Elastic studies of Glass Materials Studied by Ultrasonic Technique

Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties |
Conclusion
Outline
• Glass in General
• Ultrasonic Waves
• Physical Properties of Glass
– Preparation
– Density and Molar Volume
• Elastic Properties
– Compositional Dependence
– Temperature Dependence
– Hydrostatic Pressure Dependence
• Conclusion
Glass prism

Conclusion
Glass – An Introduction
What is a glass?
Glass - hard, brittle solid material that is
normally lustrous and transparent in
appearance and shows great durability
under exposure to the natural elements.
The latin term glesum, probably originated from
a Germanic word for a transparent,
lustrous substance.
The term glass developed in the late Roman
Empire.
Natural heat-producing processes like volcanoes
and lightning strikes are responsible for
creating various forms of natural glass.
Obsidian - super-heated sand or rock
that rapidly cooled.
Moldavite formed by meteorite
impact (Besednice, Bohemia)

Conclusion
General Introduction
• These three properties—
lustre, transparency, and
durability
— make glass a favoured
material for such
household objects as
windowpanes, bottles, and
lightbulbs.
Clear glass for
Incandescent light
bulb
Thermal
Insulation
Glass

Conclusion
Glass Application
Special properties of glass make it
suitable for folllowing applications
– flat glass
– Tempered glass
– Annealed glass
– Laminated glass
– container glass
– optics and optoelectronics
material
– laboratory equipment
– thermal insulator (glass wool)
– reinforcement fiber (glass-
reinforced plastic, glass fiber
reinforced concrete)
– and art.

Conclusion
Glass Technology
Glass building
Energy saving mirror

Conclusion
Glass Arts
Decoration Glass- Venetian millefiori.
Chinese ring
Glass beads are made with silica (usually from sand).
Cross section of Korean broken beads

Conclusion
Glass Art
Roman Cage Cup
from the 4th century
A.D.
Roman glass A 16th-century stained
glass window.
A vase being created at
the Reijmyre
glassworks, Sweden
Stained glass

Conclusion
Next-generation large-scale panels
Glass substrates for LCDs
To form various functional films on glass substrates.
ASAHI
Glass,
Japan

Conclusion
Specific Potential Application
of Glassy Materials
CD memory device
Optical
switching
device
Non-linear optical
devices
Electrochemical devices
Laser host
Infra-Red Fiber Optics
Optical waveguides

Conclusion
Outline
– Definition
– Preparation
• Conclusion
Glass prism

Conclusion
.
Glass Definition
♦ Glass is an inorganic product of
fusion that has cooled to a rigid
condition without crystallization
(American Society for Testing Materials ,1945)
True for most commercial materials (e.g.,
soda-lime-silica) but ignores organic, metallic,
H-bonded materials, ignores alternate
processing routes (sol gel, CVD, electron or
neutron -bombardment, etc.)
♦ Glass is an X-ray amorphous
material which exhibits a glass
transition. (Wong and Angell, 1976)
Not all amorphous solids are glasses; wood,
cement, a-Si, thin film oxides, etc. are
amorphous but do not exhibit the glass
transition.
♦Glass is an undercooled liquid."
Problems: glasses have 'solid'
properties (e.g., elastic material)
No flow at room temperature
♦ Glass as any isotropic material,
whether inorganic or organic,
which lacks three dimensional
atomic periodicity and has a
viscosity greater than about 1014
poise (Mackenzie, 1960)

Conclusion
Zachariasen’s model
According to Zachariasen, in order for a
given oxide AmOn to form a glassy
solid, it must meet the following
criteria:
(1) the oxygen should be linked to no
more than two atoms of A,
(2) the coordination number of the
oxygen about A should be small, on
the order of 3 or 4,
(3) the cation polyhedra must share
corners only, and
(4) at least three corners must be
shared.
In 1932, physicist W.H. Zachariasen
defined glass is an extended, three-
dimensional network of atoms
that form a solid which lacks the
long-range periodicity (or
repeated, orderly arrangement)
typical of crystalline materials.

Conclusion
Definition
• These criteria are useful guidelines for
the forming of conventional oxide
glasses, but unsuitable for nonoxide
glasses.
• Chalcogenide glasses
– for instance, are chains of random lengths
and random orientation formed by the
bonding of the chalcogen elements sulfur,
selenium, or tellurium.
– Ions of these elements have a 2-
coordination requirement, and the chains
are cross-linked by 3- or 4-coordinated
elements such as arsenic, antimony, or
germanium.
♦ Glass is a solid that
possesses no long range
atomic order and, upon
heating, gradually softens
to the molten state.
Non-crystalline structure
Glass transformation
behavior

Conclusion
Outline
• Basic Ultrasonics
– Preparation
• Conclusion
Glass prism

Conclusion
Basic Ultrasonics
• “Ultrasonic" refers to sound that
above the frequencies of
audible sound, (beyond 20 kHz)
• Ultrasonic can be produced by
transducers
– piezoelectric effect
– magnetostrictive effect
• Piezoelectricity is the ability
of some crystals (quartz) and
certain ceramics materials to
generate an electric
potential in response to
applied mechanical stress.
• Magnetostrictive
transducers use magnetic
strength to produce high
intensity ultrasonic sound in
the 20-40 kHz range for the
ultrasonic cleaning and also
other mechanical applications

Conclusion
Ultrasonic wave are able to
propagate in medium by
method such as:
• Reflection
• Refraction
• Propagation
• Transmission
• Dispersion
• etc
Advantages of ultrasonic
wave
• ability to form coherent
wave in which amplitude,
frequency,
• direction of propagation
can be controlled
Advantages of ultrasonic wave

Conclusion
Type of ultrasonic wave
2 type of ultrasonic
wave traveling in
solid such as glass:
 longitudinal wave
 shear wave
Longitudinal wave also known as
compressional waves
•the oscillation of the particle is
forward and backward, compressing,
and depressing.
Shear wave also known as transverse
wave
•the oscillation of particle in medium is
at right angles to the direction of
propagation.
•Shear wave can only propagate
through solid and cannot propagate in
liquid and gas.
N
N
U
U

Conclusion
Outline
– Glass Preparation
• Conclusion
Glass prism

Conclusion
2 methods of preparing glass samples
Glass Preparation
Conventional Method
 Cooling from the liquid
state/ Melt quenching
technique
 Condensation from the
vapor
 Pressure quenching
 Solution hydrolysis
Unconventional Method
Unconventional melting
Solution methods
Deposition methods
Solid-state transformations

Conclusion
Glass Formation
Normally, glass is formed upon the cooling of
a molten liquid in such a manner that the
ordering of atoms into a crystalline
formation is prevented.
Instead of the abrupt change in structure that
takes place in a crystalline material such
as metal as it is cooled below its melting
point
in the cooling of a glass-forming liquid there
is a continuous stiffening of the fluid until
the atoms are virtually frozen into a more
or less random arrangement similar to the
arrangement that they had in the fluid
state.

Conclusion
Crystal vs Glass
Glasses
•lack of long-range order
results in larger volumes
(lower density), higher
energies;
atoms could rearrange to
form denser structures if
given enough thermal energy
and time.
•thermodynamically
metastable phase
Crystals
ordered atomic
structures mean
smaller volumes
(high density) &
lower energies
•thermodynamically
stable phase

Conclusion
Glass Structure
Glass
• amorphous
• isotropic macroscopic physical
properties
• no grain structure when viewed
under an optical microscope.
Glass structure relates to various
physical properties such as density,
thermal expansion, viscosity, surface
tension
and also miscellaneous mechanical
(including elastic), chemical and
electrical properties of glass.

Conclusion
Glass Structure
Two-dimensional representation of (a) an oxide
crystal and (b) a glass of the same chemical
composition (A2O3) due to Zachariasen (1932)
Schematic two-dimensional representation of the microscopic
structure of binary oxide glass; (a) composed of basic glass
former and glass former; (b) showing the effect of network
modifying cations on the network of the glass former.

Conclusion
Structure of Binary Borate
Glass
Some structural groupings in
borate glasses as indicated from
nuclear magnetic resonance
experiments (Bray 1985). Small
solid circles represent boron
atoms, open circles oxygen
atoms and an open circle with
negative sign indicates non-
bridging oxygen.

Conclusion
Outline
– Preparation
• Conclusion
Glass prism
Quartz sand (silica)
as main raw material
for commercial glass
production.

Conclusion
Substance is weight First Furnace
400 C for 30 min
Second Furnace
750-800 C for 60 min
Pour melt into mould Placed molten
and mould in
First Furnace and
annealed at 400 C
Removed the mould
after the melt
was hard enough
Cut and polished sample
GLASS PREPARATION PROCESS

Conclusion
Preparing Commercialized Glass
• Pure silica (SiO2) melts at a viscosity of
10 Pa s (100 P)— of over 2300 °C
(4200 °F).
• Sodium carbonate (Na2CO3) lowers the
melting point to about 1500 °C
(2700 °F) in soda-lime glass
• Soda makes the glass water soluble,
which is usually undesirable, so lime
(calcium oxide (CaO), some
magnesium oxide (MgO) and
aluminium oxide are added to provide
for a better chemical durability.
• The resulting glass contains about 70
to 74 percent silica by weight and is
called a soda-lime glass.Soda-lime
glasses account for about 90 percent of
manufactured glass.
Lead glass, such as lead crystal
or flint glass, is more 'brilliant'
because the increased refractive
index causes noticeably more
"sparkles",
while boron may be added to
change the thermal and electrical
properties, as in Pyrex.
Marlinda Daud, Pusat Minerologi Ipoh

Conclusion
Special Glass
• Adding barium also increases the
refractive index.
• Thorium oxide gives high
refractive index and low dispersion,
(for high-quality lenses) but due to
its radioactivity has been replaced
by lanthanum oxide in modern eye
glasses.
• Large amounts of iron are used in
glass that absorbs infrared energy,
such as heat absorbing filters for
movie projectors,
• cerium(IV) oxide for absorbs UV
wavelengths (biologically damaging
ionizing radiation).
Finally, fining agents such
as sodium sulfate, sodium
chloride, or antimony oxide
are added to reduce the
bubble content in the glass.

Conclusion
Other Types of Glass
Besides common silica-
based glasses, many
other inorganic and
organic materials may
also form glasses,
including
– plastics (e.g., acrylic glass)
– phosphates,
– borates,
– chalcogenides,
– fluorides,
– germanates (glasses based
on GeO2),
•tellurites (glasses based
on TeO2),
• antimonates (glasses
based on Sb2O3),
• arsenates (glasses
based on As2O3),
• titanates (glasses
based on TiO2),
• tantalates (glasses
based on Ta2O5),
• nitrates, carbonates
and many other
substances.

Conclusion
Colored Glass
• Color in glass may be obtained by addition
of electrically charged ions and by
precipitation of finely dispersed particles
(such as in photochromic glasses).[
• Ordinary soda-lime glass appears
colorless
• iron(II) oxide (FeO) impurities of up to 0.1
wt%produce a green tint
• Further FeO and Cr2O3 additions may be
used for the production of green bottles.
• Sulfur, together with carbon and iron
salts, is used to form iron polysulfides and
produce amber glass ranging from
yellowish to almost black.
• Manganese dioxide can be added in
small amounts to remove the green tint
given by iron(II) oxide.

Conclusion
Colored Glass
Ion
Silicate-based
Glass
Phosphate-based Glass
Fe+2
deep blue-green slight greenish blue
Fe+3
yellowish-brown slightly brownish
The color of a glass may depend
upon the nature of the glass as
well as the coloration ion.
For example, iron ions have the
following color influences:

SEM Photos XRD Pattern of
Starting Materials
TeO2 powder
TeO2 glass
ZnO Powder
TeO2-ZnO glass
0
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
2400
2600
2800
3000
3200
3400
10 20 30 40 50
2 theta
Intensity(a.u)
0
5000
10000
15000
20000
25000
30000
35000
40000
45000
50000
10 20 30 40 50
2 Theta
Intensity(a.u)
0
5000
10000
15000
20000
25000
30000
35000
10 20 30 40 50
2 Theta
Intensity(a.u)
TeO2-ZnO-AlF3
glassAlF3 (97.0%)
Powder

Conclusion
XRD patterns
100
600
1100
1600
2100
10 20 30 40 50
2 theta
Intensity(a.u)
TZ7
TZ6
TZ5
TZ4
TZ3
TZ2
TZ1
TZ0
• no discrete or continuous sharp peaks
• but broad halo at around 2 260
- 300
, which reflects the
characteristic of amorphous materials.
• absence of long range atomic arrangement and the
periodicity of the 3D network in the quenched material
400
600
800
1000
1200
1400
1600
1800
10 20 30 40 50
2 theta
Intensity(a.u)
S5
S4
S3
S2
S1
TeO2)1-x (ZnO)x (x = 0.1 to 0.4 in 0.05) (TeO2)90(AlF3)10-x(ZnO)x (x = 1 to 9)
binary ternary

Conclusion
Glass Forming Region

Conclusion
Density & Molar Volume
ρ
M
V =
Molar volumes
ac
aca
a
s
ww
w ρρ 





−
=
Density Measurement
(Archimedes Method)

Conclusion
Variation of density and molar volume with mol% Bi2 O3
in Bi2 O3–B2 O3 glass systems.
The increase of the density of the glasses
accompanying the addition of Bi2 O3 is
probably attributable to a change in cross-link
density and coordination numbers of Bi3+ ions.
26
26.5
27
27.5
28
28.5
29
0.55 0.6 0.65 0.7 0.75 0.8 0.85
Mole fraction of TeO2
Molarvolume(cm3
mol-1
)
4650
4700
4750
4800
4850
4900
4950
5000
Density(kgm-3
)
Density and molar volume of TeO2.B2O3 glasses
28
28.5
29
29.5
30
30.5
0.05 0.10 0.15 0.20 0.25 0.30 0.35
Pecahan Mol Ag2
O
Isipadumolar(cm3
)
4800
4900
5000
5100
5200
5300
Ketumpatan(kg/m3
)
Density and molar volume of [(TeO2)x (B2O3)1-x)]1-y [Ag2O]y

Conclusion
Density and Molar Volume
3500
4500
5500
6500
7500
0 20 40 60 80
Bismuth Oxide (mol%)
Density(kgm-3)
Dependence of density on the composition of bismuth oxide
glass systems as measured by El-Adawy and Moustafa (1999)
(5 - 45 mol%), Wright et al (1977) (20 – 42.5 mol%) and
present works (40 – 70 mol%).

4700
4800
4900
5000
5100
5200
5300
5400
0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4
Mole fraction of ZnO
Density(kg/m3
)
22
24
26
28
30
32
34
0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4
Molarvolume(10-6
m3
mol-1
)
•The increase in density indicates
zinc ions enter the glassy network
•The decreases in the molar volume
was due to the decrease in the
bond length or inter-atomic spacing
between the atoms
• The stretching force constant (216
N/m – 217.5 N/m) of the bonds
increase resulting in a more
compact and dense glass.
• Atomic Radius (Shelby, 2005).
•R(Zn2+
)(0.074 nm) << R(Te2+
)
(0.097 nm)
•there is no anomalous structural
change (non-linear behaviour)

Conclusion
Outline
– Preparation
– Theory
• Conclusion
Glass prism
A modern
greenhouse in Wisley
Garden, England,
made from float
glass.

Conclusion
Elastic Properties of Materials
Application of external forces to a
solid body produces complex
internal forces which cause
– motion of the body,
– in the form of linear translation,
rotation and deformation.
The body is in a condition of
stress and any changes in the
shape or volume are then
referred to as strain
Elastic body - after removal
of the external force, the
material returns to its original
unstressed condition.
To study of elasticity we
consider infinitesimal
elastic deformations, where
stress is linearly proportional
to strain, as stated in Hooke's
law.

Conclusion
Elastic Properties of Materials
Elastic constants connect stress
and strain
Elastic constant can be
determined by propagating
ultrasonic elastic waves travel
through a medium.
The velocity of these waves and
density of the sample can be
used to determine the values of
these elastic constants.
The concept of elastic continuum is
applied to explain quantitatively the
elastic behavior of a solid body,
under external stresses
(temperature and hydrostatic
pressure)
Materials are assumed to behave like a
homogeneous continuous medium.
This approximation valid for elastic
waves of wavelengths λ longer than
10-6
cm, i.e. frequencies below 1012
Hz, and ultrasonic waves fulfill this
criterion.

Conclusion
Theory of Elasticity
Theory of elasticity and the
anharmonicity of solids,
both crystal and
noncrystalline (glass)
systems
The propagation of elastic
waves in crystals,
including the
thermodynamic definition
of elastic constants
The concept of
anharmonicity is also
outlined.
The effect of hydrostatic
pressure and temperature
on the elastic

Conclusion
Elasticity and Hooke's Law
• For sufficiently small deformations of
the solid body, each component of
stress is linearly related to each
component of strain by Hooke's law
σij=Cijkl ( i,j, k,l= 1,2,3)ϵ
6 components of stress
6 components of strain
σij=Cijklϵ ( i,j, k,l= 1,2,3)

Conclusion
Thermodynamic Definition of
Elastic Constants
Elastic constants can be also defined
thermodynamically i.e. with respect to
thermodynamic parameters (Brugger,
1964).
4 main thermodynamic potentials can be
involved,
U - internal energy
F - Helmholtz free energy
H - enthalpy and
G - Gibbs free energy
Each of these to be a function of entropy S,
temperature T, thermodynamic tension
components tij and reduced Lagrangian
strain components ηij/ρo where ρo,
represents the density of the
unstrained solid.
ijijdηt
ρ
1
TdsU 





+=

d
ijijdηt
ρ
1
SdTF 





+−=

d
ijijdt
ρ
1
TdsH η





−=

d
ijijdt
ρ
1
SdTG η





−−=

d
0',
ijkl
s
...
U
C
=








∂∂
∂
=
η
ηη
ρ
Sklij
n
o
0',
ijkl
T
...
F
C
=








∂∂
∂
=
η
ηη
ρ
Tklij
n
o
0',
ijkl
S
...
H
S
=








∂∂
∂
−=
tSklij
n
o
tt
ρ
0',
ijkl
T
...
G
S
=








∂∂
∂
−=
tTklij
n
o
tt
ρ

Conclusion
Elastic Constant
.........
6
1
2
1
)(
5
5
o
+





+






=
mnkljijklmn
klijlijk
iC
CU
ηηη
ηηηρ
Energy density of the
solid may then be written
as
0'
ijkl
s
...
U
C
=








∂∂
∂
=
η
ηη
ρ
klij
n
o
0'
3
ijklmn
s
C
=
∂∂∂
∂
=
η
ηηη
ρ
mnklij
o
U
Second Order
Elastic
Constant
Third Order
Elastic Constant
Since the form of this expansion is
similar to the expansion of potential
energy in terms of interatomic
displacement,
It is possible to relate the elastic
stiffness constants to the interatomic
forces in a solid.

Conclusion
Propagation of Elastic Waves In Solid
One way to determine the elastic
properties of any solid is through a
dynamic test in which elastic waves
are propagated in the solid.
Assumption
• Propagated waves behave
adiabatically:
• Entropy is conserved;
• Wavelengths are much greater
than the interatomic spacing
• Small displacement of the atoms
To ensure that the deformation is
elastic and Hooke's law is obeyed.
j
iji
o
xt
u
∂
∂
=
∂
∂ σ
ρ 2
2















 ∂
+
∂
∂
∂
∂
=
∂
∂
i
j
j
i
ijkl
k
i
o
dx
u
x
u
C
xt
u
2
1
2
2
ρ
kj
i
ijkl
i
o
xx
u
C
t
u
∂∂
∂
=
∂
∂ 2
2
2
ρ
( ) 02
=−∂ oljkolijklilo UNNUCvρ
Christoffel's equation
For a specific combination of N and U,
the equation of motion will provide only
three solutions of wave velocities, one of
which resembles a longitudinal and two
shear waves.
N - Propagation Direction
U - Polarization direction

Conclusion
Elastic Contants – Wave Velocity
Mode No
Propagation Direction
N
Polarization direction
U
(ρv2
)
1 [100] [100] C11 (L)
2 [100] In [100] plane C11
3 [110] [110] (C11+C12+2C44)/2
4 [110] [001] C44 (G)
5 [110] [1 0] C’=(C11-C12)/2
6 [111] [111] (C11+2C12+4C44)/3
7 [111] In [111]plane (C11+C44-C12)/3
1
Ultrasonic wave velocity and elastic stiffness constant relationships for a cubic crystal

Conclusion
Elastic constants of the glasses
Longitudinal modulus
Shear modulus
Bulk modulus
Poisson’s ratio
Young’s modulus
Debye Temperature
2
lVL ρ=
2
sVG ρ=






−=
22
3
4
sl VVK ρ
( )
( )22
22
2
2
sl
sl
VV
VV
−
−
=σ
( )
22
222
43
sl
sls
VV
VVV
E
−
−
=
ρ
mDt V
M
Np
k
h 3
1
4
9






=≈
π
ρ
θθ
3
1
33
12
−








+=
lS
m
VV
V

Conclusion
Ultrasonic System
Schematic representation of (a)
simple pulse ultrasonic system.
(b) Envelope of pulse echo train
and (c) detail of each echo as
seen on oscilloscope display

Conclusion
Ultrasonic Pulse Echo Overlap System
Pulse echo overlap system
Pulse echo overlap waveforms
Block diagram of the experimental
set up – ultrasonic wave velocity
and attenuation measurement
(Mepco Engineering College,
INDIA)

Conclusion
Ultrasonic System
Ultrasonic – MBS 8000
Ultrasonic Data Acq.
System

Conclusion
Interatomic Potential Energy
In a simple lattice dynamical model, the
restoring forces between atoms and
hence their potential energy are
generally considered to be a function of
the atomic displacement from
equilibrium positions.
In the harmonic and anharmonic lattice
vibration models for a solid
TOEC play an important role in
accounting for the anharmonic and
nonlinear properties of solids in
the long wavelength acoustic
modes.

Conclusion
Wave Velocity
Compositional dependence of the velocity of
longitudinal and shear acoustic waves in Bi2
O3–B2 O3 glass systems.
Both increase at ﬁrst with increasing Bi2
O3 mol% up to a maximum at 25 mol%
Bi2 O3 and then decrease as the Bi2 O3
mol% increases further.
1000
1500
2000
2500
3000
3500
4000
0.05 0.10 0.15 0.20 0.25 0.30 0.35
Pecahan mol of Ag2O
Halajuultrasonik(m/s)
Compositional dependence of the velocity of
longitudinal and shear acoustic waves in [(TeO2)x
(B2O3)1-x)]1-y [Ag2O]y glass
1500
2000
2500
3000
3500
4000
0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4
Velocity(m/s)
Longitudinal
Longitudinal
Shear
Shear
Compositional dependence of the velocity of longitudinal and
shear acoustic waves in [(ZnO)(TeO2) glass

Conclusion
Lead Magnesium Chloride
Phosphate Glass

Conclusion
Elastic Modulus
Dependence of longitudinal modulus on
the composition of Bi2 O3–B2 O3 glass
systems.
One reason for this difference may come from the
volume effect, in that C44 expresses the
resistance of the body to deformation where no
change in volume is involved, while C11 expresses
the resistance where compressions and
expansions are involved.
10
20
30
40
50
60
70
0.05 0.10 0.15 0.20 0.25 0.30 0.35
Pecahan mol Ag2O
Moduluskenyal(GPa)
L
E
K
G
Compositional dependence of the longitudinal and shear
modulus of [(TeO2)x (B2O3)1-x)]1-y [Ag2O]y glass

Conclusion
15
20
25
30
35
40
45
50
55
60
0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4
Mole fractionof ZnO
ElasticModuli(GPa)
Longitudinal Modulus, L
Young’s Modulus, E
Bulk Modulus, K
Shear Modulus, G

Conclusion
Elastic Properties
Mole fraction, x 0.3 0.4 0.45 0.5 0.6
Elastic stiffness (GPa)
C11
C44
C12
48.9
18.0
12.9
48.8
18.0
12.7
47.5
17.4
12.7
47.3
17.5
12.3
47.3
17.2
13.0
Young's modulus, E
(GPa)
43.5 43.5 42.2 42.2 41.8
Bulk modulus, B (GPa) 24.9 24.7 24.3 24.0 24.4
Poisson's ratio, σ 0.208 0.207 0.211 0.207 0.215
Fractal dimension 2.90 2.92 2.87 2.92 2.82
Molar volume, V
(cm3
/mole)
34.2 33.8 34.2 33.9 33.3
Number of atoms per
volume (x1028
atoms/m3
)
9.67 8.90 8.37 8.00 7.24
Debye Temperature (K) 291 275 263 255 238
The room temperature elastic
properties of (PbO)x(P2O5)1-x glasses
Mole fraction, y 0.04 0.06 0.07 0.1
Elastic stiffness (GPa)
longitudinal, c11
shear, c44
c12
50.4
17.1
16.3
44.3
16.0
12.3
43.0
15.9
11.2
35.7
14.8
6.03
Young's modulus, E
(GPa)
42.4 39.0 38.4 33.9
Bulk modulus, B (GPa) 27.6 23.0 21.8 15.9
Poisson's ratio, σ 0.244 0.217 0.206 0.145
Fractal dimension 2.47 2.79 2.92 3.73
Molar volume, V
(cm3
/mole)
33.5 33.5 33.3 33.4
Number of atoms per
volume (x1028
atoms/m3
)
9.60 9.65 9.72 9.78
Debye Temperature (K) 276 266 264 251
Room temperature elastic properties of
(PbCl2)y(PbO.2P2O5)1-y glasses

Conclusion
Elastic Properties

Conclusion
Outline
– Preparation
– Theory
• Conclusion
Glass prism

Conclusion
Temperature Dependence
Low temperature dewar
system
Sample holder

Conclusion
Temperature Variations of the SOEC
The dependence of elastic constants
upon temperature is another
consequence of anharmonicity of the
interatomic potential energy in solids.
The normal behaviour of the thermal
variations of the SOEC of most
crystals,, is characterized by two
general features;
•a linear increase with decreasing
temperature and
•a zero slope in the region where the
temperature approaches zero Kelvin.
The linear dependence of elastic
constants on temperature, especially
above the Debye temperature θD ,is
due to the anharmonic nature of the
lattice vibrations.
The linearity of this dependence may
break down in the vicinity of a phase
transition.
Typical curve of second order elastic
constant versus temperature
))/(1( DoJI TLFCC θ−=
{ }∫ −=
T
DD
D
dxxxTTF
/
0
34
1)exp()/(3)/(
θ
θθ
3
2 v
o
T
IJ
JI
dT
df
f
C
dT
dC α
−





=

Conclusion
Variation of velocity and elastic moduli with temperature of Lead
Bismuth Tellurite (BTP) Glasses

Conclusion
At sufficiently low temperatures it is
expected that in most crystalline
solids the slope of dCIJ/dT would
decrease i.e. dCIJ/dT →0 as T →0
which is a direct consequence of
the third law of thermodynamics.
However in certain materials like
glasses, this particular feature is not
always observed; instead of
showing a zero slope of dCIJ/dT,
the elastic constant increases to a
maximum value at low temperature
(~1K).
This behaviour has been ascribed
to interactions with two-level
systems (Anderson et al. 1972,
Phillips 1972).

Conclusion
At very low temperatures where only ground states
have to be considered, the groups of atoms are still
able to tunnel through a barrier. This gives rise to
an energy splitting of the ground state for this two-
level system given by
2
0
2
∆+∆=E
)exp(00 λω −=∆ 
2
/2 mVd=λ
where
The parameter Δ designates the asymmetry of
two-level potential, Δo represents the tunneling
energy and λ is a tunnelling parameter
describing the overlap of the wavefunctions of
two states in a quantum mechanical theory
(Phillips 1981). The parameter ωo is the
frequency of oscillation in an individual well.
Schematic representation of a double well
potential, sometimes known as the two level
system, characterized by a barrier V,
asymmetry energy LI and distance d.

Conclusion
Debye Temperature
3
1
3
3
3
2
3
1
3
1
1 111
4
9
−







 Ω






+











= ∫ ππ
θ
d
vvvk
h
V
Ne
D
The Debye temperature θD is useful in
describing the thermal behaviour of
solids and it plays an important role in the
theory of lattice vibrations.
θD measure of the separation of the low
temperature quantum mechanical region,
where the vibrational modes begin to be
"frozen out", from the high temperature
region where all modes begin to be
excited according to classical theory.
θD can be obtained directly from heat
capacity measurements, and it can be
also derived from a set of the elastic
constants.
3
1
33
21
3
1
−














+=
SL VV
Vm
VL (= (C11/ρ) 1/2
) and VS= (=C44/ρ) 1/2
m
e
D V
k
h
V
N












=
3
1
1
4
9
π
θ

Conclusion
Pressure Dependence
To compare between the
measured values of (ρW2
)'p=0
and the pressure derivatives
of the effective SOEC (ρV2
)',
the following relations has to
be employed,
dP
WVd
W
dP
d
W
dP
dW
W
dP
V
d oo
o
oooo
)/()/(
2)(
22
22
2
ρ
ρρ
ρρ
ρ
++=






−+= kmiimk
T
o
IJ
IJ
SNN
dP
df
f
C
dP
dC
2
2
β
Here Co
IJ represents the SOEC at ambient
condition, df/dP is the gradient of measured
frequency in the pulse echo overlap experiment
(see section 3.5) versus pressure, fo is the overlap
frequency and βT
and Skmii are the isothermal
volume compressibility and the elastic compliances
respectively.
Hydrostatic pressure cell and sample holder

Conclusion
Mode Grüneisen Parameters
The mode Grüneisen parameter is
an important tool for investigation
of anharmonic effect in solid.
One way to derive the Grünisen parameter is
by considering the entropy of the system in
the quasiharmonic form (Barron 1995)
T
TV
SS i
i
i
),(ω
∑=
1
ln
ln
1
ln
)(
−
∂
∂
−
∂
∂
−= ∑ TV
TC ii
i
i
ωω
Vd
d i
i
ln
lnω
γ −=
1
1
)(
−
−
∂
∂
∂
∂
−=
∂
∂
∑ TTVT
TC
V
S i
V
i
T
i
i
i
V
ωωω
VT
th
C
V
V
S
∂
∂
=γ V
T
VP
S
V CVCV βαβα // ==
α is the coefficient of volume thermal
expansion, V is the volume, and is
isothermal and adiabatic compressibility
respectively and Cv and Cp are specific
heats at constant volume and constant
pressure respectively
dP
vd
Tl
1ln1
3
1
β
γ +=
dP
vd
Ts
1ln1
3
1
β
γ +=
( )
3
21 s
el γγ
γ
+
=

Conclusion
Relation between SOEC and TOEC
Even though we have not measured
a set of individual TOEC, the TOEC
can be obtained from the pressure
derivatives of the second order
elastic constants
)2(
)22(
1211
16614444121144
CC
CCCCC
P
C
+
++++
=
∂
∂
)2(2
)233(
1211
1231111211
'
CC
CCCC
P
C
+
−++
=
∂
∂
)2(3
)26(
1211
123112111
CC
CCC
P
B
+
++
=
∂
∂

Conclusion

Conclusion
Conclusion
• The general discussion on basic
glass and its preparation, as well
as the fundamental of elastic
properties have been discussed
• Experimental shows the physical
and elastic properties of glasses
were found slightly affected by the
changes in the glass composition.
• The densities of most glasses
increases as the glass modifier
content was added to substitute the
glass former content while their
molar volume increases or
decreases due to the composition.
•The experimental setup has
been discussed for evaluating the
ultrasonic and elastic properties
of materials at low temperatures
and high pressure.
•There are possibility in
evaluating the elastic properties
of any glass based materials at
elevated temperatures and
pressure in order to obtain their
elastic behaviour.

Conclusion
Acknowledgement
Glass Research Group
• Dr Halimah Ahmad Kamari
• Prof Madya Dr Zainal Abidin Talib
• Prof Madya Dr Wan Daud Wan Yusof
• Dr Khamirul Amin Matori
• Prof Dr Abdul Halim Shaari
• Our postgraduate students
Special thanks to MOSTI and UPM for financial
support.

Conclusion
Thank you for
your attention
drsidekaziz@gmail.com

Elastic studies of Glass Materials Studied by Ultrasonic Technique

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