure and then one or more crystal phases
are formed and additionally their properties have a strong influence from their
thermal history. The second fact has to do with structural relaxation, a type of
physical aging, which for example may change the properties of a glass when it is
reheated in glass transformation range. In order to explain structural relaxation it
would be very useful to introduce another diagram, Fig. 2.
Fig.2. Volume-versus-temperature diagram of a glass forming material.
One could envisage an alteration in volume by causing a specific treatment to a
metallic glass. For example, if a fast-cooled glass is reheated to a temperature
between the glass transformation range, but below the fictive temperature, then its
new structure would be analogous to this new temperature. At this example a
reduction in volume is achieved and the difference of volume is usually called excess
volume. Also a slight change in density could be observed. Although, this can play an
important role in the mechanical properties of a metallic glass. So it is crucial to
know the so-called thermal history of the glass before using it, which is the way it
was produced.
Subsequently, a deepening in metallic glass formation will be achieved by
investigating nucleation and growth of crystal state in a crystalline diffusion couple.
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A physical mixture of these two metals has a free energy given by the dotted line in
Fig.3.
Fig. 3. Free energy diagram for the
Au-La system at 300 K.
It is obvious that free energy decreases by the formation of glass from the
crystalline metals over a range of composition. The dashed lines represent the
common tangent of the final solutions with the amorphous phase and separate
Au-amorphous from La-amorphous fields for metastable equilibrium of
amorphous alloy with the metals. Circled crosses give give free energy of
intermetallic compounds. Open circles indicate compositions where a single
phase product yields. And left filled (right filled) circles represent multilayers in
which Au (La) metal remained in metastable equilibrium with the amorphous
product. By the same time a different experiment was conducted and similar
phenomena in Ni-Zr binary alloy. In contrast with previous alloy, now
formation of a planar layer of the intermetallic compound ZrNi occurred after
reaction of the couple for 12 hours. The nucleation and growth of this
compound separates the amorphous layer from the remaining Zr metal layer.
Also the contact between the amorphous layer and Ni is reduced by voids, that
are connected to Kirkendall effect. More specifically, growth of the amorphous
layer is accompanied by gradual formation of the above mentioned Kirkendall
voids, at the interface between Ni and the amorphous interlayer. Further
differences of these two alloy systems are envisaged through comparison
between their free energy diagrams. Fig. 4 depicts the excess free energy of
mixing of the Ni-Zr system at a temperature of 550 K, where metallic glasses
form and grow in thin film diffusion couples.
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Fig. 4. Free energy diagram for the binary Ni-Zr system at 550 K.
As before the six intermetallic compounds, in respect with the equilibrium phase
diagram, are marked as crosses. In contrast to the Au-La diagram, all solid solution
phases have a negative free energy of mixing, which means that these phases can
form spontaneously. Due to this characteristic the ability of spontaneous alloying to
a solution with free energy above that of glass, while solution composition lays
outside the To lines that define the thermodynamic limits of homogenous metastable
crystalline phases, is possible. So a metastable crystalline solution is formed by
normal downhill thermal diffusion. But in the Au-La system the above described
situation can occur only inside the respective To(C) lines. As a result, a glassy
interlayer phase can be formed in two ways. At first, spontaneous dissolution of the
Ni in hcp-Zr or Zr in fcc-Ni is possible in very dilute concentrations which lie with the
respective To lines. The transform of the solutions to glass can be achieved either bi
heterogeneous nucleation of the glass at a preferred location in the diffusion couple
or by destabilization and catastrophic vitrification. On the other hand, in the Au-La
case the glass phase must form by nucleation at the original Au-La interface or at
some other preferred place. For further explanation the above phenomena will be
examined by kinetic aspects. It has been demonstrated that during the form of the
glass interlayer no presence of intermetallic compounds was observed, but no logical
explanation could be given by thermodynamic aspect. A good assumption would be
that forming of a critical nucleus is restricted due to the absence of mobility of one
of the atomic species. Another restriction would be the absence of a potentially low
energy or coherent interface between the intermetallic compound crystal and the
parent metals of the diffusion couple. This “kinetic barrier” is enhanced by the fact
that the successive atomic rearrangements needed for growth of an intermetallic
compound requires many correlated atomic jumps and as a result glass growth is
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preferred. In order to model the kinetics behind the growth of a glassy interlayer a
set of phenomenological macroscopic equations can be used. For one-dimensional
amorphous interlayer growth the following set of coupled differential equations
would provide critical answers.
𝜕𝐶
𝜕𝑡= �̃�
𝜕2𝐶
𝜕𝑋2
𝐷 ̃𝜕𝐶
𝜕𝑋 = (1 − 𝐶1)
𝑑𝑋1
𝑑𝑡
−�̃� 𝜕𝐶
𝜕𝑋 = C2
𝑑𝑋2
𝑑𝑡
𝑑𝑋2
𝑑𝑡= 𝑓2(𝐶2 − 𝐶2
ₒ ≈ 𝜅2(𝐶2 − 𝐶2ₒ) + ⋯
𝑑𝑋1
𝑑𝑡= 𝑓1(𝐶1 − 𝐶1
ₒ ≈ 𝜅1(𝐶1 − 𝐶1ₒ) + ⋯
�̃� = the metal interdiffusion constant in the amorphous phase
C = C(X) = the concentration profile of metal no. 1 in the amorphous phase
𝐶1ₒ(𝐶2
ₒ) = the concentration of metal no. 1 (no. 2) in the amorphous phase which gives
equilibrium with “pure” metal no. 1 (no. 2)
X1(X2) = position of the interface separating the amorphous interlayer from metal no.
1 (no. 2)
C1(C2) = C(X1) (C(X2))
κ1(κ2) = kinetic response parameter for interface no. 1 (no. 2)
The metal interdiffusion constant �̃� was taken to be independent of composition of
the amorphous alloy. The parameters κ1 and κ2 are linear response parameters
which couple the interface motion to the degree of chemical non-equilibrium at the
interfaces. They have the dimensions of velocity. The first equation is the Fick
diffusion law in the amorphous interlayer, the two following equations are continuity
equations for fluxes at the interfaces and the two latest couple the concentration
profile to the moving interfaces. The above set of equations has been solved by
numerical methods and some interesting conclusions have been extracted. For long
times (𝑡 → ∞) the solution is
X2 = -�̃�/κ2 + √2𝑎�̃�𝑡 + …
where a is a constant in order of unity. So, this predicts a “shifted 𝑡1
2 “ law and this is
called interface-limited growth. At short times (t→0) the solution is
X1
X2
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X2 = constant κ2t + …
At this instance growth of the amorphous interlayer is linear in time with rate
proportional to κ2 and this is referred to a diffusion-limited growth. At last the
relation of �̃� and temperature has to be taken into consideration. After studying the
growth of the amorphous interlayer in the binary Ni-Hf system the collected data
were fitted to the above solutions. So, estimates for �̃� can be made as shown in Fig.
5 below.
Fig.5. Arrhenius plot of intediffusion
constant vs. T-1 for interdiffusion of Ni
and Hf in a growing amorphous
interlayer.
As far as the diffusion a differentiation must be made between conventional and
bulk metallic glasses.
Conventional metallic glasses
The below data take into consideration structural relaxation, because it can induce
changes in the final results.
Fig. 6. Diffusion profiles of Fe in as-quenched
Fe40Ni40B20 after various annealing times.
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In the above diagram each sample is showed by a curvature with the information of
the annealing time. The straight line prove the thin-film solution (Gaussian solution)
for Fick’s second law
c(x,t) = 𝑆˳
√𝜋𝐷𝑡exp (−
𝑥2
4𝐷𝑡)
Probably, diffusion coefficients have a relation with time, because in different way
the profiles would be the same and Fig. 7 provides persuasive evidence.
Fig. 7. Time-averaged diffusivities as functions of the annealing time.
Obviously one could expect a decrease in diffusivity of a fast-quenched glass after
annealing at a temperature below the fictive temperature of the as-quenched glass,
because then volume is derated and so the structure is more dense. By adding the
concept of quasivacancies, which cause the excess volume and are mentioned as
localized defects that are stable over several jumps, a could explanation could be
given. It is known that in crystalline metals vacancies are necessary for self-diffusion,
but in as-quenched amorphous alloys the so-called quasivacancies anneal out when
they become mobile. So a decrease in the diffusivities is expected, until they reach
their relaxes-state values.
Bulk metallic glasses
Discovery of bulk metallic glasses opened the field of investigation for diffusion in
metallic glasses and their supercooled melts. Bulk metallic glasses offer the ability of
annealing for some time in the supercooled liquid state, beacause their
crystallization temperature Tx exists above Tg, while conventional glasses undergo
crystallization before the glass-transition temperature is reached. One widenly used
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bulk metallic glass is the five-component alloy Zr46,75Ti8,25Cu7,5Ni10Be27,5 , known as
Vitreloy 4. The utility of this material lays in the fact that no sign of decomposition is
envisaged in the temperature range of glass transition, while other bulk metallic
glasses undergo spinodal decomposition into two amorphous phases. For example
Vitreloy 1 decomposes around 623 K within a few hours. In contrast, Vitreloy 4 lies
outside the miscibility gap. Additionally, many bulk metallic glasses exhibit a
“nonlinear” Arrhenius behavior. For example, the diffusivity in the glassy state is
higher than that predicted by a normal Arrhenius behavior, due to the fact that the
effective activation enthalpy and preexponential factor above the glass-
transformation temperature Tg are higher than below Tg. More research on Vitreloy
4 has proved that the diffusion times at low temperatures were too short in order to
catch the metastable state of the supercooled liquid at these temperatures, as
shown in Fig. 8.
Fig. 8. Time-
Temperature-
Transformation
diagram of
Vitreloy 4.
During every diffusional annealing depicted, crystallization was avoided and for further explanation open symbols correspond to annealing parameters that led to diffusivities below Tg, related to glassy state, while solid symbols and crosses are connected with conditions above the transition temperature, related to supercooled liquid state.
Preparation of metallic glasses
After having clarified the basic concept behind nucleation a growth in metallic glasses it would be understandable to analyze the preparation of them. Various methods have been developed for the preparation of conventional amorphous metals. They can be quenched from the liquid state, e.g., by melt spinning or splat quenching, and can be produced by vapor condensation and sputter deposition. Moreover, it is possible to transform crystalline solids into the amorphous state by
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solid-state reaction, ion implantation, neutron irradiation, ball milling, high-pressure application, and other techniques. Melt spinning Melt spinning is one method of rapidly solidifying liquid metals to produce either
amorphous or microcrystalline microstructures, depending on such variables as melt
composition and cooling rate. A radio-frequency induction coil is used to heat the
metal in a crucible. When molten the alloy is ejected through either a single hole or a
row of holes onto a rotating brass wheel. The solid metal produced is spun in the
form of a ribbon.
Fig. 9. Melt spinning
Melt temperature : 350°-
400°C
Estimated cooling rate : 105-
106 Ks-1
Of course, before proceeding to the above procedure one must take the TTT diagram
for glass-forming alloys into consideration.
Fig. 10. Time-
temperature-
transformation
diagram for glass-
forming alloys.
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In fact, the big rate of cooling achieved by melt spinning allows the glass
transformation, as the crystallization “nose” is avoided. In case of bulk metallic
glasses, additional components play the role of stabilizers for the glassy phase,
because the existence shift the crystallization “nose” and glass formation can be
achieved by smaller cooling rates.
Ball milling
The process of ball milling is illustrated in Fig. 11. Powders are placed together with
hardened steel or WC balls in a sealed container which is shaken or violently
agitated. The powders are severely deformed, fractured and mutually cold welded
during collisions of the balls. The successive deformation and welding of grain leads
to a progressively refined lamellar type of domain structure when two elemental
metal powders are mechanically alloyed.
Fig. 11. Illustration of the process of
high energy ball-milling of a mixture
of two metal powders.
The process of amorphization by alloying of elemental powders leads to an ultrafine
composite in which a solid-state amorphizing reaction takes place. High dislocation
densities produced by sever deformation enhance atomic mobility in the interfacial
regions of the two metals. Together with the deformation itself and the expected
local temperature rises during collision events sufficient diffusion is permitted and
allows the amorphizing reaction to occur in the solid-state. The driving force in this
explanation is composition-induced destabilization of the crystalline solutions.
Rapid discharge forming
The heat of the material above the Tg temperature happens through ohmic heating,
while a short and intense pulse of electrical current is fired and delivers an energy
surpassing 1,000 joules in about 1 milisecond, about one megawatt of power. Now
the heated rod of the metallic glass can be injected into a mold and cooled with the
whole procedure lasting a few milliseconds. Despite being formed in open air the
molded rod is free of flow defects and oxidation. Thanks to this method metallic
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glasses can be studied in their molten state and the crystallization process can be
examined on millisecond time scales.
Fig. 12. The metallic-glass rod
before heating and shaping (left),
the molded part (middle), the
final part trimmed of excess
material (right).
At last, little information can be given about the mechanical properties of metallic
glasses, but this is not the main purpose of this study. Superior strength and
hardness, and excellent corrosion and wear resistance, combined with their general
inability to undergo homogeneous plastic deformation are the main advantages that
are closely related to the above described phenomena. In contrast, the lack of
defects in the microstructure of metallic glasses makes them brittle and as result
they are weak against fatigue.
Fig. 13. Typical strengths and elastic limits for various materials.
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CONCLUSIONS
Amorphous metallic alloys, also termed metallic glasses, are the paradigm of dense random packing. Conventional metallic glasses are very prone to crystallization and do not lend themselves for diffusion studies above the glass transition temperature. With the discovery of novel bulk-glass-forming alloys, diffusion in metallic systems can now be investigated from the glassy state up to the equilibrium melt. This is of considerable interest not only from the technological point of view but also in terms of fundamental science, particularly in connection with the glass transition. The construction of free energy diagrams that describe the variation of the enthalpy and Gibbs free energy of the crystalline phase in non-equilibrium states added essential thermodynamic evidence throughout the study. In all of the examples discussed, the concepts of a To and a Tm line play a key role in allowing one to determine when the crystalline phase becomes metastable in respect to a glass transformation. Also, a quick reference in the production methods of metallic glasses proved that progress in theoretical studies has great impact on practical issues. Besides, the main purpose of tis study, which has to do with thermodynamic and kinetic aspects, little information were given about mechanical properties of metallic glasses.
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REFERENCES
G. N. Haidemenopoulos, (2000), Physical Metallurgy, Publications of University of
Thessaly
William L. Johnson, Thermodynamic and kinetic aspects of the crystal to glass
transformation in metallic materials, (1986)
Franz Faupel & Werner Frank et al., Diffusion in metallic glasses and supercooled
melts, REVIEWS OF MODERN PHYSICS, VOLUME 75, JANUARY 2003
A. Inoue, X.M. Wang and W. Zhang, Developments and applications of bulk metallic glasses, February 28, (2008) Michael Miller & Peter Liaw, (2008), Bulk metallic glasses, Springer publications K. L. Ngai, (2011), Relaxation and diffusion in complex systems, Springer publications Paul Heitjans & J�̈�rg K�̈�rger, (1998), Diffusion in condensed matter, Springer publications Helmut Mehrer, (2007), Diffusion in solids, Springer publications D. B. Miracle, A structural model for metallic glasses, Nat. Mater. 3(10), (2004) Phys.org , last access in 12/01/16