Volumetric Dilatometry

The ability to measure and characterize the volumetric behavior of new and existing materials

as a function of temperature and time is of great importance. This is due to the fact that there

are a variety of physical phenomena that result in dimensional change (i.e. crystallization,

melting, glass formation, secondary transitions and physical aging). No where is this statement

more valid than in the field of polymer science.[1]

Thermal Expansion

The coefficient of linear expansion, also known as expansivity, is the ratio of the change in lengt

-h per ◦C to the length at 0◦C. The coefficient of volume expansion for solids is approximately

three times the corresponding linear coefficient. The coefficient of volume expansion of a liquid

is the ratio of the change in volume per degree, to the volume at 0◦C. The value of thecoefficient

varies with temperature.The coefficient of volume expansion for a gas under constant pressure is

nearly the same for all gases and temperatures, and is equal to 0.00367.[2]

1. Linear expansion in solids. A bar of length L0 at temperature T0 expands to a length L when

heated to a temperature T. The change in length ΔL (i.e. L – L0) is related to the change in

temperature ΔT (i.e.T – T0) and the original length L0 by a constant that depends on the material.

This constant is the coefficient of linear expansion (also called the coefficient of thermal

expansion), α.

a. The change in length is directly proportional to the change in temperature: ΔL ∝ ΔT.

b. The change in length is directly proportional to the original length: ΔL ∝ L0.

c. The change in length is directly proportional to the coefficient of linear expansion: ΔL α.∝

d. Together, these proportionalities form the equation ΔL = αL0ΔT.

2. Volume expansion in solids and liquids. A volume V0 of solid or liquid at temperature T0

expands to a volume V when heated to a temperature T. The change in volume ΔV (i.e. V – V0) is

related to the change in temperature ΔT (i.e. T – T0) and the original volume V0 by a constant

that depends on the material. This constant is the coefficient of volume expansion, β.

a. The change in volume is directly proportional to the change in temperature: ΔV ∝ ΔT.

b. The change in volume is directly proportional to the original volume: ΔV ∝ V0.

c. The change in volume is directly proportional to the coefficient of volume expansion: ΔV β.∝

1

d. Together, these proportionalities form the equation ΔV = βV0ΔT.

e. For solids whose coefficient of linear expansion is known, the equation ΔV = 3αV0ΔT may be

used.

3. Volume expansion in gases. The volume V of a gas is related to its temperature and the

pressure at which it is contained. Raising the temperature of the gas from T0 to T increases the

volume from V0 to V if the pressure P is held constant (Charles’ Law). Reducing the pressure

from P0 to P of a gas increases the volume of a gas from V0 to V if the temperature is held

constant (Boyle’s Law). Taken together, these proportionalities form “Charboyle’s Law” (a. k. a.

The Ideal Gas Law): P0V0/T0 = PV/T.[10]

Methods for measurement of thermal expansion

Solids

-(Mechanical) Dilatometry

 - Thermomechanical

Analyser

-   Interferometry

-   X-Ray diffraction

-   Line-width camera

-   Strain gauge technique

Liquids

-   Magnetic suspension

-   Rise of meniscus in capillary

Fig 1

Dilatometers (an early version is shown above)

are the most common measurement devices

for thermal expansion measurement.

Expansion measurement methods for solids

The most commonly used technique on a suitable test-piece is one based on mechanical

dilatometry – the change in length of a known length is recorded as a function of temperature by

a contacting push-rod. The movement of this push-rod is determined by one of several

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techniques, including a simple dial gauge, a capacitance transducer, an LVDT or interferometer.

This technique works well from liquid helium temperature to over 2000 °C, provided that the

materials of the supporting system and the push-rod are stable. There are commercial

instruments that make direct measurements on individual test-pieces, or compare the movement

in an unknown with that in a reference material.

The accuracy of such instruments is

typically no better than ± 0.1 x 10-6 °C in

expansion coefficient or expansivity, for data

obtained over a 100 °C temperature interval. In

the polymer field, e Thermomechanical

Analyser is a simple form of dilatometer, but is

not capable of the same level of accuracy as

purpose-built dilatometers on materials of low

thermal expansion.

Fig 2

Commercial dilatometers are available

from various suppliers, like that shown

above .

The use of interferometry to measure length

change directly from the test-piece is less

common but potentially more accurate since it

is less reliant on mechanical contact

movements. The test-piece is placed on a

mirror, has a small mirror placed on top, and the

relative movement of the mirrors as the test-

piece is heated and cooled is determined by

multiple beam interferometry. Preferably, the

test-piece itself is made with mirror surfaces.

The accuracy of this type of arrangement is

perhaps an order of magnitude improvement

over mechical dilatometry,but is limited by

achievable temperature homogeneity. The

technique is also more expensive, more limited

in temperature range, and more restricted in

terms of test-piece type and geometry. Fig 3

3

Laser interferometer for expansion

measurement on pulse-heated samples at OGI,

Austria.

Direct optical expansion measurement is in use for high-expansion plastics materials and has

been used extensively in the past. In fact, certified reference materials have been calibrated using

this method. Fiducial marks are placed on a long test-piece and viewed laterally using a long

focal length microscope attached to an accurately calibrated length scale parallel to the test-piece.

As the test-piece is heated or cooled, the position of the fiducial marks are recorded manually.

Modern versions of this method involving analysis of video-images have also been employed for

complex structures.

There are a number of other techniques that have their place, but are less commonly used

for data generation, and they include:

X-ray diffraction – measures lattice cell expansion, but may not produce the same

results as whole body methods because the effects of local residual stresses may not be

taken into account

electrical heating with servo displacement – allows expansion to be measured when

subjected to a given force

line-width camera – useful for measuring size changes of very hot objects which can be

imaged, but where other direct dilatometric methods are not appropriate, but the accuracy

may be limited by resolution limitations

strain gauge – this technique has value for determining local behaviour of complex

bodies, such as composite structures, but the gauges have to be carefully calibrated for

their response with respect to changing temperature.

Expansion measurement methods for fluids

Techniques for the direct measurement of fluid volume are less well developed than for linear dim

-ensions. The volume of a known mass of liquid can be tracked as a function of temperature as its

meniscus rises up a capillary exiting from a filled rigid vessel.

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More sophisticated magnetic suspension devices that operate over wide ranges of temperature

and pressure are available for accurate determinations.[3]

Dilatometers

dilatometers, measure the dimensional changes as a function of temperature. The instruments of

this family may differ in the way they measure dimensional changes of the sample. One very

relevant difference is if there is contact with the sample or not.

All the mechanical or electronic dilatometers use a push rod in touch with the sample to transfer

the dimensional change of the sample from the internal of the fumace to the transducer (dial

gauge, differential transformer, capacitive) (Fig. 4) [4]

Fig 4 (Lop) Scheme of a traditional Dilatometer With a push-rod and A displacement

transducer

The sample rests between the tips of a fixed quartz rod and a similar frictionless sensing rod in th

-e centre of a high–frequency induction furnace. Length changes are transmitted through the frict

-ionless rod to an electronic transducer which in turn drives the recording system.

The thermocouple is spot welded to the sample, and referenced at 40◦C by means of a constant

temperature bath. [2]

The use of a push rod in mechanical contact with the sample requires to correct the measured

data to take in account the expansion of the push rod, but now a day, with computerised systems,

this operation is carried out automatically. As long as the System is kept calibrated, the

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measurements are very reliable even if sometimes the correction amounts for twice as much as

the measured value.

The push rod dilatometer can follow the sample only as long as it is rigid enough not to be

deformed by the pressure of the rod. When a sample is too thin to be pushed or loo fragile to be

pulled, or it is almost incoherent or softened, it cannot! be measured using this kind of

dilatometer. it is necessary to use a non contact measuring system,

Optical dilatometers use a beam of light to measure the dimensional changes and so the sample

is not in touch with the measuring system. There are several methods for measuring the

dimensional changes of the sample with a beam of light and they can be summarised in two

categories: reflected beam and direct beam.

The first optical dilatometer was invented by Abbe and Fizeau in the second half of the 19th

century. This design uses a reflected beam of monochromatic light and the measurement of the

displacement is carried out by courting the interference fringes between the forward going beam

and the reflected team. After the Abbe invention, many improvements were achieved on the

original design and now a day there are many models on the market, which use new optics and

design. But in order to measure thermal expansion up to high temperatures the sample has to be

set on a sample holder inside the fumace and also the sample holder has its own thermal

expansion. In order to achieve a good accuracy it is necessary to measure the expansion of the

sample holder and to subtract it from the actual expansion of the specimen.

The best way to do is to split the laser beam into two beams of light, which are reflected by the

top of the sample and by the sample holder or by both ends of the specimen (Fig. 5).

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Fig 5Scheme of a double Beam interferometric dilatometer

Measuring the sample from both ends the measure is absolute and there is no need for any

correction. This is the most accurate way of measuring thermal expansion and it may reach a

nano-metric resolution. This is the type of instrument used by the suppliers of standard materials

for the thermal expansion. For example, the National Institute for Standards and Technology

(NIST) uses a Fizeau double beam interferometer to certify the thermal expansion of their

Standard Reference Materials for thermal expansion.

This method proved to be very accurate, with a resolution of a fraction of the wave length of the

incident light, but it is limited by the reflectance of the surface of the specimen, if the specimen

is not reflective, or it becomes not reflective during the test, it is then necessary to use a

mirror ,which is put in touch with the specimen using a refractory push rod. Managing in this

way, this method looses the advantage of being non contact and becomes substantially similar to

the electronic dilatometer.

The direct beam measuring System overcomes this problem becausethespecimenis measured by

the image that it projects on a CCD when it is lighted by a direct beam of light. Using a beam of

light with short wave length and a very high resolution CCD it is possible to achieve a good

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resolution. For example, using a blue light with a wave length below 0,5 µm, it is possible to

have an image with an actual resolution of 0,5 µm per pixel of the camera (not an interpolated

resolution but an actual resolution). With a sample of 50 mm of length the resolution becomes

one part over 100 000. Using two beams of light, which illuminate both the ends of the specimen

it is then possible to achieve an absolute measurement of the dimensional changes of the sample

during the heat treatment. (Fig. 6).

Fig 6Scheme of a double beam optical dilatometer with two direct beams of light

The specimen is completely free to expand or contract, there is no measuring System in touch

with it, but only a sample holder, to keep it in place inside the fumace. The displacement of the

sample holder is not relevant for the result of the measurement because the optical system is

watching both the ends of the sample.[4]

New Fields of Research

Now the ceramic scientist has the possibility to follow the behaviour of the sample during the

heat treatment without interfering with the process. The applications brake the limits of

traditional dilatometry in many fields of research:

Incoherent materials, like the expansion and contraction of an Incoherent granular frit, as

applied on a raw tile.

Softened materials, like the behaviour of a glass above the transition temperature, where

the surface tension starts to pull the edges and to make the sample shorter.

Sintering kinetics; studying the relationship between time and temperature during a

sintering process

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Extremely thin samples, like thermal expansion and sintering behaviour of the extremely

thin. layer of glaze as applied on a ceramic tile.[4]

Exsamples of Push_Rod Dilatometers:

Differential Dilatometer

The instrument, DIL 802, from Bähr, is a differential dilatometer

designed for highest accuracy and for use under vacuum or inert gas atmosphere

within a temperature range of 293 K to 1773 K. With this instrument the

difference in length between the specimen to be investigated and a reference

sample is measured, which results in a resolution of ± 0.01 µm. The sample

holder ( pushrod ) is made of sapphire. Specimens with a diameter of 5 mm and

length of 10 mm are usually investigated. The dilatometer performs length-

change measurements at constant heating and cooling rates ( max. 20 Kmin-1)

and temperature measurement at an accuracy of ±1 K. The linear thermal

expansion coefficient can be obtained with an accuracy of ±0.01·10-6 K-1. On the

basis of the measured length changes, which are directly correlated to volume

changes, kinetic properties of solid state phase transformations can be

researched using the dilatometer.

Fig 7

The differential dilatometer

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Quenching- and Deformation Dilatometer

The instrument, DIL 805A/D, from Bähr, is a dilatometer designed for

measuring length changes at high heating rates ( max. 4000Kmin-1 ) and cooling

rates ( max. 2500 Kmin-1 ) and under mechanical load (deformation). The

sample length is directly measured with a resolution of ± 0.05 µm. The

electrically conductive solid specimen is heated by an induction coil and can be

actively cooled by controlled inert gas flow. High heating and cooling rates can

be achieved using hollow specimens. A hydraulic system provides a constant

applied load (compression and tensile mode) of maximal 5 kN with a resolution

of 0.5N. The influence of high heating and cooling rates and of applied load on

the kinetics of solid state phase transformations can be researched using this

instrument. [5]

Fig 8 Detailed view of the inductive heating section of the quenching- and

deformation dilatometer [induction coil with an inner coil for controlled inert

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gas cooling; push rods( fused silica ); specimen, 5mm in diameter and 10 mm in

length, with a spot welded thermocouple in the centre, is surrounded by the

induction coil]

Specimen Design

Specimens for use in high–speed dilatometry are usually in the form of hollow

rods, with internal and external diameters of 1.5 and 3.0 mm respectively; the

length is limited by the extent of the furnace to a maximum of about 3 cm.

These dimensions are somewhat arbitrary, but experience suggests that they

satisfy the following requirements:

1. The specimen should be sufficiently thick to prevent free surface effects from

altering transformation kinetics. The tests should reflect what happens in

equivalent bulk samples. Nickel plating the specimens (to a thickness of about

0.08 mm) helps to reduce surface nucleation. Contrary to popular belief, this is

not an effective way of preventing decarburisation in steels. To reduce

decarburisation, the specimen should be copper plated; carbon is only sparingly

soluble in copper. The plating material should be chosen so as not to interact

with the sample, for example by penetration into the grain boundaries of the

substrate.

2. The specimen dimensions must be small enough to allow rapid changes in

temperature. The specimen should obviously be representative of bulk material.

Its ends should be ground flat and parallel to give a true cylindrical shape.

Otherwise, slip at the specimen–quartz interface can lead to erroneous

interpretation especially under the influence of the high–pressure quench–gas

jets.

It is normal to isolate the specimen from the RF coil with a length of quartz

tubing, not only to avoid contaminating the coil, but also to guard against the

potentially disastrous consequences of accidental specimen melting. High–

speed dilatometers generally do not have long term electronic or mechanical

stability.

Equipment like this cannot be used for tests lasting more than a few hours.

Prolonged holding at high temperatures can also lead to slag–forming reactions

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between the specimen and quartz retaining–rods. A certain amount of pressure

is always necessary to hold the specimen between the quartz retaining rods and

to remove backlash, so care should be taken to ensure that any resulting creep

effects are negligible.[2]

Calibration

The temperature calibration is similar to that of differential scanning calorimeter

and is not discussed further. However, for the calculation of thermal expansion

coefficients, and for the purposes of absolute dilatometry, it may be necessary to

calibrate the magnification of the displacement transducer.

There are two ways of doing this:

1. A pure platinum specimen with known expansion characteristics is heated at

a sufficiently slow rate over the temperature range of interest. The

magnification M is then given by:

M = (6)

where Δl is the deflection of the length recording pen, ΔT is the difference

between the initial and final temperatures T1 and T2 respectively of the test, lPt

is the length of the Pt specimen at T1, ePt the linear expansively of Pt

(obtainable from standard handbooks). This method can be accurate, but does

not take account of the expansion of the part of the quartz rods within the

furnace assembly.

2. A micrometer attachment on the dilatometer allows the transducer to be

stimulated independently of specimen movement. The magnification is then

simply Δl/micrometer movement. Having calculated the magnify.[2]

Δl = M( ) (7)

Application of Dilatometric

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Determination of specific volume as a function of temperature and/or time

(Vsp(T,t)).

Determination of temperature transitions (melt transitions (Tm), glass

transitions (Tg) and secondary transitions (Tك))

Determination of primary and secondary crystallization kinetic

parameters.

Determination of physical aging rates (كv).[1]

Exsamples of Researches Using Dilatometric

Experimental aspects of temperature-modulated dilatometry of polymers:

Polymers are materials marked by specific physical properties, different from

those such as metals, alloys or ceramics. Temperature-modulated temperature

profile in the investigation of polymers by dilatometry may have many

outstanding features, similar to those of temperature modulated DSC. However

the experimental conditions are more stringent than those of conventional

dilatometry. An overview of dilatometer types is presented. Taking into account

specific properties of the sample such as softness and heat transfer, an optimal

choice of dilatometer was made and experimental conditions were established.

[6]

Application of dilatometric analysis to the study of solid–solid phase

transformations in steels:

This article outlines the use of dilatometry in solid–solid phase transformation

research in steel. It describes how dilatometric data are interpreted, with an

emphasis on continuous heating and cooling transformation diagrams. These

diagrams show the microstructural constituents that result from given heating

and cooling conditions, and are an invaluable tool for the metallurgist in

characterizing steels with respect to their response to heat treatments. Several

practical examples and applications of dilatometry in steel research are briefly

described in this work.[7]

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Many existing concrete dams are at present deteriorated by the

chemical-physical process called alkali-silica reaction and/or by past extreme

loading. Diagnostic analyses intended to quantify possible structural damages in

large dams can be carried out in overall or in local terms. This paper describes a

novel procedure for local diagnostic analysis. It is based on a combination of

experiments consisting of hole digging, hole pressurization and dilatometric

measurements with computer simulation and inverse analysis centered on least-

square first-order algorithm and artificial neural networks. The proposed

procedure provides estimates of parameters which characterize local stress state

and possibly deteriorated mechanical properties, including tensile strength and

fracture energy.[8]

A Dilatometric Study of the Order-Disorder Transformation in Cu-Au

Alloys:

The order-disorder transformation in single crystals of Cu-Au alloys, containing

22, 25, and 30 atomic percent Au, has been studied by dilatometric means. The

plots of true coefficient of thermal expansion versus temperature for previously

well-ordered alloys display a slow rise from -190°C to about +50°C, followed

by a flat plateau to about 250°C. From the flat plateau they rise rapidly to a peak

at the critical ordering temperature Tc, followed by a fall to a second flat plateau

which extends to at least 450°C above Tc. The lower portion, that portion below

the flat plateau, can be well represented by a Grueneisen equation if one

assumes additivity for the constants taken from the equation for the pure metals

Cu and Au. The presence of the flat plateau above Tc is in disagreement with

Bethe-Peierls' theory of the vanishing of short range order. Plots of true

coefficient of expansion versus temperature, for specimens previously quenched

from above Tc, display valleys similar to those in the comparable specific heat

curves of Sykes and Jones.[9]

References

14

[1] www.Stellarnet low cost spectrum.com

[2] H. K. D. H. Bhadeshia,Materials Science & Metallurgy, University of

Cambridge

[3]www.Wikipedia.org

[4]www.Expertsystemsolution.com

[5] www.Max Planck Institute for Metals Research.com

Thermochimica Acta[6]

Volume 442, Issues 1-2, 15 March 2006, Pages 48-5

[7] Materials Characterization

Volume 48, Issue 1, February 2002, Pages 101-111

[8]www.sciencedirect.com

[9]www.prola.com

[10]www.mac.com

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