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448 Part C Materials Properties Measurement

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7.325 EN 10225:2001: Annex E, Weldability Testing for Steels

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Part C 7

452 Part C Materials Properties Measurement

7.326 BS 7448-1997: Fracture Mechanics Toughness Tests,

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Part C 7

453

Thermal Prop

8. Thermal Properties

If materials – solids, liquids or gases – are heated

or cooled, many of their properties change. This

is due to the fact that thermal energy supplied to

or removed from a specimen will change either

the kinetic or the potential energy of the con-

stituent atoms or molecules. In the ﬁrst case, the

temperature of the specimen is changed, since

temperature is a measure of the average kinetic

energy of the elementary particles of a sample.

In the second case, e.g. the binding energy of

these particles is altered, which may cause a phase

transition.

Thermal properties are associated with

a material-dependent response when heat is

supplied to a solid body, a liquid, or a gas. This re-

sponse might be a temperature increase, a phase

transition, a change of length or volume, an initi-

ation of a chemical reaction or the change of some

other physical or chemical quantity.

Basically, almost all of the other materials

properties treated in Part C, namely mechani-

cal, electrical, magnetic, or optical properties, are

temperature-dependent (except a material that is

especially designed to be resistant to temperature

variations). For example, temperature inﬂuences

mechanical hardness, electrical resistance, mag-

netism, or optical emissivity. Temperature is also

of importance to the characterization of mater-

ial performance (Part D) as it inﬂuences materials

integrity when subject to corrosion, friction and

wear, biogenic impact or material–environment

interactions. Temperature effects related to these

areas are dealt with in the other chapters of this

book dedicated to those topics. Only if those prop-

erties are needed to explain measuring methods

within this chapter are they are outlined in the

following sections.

In this chapter, a number of materials prop-

erties are selected and called thermal properties,

where the effect of thermal energy treatment plays

the major role compared to electrical, magnetic,

chemical or other effects. The presentation

of measurement methods for thermal properties is

organized into ﬁve parts, referring to:

1. Thermal transport properties, such as thermal

conductivity, thermal diffusivity or speciﬁc heat

capacity, characterizing the ability of materials

to conduct, transfer, store and release heat.

2. Phase transitions and chemical reactions of

materials. Various calorimetric methods are

presented, which are used to investigate e.g.

phase transitions, adsorption, and mixing

processes. Typical examples are ﬁrst-order

transitions such as boiling and melting, but

also combustion and solution processes.

3. Physical properties, which are affected when

heat is supplied to a body. The determina-

tion of the temperature dependence of these

quantities requires knowledge of thermal mea-

surement methods. Among the many different

physical quantities the most important for

applications in materials science and engi-

neering are length and its relation to thermal

expansion.

4. Thermogravimetry, which is important in

chemical analysis, see Chap. 4.

5. Temperature measurement methods, since

these techniques are essential for all the

other measurements described above. Tem-

perature scales and the principles, types

and applications of temperature sensors are

compiled.

8.1 Thermal Conductivity

and Speciﬁc Heat Capacity ..................... 454

8.1.1 Steady-State Methods .................. 456

8.1.2 Transient Methods........................ 458

8.1.3 Calorimetric Methods.................... 461

8.2 Enthalpy of Phase Transition, Adsorption

and Mixing .......................................... 462

8.2.1 Adiabatic Calorimetry ................... 464

8.2.2 Differential Scanning Calorimetry ... 465

Part C 8

454 Part C Materials Properties Measurement

8.2.3 Drop Calorimetry .......................... 466

8.2.4 Solution Calorimetry ..................... 467

8.2.5 Combustion Calorimetry ................ 468

8.3 Thermal Expansion

and Thermomechanical Analysis ............ 469

8.3.1 Optical Methods ........................... 469

8.3.2 Push Rod Dilatometry ................... 470

8.3.3 Thermomechanical Analysis........... 470

8.4 Thermogravimetry ................................ 471

8.5 Temperature Sensors ............................ 471

8.5.1 Temperature

and Temperature Scale ................. 471

8.5.2 Use of Thermometers .................... 474

8.5.3 Resistance Thermometers .............. 475

8.5.4 Liquid-in-Glass Thermometers ...... 477

8.5.5 Thermocouples ............................ 478

8.5.6 Radiation Thermometers ............... 479

8.5.7 Cryogenic Temperature Sensors ...... 480

References .................................................. 482

8.1 Thermal Conductivity and Speciﬁc Heat Capacity

There are two main material properties (thermophysi-

cal properties) associated with heat transfer in materials.

These are the ability of a material to store heat and

the ability to transfer heat by conduction. If a speciﬁc

amount of heat dQ is supplied to a thermally isolated

specimen of mass m the relationship between heat and

temperature increase dT is given by

dQ = mc

dT . (8.1)

Consequently the ability of a material to store heat is

characterized by the speciﬁc heat capacity at constant

pressure c

. If two equal volumes of different mater-

ials are compared to each other, the ability to store

heat is described by the product of density and speciﬁc

heat capacity c

. This product is used if simultaneous

heat conduction and storage processes are investigated

by means of the transient heat conduction equation. In

many cases the density of a material or the mass of

a specimen is well known or can be easily determined

with sufﬁcient accuracy. Therefore, the problem is re-

duced to the determination of the speciﬁc heat capacity.

For gases and some liquids a distinction between the

speciﬁc heat capacity at constant pressure c

and at

constant volume c

is made. This is due to the work

required for the thermal expansion of the gas or liquid.

For solids this contribution is very small in comparison

to the measurement uncertainty and can be neglected.

The thermal conductivity λ is the material prop-

erty associated with heat conduction and is deﬁned by

Fourier’s law

q =−λ

∂T

∂x

=−λ

ΔT

. (8.2)

Here, q is the heat ﬂux, the heat conducted during

a unit time through a unit area, driven by a temperature

gradient ∂T/∂x. In practice, for thermal conductivity

measurements the temperature difference ΔT between

two opposite surfaces of a sample with a separation of d

is determined. The quotient of distance and thermal con-

ductivity is the thermal resistance R

. In contrast to the

storage of heat, conduction is considered as a steady-

state process, i. e. the temperature ﬁeld and the heat ﬂux

within heat-conducting materials are not a function of

time.

But, in most cases both heat conduction and heat

storage are simultaneously occurring processes. This

is taken into account by the transient heat conduction

equation. The temperature ﬁeld T(x, t) in one dimen-

sion is dependent on the location x and time t

∂T

∂t

∂

∂x

. (8.3)

The thermal diffusivity a is given as the ratio of the ther-

mal conductivity and the product of density and speciﬁc

heat capacity

a =

c

. (8.4)

From its physical meaning thermal diffusivity is asso-

ciated with the speed of heat propagation. In analogy

to Einstein’s relation, which connects random walks

and diffusion, the mean square displacement





a thermal pulse is proportional to the observation time t

(one-dimensional diffusion)

a =





. (8.5)

A further thermal property is the thermal effusivity e.

The thermal effusivity is a measure of a material’s abil-

Part C 8.1

Thermal Properties 8.1 Thermal Conductivity and Speciﬁc Heat Capacity 455

ity to exchange heat with the environment (thermal

impedance) and is deﬁned according to

e =



λc

. (8.6)

Knowing the thermal diffusivity and thermal effusivity,

other complementary materials properties, e.g. λ and

c

, can be calculated.

Based on the fundamental laws of heat conduc-

tion and storage three different attempts to measure

these thermophysical properties can be distinguished.

The ﬁrst one is the steady-state approach using (8.2)

in order to determine the thermal conductivity. Steady-

state conditions mean that the temperature at each point

of the sample is constant, i. e. not a function of time.

The determination of the thermal conductivity is based

on the measurement of a heat ﬂux and a temperature

gradient, i. e. mostly a temperature difference between

opposite surfaces of a sample. If the speciﬁc heat cap-

acity is the property of interest, a calorimetric method

Table 8.1 Comparison of measurement methods for the determination of thermal conductivity and thermal diffusivity

Method Temperature Uncertainty Materials Merit Demerit

range

Guarded hot 80–800 K 2% Insulation materials, High accuracy Long measurement time,

plate plastics, glasses large specimen size,

low conductivity materials

Cylinder 4–1000 K 2% Metals Temperature range, Long measurement time

simultaneous determination of

electrical conductivity and

Seebeck-coefﬁcient possible

Heat ﬂow meter −100–200

◦

C 3–10% Insulation materials, Simple construction Measurement uncertainty,

plastics, glasses, and operation relative measurement

ceramics

Comparative 20–1300

◦

C 10–20% Metals, ceramics, Simple construction Measurement uncertainty,

plastics, plastics and operation relative measurement

Direct heating 400–3000 K 2–10% Metals Simple and fast measurements, Only electrically

(Kohlrausch) simultaneous determination conducting materials

of electrical conductivity

Pipe method 20–2500

◦

C 3–20% Solids Temperature range Specimen preparation,

long measurement time

Hot wire, 20–2000

◦

C 1–10% Liquids, gases, low Temperature range, Limitedtolow

hot strip conductivity solids fast, accuracy conductivity materials

Laser ﬂash −100–3000

◦

C 3–5% Solids, liquids Temperature range, most Expensive, not for

solids, liquids and powders, insulation materials

small specimen, fast, accuracy

at high temperatures

Photothermal 30–1500 K Not sufﬁ- Solids, liquids, Usable for thin ﬁlms, Nonstandard, knowledge

photoacoustic

ciently gases, thin ﬁlms liquids and gases about accuracy

known

based on (8.1) is used. In this case, heat is supplied

to a sample that is isolated from the surroundings,

and the change of the (mean) sample temperature is

measured. The third approach is the simultaneous de-

termination of both properties by a transient technique.

For that purpose numerous solutions of the transient

heat conduction equation based on one- (8.3), two-, or

three-dimensional geometries have been derived.

The main experimental problem for all methods for

the determination of thermal properties is that ideal ther-

mal conductors or insulators do not exist. In comparison

to electrical transport the ratio of thermal conductivities

of the best conductors and the best insulators is many or-

ders of magnitudes smaller. Therefore, instruments for

the determination of thermal properties are often opti-

mized or restricted for a speciﬁc class of materials or

temperature range [8.1]. Table 8.1 gives an overview of

the most important methods used for the measurement

of thermal conductivity and thermal diffusivity.

Part C 8.1

456 Part C Materials Properties Measurement

8.1.1 Steady-State Methods

The principle of (one-dimensional) steady-state methods

for the determination of the thermal conductivity is de-

rived from (8.2) and based on the measurement of a heat

ﬂux and a temperature difference according to

λ =

−T

A (T

−T

)

. (8.7)

In many cases the heat ﬂux q is determined by the meas-

urement of a power P released in an electrical heater

divided by the area A of the sample. The temperature

difference T

−T

is determined between two opposite

surfaces of the specimen having a separation of d.

The typical sample geometry and the conﬁgura-

tion of a measurement system for thermal conductivity

measurements depend most strongly on the magnitude

of the thermal conductivity. When the thermal conduc-

tivity of a material is low, the samples are usually ﬂat

disks or plates. In the case of a high thermal conduc-

tivity the sample geometry is formed by a cylinder or

rod. According to the relationship between the sample

geometry (assumed to be cylindrical) and the direction

of the heat ﬂow, axial and radial heat ﬂow methods of

measuring the thermal conductivity are distinguished.

Guarded Hot Plate and Cylinder Method

The guarded hot plate method can be used for the de-

termination of the thermal conductivity of nonmetals

such as glasses, ceramics, polymers and thermal insu-

lation materials but also for liquids and gases in the

temperature range between about 80 K and 800 K. The

geometry of the sample or sample chamber is a plate

or a cylinder with axial heat ﬂow. Depending on the

thermal conductivity and homogeneity of the material

under investigation, the sample thickness varies be-

tween a few millimeters and a few decimeters. There are

two different types of guarded hot plate instruments: the

Guarded heater

hot plate

Specimen

Cold-plate

Insulation

Auxiliary heater

Fig. 8.1a,b Principle of the guarded hot plate method. (a) two-

specimen apparatus.

(b) single-specimen apparatus

two-specimen and the single-specimen apparatus shown

in Fig. 8.1.

Guarded hot plate instruments consist of one or two

cold plates, a hot plate and a system of guard heaters and

thermal insulation. The cold plates are liquid-cooled

heat sinks, the hot plate is electrically heated. To make

sure that the heat released in the hot plate is passed only

through the sample, the hot plate is surrounded by guard

heaters and thermal insulation. This minimizes the heat

losses from the hot plate and ensures the high accu-

racy of this method. With guarded hot plate instruments

relative expanded uncertainties of thermal conductivity

measurements of about 2% can be achieved. There are

two main sources of uncertainty in thermal conductivity

measurements: the heat ﬂux and the temperature dif-

ference determination. The major contributions to heat

ﬂux errors are heat losses from the hot plate and the

heat exchange between the sample and the surround-

ing medium. With increasing thermal resistance of the

sample (insulation materials) these sources of uncer-

tainty become dominant.

The advantage of the two-specimen apparatus is

that heat losses from the hot plate can be controlled

more effectively because of the symmetric specimen ar-

rangement. In contrast to the single-specimen method,

only solid materials can be investigated. This is because

of the inﬂuence of convection on thermal conductivity

measurements. In order to avoid convection, the sample

must be heated from the top.

The cylinder method with axial heat ﬂow can be

used for thermal conductivity measurements of met-

als with thermal conductivities up to 500 W m

−1

in a temperature range between about 4 K and 1000 K.

Comparing the principle of operation and the mathe-

matical model, the cylinder method and the guarded

hot plate method fully agree. The most important dif-

ference is the sample geometry, which is a ﬂat plate or

disk for the guarded hot plate method and a long cylin-

der or rod for the cylinder method. This is due to the

fact that the main difﬁculty for measurements of ma-

terials with high thermal conductivity (e.g. metals) is

the determination of the temperature difference. In this

case the contact resistances between the sample and the

heater and between the sample and the cold plate must

be considered. The minimization and determination of

the resulting temperature drop across these thermal con-

tact resistances is the most important criterion for the

optimization of this type of instrument.

Therefore, guarded hot plate and cylinder method

are realizations of the same measurement principle op-

timized for different ranges of thermal conductivity.

Part C 8.1

Thermal Properties 8.1 Thermal Conductivity and Speciﬁc Heat Capacity 457

Heat Flow Meter and Comparative Method

The main disadvantage of steady-state methods is that

they are very time consuming. This is because the whole

system of specimen and guard heaters must reach ther-

mal equilibrium in order to avoid unaccounted heat

losses and deviations from steady-state conditions. The

basic idea of the heat ﬂow meter and the comparative

method is the determination of the (axial) heat ﬂux by

means of the measurement of a temperature drop across

a thermal resistor. This is in analogy to the determi-

nation of a current by the measurement of a voltage

drop across an electrical resistor. The implementation

of this idea for heat ﬂux measurements is carried out ei-

ther by the use of a reference sample with well-known

(certiﬁed) thermal resistance or by means of a heat ﬂux

sensor. Most heat ﬂux sensors consist of a series con-

nection of thermocouples across a thermal resistor, e.g.

a thin ceramic or plastic plate. The measured signal is

a thermovoltage proportional to the temperature drop

across the plate. Usually a heat ﬂux sensor is calibrated

in a steady-state temperature ﬁeld with well-known heat

ﬂux, e.g. in a guarded hot plate apparatus.

The design of a heat ﬂow meter apparatus is very

similar to that of the single-specimen guarded hot plate

instrument. Instead of the main heater a heat ﬂux sensor

is used. In some cases a second heat ﬂux sensor at the

cold plate is applied to determine radial heat losses and

to reduce the measurement duration. This is of particu-

lar advantage for measurements of insulation materials.

To avoid radial heat losses the lateral surfaces of the

sample are surrounded by thermal insulation or addi-

tional guard heaters.

If a reference sample for heat ﬂux measurements is

used, the sample and reference samples are piled upon

one another in a temperature ﬁeld (series connection of

thermal resistors). The temperature drops across both

sample and reference sample are measured and com-

pared (comparative method). To correct for radial heat

losses two reference samples are mostly used and the

investigated sample is sandwiched between them. Un-

der steady-state conditions the heat ﬂux at each point

of the stack is the same. In that case the ratio of the

thermal resistances of the sample and reference sample

is equal to the ratio of the corresponding temperature

drops. In contrast to the guarded hot plate method the

heat ﬂow meter and the comparative method are relative

and not absolute methods. The heat ﬂow meter method

is mostly used for insulation materials and polymers

(λ<0.3Wm

−1

), in some cases for glasses and ce-

ramics, i. e. for materials with thermal conductivities

less than about 5 W m

−1

. In contrast, the typical

application range of the comparative technique is the

investigation of metals, ceramics and glasses having

thermal conductivities above 1 W m

−1

. Typical up-

per temperature limits are about 200

◦

C for the heat ﬂow

meter method and about 1300

◦

C for the comparative

method. The measurement uncertainties are about 3%

for insulation materials near room temperature and be-

tween 10 and 20% at high temperatures.

Direct Heating (Kohlrausch) Method

The disadvantages of steady-state thermal conductivity

measurement methods are the long equilibration time

needed to reach steady-state conditions and the difﬁ-

cult quantiﬁcation of heat losses, in particular at high

temperatures. These can be avoided using the direct

heating method, although this can only be used for

materials with sufﬁciently high electrical conductivity,

such as metals. Typically samples are wires, pipes or

rods with a diameter d between 0.5 and 20 mm and

a length l between 50 and 500 mm. Figure 8.2 shows

the schematic of the most popular design of the direct

heating method.

The sample is placed in a vacuum chamber, clamped

between two liquid-cooled heat sinks and heated by

a sufﬁciently high electrical current I

to achieve

sample temperatures in the range 400–3000 K. Temper-

atures and voltage drops are measured at three positions;

one position is in the middle of the rod, while the oth-

Power supply

Vacuum

enclosure

Cylindrical

guard heater

guard

Specimen

, T

–U

Fig. 8.2 Principle of the direct heating method

Part C 8.1