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Sinan Özgün, Abdül Kadir Eren
Anadolu Universitesi Malzeme Bilimi ve Mühendisliği Bölümü, 2011
1
A Report on
VISCOSITY OF GLASS MELTS / GLASS FORMING LIQUIDS Sinan Özgün, Abdul Kadir Eren
Course Instructor: Asst. Prof. Emrah Dölekçekiç
Anadolu University, Materials Science & Engineering Department Eskisehir-Turkey
December 25th, 2011
Abstract:
This report reviews the viscosity phenomena, the viscosity of glass melts and glass
forming liquids in undergraduate level, as part of the MLZ 320 Glass Technology technical
elective course given at Anadolu University, Materials Science & Engineering Department
prior to presentation. In the introduction part, general definition and terminology of the
phenomenon is introduced. In the following parts definitions of viscosity and other related
concepts, temperature, thermal history, compositional dependence of viscosity and effect of
crystallization on viscosity are examined, respectively. In the third part viscosity measurement
techniques are introduced, namely: Parallel Plate Viscometry, Beam–Bending Viscometers,
Fiber Elongation Viscometers, Falling Sphere Viscometers and Rotation viscometers.
Table of Contents:
1. Introduction
1.1.Definition of Viscosity
1.2.Terminology
2. Factors Affecting Viscosity of Glass
2.1. Temperature Dependence of Viscosity
2.2. Compositional Dependence of Viscosity
2.3. Effect of Thermal History on Viscosity
2.4. Effect of Phase Separation on Viscosity
2.5. Effect of Crystallization on Viscosity
3. Viscosity Measurement Techniques
3.1. Rotation viscometers
3.2. Falling Sphere Viscometers
3.3. Fiber Elongation Viscometers
3.4. Beam –Bending Viscometers
3.5. Parallel Plate Viscometry
4. Conclusions
Sinan Özgün, Abdül Kadir Eren
Anadolu Universitesi Malzeme Bilimi ve Mühendisliği Bölümü, 2011
2
1. Introduction
Viscosity plays a major role in determining the formation of all melts and the melting
conditions for a homogenous melt which then be used for the shaping processes. Also
annealing temperature and the temperature range of forming commercial products depend on
viscosity. For glasses the most favorable conditions are:
a. Very high viscosity at the melting temperature of the crystalline phase which would
form from the melt
b. Viscosity of the melt increases very rapidly with decreasing temperature.
In both of the cases, crystallization is prevented by the kinetic barrier that restricts
atomic rearrangement which results from a high viscosity.(1.a)
Before directly going into the concept of the viscosity of glass, it is necessary to visit
numerous definitions for the term viscosity, and also introduce related terminology to enhance
the understanding and comprehension of the subject. Following two sections are dedicated to
this necessary preliminary objective.
1.1.Definition of Viscosity
The viscosity (denoted by ƞ) is a general property for all types of non-crystalline
materials, including polymers, non-crystalline ceramics, glass and glass ceramics. It is the
property which makes viscous flow (plastic deformation of amorphous structures) possible for
non-crystalline materials, since dislocation motion is not possible due to the irregular atomic
structure, these materials deform in the same manner as liquids. The most widely used
definitions are as follows;
“Viscosity is a measure of non-crystalline material’s resistance to deformation.”(2a)
“Viscosity is a measure of the resistance of a liquid to shear deformation, ie. a measure
of the ratio between the applied shearing force and the rate of flow of the liquid.”(1.a)
“The ratio of the magnitude of an applied shear stress to the velocity gradient that it produces; that is, a measure of a noncrystalline material’s resistance to permanent deformation.”(2.c)
“Internal resistance to flow of a solid (powder), liquid, or gas at a specified temperature. Viscosity is a definite measurement for the consistency of a material.”(3)
1.2.Terminology
Viscosity is denoted by the symbol ƞ, and the units used to express the magnitude of
viscosity are poise (P) and pascal-seconds (Pa.s); the relation between these units is,
10P=1Pa.s. The general formula can be expressed as: If a tangential force difference, F, is
applied to two paralel planes of area, A, which are separated by a distance, d, and the relative
velocity of planes is denoted with v, the viscosity is given by the expression: (1.a)
Sinan Özgün, Abdül Kadir Eren
Anadolu Universitesi Malzeme Bilimi ve Mühendisliği Bölümü, 2011
3
ƞ = ����
Glass : A glass is a non-crystalline material (lacking long range repeatable order)
which exhibits glass transition. Glasses are typically produced from a glass forming liquid by
continuous cooling with a sufficiently enough cooling rate.
Glass Modifying Oxides : Oxides that break up the glass network. (2.b)
Intermediate Oxides : Oxides which cannot form a glass network by themselves but
can join into an existing network. (2.b)
Shear : Deformation of a solid body in which a plane in the body is displaced parallel
to itself relative to parallel planes in the body, it is the displacement of any plane relative to a
second plane.(4) Shear stress is denoted by τ.
Annealing of Glass : A process applied to final products in order to remove internal
stresses.
Viscous Flow : A type of plastic deformation observed in amorphous materials in
response to an applied shear stres. Atoms or ions slide past one another by the breaking and
re-forming of interatomic bonds.(2.a)
Viscoelasticity : A combination of viscous and elastic properties in a material, with the relative contribution of each dependent upon time, temperature, stress, and strain rate.(3)
Glass Transition Temperature (Tg) : Tg is the temperature of reversible transition
in amorphous materials (or in amorphous regions within semicrystalline materials) from a
hard and relatively brittle state into a molten or rubber-like state.(5)
In glassy materials, volume decreases continuously as temperature decreases. During
this process, a slight decrease in slope of the cooling curve (figure 1) is observed at what is
called the glass transition temperature. Above this point, the material under consideration is
said to be a supercooled liquid and far above it is a liquid; below the Tg it is considered as a
glass. (2.b)
Melting Point (Tm) : The melting point corresponds to the temperature at which the
glass is fluid enough to be considered as a liquid. (2.b)
Working Point : The working point represents the temperature at which the viscosity is
such that the glass is easily deformed. (2.b)
Softening Point : The maximum temperature at which a glass piece may be handled
without causing significant dimensional alterations. (2.b)
Annealing Point : The temperature which corresponds to a viscosity in which atomic
diffusion is sufficiently rapid that any residual stresses may be removed within about 15
minutes. (2.b)
Sinan Özgün, Abdül Kadir Eren
Anadolu Universitesi Malzeme Bilimi ve Mühendisliği Bölümü, 2011
4
Strain Point : For temperatures below the strain point, fracture will occur before the
onset of plastic deformation. (2.b)
Isokom Temperatures : Temperatures referring to a specified viscosity.(1.b)
The Fictive Temperature, (Tf): It is the temperature at which the liquid structure is
frozen into the glassy state.(6)
2. Factors Affecting Viscosity of Glass
Viscosity of glass depends on temperature, composition, thermal history, phase
separation, and crystallization.
2.1. Temperature Dependence of Viscosity
As daily observation along with laboratory experiments proves that the viscosity of
liquids is very low, on the other hand, glasses have extremely high viscosities at ambient
temperatures, which is accounted for by strong interatomic bonding. As the temperature is
raised, the magnitude of the bonding is diminished, the sliding motion or flow of the atoms or
ions is facilitated, and subsequently there is attendant decrease in viscosity. (1.b)
It is commonly assumed that shear viscosity is a thermally activated process. Since the pioneering work of Frenkel, fluid viscosity, η(T), has been expressed in terms of an activation energy Q (or ∆Hη) by the following Arhenian expression:
ƞ(T) = Aexp( QRT)
Sinan Özgün, Abdül Kadir Eren
Anadolu Universitesi Malzeme Bilimi ve Mühendisliği Bölümü, 2011
5
where T is temperature in K (Kelvin), R is the molar gas constant, and A (or η0) is a constant. For amorphous materials, two different regimes of flow have been identified with melts at high temperature having lower activation energy for flow than materials at lower temperatures.Within the low temperature or high temperature regimes, an Arrhenius dependence of viscosity is observed and an appropriate activation energy, QH or QL, respectively, can be defined. Asymptotically, both at low and high temperatures the activation energy of viscosity is independent of temperature.(7)
For glass type materials, Arrhenian behaviour is observed within the glass transformation range and at high temperatures where melts are very fluid but between these limiting regions the temperature dependence is decidedly non-Arhenian, with a continously varying value of Q over this intermediate region. A better equation that fits to viscosity data over the entire viscosity range is provided by a modification to the Arrhenian expression known as Vogel-Fulcher-Tamman equation derived as follows.(1.b):
The VFT equation adds a third variable, T0, to the above Arrhenian expression to account for the variability of the activation energy for viscous flow, replaces the Q with a less defined variable, B: η=η0e
B/(T - T0) (T and T0 are in ℃)
The VFT equation can be used for a wide range of temperatures but it should be kept in
mind that it always overestimates the viscosity in constant Q ranges such as the lower end of the transformation region. Also, the temperature terms can be replaced with volume terms, where B1 is a constant, V is the specific volume of the melt, V0 is the specific volume for the close packed melt: η=η0e
B1/(V -
V
0) (if � is independent of T)
And, a similar expression can be written by considering entropy of a melt, where B2 is another constant, Sc is the configurational entropy: η=η0e
B2/(TS
c) (1)
Also Sc (configurational entropy) can be expressed in terms of temperature and Cp (heat capacity under constant pressure) as:
Sc=∆Cp(T-T0)/T (2)
Additionally substituting equation (2) to (1), and taking activation energy into account, another expression can be derived which expresses the relationship between temperature and viscosity at temperatures above Tg, where the glass melt is a solution:(8)
η= η0exp�ɛ ���� ��� (ɛ and α are coefficients derived
from activation energy and Cp)
Sinan Özgün, Abdül Kadir Eren
Anadolu Universitesi Malzeme Bilimi ve Mühendisliği Bölümü, 2011
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The viscosity versus temperature
relation of a melt also determines the fragility of the melt. Melts that show near-Arrhenian behavior over entire viscosity range are termed as strong melts, while those which have a large degree of curvature are termed fragile melts. Strong melts have well-developed, high degree short range ordered structural units, at least partially covalent bonds, low changes in heat capacity upon passing through the glass transition region and they only gradually dissociate with increasing temperature, whereas fragile melts have ionic bonds, high configurational degeneracy, large changes in heat capacity
at Tg and they disintegrate rapidly with increasing temperature over Tg. (1.b)
2.2. Compositional Dependence of Viscosity
Theoretically, compositional dependence of viscosity can be expressed with the help of
solution thermodynamics by means of calculating the partial role of each constituent on
overall entropy change of a glass system and using the viscosity-entropy expression
introduced in the previous section(8), but the complexity of the process makes a more practical
approach desirable.
Sinan Özgün, Abdül Kadir Eren
Anadolu Universitesi Malzeme Bilimi ve Mühendisliği Bölümü, 2011
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Practically the compositional dependence of viscosity of glass forming melts is closely
related to the connectivity of the structure. In general, changes in composition which reduce
connectivity reduce the viscosity, while those which increase the connectivity increase the
viscosity.(1.b) In the following pharagraphs some examples of this occurance will be
introduced.
Adjusting the viscosity of glass melts is very important for glass production in terms of
adjusting the working point, softening point and melting temperature of the batch, by means
of lowering production costs. Addition of glass modifying oxides such as alkali oxides and
intermediate oxides like alumina changes the viscosity of glass melts by modyfying the
connectivity.
Alkali oxides such as Na2O and K2O and alkaline earth oxides such as CaO and MgO
lowers the viscosity of silica glass. The oxygen atoms from these oxides enter the silica
network at points joining the tetrahedra and break up the network producing oxygen atoms
with an unshared electron, resulting in a decrease in connectivity. (The remaining Na+, K+
ions fill the interstices of the network by ionic bonding and promote crystallization.)(9)
Replacement of a modest amount of alkali oxide by an alkaline earth oxide, as is often done in
commercial silicate glasses, results in small increase in viscosity due to changes in field
strength. The order of decreasing viscosity effect for alkali oxides is: Cs>Rb>K>Na>Li(1.b)
Intermediate oxides such as Al2O3 and Ga2O3 can enter the silica network as AlO44- and
GaO44- tetrahedra, replacing some of the Si O4
4- groups but do not alter viscosity
significantly.(9) Replacement of an alkali or alkaline earth oxide by these intermediate oxides
reduces the concentration of non-bridging oxygens and increases the connectivity of the
network and so the viscosity. (1.b)
Addition of alkali oxides to boric oxide shows two complex behavior in glass system.
First, even though the connectivity of the melt is increased through conversion of boron-
oxygen triangles to tetrahedra with no non-bridging oxygen formation, the fragility of the
melt increases with increasing alkali oxide concentration. Second, if we consider the
behaviour of the viscosity in the transformation region, we find that initial additions of alkali
oxide increase the viscosity, while further additions decrease it.Viscosity decreases in the
transformation region in the order Li>Na>K>Rb>Cs.(1.b)
2.3. Effect of Thermal History on Viscosity
For a glass sample, each different fictive temperature represents a different
structureand properties. So, if we alter the surrounding temperature of our sample from that of
the fictive temperature of the sample, the structure and properties will also change
accordingly. The time required fort his change will depend upon the viscosity of the melt,
which will vary as the fictive temperature changes. Since a higher fictive temperature
indicates a more open structure, the viscosity will be lower than the original temperature.(1.b)
Sinan Özgün, Abdül Kadir Eren
Anadolu Universitesi Malzeme Bilimi ve Mühendisliği Bölümü, 2011
8
2.4. Effect of Phase Separation on Viscosity
Phase separation can radically alter the viscosity of a melt. If stable immiscibility leads
to complete separation into two layers of liquid, each layer will be characterized by its own
viscosity. Viscosity measurements thus reflect the compositions of the two liquids, and have
little to do with the bulk composition of the melt.(1.b) If the phase separation is observable
necessary precautions can be taken, but in the case of a metastable immiscibility, in many
cases phase separation cannot be observed by naked eye. In such a case, if the phase with the
higher viscosity has a connected structure, the lesser one will have no importance and the
viscosity will be determined by the less mobile, higher viscosity phase. But, if the phase with
the higher viscosity exists as isolated regions within a matrix of less viscous phase, the
measured viscosity will be near that of more mobile, lower viscosity phase. In both cases any
thermal treatment which alters the connectivitiy of the phases can radically alter the measured
viscosity of the material. This effect can have unfortunate side effects in production.
2.5. Effect of Crystallization on Viscosity
Effects of crystallization on viscosity is directly related to the details of the
crystallization and the shape of the crystalls formed. If a melt crystallizes from the surface, it
will be covered by a shell of crystalls, in this situation the viscosity appears to increase to
Sinan Özgün, Abdül Kadir Eren
Anadolu Universitesi Malzeme Bilimi ve Müh
infinity. But, if the forming crystals are dispersed throughout the bulk, viscosity will be
similar to that of the complete melt. It will increase or decrease according to the r
composition of the melt and the crystals until the crystalls start to interact with each other.
After that point viscosity will increase and the flow will stop eventually. If the crystalls are in
spherical form increase in viscosity will be lower t
3. Viscosity Measurement Techniques
The measurement of viscosity
temperature range requires the use of
restricted to a limited range of viscosity values.
measurement of the viscosity using a rotation viscometer,
sphere, or the rate of deformation of a plate fiber or beam.
based on the rate of penetration in
tube under a torque or, the shearing of a thin disk between a cone and a flat plate.
3.1. Rotation viscometers
Rotation viscometers are commonly used at room temperature to measure the viscosity
of a wide variety of liquids in the range of 1 to 10000 Pa s.Use of these viscometers at
temperature up to 1600 C. Requires that the parts exposed to the melt be constructed of
platinium or platinium alloys.These viscometers consist of a small clyinder, or spindle,which
is rotated inside a large cylindirical crucible containing the melt.The viscosity range covered
by this method can be extended by measuring the time required for the spin
through a defined angle of deflection or by measuring the torque required to twist the spindle
through a small angle. This method requires use of a few hundred grams of glass to provide
a sufficient melt size for reliable measurements.In
determined from the torque, T,
3.2. Falling Sphere Viscometers
Viscosities can be measured directly through the determination of the resistance of a
liquid to the motion of a sphere falling through the liquid under the influence of gravity.
viscosity is given by the stokes law :
Where r is radius of the sphere
denote the density of the sphere.
3.3. Fiber Elongation Viscometers
The most widely used viscometers are based on measuremen
alongation of a fiber of known dimensions under a known load.This method can be used for
hendisliği Bölümü, 2011
9
infinity. But, if the forming crystals are dispersed throughout the bulk, viscosity will be
similar to that of the complete melt. It will increase or decrease according to the r
composition of the melt and the crystals until the crystalls start to interact with each other.
After that point viscosity will increase and the flow will stop eventually. If the crystalls are in
spherical form increase in viscosity will be lower than that of flake or needle like crystalls.
3. Viscosity Measurement Techniques
he measurement of viscosity of a glass melt for a given composition over a wide
temperature range requires the use of a number of different techniques,
ited range of viscosity values. Generally, viscometers are based on direct
measurement of the viscosity using a rotation viscometer, the rate of descent of a falling
or the rate of deformation of a plate fiber or beam. Less commonly used methods are
d on the rate of penetration into the surface of a melt, the torsional reflection of
, the shearing of a thin disk between a cone and a flat plate.
Rotation viscometers(1.b)
:
eters are commonly used at room temperature to measure the viscosity
of a wide variety of liquids in the range of 1 to 10000 Pa s.Use of these viscometers at
temperature up to 1600 C. Requires that the parts exposed to the melt be constructed of
m or platinium alloys.These viscometers consist of a small clyinder, or spindle,which
is rotated inside a large cylindirical crucible containing the melt.The viscosity range covered
by this method can be extended by measuring the time required for the spin
through a defined angle of deflection or by measuring the torque required to twist the spindle
This method requires use of a few hundred grams of glass to provide
a sufficient melt size for reliable measurements.In the most basic version,
T, on the spindle and use of this equation :
ƞ= ���� �
��� �
���� �
�ɷ�
Falling Sphere Viscometers(1.b)
:
Viscosities can be measured directly through the determination of the resistance of a
liquid to the motion of a sphere falling through the liquid under the influence of gravity.
viscosity is given by the stokes law :
Where r is radius of the sphere ,g is gravity, v is the velocity of the sphere and
denote the density of the sphere. This method yield values in the range 1 to 1000000 Pa s.
Fiber Elongation Viscometers(1.b)
:
The most widely used viscometers are based on measuremen
alongation of a fiber of known dimensions under a known load.This method can be used for
infinity. But, if the forming crystals are dispersed throughout the bulk, viscosity will be
similar to that of the complete melt. It will increase or decrease according to the relative
composition of the melt and the crystals until the crystalls start to interact with each other.
After that point viscosity will increase and the flow will stop eventually. If the crystalls are in
han that of flake or needle like crystalls.
for a given composition over a wide
different techniques, each of which is
Generally, viscometers are based on direct
the rate of descent of a falling
only used methods are
the torsional reflection of a hollow
, the shearing of a thin disk between a cone and a flat plate.
eters are commonly used at room temperature to measure the viscosity
of a wide variety of liquids in the range of 1 to 10000 Pa s.Use of these viscometers at
temperature up to 1600 C. Requires that the parts exposed to the melt be constructed of
m or platinium alloys.These viscometers consist of a small clyinder, or spindle,which
is rotated inside a large cylindirical crucible containing the melt.The viscosity range covered
by this method can be extended by measuring the time required for the spindle to rotate
through a defined angle of deflection or by measuring the torque required to twist the spindle
This method requires use of a few hundred grams of glass to provide
the most basic version, the viscosity is
Viscosities can be measured directly through the determination of the resistance of a
liquid to the motion of a sphere falling through the liquid under the influence of gravity. The
,g is gravity, v is the velocity of the sphere and ρ values are
This method yield values in the range 1 to 1000000 Pa s.
The most widely used viscometers are based on measurements of the rate of
alongation of a fiber of known dimensions under a known load.This method can be used for
Sinan Özgün, Abdül Kadir Eren
Anadolu Universitesi Malzeme Bilimi ve Mühendisliği Bölümü, 2011
10
viscosities ranging from 10 ^5 to 10 ^12. Pa s.It ıs alsa used for the determination of the little
ton softening and annealing reference points.Fiber elongation measurements are based on the
rate of elongation dL /dt where L is the fiber lentgh of a fiber of cross-sectional A,which is
suspended vertically in a furnace.The elogngation rate is determined by the viscosity of the
melt and the applied stress F/A ,where F is force apliied to ehe fiber.The viscosity is given by
this equation ;
ƞ =�
!"(#$#%)
3.4. Beam –Bending Viscometers(1.b)
:
Transformation range viscosities are often measured by the beam –bending method in
which a small beam of known cross-secional area, A, is placed in 3 point bending
configuration with a load M applied at the center of the beam.The viscosity is given by the
expression;
ƞ = ��&'.�)*+
�- + "�/�.0 �
Where L is the length of the specimen between thesupport spans, I is the moment of inertia of
the beam, V is the deflection rate of the mid-point of the beam and ρ is thednesity of a
material.The ease of sample preparation for the beam-bending method makes this technique
particularly suıtable for research studies.Any beam shape,including rods or tubing in addition
to square or rectangularbars, can be used,provided the moment of inertia can be calculated.
3.5. Parallel Plate Viscometry (10)
:
The principles of parallel-plate
viscometry are described by Dienes,
Gent, Fontana, and Varshneya, and described in
detail through ASTM C1351. The main parts of
the instrument are shown in Figure 5. A disk of
glass, roughly 6-12 mm diameter and 4-6 mm
high, is sandwiched between two parallel plates
inside a well-insulated furnace as shown. The
glass sample surfaces should be parallel with an
error of +/- 0.01 mm with about 600 grit
surface finish. Surface polishing with an
accuracy of +/- 0.001 mm as suggested by
ASTM C1351 is not required for practical
application. The upper pedestal (marked "load
rod") is loaded, and the rate of sagging is
recorded as a function of time through a
linearly variable differential transformer (LVDT) or similar instrument with a resolution of at
least +/- 0.005 mm. The thermal expansion of the alumina plates in Figure 5 should be
compensated. It is beneficial to avoid many interfaces between the glass sample and load
Sinan Özgün, Abdül Kadir Eren
Anadolu Universitesi Malzeme Bilimi ve Mühendisliği Bölümü, 2011
11
rod/pedestal (e.g. through additional support plates or platinum foil) due to irregular
readjustments during heating. The LVDT unit and the cold thermocouple junction always
must remain at room temperature, e.g. through auxiliary air-fan cooling, especially if the
furnace is heated up.
It is important to pay attention to the geometry of deformation during measurement. Figure 6, illustrates the extrema: either the glass sample shows a "perfect slip" on the substrates (i.e. the contact areas between sample and substrate increase, the sample remains a rectangular cylinder), or "no slip" where the contact areas to the substrates stay constant and the glass sample "bulges out". Varshneya shows that superior results are obtained if no-slip condition is assumed using alumina substrates.
Figure 6: Perfect slip and no-slip conditions during parallel plate viscosity measurement
Following assumptions are further made: - The viscous sample is incompressible, - The flow is Newtonian, - The sample does not completely fill the area between the substrates during testing, - The sample remains cylindrically symmetric during flow. Under these assumptions, the glass viscosity may be calculated from the sag rate through
Equation (1):
where = glass viscosity in Poise or Pa s; M = applied load; g = gravity acceleration; h = sample height; V = sample volume; dh/dt = deformation or sag rate; = roughly estimated linear expansion coefficient; DT = temperature change compared to room temperature. The term (1 + T) can be neglected for low expanding glasses.
Using the parallel plate technique, it is possible to measure viscosities in the glass softening range, log( / Pa s) = 4 to 10. At the lower end of the range, low loads, large diameter samples, and heating rates up to maximal 5oC/min may be needed. The heating rate should not be substantially lower than 1oC/min, else some glasses may crystallize during measurement which can lead to incorrect viscosity results.
Sinan Özgün, Abdül Kadir Eren
Anadolu Universitesi Malzeme Bilimi ve Mühendisliği Bölümü, 2011
12
4. Conclusions
Measuring and adjusting viscosity is a key necessity in glass production, since it
solitarily determines most of the important process parameters and abilities. Viscosity of a
glass melt/glass forming liquid changes in the range of 14 to 15 orders of magnitude during
the production process and the viscosity curve has a complex characteristic. As a result
different measurement techniques should be applied during processes to ensure that the
viscosity is in favorable values. And also, to adjust the viscosity of a melt, one should pay
attention to the dependencies of viscosity which we have introduced in the second part of this
report.
Sinan Özgün, Abdül Kadir Eren
Anadolu Universitesi Malzeme Bilimi ve Mühendisliği Bölümü, 2011
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REFERENCES, CITATIONS, SOURCES
(1) James E. Shelby, Introduction to Glass Science and Technology, a) p.111 b) p.120-124 c) p.117-119, Royal Society of Chemistry, 2005-UK
(2) William D. Callister, David G. Rethwisch, Materials Science and Engineering 8th Ed. SI Version, a) p.488 b) p.514 c) p.614, Wiley (Asia), 2011
(3) ASTM, Dictionary of Engineering Science & Technology 10th Ed., p.669, 2005-USA
(4) F.F.Wu, Z.F.Zhang, Shear Deformation Capability of Different Metallic Glasses, Shanyang National Laboratory for Materials Science, Institute of Metal Research, 2008-China
(5) ISO 11357-2: Plastics-DSC-Part 2, Determination of Glass Transition Temperature, 1999
(6)http://www.britannica.com/EBchecked/topic/234890/industrial-glass/76304/Glass-formation
(7) Michael I. Ojovan, Viscosity and Glass Transition in Amorphous Oxides, p.6, Hindawi Publishing Corp. Advances in Condensed Matter Physics Vol.‘08, Article ID 817829, 2008-UK
(8) I. Avramov, Viscosity of Glassforming Melts, Institute of Physical Chemistry,
Bulgarian Academy of Sciences, Elsevier - Journal of Non-Crystalline Solids 238 (1998) 6-10, 1998
(9) William F. Smith, Javad Hashemi, Foundations of Materials Science and
Engineering 4th Ed., p.622-624, Mc Graw Hill, 2006-US
(10) A. K. Varshneya, N. H. Burlingame, W. H. Schultze: "Parallel Plate Viscometry to Study Deformation-Induced Viscosity Changes in Glass", Glastechn. Ber. 63K (1990), 447-459
Figure 1 : William D. Callister, David G. Rethwisch, Materials Science and Engineering 8th Ed. SI Version, p.514, Wiley (Asia), 2011
Figure 2 : Angell, C.A. (1985). Strong and fragile liquids. In K.L. Ngai and G.B. Wright, Eds., Relaxations in complex systems, U.S. Department of Commerce National Technical Information Service, Springfield, Virginia.
Figure 3 : A. Fluegel, "Glass Viscosity Calculation”
Figure 4 : James E. Shelby, Introduction to Glass Science and Technology, p.132, Royal Society of Chemistry, 2005-UK
Figure 5 and 6 : G. J. Dienes, H. F. Klemm, "Theory and Application of the Parallel Plate Plastometer", Journal of Applied Physics 17 (1946), 458-471
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