Question 1 (25)
a) What is the distinction between an amorphous solid and a glass? In other words, what is the specific property of a glass
as opposed to a general amorphous material.
An amorphous solid is a solid which lacks long range (crystalline) order
All glasses are amorphous, but not all amorphous are glasses!
Glasses are the amorphous materials that exhibit, show, made by a glass transition.
In other words are prepared by a glass transition.
A structural glass is an amorphous solid which is capable of passing into the viscous liquid state, usually, but not necessarily,
accompanied by an abrupt increase in heat capacity (the glass transition).
Common mistake: Say that glass do not have long range order but amorphous have.
Then what is the difference between glass and amorphous?
Glasses are the amorphous materials that exhibit, show a glass transition.
In other words are prepared by a glass transition, i.e. Fast cooling.
This is a glass.
An amorphous solid prepared from liquid by fast cooling.
XRD showing a pressure-induced amorphization of CuFeS2 at
around 6.3 GPa. This is an amorphous solid but not a glass.
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b) Based on the bellow classical diagram for a glass transition, briefly explain the differences between crystallization and glass
transition in the context of thermodynamic transitions. Specifically explain (briefly) why the glass transition is not a
conventional thermodynamic transition.
➢ Slow cooling of a melt results to a liquid to crystal transition at Tm
a) This is a classical first order phase transition
b) Tm is fixed for a given material.
➢ Fast cooling bypass crystallization temperature and results to:
1) Initially to a super cooled liquid: a high viscosity (almost jello-like
or ruber) liquid.
2) At lower temperature (<Tg) to a glass solid.
a) This is neither a first nor a second order transition.
b) Two step process.
c) Tg is not fixed, depends on cooling rate; faster the cooling rate the
higher the Tg.
Tg for slow
Tg for fast
Tm
Tm=melting and crystallization temperature
Tg= glass transition temperature
Common mistake: Discuss only the dependence of Tg by cooling rate.
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c)What are the three main families of glasses? Briefly explain the models we are using to describe each family and the
prevailing bonding in each case.
1) Network Glasses: Glasses made mainly by covalent bonding between elements, e.g. SiO2, TeO2, B2O3 As2S3, AsSe4.
Ionic bonding can be present in the case of network modifiers., e.g. Na2O-SiO2 glasses. Continuous Random Network
Chalcogenide glasses
Soda-Lime glasses
2) Metallic Glasses: Glasses made by metallic bonding.
Random Close pack
3) Polymer glasses: Cross-linking of molecular chains involving van der Waals bonding between chains and
covalent intra-molecular bonding.
Common mistakes: a) Refer to Network glasses as silicate glasses and b) say that metallic glasses have ionic bond.
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Bonus!!! Could you make a general conclusion (with explanation) about the effect of the different types of bonding on the
cooling rate needed to prepare a glass? You can use the table as a guidance.
Silica and other oxide glasses (covalent bonding) have the lower cooling rate, i.e. they
are the best glass formers. This is because strong directional bonds make structural
rearrangement difficult when the liquid is cooled don to form the solid. This promote,
glass formation, instead of crystallization, that requires rearrangement (time) to find
the best (lower enthalpy) structure.
In contrast, metallic glasses have week non directional bonding, that makes
rearrangement (i.e. finding the lower enthalpy structure) easy and thus facilitate
crystallization. Thus, making glass formation difficult, requiring very high cooling rates.
Common mistake: Just say that strong bonds have lower cooling rate, while week high cooling rate.
Question 2 (25)
a) What is the effect of the cooling rate on the density and the enthalpy of a given glass?
Tg for slow
Tg for fast
Tm
Be careful: glass density is not fixed, depends on cooling rate! Lower cooling rate higher density.
H=U+PV
U=internal energy (state function):depends only on T
P=pressure
V=Volume
Common mistake: Just say that higher cooling rate results to lower density and high enthalpy.
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b) The enthalpy of a glass is always higher than that of the corresponding crystal. However, a phase transition from a glass to
crystalline is not observed in the time frame of experimental observation. How this is explained? Could this be explained under
conventional thermodynamic description?
Enthalpy of glass is higher than that of crystalline. Thus, a glass should be transformed to the corresponding crystalline phase
according to classical thermodynamic.
This is not happening in reality! Glass are stable over million of years!
This is because the glass to crystalline transition is a kinetic, rather than a
thermodynamic effect.
Thermodynamic effect: everything depends on enthalpy
Kinetic effect: there is a rate for transformation. For the glass to crystalline transition
it is vanishingly slow!
A glass is kinetically stable (means rate is extremely slow) but thermodynamically unstable.
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c) The energy-structure landscapes for three different chemical compositions are provided. Which one is expected to be the
best glass former? i.e. requiring the lowest cooling rate?
(a)
(b)
In c) the energy landscape has a plethora of local minima. Thus, more time is needed (i.e. for the atoms to rearrange) to
find the absolute minimum (i.e. the crystal structure). Thus, a glass can be formed with lower cooing rate (because time
for crystallization is high) and consequently c) is the best glass former.
To make a glass you need to cool down faster than crystallization time!
Common mistake: Say that a) is best because it has only one global minimum.
Bonus!!! Assume that you would like to synthesize an IrTe2 glass. At which pressure you will
make your attempt in order to minimize the needed cooling rate?
At 70 GPa a lot of structures have similar enthalpy. Thus, a lower cooling rate is needed,
see question C.
(a)
Common mistake: a) say 70 GPa because ΔH is zero and b) say 0 or 140 GPa because H is negative.
(b
)
IrTe2 phases.
Question 3 (25)
a) briefly explain the structure of a soda lime glass and the role of the different elements
(Si, O, Na, Ca).
Network Glasses: Glasses made mainly by covalent bonding between elements, e.g. SiO2
Ionic bonding can be present in the case of network modifiers., e.g. Na2O-SiO2 glasses
Soda–lime glass, also called soda–lime–silica glass, is the most prevalent type of glass, used
for windowpanes and glass containers. They account for about 90% of manufactured glass.
Pure silica has excellent resistance to thermal shock, its high Tg and viscosity make it difficult
to work with. Other substances are therefore added to simplify processing:
1) One is the "soda", or sodium carbonate (Na2CO3), which lowers the glass-transition
temperature. However, the soda makes the glass water-soluble, which is undesirable.
2) To provide for better chemical durability, the "lime" is also added. This is calcium
oxide (CaO), generally obtained from limestone.
b) Consider the following aluminosilicate glass: 0.15(Li2O)-0.25(Al2O3)-0.6(SiO2). Characterize (including its role) each oxide and
explain why an aluminosilicate glass cannot be formed without the introduction of an alkali oxide.
A) Glass or network formers include oxides such as SiO2 ,B2O3, GeO2, P3O5, V2O5 and
As2O3 (i.e. oxides with strong covalent bond)
B) Intermediates include Al2O3,Sb3O2, ZrO2,TiO3, PbO, and ZnO .
Some oxides cannot from a glass network by themselves but can join into an existing
network. For example, Al2O3 can join silica network as AlO4 tetrahedra replacing some
of the SiO4 units. However, the valence of Al is 3 instead of the necessary 4 for the
tetrahedra, alkali cations must supply the necessary other electrons to produce
electrical neutrality . Big difference with pure SiO2
C) Modifying oxides include MgO ,Li2O ,BaO , CaO ,SrO , Na2O , and K2O (i.e. oxides
with ionic bond). These are added to modify the properties of glass oxides. Alkali
and alkaline earth oxides are added to silica glass to lower Tg and viscosity so that it
can be worked and formed more easily.
Common mistake: say that we need Li2O to lower the Tg.
c) Assuming that the introduction of a modifier results only to the creation of non-bridging oxygens (NBO). How many NBOs per
Si atom are expected for the 0.5(Na2O)-0.5 (SiO2) glass?
1) Every Na ion produce 1 NBO per silicon atom.
If we have 2 Na per Si atom they will produce 2NBOs per silicon atom.
In the schematic the ratio between Na/Si=1, in this question Na/Si is 2.
2) This glass can be written as Na2SiO3. Thus, Si mast have 2NBOs to keep
the tetrahedral arrangement (Q unit)
Common mistake: say 1NBO per Si based on the schematic.
Bonus!!! Assuming a) no Q0 and Q1 units and b) Q3 are 50% of the units in the above
glass, what will be the ratio between Q4 and Q2 i.e. Q4/Q2?
Based on question c, the relevant unit is Q2, i.e. 2 NBOs per Si.
Half Si atoms have 1NBO (Q3) thus, the rest of Si atoms should have (average)3NBOs
This is impossible when you have only Q2 and Q4 units.
Such glass cannot exist with this distribution of units!!!! It has a lot of a modifier that disturbs the network.
Remember: Soda–lime glass, also called soda–lime–silica glass, is the most prevalent type of glass, used for windowpanes
and glass containers. They account for about 90% of manufactured glass.
1) One is the "soda", or sodium carbonate (Na2CO3), which lowers the glass-transition temperature. However, the soda
makes the glass water-soluble, which is undesirable.
2) To provide for better chemical durability, the "lime" is also added. This is calcium oxide (CaO), generally obtained
from limestone.
In addition, magnesium oxide (MgO) and alumina (Al2O3), contribute to the durability. The resulting glass contains about 7074% silica by weight.
Question 4 (25)
Consider the following diagram for the three types of bulk metallic glasses a, b, and c, and answer the questions given below:
a) What is this diagram called and what is its significance?
Time-Temperature-Transformation (TTT) Diagram.
It provides the info about the cooling rate needed to bypass crystallization and form a glass.
b) Based on above diagram which one metallic glass is a good glass former, and which is a poor glass former?
Glass C requires the lowest cooling rate thus, it is the good glass former.
Glass A requires the highest cooling rate thus, it is a poor glass former.
Common mistake: say exactly the opposite.
c) Based on above diagram which one metallic glass is expected to have the highest number of elements and which one has the
least number of elements?
The TTT curve is C shaped with a neck at a certain temperature, Tneck. We can
draw a straight line from the melting temperature such that it is tangent to this
nose. The slope of this line gives a critical cooling rate. If the melt is cooled at a
higher cooling rate, then no crystal formation would occur and a glass would
result. For oxides which form glasses this critical cooling rate is lower than the
normal cooling so that such oxides form glass easily on normal cooling.
On the other hand, the critical cooling rate may be as high as 1012 K/s for pure
metals, a very difficult to achieve rate.
What factors would lead to a low critical cooling rate and so to glass formation?
(i) Minimization of heterogeneous nucleation by elimination of impurities such as
refractory particles and minimization of the contact with the container wall.
(ii) High viscosity presents a high kinetic barrier to crystallization.
(iii) If the melt contains many different elements which have to rearrange to form
the crystalline structure, the crystal growth would be difficult and so the
critical cooling rate would be low. This is the reason that the glass forming
compositions are generally very complex.
The time-transformation-temperature
(TTT) curve for a glass forming melt.
Common mistake: say that glass (c) will have only one element because pure metals need more time to crystallize.
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d) The critical cooling rate 𝑅𝑐 for the formation of a metallic glass is given as,
∆𝑇 𝑇𝑙 − 𝑇𝑛
𝑅𝑐 =
=
𝑡𝑛
𝑡𝑛
Where, 𝑇𝑙 is the melting temperature, and 𝑇𝑛 and 𝑡𝑛 are the temperature and time at the nose of the TTT curve. Estimate the
ratio between the cooling rates of metallic glasses ‘a’ and ‘c’.
𝑅𝑐𝑎
𝑅𝑐𝑐
𝑇𝑙 − 𝑇𝑛
𝑡𝑐
𝑡𝑎
=
= ≈ 105
𝑇𝑙 − 𝑇𝑛 𝑡𝑎
𝑡𝑐
Bonus!!! Which one is more feasible to synthesize, a monoatomic BMG or a multicomponent BMG? Briefly explain your answer.
A multicomponent BMG will be much more easy to synthesize. See question c.
Common mistake: Give opposite response than question c)!!! i.e. Not make the connection that more easily means lower cooling rate.