LECTURE - 14.04.2014 - Metallic Glass.pdf

Metallic glasses

1. Lecture- 7: Amorphous, Metallic Glass and
Quasicrystalline Materials
Few major references are included here. Other references may be found in individual
chapters.
Materials Science and Engineering, V. Raghavan,
Fifth Edition, Prentice Hall of India Pvt. Ltd., New Delhi, 2004.
Materials Science and Engineering: An Introduction, William D. Callister
John Wiley & Sons, 2010.
Materials: Engineering, Science, Processing and Design, M.F. Ashby, H.R.
Shercliff and D. Cebon, Butterworth Heinemann, Oxford 2007.
 Materials Selection in Mechanical Design, 3
rd
edition, M.F. Ashby, Butterworth
Heinemann, Oxford, 2006.
REFERENCES
Materials engineer make things. They make them out of materials, using
processes.

2. What are the common types of Amorphous Materials?
Materials selection and design
Some important Amorphous Materials: Glass, Amorphous Metals (Metallic Glass)
etc.
Quasicrystalline Materials
Recent developments
What will you learn in this lecture?

3.  Oxide glasses
 Metallic glasses
 Polymers
 Silicon
Amorphous Materials

4. Semicrystalline polymers
A mixture of crystalline regions (lamellae) separated by amorphous regions
•Polymers are composed of long molecular chains which form irregular,
entangled coils.
•Some polymers retain such a disordered structure upon freezing and thus
convert into amorphous solids.
•In other polymers, the chains rearrange upon freezing and form partly ordered
regions with a typical size of the order 1 micrometer.
•Although it would be energetically favorable for the polymer chains to align
parallel, such alignment is hindered by the entanglement.
•Therefore, within the ordered regions, the polymer chains are both aligned and
folded.
lamellae
Amorphous

5. Amorphous Silicon (aSi)
Largely four-fold coordinated network, with some
free-fold coordinated atoms (inducing dangling
bonds).

To eliminate dangling bonds that act as electron
traps - aSi is hydrogenated. Hydrogen saturates
dangling bonds (a- Si-H).

Thin-film amorphous Silicon (a- Si) have good
photovoltaic characteristics, are mounted on flexible
backings are do not fracture as easily as crystalline Si,
which allows them to be formed to fit applications
with the bending inherent when used in building
materials.
Amorphous solar cells do not convert sunlight quite as efficiently as crystalline Si
cells, however, they require considerably less energy to produce, and are superior to
crystalline cells in terms of the time required to recover the energy cost of
manufacture (Pocket calculater).

Amorphous silicon is gradually degraded by exposure to light. This phenomena is
called the Staebler -Wronski Effect (SWE).

6. GLASSES
Glass
is an amorphous (non- crystalline) solid material and
typically brittle and optically transparent.

Silica(SiO
2) is a common fundamental constitute of glass.
Synthesis of glass
1.Mixture of soda ash ,limestone, sand
and broken glass in dry condition.
2.
Send to furnace and heat to 1600°C
3.Molding.
4.Annealing.
5.Shaping.
6.Marketing .
Glass is an amorphous solid material that exhibits a glass transition.
It is a state of matter in which the atoms and molecules are locked into place, but
instead of forming neat, orderly crystals, they arrange themselves randomly.

7. Similarities between a glass and a ceramic
1.Hard but brittle
2.Good electrical and heat insulator
3.Do not corrode
4.Resistant to chemical attacks
5.Can withstand compression

1.Transparent
2.Can be melted and remoulded
3.Does not have a melting point
(have a melting range)

1.Opaque
2.Cannot be melted and
remoulded
3.Have very high melting point
Glass Ceramic
Difference between a glass and a ceramic

8. Composition of Glass
•Glass is made up of silica (SiO2). Following are the other
components of glasses

•Sodium oxide
•Magnesia
•Lime
•Alumina
•Boric oxide
•Soda (Na2O)
•Lead oxide
•Potassium oxide
•Zinc oxide
•Barium oxide
•Germanium oxide

9. Glass preparation
•The main constituent of flat Glass is SiO2. This has a high melting temperature
in the region of 1600 degrees C. The basic building block of silica has a
tetrahedral pyramid shape with silicon at its centre linked symmetrically to four
oxygen atoms at its corners.

•On cooling molten silica quickly, a random organised network of these
tetrahedra is formed, linked at their corners, to give an amorphous material
known as vitreous silica.

•High melting point and viscosity of silica can be reduced by the addition of
sodium oxide. Here sodium oxide works as flux. Sodium oxide used in the form
of a carbonate and the sodium-oxygen atoms enter the silicon-oxygen network.

•These network modifiers make the structures more complex so that when the
components are melted together. In the glass making process, the cooling rate
is arranged such that viscosity increases and the mobility of the atoms are
hindered thus preventing arrangements and crystallization from occurring.

10. •First true glass was made in coastal north Syria
•The story of glass dates back to ancient Egypt where glass-making
became popular during the late Bronze Age.

•Anglo- Saxon period glass was a luxury material across England

•In 10th centaury stained glass came to usage
•In 1330 crown glass was produced in Rouen
•In 14th and 19th centauries stained glass employed in building purposes
•In 1843 Henry Bessemer invented float glass
•In 120th centaury reinforced glass and glass bricks came to usage

•Colored glasses are due to inclusion of ions of chemical elements like
iron (Fe), cobalt (Co), nickel (Ni), copper (Cu), chromium (Cr), and
manganese (Mn)

Backgrounds of Glass

11. Application of GLASSES
Borosilicate glasses formerly called Pyrex are
often used laboratory reagents due to their
resistance to chemical corrosion and heat
fancy glass started to
become significant branches
of the decorative arts.
•Flat glass is used in glazing in buildings, to car windscreens, doors and mirrors. Container
glass extensively used in beer, wine, spirits, juices, food, cosmetics.
•Borosilicate glass possesses good chemical and thermal shock resistance which make it ideal for laboratory equipment and various forms of ovenware.

12. The 4 types of glass studied here are:
a)Fused glass
b)Soda lime glass
c)Borosilicate glass
d)Lead crystal glass
Classifications of Glasses

13. Fused Glass
1.Fused quartz glass is the simplest glass.
2.Main component of glass is silica.
3.Properties of fused glass:
a)High purity and optical transparency
b)High softening point
c)Low coefficient of thermal expansion
d)Chemical durability
e)Difficult and expensive to produce

a)Laboratory glassware
b)Lenses
c)Telescope mirrors
d)Optical fibres
Uses

14. Soda Lime Glass
1.Soda-lime glass is the most common glass.
2.Produced by heating silica with sodium oxide and calcium
oxide.
3.Properties of soda-lime glass:
a)Low softening point- easy to make into different shapes
b)High thermal coefficient of expansion
c)Low resistance to chemical attacks
a)window panes
b)light bulbs
c)bottles
d)glass containers
Uses

15. Borosilicate Glass
1.Borosilicate glass is formed when boron oxide is added to soda- lime glass.
2.Was first developed by German glassmaker Otto Schott in the late 19th century.
3.Properties of borosilicate glass:
a)Very low thermal expansion coefficient
b)High softening point
c)Resistant to thermal shock
d)Chemically resistant
Otto Schott in 1890
a)Laboratory glassware such as beakers,
boiling tubes, flasks etc.
b)Cookware
c)Glass containers
Uses

16. 1.Commonly known as lead crystal.
2.Made by using lead oxide and potassium oxide.
3.Lead glass has a high refractive index and a relatively soft surface that is easy to grind,
cut and engrave.
4.Properties of lead glass are:
a)High refractive index
b)High density
c)Attractive glittery/shiny appearance

Lead Glass
Lead-crystal continues to be used in
industrial and decorative applications

17. Amorphous Metal
An amorphous metal is a metallic
material with a disordered atomic-scale
structure. In contrast to most metals,
which are crystalline and therefore have
a highly ordered arrangement of atoms,
amorphous alloys are non-crystalline.
amorphous
crystalline
Materials in which such a disordered
structure is produced directly from the
liquid state during cooling are called
"glasses", and so amorphous metals
are commonly referred to as "metallic
glasses" or "glassy metals".
Non-crystalline, amorphous structure,
no dislocations, No grain boundaries

18. Crystalline Amorphous
Liquid
Cooling
- Glass (frozen liquid )
or non-crystalline solid
- Glass with metallic elements
 Metallic Glass
Basic Concept
ΔT = 1,000,000 °C / s

19. TEM image of amorphous zirconium alloy
•Metallic glasses are made by rapid cooling of a
metallic liquid such that there is not enough time
for the ordered, crystalline structure to nucleate
and grow.
•In the original metallic glasses the required
cooling rate was as much as a million degrees
Celsius per second!
•Recently, alloys have been developed that form
glasses around 1-100 degrees per second cooling
rates.
• Typically the best glass formers are
multicomponent materials such as Zr-Ti-Cu-Ni-Al
alloy.
• Metallic glasses can be quite strong yet highly
elastic, and they can also be quite tough.
Furthermore above the glass transition
temperature a metallic glass becomes quite soft
and flows easily allowing to form complex
shapes.
Schematic of a two component glass

20. T
g=T
x
Tg Tx
T
m
Heat flow ( endo)

Temperature
DSC curve

21. Temperature

Temperature/cooling rate

22. More recently a number of alloys with critical cooling rates low
enough to allow formation of amorphous structure in thick layers
(over 1 millimeter) had been produced, these are known as bulk
metallic glasses (BMG).


More recently, batches of amorphous steel have been produced
that demonstrate strengths much greater than conventional steel
alloys.

26. Local plastic deformation and shear band
formation

27. Medical devices Fine jewelry
Hinge applications Defense applications
Electronic casting
Sporting goods
Applications
Energy Fly wheel

28. •Metallic glasses are used as transformer core material in high power
transformers.
•Due to its high electrical resistivity and nearly zero temperature coefficient of
resistance, these materials are used in making cryothermometers, magneto
resistance sensor and computer memory.
•As the magnetic property of metallic glass are not affected by irradiation they
are used in making container for nuclear waste disposal.
•These materials are used in preparation of magnets for fusion reactors and
magnets for levitated trains etc.
•Metallic glasses can also be used for making watch cases to replace Ni and
other metals which can cause allergic reactions.
•Used in cutting and in surgical instrument.
•In future ,it will be used in electronic field can yield stronger, lighter,and more
easily moulded castings for personal electronics products.
•They are used in tape recorders as heads ,in the manufacture of springs and
standard resistances.

29. High Energy
Transformers
Loaded springs Razor plades
Tape Rrcprders Surgical Instruments Bio implants

30. Background of BMGs

The first metallic glass was an alloy (Au80Si20) produced at Caltech by
Pol Duwez in 1957. This and other early glass-forming alloys had to be
cooled extremely rapidly (on the order of one megakelvin per second,
10
6
K·s
-1
) to avoid crystallization.

An important consequence of this was that metallic glasses could only
be produced in a limited number of forms (typically ribbons, foils, or
wires) in which one dimension was small so that heat could be extracted
quickly enough to achieve the necessary cooling rate. As a result,
metallic glass specimens (with a few exceptions) were limited to
thicknesses of less than one hundred micrometres.

In 1969, an alloy of 77.5% palladium, 6% copper, and 16.5% silicon was
found to have critical cooling rate between 100 K/s to 1000 K/s.

31. In 1976, H. Liebermann and C. Graham developed a new method of
manufacturing thin ribbons of amorphous metal on a supercooled fast-
spinning wheel. This was an alloy of iron, nickel, phosphorus and boron.
The material, known as Metglas , was commercialized in early 1980s
and used for low-loss power distribution transformers (Amorphous metal
transformer). Metglas-2605 is composed of 80% iron and 20% boron,
has Curie temperature of 373 °C and a room temperature saturation
magnetization of 125.7 milliteslas.

In the early 1980s, glassy ingots with 5 mm diameter were produced
from the alloy of 55% palladium, 22.5% lead, and 22.5% antimony, by
surface etching followed with heating- cooling cycles. Using boron oxide
flux, the achievable thickness was increased to a centimeter.

32. The research in Tohoku University, Japan and Caltech yielded
multicomponent alloys based on lanthanum, magnesium, zirconium,
palladium, iron, copper, and titanium, with critical cooling rate between
1 K/s to 100 K/s, comparable to oxide glasses.

In 1988, alloys of lanthanum, aluminium, and copper ore were found to
be highly glass-forming.

In the 1990s, however, new alloys were developed that form glasses at
cooling rates as low as one kelvin per second. These cooling rates can
be achieved by simple casting into metallic molds. These "bulk"
amorphous alloys can be cast into parts of up to several centimeters in
thickness (the maximum thickness depending on the alloy) while
retaining an amorphous structure. The best glass-forming alloys are
based on zirconium and palladium, but alloys based on iron, titanium,
copper, magnesium, and other metals are also known.

33. In 1992, the first commercial amorphous alloy, Vitreloy 1 (41.2% Zr, 13.8%
Ti, 12.5% Cu, 10% Ni, and 22.5% Be), was developed at Caltech, as a
part of Department of Energy and NASA research of new aerospace
materials. More variants followed.

In 2004, two groups succeeded in producing bulk amorphous steel, one at
Oak Ridge National Laboratory, the other at University of Virginia. The
Oak Ridge group refers to their product as "glassy steel". The product is
non-magnetic at room temperature and significantly stronger than
conventional steel, though a long research and development process
remains before the introduction of the material into public or military use.

34. Classification of BMGs
•Metallic glasses are of two types based on their base material used in
preparation.
1.Metal-Metal glasses.
Example: Ni -Nb, Mg-Zn, Hf-V and Cu-Zr .
2.Metal-Metalloid glasses: like Fe, Co, Ni and metalloids like B, Si, C and P are
used
.

35. Properties of BMGs

Amorphous metal is usually an alloy rather than a pure metal.
The alloys contain atoms of significantly different sizes, leading to
low free volume (and therefore up to orders of magnitude higher
viscosity than other metals and alloys) in molten state.

The viscosity prevents the atoms moving enough to form an ordered
lattice. The material structure also results in low shrinkage during
cooling, and resistance to plastic deformation.

The absence of grain boundaries, the weak spots of crystalline
materials, leads to better resistance to wear and corrosion.
Amorphous metals, while technically glasses, are also much
tougher and less brittle than oxide glasses and ceramics.

36. Structural Properties
.
Mechanical Properties
Electrical Properties

37. [ the amount of magnetic field that a magnet can produce is known as
saturation magnetisation ] Strong magnets have higher saturation.

Magnetic Properties

Chemical Properties
•Small dimensions (due to cooling)
•Raw materials expensive

Approx. from $500 per pound
•Production expensive
Limitations

38. Thermal conductivity of amorphous materials is lower than of
crystals. As formation of amorphous structure relies on fast cooling,
this limits the maximum achievable thickness of amorphous
structures.

It shares the property of both metals and alloys.
Metallic glasses are metal alloy that are amorphous.That is they
don’t have long range atomic order.
The major advantages of such glasses are that they are generelly
homogeneous in composition, offer strong and superior corrosion
resistance

39. •Summary of Properties

•High strength but lighter in weight.
•They are ductile ,malleable, brittle and opaque. Hardness is very
high.
•The toughness is very high i.e. the fracture resistance is very high.
•High elasticity.
•High Corrosion resistance.
•They are soft magnetic materials. As a result, easy to magnetisation
and demagnetisation are possible.
•Narrow hysteresis loop thus low hysteresis energy losses.
•They have high electrical resistivity which leads to a low eddy
current loss.

40. To achieve formation of amorphous structure even during slower cooling,
the alloy has to be made of three or more components, leading to
complex crystal units with higher potential energy and lower chance of
formation.

The atomic radius of the components has to be significantly different
(over 12%), to achieve high packing density and low free volume.

The combination of components should have negative heat of mixing,
inhibiting crystal nucleation and prolongs the time the molten metal stays
in supercooled state.

The alloys of boron, silicon, phosphorus, and other glass formers with
magnetic metals (iron, cobalt, nickel) are magnetic, with low coercivity
and high electrical resistance. The high resistance leads to low losses by
eddy currents when subjected to alternating magnetic fields, a property
useful for eg. transformer magnetic cores.

41. The critical casting thickness versus the years in which alloys were discovered.
Over 40 years, the critical casting thickness has increased by more than three
orders of magnitude.
Critical casting thickness

42. Amorphous alloys have a variety of potentially useful properties.
In particular, they tend to be stronger than crystalline alloys of similar
chemical composition, and they can sustain larger reversible
("elastic") deformations than crystalline alloys.
Amorphous metals derive their strength directly from their non-
crystalline structure, which does not have any of the defects (such as
dislocations) that limit the strength of crystalline alloys.
Amorphous metallic alloys combine higher strength than crystalline metal
alloys with the elasticity of polymers.
• High yield strength (7 Gpa)
• High elastic strain limit (2%)
• Excellent processibility

43. Perhaps the most useful property of bulk amorphous alloys is that
they are true glasses, which means that they soften and flow upon
heating. This allows for easy processing, such as by injection
molding, in much the same way as polymers.

As a result, amorphous alloys have been commercialized for use in
sports equipment, medical devices, and as cases for electronic
equipment.
Thin films of amorphous metals can be deposited via high velocity
oxygen fuel technique as protective coatings.

44. One modern amorphous metal, known as Vitreloy , has a tensile strength
that is almost twice that of high-grade titanium . However, metallic glasses at
room temperature are not ductile and tend to fail suddenly when loaded in
tension, which limits the material applicability in reliability-critical
applications, as the impending failure is not evident. Therefore, there is
considerable interest in producing metal matrix composite materials
consisting of a metallic glass matrix containing dendritic particles or fibers
of a ductile crystalline metal.

Vitreloy

45. In addition to direct cooling, there are several other ways in which
amorphous metals can be produced, including:

• physical vapor deposition
• solid-state reaction,
• melt spinning
• mechanical alloying.
• Laser deposition

Amorphous metals produced by these techniques are, strictly speaking,
not glasses; however, materials scientists commonly consider
amorphous alloys to be a single class of materials, regardless of how
they are prepared.
In the past, small batches of amorphous metals have been produced
through a variety of quick-cooling methods.

For instance, amorphous metal wires have been produced by
sputtering molten metal onto a spinning metal disk. The rapid cooling,
on the order of millions of degrees a second, is too fast for crystals to
form and the material is "locked in" a glassy state.
Processing Methods

46. Virtually any liquid can be turned into a glass if it is cooled quickly
enough to avoid crystallization. The question is, how fast does the
cooling need to be?

Common oxide glasses (such as ordinary window glass) are quite
resistant to crystallization, so they can be formed even if the liquid is
cooled very slowly. For instance, the mirror for the 200" telescope at
the Palomar Observatory weighed 20 tons and was cooled over a
period of eight months, but did not crystallize.

Many polymer liquids can also be turned into glasses; in fact, many
polymers cannot be crystallized at all.

For both oxides and polymers, the key to glass formation is that the
liquid structure cannot be rearranged to the more ordered crystalline
structure in the time available.

47. Melt spinning and other rapid solidification techniques have been used
to make a wide variety of amorphous and nanocrystalline metals from
the 1960s to the present. However, materials produced in this way
have a key limitation: At least one dimension must be very small, so
that heat can be extracted quickly enough to achieve the necessary
cooling rate. As a result, the early glass-forming alloys could only be
produced as thin ribbons (typically around 50 μm thick), wires, foils, or
powders.

Although some applications ( notably those that made use of the
magnetic properties of iron- and nickel-based alloys) could use metallic
glasses in these forms, structural applications were obviously
impractical.
Melt Spinning

48. Metallic glasses are another story. Because the structural units are
individual atoms (as opposed to polymer chains or the network structure
of an oxide), in most alloys it is relatively easy for crystals to nucleate
and grow. As a result, the earliest metallic glasses (which were
discovered at Caltech in the late1950s) required very rapid cooling -
around one million degrees Celsius per second - to avoid crystallization.
One way to do it is by single-roller melt spinning, as shown here:
Single Roller Melt Spinning

In this process, the alloy is melted
(typically in a quartz tube) by induction
heating, and then forced out through a
narrow nozzle onto the edge of a rapidly
rotating chill wheel (typically made of
copper). The melt spreads to form a thin
ribbon, which cools rapidly because it is
in contact with the copper wheel.

50. An ingot in the upper chamber under an inert atmosphere is melted with an
electric arc (much like in arc welding) and then sucked into a mold when the
lower chamber is opened to vacuum. One of the potentially useful properties of
metallic glasses is that they do not melt abruptly at a fixed temperature. Instead,
like ordinary oxide glasses, they gradually soften and flow over a range of
temperatures. By careful control of temperature, the viscosity of the softened
glass can be precisely controlled. This ability can be used to form metallic
glasses into complex shapes by techniques similar to those used for molding
polymers.
Suction Casting Technique

51. Water-cooled
induction coil
Vacuum
pump
Ar
Control box
Cu plate
Sensor
Fig. Schematic illustration of splat quenching apparatus.
Splat Quenching Technique
Production of amorphous glass in high vaccum, inductive levitation melting
with subsequent optoelectronic detection of the falling droplet and release of
two high velocity pistons to squeeze the sample

52. Based on atomic order quasicrystals are one of the 3 fundamental phases of matter
QUASICRYSTALS
Nobel Prize in Chemistry (2011) to Dan Shechtman
5-fold symmetry
Perfectly ordered materials that never repeat themselves

53. Some examples of crystals
Sulfur Topaz
Quartz

54. Crystal =
Lattice (Where to repeat)
+
Motif (What to repeat)
=
+
a
a
2
a
WHAT IS A CRYSTAL?
Let us first revise what is a crystal before defining a quasicrystal

55. R  Rotation
G  Glide reflection
Symmetry operators
R  Roto-inversion
S  Screw axis
t  Translation
R  Inversion R  Mirror
 Takes object to the same form
 Takes object to the Mirror images/enantiomorphic form
Crystals have certain symmetries

56. HOW IS A QUASICRYSTAL DIFFERENT FROM A CRYSTAL?

57. QUASICRYSTALS (QC)
ORDERED PERIODIC
QC ARE
ORDERED
STRUCTURES
WHICH ARE
NOT
PERIODIC
CRYSTALS
 
QC 
×
AMORPHOUS × ×

58. SYMMETRY
CRYSTAL QUASICRYSTAL
t  τ
R
C
 R
CQ
QC are characterized by Inflationary
Symmetry and can have disallowed
crystallographic symmetries*
t → translation
τ → inflation
R
C → rotation crystallographic
R
CQ → R
C + other
2, 3, 4, 6
5, 8, 10,
12
* Quasicrystals can have allowed and disallowed crystallographic symmetries

59. ICOSAHEDRAL QUASILATTICE
5-fold [1 τ 0]
3-fold [2τ+1 τ 0]
2-fold [τ+1 τ 1]
Note the occurrence of irrational Miller
indices
The icosahedral quasilattice is the 3D analogue of the Penrose tiling.
It is quasiperiodic in all three dimensions.
The quasilattice can be generated by projection from 6D.
It has got a characteristic 5-fold symmetry.
20 triangular
faces, 30 edges
and 12 vertices

60. Type of
quasicrystal
QP
+
Rank Metric Symmetry System First
Report
Icosahedral 3 D 6 τ
(√5)
m3
_
5
_

AlMn Shechtman et al.
1984
Cubic 3D 6 √3
43m
_

VNiSi Feng et al
1989
Tetrahedral 3D 6 √3
m3
_

AlLiCu Donnadieu
1994
Decagonal 2D 5 τ
(√5)
10/mmm AlMn Chattopadhyay et
al., 1985a and
Bendersky, 1985
Dodecagonal 2D 5 √3 12/mmm NiCr Ishimasa et al.
1985
Octagonal 2D 5 √2 8/mmm VNiSi,
CrNiSi
Wang et al.
1987
Pentagonal 2D 5 τ
(√5)
5m
_

AlCuFe Bancel
1993
Hexagonal 2D 5 √3 6/mmm AlCr Selke et al.
1994
Trigonal 1D 4 √3
3m
_

AlCuNi Chattopadhyay et
al.,
1987
Digonal 1D 4 √2 222 AlCuCo He et al.
1988

List of quasicrystals with diverse kinds
of symmetries

61. CRYSTAL QUASICRYSTAL
Translational symmetry Inflationary symmetry
Crystallographic rotational symmetries Allowed + some disallowed rotational
symmetries
Single unit cell to generate the structure Two prototiles are required to generate the
structure
3D periodic Periodic in higher dimensions
Sharp peaks in reciprocal space with
translational symmetry
Sharp peaks in reciprocal space with
inflationary symmetry
Underlying metric is a rational number Irrational metric
Comparison of a crystal with a quasicrystal

62.  WEAR RESISTANT COATING (Al -Cu-Fe-(Cr))
 NON-STICK COATING (Al-Cu-Fe)
 THERMAL BARRIER COATING (Al -Co-Fe-Cr)
 HIGH THERMOPOWER (Al -Pd-Mn)
 IN POLYMER MATRIX COMPOSITES (Al -Cu-Fe)
 SELECTIVE SOLAR ABSORBERS (Al -Cu-Fe-(Cr))
 HYDROGEN STORAGE (Ti -Zr-Ni)
APPLICATIONS OF QUASICRYSTALS

63. Symmetries
Rotations:
2-fold:
3-fold:
4-fold:
6-fold:

64. Symmetries
Translations: Reflections:

65. Symmetries
Combinations of reflections and rotations:

66. Symmetries
Combinations of translations, reflections and rotations:
The symmetry “space group”
6-fold symmetry
Translations
Group is closed under combinations

67. Symmetries
What happened to 5- fold symmetry?
Rotation Translation (shortest)
Combination: New translation (shorter)
Translationally periodic structure cannot have 5x axis
τ = (1+√5)/2 = 1.61803…
is the Golden Mean, the
“most irrational number”.

68. Flux-grown Quasicrystals
AlGaPdMn
ZnMgHo
AlCoNi
Dodecahedron lattice: It
has 20 vertices, 30 edges
and 160 diagonals

69. Penrose Tiling (1974)
I L I S I L I L I S I
A Penrose tiling is a non-periodic tiling generated by an aperiodic set of prototiles.
The aperiodicity of the Penrose prototiles implies that a shifted copy of a Penrose tiling
will never match the original. A Penrose tiling may be constructed so as to exhibit
both reflection symmetry and fivefold rotational symmetry, as in the diagram at the right.

70. Bachelor Hall, Miami University of Ohio, 1979

71. Penrose Quilt, Newbold (2005) Penrosette doily, Jason (1999)
Penrose arts & crafts

72. Quasicrystal Diffraction Patterns
Decagonal Al-Co-Ni
(10000 0)
(01000 0)
(00001 0)
(01001 0)

73. Penrose Tiling Projected from 5D

74. Next Lecture
Electronic Materials

- Si, Ge, etc
-LED, Li-ion batteries
- Recent developments