a report on viscosity of glass melts and glass forming liquids - s.Özgün, a.k.eren

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



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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)



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)



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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)



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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)



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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.



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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)



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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


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


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


similar to that of the complete melt. It will increase or decrease according to the r



spherical form increase in viscosity will be lower than that of flake or needle like crystalls.


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



m or platinium alloys.These viscometers consist of a small clyinder, or spindle,which


by this method can be extended by measuring the time required for the spin


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)

:


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



similar to that of the complete melt. It will increase or decrease according to the relative



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



m or platinium alloys.These viscometers consist of a small clyinder, or spindle,which


by this method can be extended by measuring the time required for the spindle to rotate


This method requires use of a few hundred grams of glass to provide

the most basic version, the viscosity is


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




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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



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.



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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.



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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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