Czichos H., Saito T., Smith L.E. (Eds.) Handbook of Metrology and Testing

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458 Part C Materials Properties Measurement

ers are placed symmetrically at equal distances from

the middle position. In most cases thermocouples are

used because of their dual usability as temperature sen-

sors and for voltage-drop measurements. The result of

measurements by the direct heating method is the prod-

uct of the thermal conductivity and the speciﬁc electric

resistivity λρ

λρ

(

−U

)



−

(

)



(8.8)

The speciﬁc electrical resistivity can be determined

from the length l and cross-sectional area A of the sam-

ple, heating current I

and voltage drop U

according

. (8.9)

Pipe and Hot Wire Method

The characteristic of this class of methods is radial heat

ﬂow in a cylindrical sample (diameter d

, length l). Fig-

ure 8.3 shows the principle of the pipe method.

A hole on the central axis of the sample con-

tains the core heater (diameter d

), which is a rod,

Muffle heater Specimen

Temperature sensors

Water cooled

cylindrical chamber

InsulationCore heater

Muffle heater

Fig. 8.3 Principle of the pipe method

tube or wire. Depending on the temperature range of

interest the sample is surrounded by a liquid-cooled

heat sink or a combination of mufﬂe heater and water

jacket. Axial heat losses can be minimized by additional

end guard heaters or a special sample geometry, i. e.

a large length-to-diameter ratio. The thermal conduc-

tivity is determined by the measurement of the radial

heat ﬂow Φ and the temperature difference between the

inner and the outer surface of the sample according to

λ =

Φ ln





2πl (T

−T

)

. (8.10)

Because of its simple design modiﬁed versions of this

technique have been used for solids covering the ther-

mal conductivity range between insulation materials



20 mW m

−1



and metals



200 W m

−1



for

temperatures between room temperature and 2770 K.

Transient modiﬁcations to this technique for the simul-

taneous determination of thermal conductivity and ther-

mal diffusivity are of increasing interest (Sect. 8.1.2).

8.1.2 Transient Methods

With the availability of modern computers and data

acquisition systems transient methods have become in-

creasingly popular. The advantages of transient methods

are that much less time is needed for the experiments

and that various thermal properties can be determined

in the same measurement cycle. A typical measurement

duration of one hour for steady-state methods is reduced

to a few minutes or to a subsecond interval for transient

methods. In many cases the temperature measurement

at two opposite surfaces of the sample is replaced by

a temperature measurement as a function of time at only

one position. This makes the design of instruments for

transient measurements straightforward in comparison

to steady-state methods and can improve the accuracy

of the results.

Transient Hot Wire and Hot Strip Method

Most thermal conductivity measurements of liquids,

gases and powders are carried out by means of the tran-

sient hot wire method, a modiﬁcation of the steady-state

pipe method with a cylindrical specimen geometry and

radial heat ﬂow. The pipe is replaced by a thin platinum

wire or nickel strip [8.2,3]. For measurements on solids

the wire is embedded in grooves between two equally

sized specimens. Considerable care is needed in the

sample preparation to achieve sufﬁciently low thermal

contact resistances between solid samples and the heat-

ing wire. Therefore, the use of a thin metal foil strip (hot

Part C 8.1

Thermal Properties 8.1 Thermal Conductivity and Speciﬁc Heat Capacity 459

strip method) instead of the heating wire has become in-

creasingly popular for measurements on solids. In this

case the sample preparation is simpliﬁed by the use of

a heat sink compound. The disadvantage of deviations

from the radial symmetric temperature ﬁeld in compar-

ison to the wire method is compensated by an adequate

mathematical model and evaluation procedure [8.2,4,5].

In the standard transient hot wire technique

(Fig. 8.4) the platinum wire has two functions, as

a heater and as a temperature sensor.

The heat source is assumed to have a constant out-

put, which is ensured by a stabilized electrical power

supply. From the slope of the resulting linear tem-

perature rise as a function of elapsed time the thermal

conductivity λ of the specimen is determined. The ther-

mal diffusivity a can be found from the intercept of

this linear temperature dependence. To eliminate the

effect of axial conduction via the large-diameter cur-

rent supply leads attached to the ends of the hot wire,

two hot wires of differing lengths are often operated

in a differential mode. Further modiﬁcations of this

technique are the cross-wire and the parallel-wire tech-

niques, where the heater and temperature sensor are

separated from each other. For the cross-wire technique,

Fig. 8.4 Principle

of the hot wire

method

the heating wire and legs of a thermocouple are in di-

rect contact with each other and form a cross. The

advantage of the parallel wire method is that it can be

used for anisotropic materials and for materials having

a thermal conductivity above 2 W m

−1

. Further de-

velopments are the use of modulated heat input, e.g.

pulse or sinusoidal modulation.

Relative expanded (k =2) uncertainties of the meas-

ured values of 0.38% for thermal conductivity and 1.7%

for thermal diffusivity (resp. ρc

) of liquids have been

achieved [8.5].

Laser Flash Method

The most frequently used method for the determina-

tion of thermal transport properties of solids is the laser

ﬂash method. The main reason is that it can be used

in a wide temperature and thermal diffusivity range.

Measurements in a temperature range between −100

◦

and about 3000

◦

C are possible. In contrast to most

other methods different material classes, such as poly-

mers, glasses, ceramics and metals, can be investigated

without signiﬁcant limitations on the achievable mea-

surement uncertainty.

Using this method the thermal diffusivity a is deter-

mined. If the speciﬁc heat capacity and the density of

a material are known, the thermal conductivity can be

calculated by using (8.4). Therefore, thermal diffusivity

measurements are often supplemented by calorimetric

measurements for the determination of the speciﬁc heat

capacity.

The principle of the laser ﬂash method is based on

the heating of a specimen by a short laser pulse on

the front side of the specimen and the detection of the

temperature increase at its rear side (Fig. 8.5).

If the laser pulse can be considered to be instanta-

neous and if the sample is kept at adiabatic conditions,

the thermal diffusivity a can be calculated according to

a =0.1388

1/2

. (8.11)

The thermal diffusivity is calculated from the thick-

ness d of the specimen (typically 2 mm) and the

time t

1/2

. This is the time needed for the temperature

of the rear specimen surface to reach half its max-

imum value. Several improvements of the evaluation

methods have been developed since the introduction of

this method by Parker et al. in 1961 [8.6]. These are

the consideration of three-dimensional heat ﬂow, heat

losses, ﬁnite pulse duration, nonuniform heating, com-

posite structures and radiation contributions to the heat

transfer. In addition several modiﬁcations, e.g. for the

Part C 8.1

460 Part C Materials Properties Measurement

500νs

Laser power Temperature

Time

5 ms–10s

1/2

Laser SpecimenFurnace

Radiation

thermometer

Fig. 8.5 Principle of the laser ﬂash method

measurement of the speciﬁc heat capacity or for the

direct determination of the thermal conductivity, have

been developed.

The most important advantage of the laser ﬂash

method is that, for the determination of a thermal

property, neither absolute temperatures nor heat meas-

urements are necessary. The thermal diffusivity mea-

surement is carried out by determination of the relative

temperature change as a function of time only. This is

the main reason why relative measurement uncertain-

ties in the 3–5% range can be achieved even at high

temperatures [8.7–9].

Photothermal Methods

The principle of these methods is based on the investi-

gation of a light-induced change in the thermal state of

a material in solid, liquid or gaseous state. If light is ab-

sorbed by a sample, subsequent changes in temperature,

pressure or density are detected. There are methods in

which the sample is in contact with the detection system

and others that involve remote, noncontact detection

systems.

Photothermal and photoacoustic methods for the de-

termination of optical absorption and thermal properties

of materials can be classiﬁed according to the detection

technique used. These are based on the measurement of

changes in:

•

Temperature: Changes in temperature are usually

investigated by means of contact thermometry (e.g.

the photopyroelectric technique), radiation ther-

mometry or calorimetric methods.

•

Pressure: Pressure changes are determined via

acoustic methods.

•

Density: The investigation of density changes in-

clude the detection of refractive index variations or

of surface deformations. The most important tech-

niques are the thermal lens method, thermal wave

technique, beam deﬂection, refraction or diffraction

methods.

The general idea of thermal diffusivity measurement by

photothermal methods is modulated heating of a sample

surface and detection of the amplitude and phase of the

temperature at the opposite sample surface as a func-

tion of modulation frequency. This technique can be

modiﬁed by simultaneous heating of both surfaces with

a single modulation frequency and measurement of the

phase difference between both surface signals.

Photoacoustic Technique. Typically the sample is

placed in an acoustically sealed cell containing a con-

tact gas and a microphone. A monochromatic light

source periodically heats the sample and the resulting

expansion causes a pressure wave which is sensed with

the microphone pressure transducer. Liquid or solid

samples can be measured either by direct coupling of

the acoustic wave to the microphone or via a gas (cou-

pling ﬂuid). A great variety of photoacoustic conﬁgura-

tions have been developed depending on the aggregate

state of the sample, the property to be measured (e.g.

thermal diffusivity, effusivity, optical properties) or the

temperature and pressure range of interest.

Optical Beam Deﬂection Technique. An excitation

beam heats the material periodically while a continuous

wave (cw) probe beam is used either in order to detect

density changes of the gas near the sample surface or

to probe the sample directly. Depending on the relative

position between excitation and probe beam, collinear

and perpendicular conﬁgurations are distinguished. If

the sample surface temperature is different from that of

the surrounding gas, this results in a temperature gra-

dient between the gas near the sample surface and the

bulk gas. Since the density of a gas is temperature de-

pendent, a gradient of the refractive index of the gas is

observed. This method, also known as the optical mi-

rage technique, is based on the refraction of the probe

beam caused by the dependence of the speed of light on

the gas temperature.

Part C 8.1

Thermal Properties 8.1 Thermal Conductivity and Speciﬁc Heat Capacity 461

Thermal Lens Technique. This method is of particu-

lar interest for the determination of thermal properties

of transparent liquids and solids, such as glasses, poly-

mers or liquid crystals. The photothermal lens is created

through the temperature dependence of the refractive

index of the sample resulting from the heating of the

sample by an excitation laser beam. Typically the lens

causes a laser beam divergence which is detected as

a time-dependent decrease in power at the center of the

beam.

Thermal Wave Technique. The principle of the thermal

wave technique is based on measurements of tempera-

ture ﬂuctuations in a (gaseous) sample following the

absorption of intensity-modulated light. The thermal

diffusivity is determined from frequency- and time-

domain behavior of a thermal wave in a ﬁxed volume.

An improvement of this technique is the development

of the thermal wave resonant cavity, which has been

used for the measurement of the thermal diffusivity of

gases with very high precision. A thermal wave cav-

ity consists of two parallel walls. One wall is ﬁxed

and periodically heated by a laser beam or resistive

heating. The other one consists of a pyroelectric thin-

ﬁlm transducer, which is used to monitor the spatial

behavior of the thermal wave by means of cavity-

length scans. By this method the thermal conductivity

and thermal diffusivity of the gas in the cavity can be

measured.

For a more detailed discussion we refer to [8.10].

8.1.3 Calorimetric Methods

The general principle of all calorimetric methods for

the determination of the speciﬁc heat capacity is based

on (8.1), i. e. the measurement of a speciﬁc amount of

heat dQ and the resulting temperature increase dT.In

most cases two experiments are necessary, a ﬁrst one

with the empty calorimeter in order to determine the in-

strument’s heat capacity and for the correction of the

remaining heat losses and a second one with the ﬁlled

calorimeter including the sample.

Numerous types of calorimeters have been devel-

oped for the determination of speciﬁc heat capacities of

materials. Table 8.2 shows the most important of these

and their typical application range.

The most accurate methods for speciﬁc heat cap-

acity measurements are adiabatic calorimetry and drop

calorimetry (for details see Sect. 8.2). Construction of

these high-precision instruments, which are not com-

mercially available, requires considerable effort and

money, while their operation demands substantial ex-

perience and time.

Therefore, probably more than 90% of speciﬁc heat

capacity measurements of solids and liquids are car-

ried out by means of a differential scanning calorimeter

(DSC, for a detailed description see Sect. 8.2.2). A DSC

is operated in dynamic mode, which means that the fur-

nace is heated or cooled with a constant scanning rate

of, typically, 20 K/min. The measured quantities are

the heat ﬂow rate Φ = dQ/ dt and the corresponding

sample temperature T. Usually, three experiments are

necessary: the measurement of the empty calorimeter,

the sample measurement and the calibration sample

measurement.

A calibration is needed because differential scan-

ning calorimetry is a relative method. There are two

materials that are considered as standards for the test or

calibration of calorimeters used for the determination of

speciﬁc heat capacities of solids. These are copper for

the temperature range 20–320 K [8.11] and synthetic

sapphire for the temperature range 10–2250 K [8.12].

The relative measurement uncertainties are less than

0.1% for copper, and less than 0.1% for sapphire in the

temperature range 100–900 K and in the range 1–2% at

higher temperatures.

In many cases a certiﬁed reference material such as

synthetic sapphire (e.g., SRM 720 from the National

Institute of Standards and Technology, Gaithersburg,

USA) is used as the calibration material.

If the heating rates of the sample (s), calibration

sample (cal) and empty (0) measurement are identical,

the speciﬁc heat capacity of the sample c

p,s

is given by

p,s

cal

p,cal

−Φ

cal

−Φ

. (8.12)

Here m

and m

cal

are the masses of the sample and

calibration sample and the corresponding heat ﬂow

rates are Φ

and Φ

cal

. There are several commer-

cially available instruments that can be used in different

temperature ranges between 100 K and 1900 K. For

most DSCs disk-typed samples with diameters of about

6 mm and heights of 1 mm are used. But there are

also cylinder-type DSCs (known as Calvet-type de-

vices) having sample container volumes in the range

1.5–150 ml. For measurements on liquids a measure-

ment or control of the vapor pressure and of the sample

volume is necessary. This is carried out by special sam-

ple cells in cylinder-type instruments or DSCs specially

developed for the purpose.

The typical measurement uncertainties of speciﬁc

heat capacity measurements of solids by means of DSCs

Part C 8.1

462 Part C Materials Properties Measurement

Table 8.2 Different types of calorimeters used for the determination of speciﬁc heat capacities

Type of calorimeter Quantities Typical tempera-

ture range (K)

Uncertainty

(%)

Merit Demerit

Differential scanning

calorimeter

Speciﬁc heat capacity,

enthalpy of phase

transition of solids and

liquids

100–1900 1.5–10 Standardized,

easy to use, fast

Relative method

Adiabatic calorimeter Speciﬁc heat capacity,

enthalpy of phase

transition of solids, liquids

and gases

1–1900 0.05–2 High accuracy Long measurement

time, expensive

Drop calorimeter Speciﬁc heat capacity,

enthalpy of phase

transition of solids and

liquids

273–3000 0.1–2 High accuracy Expensive

Pulse calorimeter Speciﬁc heat capacity,

enthalpy of phase

transition of solids and

liquids

600–10 000 2–3 Fast, high

temperature

Only electrically

conducting

materials, expensive

Flow calorimeter Speciﬁc heat capacity and

enthalpy measurements of

liquids and gases

100–700 0.05 − −

Bomb calorimeter Heat of combustion of

solids, liquids and gases

300 0.01 Standard method

for solids, liquids

Low accuracy for

gases

Gas calorimeter Heat of combustion of

gases

300 0.03–0.5 Standard method

for gases

−

are about 5% below 700

◦

C and up to 10% at high

temperatures. A higher accuracy requires considerable

more time and effort to be spent on a proper calibra-

tion and evaluation procedure. In those cases a relative

uncertainty of about 1.5% is achievable using this tech-

nique [8.13].

At high temperatures there are considerable prob-

lems with most calorimetric techniques due to heat

losses by thermal radiation, mechanical, electrical or

chemical properties of the sample and the construction

material of the calorimeters. Therefore, for measure-

ment at temperatures above 2000 K, pulse calorimetry

is advantageous [8.1, 14], but can only be used for ma-

terials having a sufﬁciently high electrical conductivity.

The principle of the pulse method is based on a rapid re-

sistive self-heating of a rod- or wire-type specimen by

the passage of an electrical current pulse through it. For

the determination of the speciﬁc heat capacity measure-

ments of the current through the specimen (typically in

the range 100–10 000 A), the voltage drop across the

specimen and of the specimen temperature with submil-

lisecond resolution are necessary. If the heating rate is

sufﬁciently large, investigations in the liquid state are

possible. Modiﬁcations of this technique allow the ad-

ditional determination of the emissivity, the electrical

and thermal conductivity and of the enthalpy of fusion.

The temperature range of this technique is ap-

proximately 600–10 000 K. For speciﬁc heat capacity

measurements by pulse calorimetry relative uncertain-

ties of 2–3% can be achieved.

8.2 Enthalpy of Phase Transition, Adsorption and Mixing

According to the ﬁrst law of thermodynamics the

change in the internal energy of a thermodynamic sys-

tem dU is equal to the difference between the heat

transfer into the system dQ and the mechanical work

done by the system dW (other energy forms are ne-

glected here).

dU = dQ + dW = dQ − pdV

(8.13)

The enthalpy of a thermodynamic system is deﬁned

according to H =U + pV and the resulting enthalpy

change dH is

dH = dU +pdV +V dp = dQ +V dp . (8.14)

Equation (8.14) describes the relationship between

the measured quantity, the exchanged heat dQ,and

the quantity assigned to the material, the enthalpy

Part C 8.2

Thermal Properties 8.2 Enthalpy of Phase Transition, Adsorption and Mixing 463

change dH. The relationship between these quantities

as a function of the variables of state, namely pres-

sure p, temperature T and composition ξ, is given by:

dQ =



∂H

∂p



−V



T,ξ



∂H

∂T



p,ξ

dT +



∂H

∂ξ



T, p

dξ. (8.15)

In many cases the pressure change is very small and

the ﬁrst term of (8.15) is negligible. The second term

is the heat capacity at constant pressure of nonreact-

ing systems. The third term describes the isothermal

and isobaric enthalpy change due to phase transitions,

mixing or chemical reactions. At constant pressure and

in the absence of other energy conversions (e.g. defor-

mation, oxidation or surface energy transformation) the

enthalpy of transition of a material Δ

trs

H is equal to the

heat of transition Q

trs

To understand the general principles of calorimetric

measurements it is helpful to separate a calorimeter into

three parts: (a) the calorimeter vessel with sample, cru-

cible, thermometer and additional equipment for heat

measurement, (b) the immediate surroundings of the

calorimeter vessel, e.g. a temperature-controlled liquid

bath or metal block and (c) a means for initiation chem-

ical reactions, mixing, solution or adsorption processes.

Often a calorimeter is characterized according to its

mode of operation, being either adiabatic, isothermal

or isoperibol. Adiabatic means that the heat exchange

between calorimeter vessel and surroundings is consid-

ered to be zero. In isothermal mode the temperature

of the calorimeter vessel remains constant. In isoperi-

bol mode the temperature of the surroundings is kept

constant.

There are numerous types of calorimeters in use

and, as a consequence, several classiﬁcation systems

have been proposed. Typical criteria for the classiﬁca-

tion are the following:

Principle of (Heat) Measurement.

•

Heat-compensation calorimeters

The heat to be measured is determined, e.g., by

Joule heating, Peltier cooling or by means of the

latent heat of a phase transition (e.g., Bunsen ice cal-

orimeter). The measurements are mostly carried out

under isothermal or quasi-isothermal conditions.

•

Heat-accumulation calorimeters

The heat is determined by means of a temper-

ature change measurement. It is based on the

fact that the temperature increase of a calorime-

ter is proportional to the amount of heat added.

The proportionality factor must be determined by

calibration with a known amount of heat. This prin-

ciple of measurement requires the minimization of

heat losses. Therefore, measurements are prefer-

ably carried out under adiabatic or quasi-adiabatic

conditions.

•

Heat-conduction calorimeters

In this type of calorimeter the heat is exchanged

between the calorimeter and its surroundings via

a well-deﬁned heat conduction path. The corres-

ponding heat ﬂow rate (with dimensions of power)

is measured, e.g., by means of heat ﬂux sensors

(thermopiles). Heat is determined by integration

of the measured heat ﬂow rate as a function of

time. Instruments of that type are often operated

at isoperibol conditions, i. e. the temperature of the

surroundings remains constant.

Mode of Operation.

•

Static mode

This mode includes adiabatic, isothermal or isoperi-

bol operation.

•

Dynamic mode

Either the temperature of the calorimeter vessel

or that of the surroundings is changed. The linear

scanning mode (constant heating rate) is most of-

ten used, i. e. the temperature of the calorimeter

vessel is a linear function of time. During recent

years an increasing number of variable heating rate

techniques was developed. Typical modes of oper-

ation are stepwise heating or the superposition of

a constant heating rate by sinusoidal or sawtooth

temperature changes.

Construction Principles. These are single, twin or dif-

ferential calorimeters.

Methods of Reaction, Solution, Mixing or Adsorp-

tion Initiation. Examples are continuous (e.g. ﬂow

calorimeters), discontinuous or incremental working in-

struments (e.g. incremental titration).

The use of certiﬁed reference materials or pure

substances with well-known thermodynamic proper-

ties [8.15–18] to check the proper functioning of

a calorimeter, the calibration of the instrument, and

for validation of the reliability of the measurement

uncertainty budget is highly recommended. Certiﬁed

reference materials for calorimetry are available from

the National Institute of Standards and Technology

(NIST, USA), the Physikalisch-Technische Bundes-

Part C 8.2

464 Part C Materials Properties Measurement

anstalt (PTB, Germany) and the Laboratory of the

Government Chemist (LGC, UK).

8.2.1 Adiabatic Calorimetry

Adiabatic calorimetry is one of the most accurate ther-

mal methods. Relative uncertainties of less than 0.1%

for enthalpy of fusion or speciﬁc heat capacity measure-

ments can be achieved. To reach this level, substantial

expenditure on the construction, measurement and con-

trol of the system is required [8.19, 20]. Typically an

adiabatic calorimeter can be divided into three parts:

a cylindrical inner part surrounded by a system of adia-

batic shields and a furnace (Fig. 8.6).

The inner part of the calorimeter consists of a ther-

mometer, crucible(s), sample, heater and inner radiation

shields. In contrast to other calorimeters standard plat-

inum resistance thermometers are mostly used. This

allows the determination of transition temperatures with

the highest accuracy (ΔT ≈ 1mK).

For the realization of adiabatic measurement con-

ditions (prevention of heat exchange with the surround-

ings) the inner sample part of the calorimeter is enclosed

by a heated adiabatic shield, controlled to the same tem-

perature as the inner part. For proper control of the

adiabatic conditions and to ensure sufﬁcient tempera-

ture homogeneity further guard and radiation shields

Heater Thermometer

Adiabatic shield

Furnace

Guard

Fig. 8.6 Principle of an adiabatic calorimeter

are concentrically arranged around the adiabatic shield.

The outer part of an adiabatic calorimeter is the furnace

(or cryostat) and an enclosure for measurements in vac-

uum or at controlled inert gas ﬂow. To minimize heat

losses and temperature gradients within the calorimeter,

construction materials must have a very high thermal

conductivity and low emissivity in the infrared range

(e.g. silver).

The basic principle of adiabatic calorimetry is the

measurement of the temperature increase of the sam-

ple due to the supply of a known amount of heat.

Therefore, the typical mode of operation consists of al-

ternating heating and equilibration periods, but there are

also several adiabatic calorimeters that operate in scan-

ning mode at very low scanning rates. Under adiabatic

conditions the enthalpy increment is equal to the sup-

plied heat, which is determined by an electrical energy

measurement of high accuracy (P

t = Q, P

:power,

t: time). Determination of the speciﬁc heat capacity of

a material is reduced to the basic relation

mΔT

. (8.16)

In real measurements very small heat losses remain,

which can be determined and corrected by means

of additional experiments. For that purpose in a ﬁrst

empty run the heat capacity of the calorimeter without

a sample is measured. In a properly designed adiabatic

calorimeter the heat losses are equal in the empty and

ﬁlled state. Therefore, the empty measurement is also

the basis for the correction of the remaining heat losses.

A measurement procedure for the determination of

the enthalpy of fusion also consists of different runs and

again a step heating procedure with alternating heat-

ing and equilibration periods is used. For experimental

reasons each fusion experiment starts below and stops

above the fusion temperature. Therefore, the heat cap-

acity contributions of the (ﬁlled) calorimeter must be

considered. Further experiments are needed to deter-

mine the fusion temperature of the material. For that

purpose the method of fractional fusion is used.

Adiabatic calorimeters are used from temperatures

below 1 K up to about 1900 K [8.21]. At high tempera-

tures the main problems are deviations from adiabatic

conditions because of thermal radiation. This results in

measurement uncertainties of a few percent for enthalpy

of fusion and speciﬁc heat capacity measurements at

temperatures above 1000 K. In the low-temperature

range the speciﬁc heat capacity of materials and the

sensitivity of most high-precision thermometers rapidly

decrease as a function of temperature. This leads to the

Part C 8.2

Thermal Properties 8.2 Enthalpy of Phase Transition, Adsorption and Mixing 465

requirement for considerable effort for the measurement

of the temperature difference of the sample and for the

control of the adiabatic shield. The lowest uncertainties

for enthalpy of fusion measurements of less than 0.1%

are achieved in the 100–900 K range.

8.2.2 Differential Scanning Calorimetry

Differential scanning calorimeters (DSCs) are twin-

type systems consisting of identical measuring systems

for the sample and a reference sample [8.22]. These

are mounted in the same furnace and commonly sub-

jected to a controlled temperature program (heating or

cooling). During heating or cooling heat is exchanged

between the furnace and sample part of the calorim-

eter (corresponding heat ﬂow rate Φ

) and in the same

manner between the furnace and reference part of the

calorimeter (corresponding heat ﬂow rate Φ

). The

difference between these heat ﬂow rates (ΔΦ =Φ

−

) is measured and used for the determination of the

quantity of interest, e.g. the enthalpy of fusion of the

sample. A differential scanning calorimeter measures

two quantities, the heat ﬂow rate ΔΦ (with dimensions

of power) and the corresponding sample temperature.

For the measurement of temperatures either platinum

resistance thermometers or thermocouples are used.

Heat ﬂow rates are measured either by direct electrical

power measurements or by means of thermocouples or

thermopiles. The use of thermocouples or thermopiles is

based on the determination of a temperature drop across

a thermal resistor, in analogy to the determination of

electrical currents by the measurement of the voltage

drop across an ohmic resistor.

Using DSC, both the determination of a transition

temperature and the determination of a heat of transition

is possible. The transition temperature is determined

from the extrapolated peak onset temperature T

and the

transition enthalpy from the peak area of the heat ﬂow

rate curve (Fig. 8.7).

To determine the peak area the baseline must be sub-

tracted. The proper choice of the baseline has a major

inﬂuence on the measurement uncertainty of the transi-

tion enthalpy.

A further feature of differential scanning calorime-

try is the dynamic mode of operation. Typically

a temperature program consists of three segments:

an initial isothermal segment, followed by a scan-

ning segment (heating or cooling) with a constant rate

and a ﬁnal isothermal segment. Scanning rates in the

range ±0.1–500 K/min in a temperature range between

−150

◦

C and 1600

◦

C are used for the determination

Heat flow rate

Time

Fig. 8.7 Heat ﬂow rate signal of a DSC during a transition

in heating mode with extrapolated peak onset tempera-

ture T

of enthalpies of phase transitions and speciﬁc heat

capacities.

A further development is the variable heating rate

DSC, where a temperature modulation is superimposed

on the constant heating or cooling rate of a conven-

tional DSC. The simplest and most commonly used

modulation type is periodic, e.g. sinusoidal, sawtooth

or stepwise heating. This technique has been success-

fully applied for the separation of superimposed effects

such as glass transitions and enthalpy relaxations or the

determination of speciﬁc heat capacities during phase

transitions.

There are two basic types of DSCs, the heat ﬂux

DSC and the power compensation DSC. The principle

of the heat ﬂux type of DSC is based on the measure-

ment of the difference of the heat ﬂow rates ΔΦ as

described above. The heat ﬂux within the DSC takes

place via a well-deﬁned heat conduction path with low

thermal resistance. There are two different principles of

construction of heat ﬂux DSCs, namely disk-type and

cylinder-type systems (Fig. 8.8).

A power compensation DSC consists of two iden-

tical microfurnaces (for sample and reference sample)

which are heated separately according to a prescribed

temperature program. The temperature difference be-

tween the two microfurnaces is measured and controlled

to achieve the same program of temperature versus time

for the sample and reference sample. The compensat-

ing heating power is a measure of the heat ﬂow rate

difference ΔΦ.

Several modiﬁed DSCs have been developed for

special applications. Among these are the high-pressure

DSC [8.23], photo DSCs for the investigation of light-

Part C 8.2

466 Part C Materials Properties Measurement

Disk-type DSC

Cylinder-type DSC

Reference Sample

~Δ

ReferenceSample

~Δ

Fig. 8.8 Different types of heat ﬂux DSCs

induced reactions [8.24]andDSCs for measurements

on ﬂuids [8.25, 26]. Cylinder-type instruments can be

modiﬁed to investigate mixing, solution or adsorption

processes.

The basic requirement for reliable measurements

by means of DSC is the calibration of the instrument,

for several reasons. These are the possible drift of sen-

sors and other parts of the measuring system but more

importantly the dependence of the calibration on tem-

perature, heating rates, sample holder and crucible or

sample properties, e.g. mass, thermal conductivity. It

is generally recommended that the calibrations be car-

ried out at conditions similar to those of the actual

measurement. A typical example is the heat ﬂow rate

calibration. In principle, a cylinder-type DSC could be

calibrated using a number of methods, e.g. electrically

by means of a calibration heater, by means of a refer-

ence material with known speciﬁc heat capacity or by

means of a material with known enthalpy of fusion. One

would expect it to be sufﬁcient to calibrate the instru-

ment by any of these methods. But, depending on the

actual measurement problem, very different measure-

ment uncertainties would be achieved. Therefore, the

German Society for Thermal Analysis (GEFTA) recom-

mends [8.15, 27] to distinguish between the heat and

the heat ﬂow rate calibration of a DSC, even though

the same sensor and electronics are used for both types

of measurement. As an example, if the enthalpy of

fusion of an unknown material is measured, a heat cal-

ibration of the DSC by means of a reference material

with known enthalpy of fusion at a temperature close

to the fusion temperature of the unknown material is

recommended.

A metrologically ﬂawless calibration of a DSC is

very time consuming but can improve the accuracy of

results by about one order of magnitude. Basic require-

ments for DSC calibrations are given by international

standards and more detailed procedures have been pub-

lished by GEFTA or the International Confederation for

Thermal Analysis and Calorimetry.

With carefully calibrated instruments relative meas-

urement uncertainties of about 1% for enthalpy of

fusion measurements and 1.5% for speciﬁc heat cap-

acity measurements can be achieved. For routine work

relative uncertainties in the 5–10% range are more

typical.

8.2.3 Drop Calorimetry

Drop calorimeters are used for the determination of en-

thalpy increments and speciﬁc heat capacities of solid or

liquid materials in a temperature range between room

temperature and more than 3000 K. The only require-

ments are that the sample should be nonreactive with its

container and have a low vapor pressure to avoid mass

loss and signiﬁcant contributions from heat of reaction

or vaporization.

The basic principle of a drop calorimeter is the

rapid translation (drop) of a sample from some exterior,

temperature-controlled zone (furnace) with tempera-

ture T

into a calorimeter with temperature T

,which

is used for the measurement of the heat transfered.

If the instrument is properly designed then the

heat loss during the translation from the furnace to

the calorimeter is negligible and relative measurement

uncertainties of less than 0.1% are possible [8.28].

A disadvantage of that technique is that an initial

cooling rate of the sample of up to 2000 K/s is pos-

sible. In that case the sample might become frozen in

a metastable state.

Part C 8.2

Thermal Properties 8.2 Enthalpy of Phase Transition, Adsorption and Mixing 467

The calorimeter is typically an adiabatic, isoperi-

bol or isothermal instrument. These can be considered

as consisting of two parts: the central measuring part

and its enclosing surroundings. In adiabatic calorime-

ters at any time the temperature of the surroundings

is controlled to the same value as that of the cen-

tral (sample) measuring part. Consequently, no heat

losses occur (adiabatic conditions), and adding of

heat results in a temperature increase that is used

as a measure of that heat. The relationship between

heat and temperature increase and the heat capacity

of the empty calorimeter are determined by electrical

calibrations.

An isoperibol mode of operation means that the

temperature of the surroundings is kept constant. In

that case two processes occur, if heat is added, ﬁrstly

the temperature of the calorimeter is increased (heat is

stored) and secondly heat is exchanged with the sur-

roundings. The lowest measurement uncertainties are

achieved if the amount of stored heat is considerable

larger than the exchanged heat.

Several methods are in use for the determination of

the heat loss correction. These are based on the validity

of Newton’s law of cooling



/dt =−k(T

−T

)



The basic idea of most methods for the correction of

heat losses in adiabatic and isoperibol calorimeters is

the back and forward extrapolation of the ﬁnal and ini-

tial temperatures over time (Fig. 8.9). This allows the

determination of the adiabatic temperature difference

ΔT

adiab

(without heat losses) at the time where areas A

and A

are equal.

In a calorimeter working in isothermal mode, both

the temperature of the surroundings T

and the tempera-

ture of the central measuring part T

remain constant.

This is achieved by using a thermostat to keep the tem-

Tem p e r a t u r e

Time

ΔT

adiab

= A

)

Fig. 8.9 Principle of the heat loss correction based on

Newton’s law of cooling

perature of the surroundings constant and a two-phase

system as the working substance for the measuring

part. Using a two-phase system (usually a solid–liquid

phase transition) for temperature control means that

adding heat to the measuring part of a calorimeter re-

sults in a change of the phase distribution (melting of

some material) at constant temperature. The amount of

melted material is determined either by weighing or

by a volume change measurement. The volume change

measurement is based on density differences of the

working substance between its solid and liquid state

(e.g. Bunsen ice calorimeter). On this basis heat meas-

urements with relative uncertainties of 0.02% have been

made.

8.2.4 Solution Calorimetry

The determination of heat of solution, mixing, or ad-

sorption [8.29] is of interest in different ﬁelds of

materials research, e.g. for investigation of polymers,

pharmaceutical products or ceramics. Differences in the

heat of solution between different batches of a ma-

terial can reﬂect variations in polymorphism, moisture

content, degree of crystallinity, surface area or sur-

face energy. Instruments can be classiﬁed according

to the state of aggregation of the interacting materials

or whether a continuous (ﬂow calorimeters) step mode

(e.g. titration) or discontinuous mode of operation is

used.

A further classiﬁcation scheme is the mode of

operation resulting from the coupling between the cen-

tral part of the calorimeter, which is used for the

caloric measurements, and the surroundings. Solution

calorimeters are operated either in adiabatic, isothermal

or isoperibol mode.

Speciﬁc problems are the separation and the tem-

perature control of the components before the start,

complete mixing over the course of the investigations

and the change in the vapor pressure during mix-

ing. Calorimeters for discontinuous operation consist

of a reaction vessel, a thermometer, a mixing unit or

ampoule-breaking system, the stirrer and a resistance

heater for electrical calibration. Typically thermometers

are thermistors, platinum resistance (Sect. 8.5) or quartz

thermometers. The principle of a quartz thermometer is

based on the resonant frequency dependence of a quartz

oscillator as a function of temperature. Often one of the

samples is sealed in a thin-walled glass ampoule. Af-

ter the system is in thermal equilibrium, the solution or

reaction process under study is started by breaking the

glass ampoule.

Part C 8.2