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Functional Solid State Materials
Electrical properties
Optical properties
Magnetic properties
Mechanical properties
“the secret for transmuting base metals into precious gold”
Materials & History
Stone age
Bronze age
Iron age
Silicon age
Alchemist Material Chemist
Development of Materials vs Human Society
The history of human society can be marked with inorganic
materials.
Historical Perspective
Stone → Bronze → Iron →steel → Advanced materials
Beginning of the Material Science ? People began to make tools
from stone ? Start of the Stone Age about two million years ago.
Natural materials: stone, wood, clay, skins, etc.
The Stone Age ended about 5000 years ago with introduction of
Bronze in the East Asia. Bronze is an alloy (copper + < 25% of tin
+ other elements).
Bronze: can be hammered or cast into a variety of shapes, can be
made harder by alloying, corrode only slowly after a surface oxide
film forms.
The Iron Age began about 3000 years ago and continues today.
Use of iron and steel, a stronger and cheaper material changed
drastically daily life of a common person.
Age of Advanced Materials: throughout the Iron Age many new
types of materials have been introduced (ceramic, semiconductors,
polymers, composites… ). Understanding of the relationship among
structure, properties, processing, and performance of materials.
Intelligent design of new materials.
Historical Perspective
A better understanding of
structure-composition-
properties relations has lead
to a remarkable progress in
properties of materials.
Example is the dramatic
progress in the strength to
density ratio of materials,
that resulted in a wide variety
of new products, from dental
materials to tennis racquets.
Structure-Composition-Properties Types of MaterialsLet us classify materials according to the way the atoms are
bound together.
?Metals: valence electrons are detached from atoms, and
spread in an “electron sea”that “glues”the ions together.
Strong, ductile, conduct electricity and heat well, are shiny if
polished.
?Semiconductors: the bonding is covalent (electrons are shared
between atoms). Their electrical properties depend strongly on
minute proportions of contaminants. Examples: Si, Ge, GaAs.
?Ceramics: atoms behave like either positive or negative ions,
and are bound by Coulomb forces. They are usually
combinations of metals or semiconductors with oxygen,
nitrogen or carbon (oxides, nitrides, and carbides). Hard, brittle,
insulators. Examples: glass, porcelain.
?Polymers: are bound by covalent forces and also by weak van
der Waals forces, and usually based on C and H. They
decompose at moderate temperatures (100?400°C), and are
lightweight. Examples: plastic, rubber.
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Materials Tetrahedron
Performance
Properties
Structure
and
Composition
Synthesis
and
Processing
[chemistry & engineering]
[chemistry & physics]
[engineering]
[chemistry]
Life Cycle of Materials
Synthesis
and
Processing Engineered
Materials
Product Design
Manufacture
Assembly
ApplicationsWaste
Recycle/Reuse
Raw
Materials
Properties are the way the material responds to the
environment and external forces.
Mechanical properties ? response to mechanical forces,
strength, etc.
Electricaland Magnetic properties ? response electrical
and magnetic fields, conductivity, etc.
Thermal properties are related to transmission of heat
and heat capacity.
Opticalproperties include to absorption, transmission and
scattering of light.
Chemical Stability in contact with the environment ?
corrosion resistance.
Properties
Electric Properties of Crystals
Crystals can be classified by electric properties:
Conductors
Dielectric crystals
Semiconductors
Superconductors
Dielectric Properties
The biggest difference between dielectric
materials and conductors is that the transfer
ways of electrons are totally different:
Dielectric??in manner of induced polarization
conductor ??in manner of conduction
Dielectric Material
A dielectric material is an insulator in which
electric dipoles can be induced by the electric
field (or permanent dipoles can exist even
without electric field), that is where positive
and negative charge are separated on an
atomic or molecular level
+ _+ _
+_
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Dipole formation and/or orientation along the external
electric field in the capacitor causes a charge
redistribution so that the surface nearest to the positive
capacitor plate is negatively charged and vice versa.
+ + + + + + + +
- - - - - - - - -
-+-+ -+ -+ -+ -+ -+-+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
Q0+Q’
-Q0-Q’
region of no
net charge
net negative charge
at the surface, -Q’
net positive charge at
the surface, Q’= PA
P
Dielectric Materials
The process of dipole formation/alignment in electric
field is called polarization and is described by P = Q’/A
electronic polarization
ionic polarization
molecular (orientation) polarization
Mechanisms of
Polarization
Dipole Moments
Orientation of dipole moments
Basic Conception
Dielectric? material that is electrically insulating or
can be made to exhibit an electric dipole.
§ Permittivity ? ratio of the electric displacement in a
medium to the intensity of the electrical field producing
it.
§ Capacitance ? The ratio of charge to potential on an
electrically charged, isolated conductor
§ Dielectric strength ? magnitude of the electric field
necessary to produce breakdown .
Relative Permittivity
The resultant capacitance can then be
measured due to the dielectric:
C = εrA/d
§ the dielectric constant εr= ε/ ε0
§ the dielectric constant, or relative
permittivity, is the ratio of the permittivity of
the material to the permittivity of free space
(ε0=8.854x10-12 F?m-1)
Dielectric Strength
Very high electric fields (>108 V/m) can excite
electrons to the conduction band and accelerate
them to such high energies that they can, in turn,
free other electrons, in an avalanche process (or
electrical discharge). The field necessary to start
the avalanche process is called dielectric strength
or breakdown strength.
The dielectric strength is a measure of how much
voltage can be applied to a dielectric before electric
current begins to arc across the dielectric
Arcing across the dielectric is known as dielectric
breakdown.
Dielectric strength has the units of V/m.
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Dielectric Material
A dielectric material is a material that is nonmetallic and
exhibits or may be made to exhibit an electric dipole
structure.
A dielectric material is characterized and selected according
to its dielectric constant, Σ r, often called the relative
permittivity.
There are many ceramics and polymers that exhibit
dielectric behavior.
Applications for dielectric materials
–Dielectric materials to insulate electrical conductors
–Dielectric materials used in capacitors
–Communications (radio, radar and microwave)
–Microelectronics
The Relations of Dielectric Crystals
The dielectric crystals
can be classified as:
dielectric
piezoelectric
pyroelectric
ferroelectric
The number in the
parentheses is the point
groups that the crystal
possibly exist
Piezoelectricity
In some ceramic materials, application of external
forces produces an electric (polarization) field and vice-
versa
piezoelectric effect and converse piezoelectric effect:
Some dielectrics have a crystal structure with one polar
axis. mechanical deformation of the crystal lattice
causes electric displacement. On the other hand, the
polar axis causes a deformation of the crystal lattice
when electric charges are being displaced. This is
called converse piezoelectric effect.
Piezoelectric materials include barium titanate
BaTiO3, lead zirconate PbZrO3, quartz.
Piezoelectricity
The piezoelectric effect was first mentioned in 1817 by the
French mineralogist Rene Just Hauy. It was first
demonstrated by Pierre and Jacques Curie in 1880.
The direct piezoelectric effect consists of the ability of certain
crystalline materials (i.e. ceramics) to generate an electrical
charge in proportion of an externally applied force.
Applications of piezoelectric materials is based on conversion
of mechanical strain into electricity (microphones, strain
gauges et al.)The direct piezoelectric effect has been widely
used in transducers design (accelerometers, force and pressure
transducers ...).
According to the inverse piezoelectric effect, an electric field
induces a deformation of the piezoelectric material. The inverse
piezoelectric effect has been applied in actuators design.
Piezoelectric Effect Basics
Apply mechanical stress ? Electric charge produced
Apply electric field ? Mechanical deformation produced
Dipole: each molecule has a polarization, one end is more
negatively charged and the other end is positively
charged.
Monocrystal: the polar axes of all of the dipoles lie in one
direction. ?? Symmetrical
Polycrystal: there are different regions within the
material that have a different polar axis. ??
Asymmetrical
Piezoelectric Effect Basics
§ How to produce piezoelectric effect
a) Material without stress / charge
b) Compress ? same polarity
c) Stretched ? opposite polarity
d) Opposite voltage ? expand
e) Same voltage ? compress
f) AC signal ? vibrate
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Piezoelectricity
(Greek: piezo "to press")
Some ionic crystals with polar axis
show a piezoelectric effect.
The Piezoelectric
Effect vs Crystal
Structure
If all tetrahedra have the same
orientation or some other
mutual orientation that does not
allow for a compensation, then
the action of all dipoles adds up
and the whole crystal becomes a
dipole.
Two opposite faces of the
crystal develop opposite electric
charges.
Crystals can only be
piezoelectric if they are non-
centrosymmetric.
Sphalerite, tourmaline,
ammonium chloride and quartz
are examples.
external pressure causes
deformation and results in
electric dipole
Piezoelectricity
Piezoelectric materials have crystal structures that lack
inversion symmetry but show NO spontaneous polarization
? When the crystal is stressed however it develops a NET
polarization
in an unstressed piezoelectric
crystal, the net polarization is
equal to zero (arrows indicate the
magnitude of the dipole moments
along the three symmetry
directions of the crystal)
application of stress to
the crystal gives rise to a
net polarization p
STRESS
P
Application of pressure to a piezoelectric crystal
displaces the crystal ions with respect to each other
and so causes a change in polarization.
This change of polarization can be detected as a
voltage across the crystal and this effect is referred to
as piezoelectricity. Piezoelectric crystal serve whenever
mechanical pulses are to be concerted to electrical
signals, e.g. in microphones.
The opposite effect to piezoelectricity is
electroconstriction which is an effect in which an
electric field is used to produce a change in the
dimensions of a piezoelectric crystal: e.g. Mechanical
vibrations are induced in the quartz with the aid of
electric pulses.
Piezoelectricity
Crystals where electrical polarization generated
by mechanical stress ?? in general, they are non-
centrosymmetric.
Strain shifts the relative positions of the positive
and negative charges, giving rise to a net electric
dipole.
In 32 crystallographic point groups, 21 do not
possess inversion symmetry elements, plus one
cubic has a combination of symmetries, thus, only
20 groups can be piezoelectric.
Many crystals with tetrahedral structure units
(SiO2, ZnO etc.),shearing stress causes distortional
strain of tetrahedra.
Applications of Piezoelectric Crystals
§ Mechanical to Electrical Conversion
–Phonograph cartridges
–Microphones
–Vibration sensors
–Accelerometers
–Photoflash actuators
–Gas igniters
–Fuses
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Applications of Piezoelectric Crystals
§ Electrical to Mechanical Conversion
–Valves
–Micropumps
–Earphones and speakers
–Ultrasonic cleaners
–Emulsifiers
–Sonic transducers
Applications of Piezoelectric Crystals
§ Electrical-Mechanical-Electrical Conversion
–Surface acoustic wave devices
–Filters
–Oscillators
–Transformers
Electroconstriction is exploited to convert electrical
signals into sound in earphones
Another important application is quartz resonators
which may be used as frequency selective elements
Piezoelectric materials such as PZT (PbZrTiO3) are
used to control the motion of the scanning tip in the
scanning tunneling microscope (STM)
STM image of a corrals of atoms arranged using an STM
Applications of Piezoelectricity Quartz Crystal
Quartz is a piezoelectric material, meaning that it
generates an electrical charge when mechanical pressure is
applied. These crystals also vibrate when a voltage from an
outside source, such as a battery, is applied. In the early
1920s W.G. Cady recognized that, due to their elastic
qualities, mechanical strength and durability, quartz
crystals could be used to fabricate very stable resonators.
Cady also concluded that the crystal could be cut in specific
ways that would create resonators of almost any frequency
that were practically independent of temperature variations.
Quartz crystals were first used as a time standard by
Warren Marrison, who invented the first quartz clock in
1927. Juergen Staudte invented a method for mass-
producing quartz crystals for watches in the early 1970s.
The frequency of the quartz oscillator is
determined by the cut and shape of the
quartz crystal.
The quartz crystals inside watches today
come in various shapes and frequencies.
The most common crystals are miniature
encapsulated tuning forks which vibrate
32,768 times per second. Other types of
crystals vibrate at more than 50 million
times per second.
The oscillations of the balance wheel
provide the time standard in mechanical
timepieces.
In contrast, in the history of mechanical
watches, the balance wheel oscillated first
at 2.5, then at 3, and finally at 5 cycles per
second.
Scanning Tunneling Microscope
Ability to probe
the geometric
and electronic
structure of a
surface in-situ at
the atomic level
in real space.
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Piezoelectricity
AmplifierBumps in the record groove
bounce the
stylus up and
down
Stylus motion squeezes a piezoelectric that
in turn generates an electric current
Amplified current
flexes a second
piezoelectric back and
forth, generating sound
Example: phonograph
Another area of application for dielectric materials is in
micro-electro-mechanical systems (MEMS)
Dielectrics are used to make microscopic gear structures
for a range of applications
In the transducer, stress exerted on some cantilever
structure is converted into an electrical signal via the
piezoelectric effect
microscopic gear wheels
formed in PMMA (size
scale is 100 mm!)
cantilever structure of width 10
mm and length 140 mm
patterned in a silicon substrate
Sensor technology
force sensors
Typical applications for piezoelectricity can be found
in every household. One example are lighters. In this
case a tiny prestressed hammer hits a piezoelectric
material thus igniting a spark.
Gas and cigarette lighters
Applications of Piezoelectric Crystals
Pyroelectrics
a subset where spontaneous polarization is
caused by intrinsic internal strain
accompanied by a lowering in symmetry to
a different crystal structure
Pyroelectricity results from the
temperature dependence of the
spontaneous polarization of polar materials
Pyroelectricity
Greek: pyro "to burn"
Some piezoelectric ionic crystals additionally show a
pyroelectric effect.
Pyroelectric materials possess a temperature dependent
macroscopic electrical polarization.
Temperature dependence of the spontaneous
polarization of triglycerin sulfate.
Examples for Application
Sensor technology
motion detectors
Pyroelectric materials are very sensitive! For
instance thermal radiation of an human being is
sufficient to create measurable electric voltage.
This is widely used for commercial motion
detectors.
Motion detector
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The Pyroelectric Effect of
Tourmaline (Calcium Carbide)
Calcium Carbide: trigonal crystal, C3n point
group, have only 3-fold rotation axis. The
Pyroelectric effect happens on the direction of 3-
fold rotation axis.
Examples: Pouring the mixture of sulfur powders
(yellow) and PbO powders (red) through a sieve
on a heated calcium carbide (CaC2) crystal. Due
to the friction effect of the sieve, the PbO have
positive charge and sulfur powders have negative
charge, they will cover the two tops along the 3-
fold rotation axis of CaC2, indicating that heating
makes the two tops of CaC2 crystal have different
charges along the 3-fold axis.
Heat Sensors
§Temperature change
? differential change in the remnant
polarization
–Remnant polarization is sensitive to
temperature change
§Pyroelectric heat sensor
KJ/kg in slab ricferroelect the of heat specific the :s
kg/m in slab ricferroelect the of density the :
m in slab the of thickness :h
m in slab the of area :A
J in energy heat in change the :H
)shA/(HT
p
3
0
1
2
s
p01s
*
?
ρ
?
ρ?=?
Ferroelectrics
a subset of pyroelectrics
electrical polarization can be reversed by
the application of external electric field
A pyroelectric crystal is also ferroelectric if
the direction of the spontaneous
polarization can be reversed under an
applied electric field.
Ferroelectricity
Pyroelectricity have a permanent net electric dipole
in each primitive unit cell. e.g. ZnO is pyroelectric
because ZnO4 tetrahedra, each possessing a net dipole
moment, all point in the same direction.
Ferroelectric is a pyroelectric solid in which the
spontaneous electrical polarization in a unit cell can
be reversibly changed between ± Ps, by application of
and E field of suitable polarity.
Ferroelectricity
Ferroelectricity derives its name from
ferromagnetic.
A magnetization can be observed that is
reversible by applying a certain magnetic field.
Ferroelectrics show a reversibility, but dealing
with applied electric fields to reverse a material’s
polarization.
Ferroelectricity
Ferroelectricity is a phenomena which was
discovered in 1921.
Ferroelectricity has also been called Seignette
electricity, as Seignette or Rochelle Salt (RS) was
the first material found to show ferroelectric
properties.
A huge leap in the research on ferroelectric
materials came in the 1950's, leading to the
widespread use of barium titanate (BaTiO3) based
ceramics in capacitor applications and piezoelectric
transducer devices.
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Atomic Arrangement and Ferroelectricity
§ The arrangement of the atoms in all
ferroelectric crystals result in an equally stable
state but with reoriented Ps.
§ A simple example is BaTiO3 for which the
prototype is cubic.
§ The paraelectric to ferroelectric transformation
at Tc may be viewed in terms of a low-frequency
temperature-dependent mode of the crystal
lattice, observable by optical or neutron
spectroscopy.
Ferroelectricity
+ + + +
- - - -
Normal Capacitor
+ + + +
- - - -
+ + + ++ + + ++ + + +
- - - -- - - -- - - - - -
- - -- -- - -
+ + + ++ + ++ + +
- - -
Ferroelectric Capacitor
Ferroelectric materials exhibit spontaneous
polarization. This polarization can be aligned by an
electric field, and will remain aligned even after the
field is removed. It occurs from the nonsymmetric
shape of the complex ferroelectric’s unit cell.
Ferroelectrics are principally used to improve the
performance of capacitors.
Ferroelectric Transitions
Curie Temperature, Tc: transition from
randomized paraelectric and ordered ferroelectric
phase.
Ferroelectric
Paraelectric
Ferroelectricity
Previously we saw that dielectric
crystals develop a net polarization
in the presence of an applied
electric field.
In certain crystals known as
ferroelectrics however the
polarization can persist when the
applied electric field is removed!
Ferroelectric behavior is only
observed below a critical
temperature known as the Curie
temperature TC
? At temperatures above this
normal dielectric behavior is
obtained
MATERIAL TC (K) Ps
( mCcm-2)
BaTiO3 408 26.0
SrTiO 3 110
KNbO3 708 30.0
PbTiO 3 765 >50
LaTaO3 938 50
LiNbO3 1480 71
GeTe 670
Ferroelectric Domains and Hysteresis Loop
Ferroelectric crystals
possess regions with
uniform polarization
calledferroelectric
domains.
Polarization vs. Electric
Field (P?E) hysteresis
loop for a typical
ferroelectric crystal is
shown on the right.
The characteristic signature of ferroelectric crystals is the
observation of hysteresis in their Polarization vs. Electric field
curves.
Prior to applying the electric field, the crystal is unpolarized
since the permanent dipoles in the crystal are randomly
oriented.
However, with a strong applied electric field, the permanent
dipoles polarize and saturation of the polarization is observed.
When the field is then lowered back to zero a remnant
polarization then remains.
Variation of polarization with electric field for a
ferroelectric crystal below the curie temperature
Starting from zero polarization at zero field, the
electric field is increased and the polarization
eventually saturates at the value ps
When the field is lowered back to zero the
polarization does not return to zero but exhibits a
remnant polarization p r
Pr
P
1
E
Ps2
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With the ferroelectric crystal now polarized at zero field, it
is necessary to apply a finite coercive field in the opposite
direction to return the polarization to zero.
If the reversed electric is then further increased beyond the
coercive field, saturation of the polarization will occur again.
? however, now the polarization will be oriented in the
opposite direction to that obtained originally
? the polarization vs. electric field curve is therefore said to
exhibit hysteresis
P
E
Ec
the polarization-field curve of
ferroelectric crystals typically shows
hysteresis
on the figure we indicate the coercive
field ec required to remove a net positive
polarization in the crystal
the area enclosed by the curve provides
an indication of the energy dissipated by
the field once a full cycle of the hysteresis
loop has been achieved
curve s: when E is large enough, the
whole crystal is one large domain
when E is removed, a remnant
polarization Pr remains, i.e. the crystal
now is an electret.
when a coercive field (?Ec) is applied,
Pr can be removed. Ps is the
spontaneous polarization corresponding
to the polarization within a domain.
No external E: the dipole moments of
different domains compensate each
other
curve j: the total polarization of the
crystal (if an increasing external
electric field acts on the sample, those
domains whose polarization
corresponds to the direction of the
electric field will grow at the expense of
the remaining domains).
Hysteresis
Loop
At a microscopic level,
ferroelectrics can be understood to
be those materials whose crystal
structures contain charged ions that
are displaced from high-symmetry
points.
This displacement in turn gives
rise to a net polarization of the
crystal unit cell.
A good example of a ferroelectric
crystal is barium titanate (BaTiO3)
which features two positively-
charged ions and one negatively-
charged ion.
Above the Curie temperature these
ions are distributed in a perovskite
crystal structure and the crystal
behaves as a normal dielectric with
no spontaneous polarization.
crystal structure of barium
titanate at temperatures
above the Curie temperature
in this crystal configuration
there is no net polarization of
the unit cell and the crystal
behaves as a normal
dielectric
at temperatures above the
curie temperature
ferroelectric materials are
said to be paraelectric
Barium
Titanate
lBarium –Titanate (BaTiO3) ? the first material to be
developed as a Ferroceramic
lavailable in single crystal form
lThe absence of center symmetry in crystal structure
gives rise to spontaneous polarization
lCubic above Curie temperature; tetragonal as it cools
down
As the temperature is lowered below the curie temperature,
the crystal structure deforms and the unit cell develops a net
dipole moment along the vertical axis of the unit cell.
In the ferroelectric state, a large number of dipoles align to
form ferroelectric domains that are typically randomly oriented
at zero field.
An electric field may be used to align the domains with
respect to each other.
random alignment of the dipoles of
different domains in aferroelectric
crystal with no applied electric fieldc/a=1.04
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a
a
a
T>120°C
a
c
a
5°C <T<120°C
a a
a
α
T<?90°C
a
b
c
?90°C <T<5°C
Cube
Tetragonal
Orthorhombic
Rhombohedral
Temperature Dependence of
Barium Titanate Crystal Structure In SrTiO3, Ti?O~1.95?a typical bond length for Ti-O;
stable as a cubic structure
In BaTiO3, Ti?O is stretched,
>2.0?. Too long for a stable
structure.
Ti displaces off its central
position towards one oxygen
→ square pyramidal
coordination
larger
This creates a net dipole moment:
Displacement by 5?10% Ti?O bond length
Random dipole orientations paraelectric
Aligned dipole orientations ferroelectric
Under an applied electric field, dipole orientations can be
reversed, i.e. the structure is polarizable.
Dipoles tend to be ‘frozen in’at room temperature; as increase
temperature, thermal vibrations increase the polarizability
Ferroelectric Crystal
of NaNO2
structure below Tc
structure above Tc
macroscopic dipole moment in
ferroelectirc form
paraelectirc form
In sodium nitrite the ferroelectric
polarization only occurs in one
direction.
Applications of Ferroelectricity
Ferroelectric materials have a number of different
applications in technology:
The hysteresis curve that these materials exhibit
can be utilized for memory devices in computers
The dielectric constant of ferroelectrics is orders of
magnitude larger than that of normal dielectrics ?
They may therefore be used as dielectric materials in
ultra -compact and high-efficiency capacitors
The dielectric constant and so the refractive index of
these materials may be tuned by varying an external
electric field ? this allows the use of these materials
as optical switches
Capacitors
Parallel plate capacitor
apply a voltage; charge Q
accumulates on the plates
Place a polarizable
material between the
plates ?
Q increases
e.g. H2O
12
Define the permittivity or dielectric
constant of a material by:
H2O is a polar liquid: ε′ ~80
Typical ionic solids: ε′ ~10
Air: ε′ ~1
BaTiO3:
vacQ
Q=ε′
Below 120°C, BaTiO3 is
ferroelectric with aligned
dipoles. Residual dipole
disorder gives ε′ ~200-1000
At~120°C, tetragonal →
cubic phase transition.
Dipoles randomize and
ε′ increases to ~5,000-10,000
For capacitor applications, need to increase capacitance
[energy stored/mass or volume] by increasing Q and thus
increasing ε′
How to do this? BaTiO3 is very good at 120°C but want
high ε′ at room temperature!
Solution: Partial substitution of Ba by a smaller M2+ ion -
Sr2+ ; unit cell volume decreases and the phase transition
temperature decreases
