Bsi bs en 00821 2 1997 (2000)

BRITISH STANDARD

Advanced technical
ceramics —
Monolithic ceramics —
Thermo-physical
properties —
Part 2: Determination of thermal
diffusivity by the laser flash (or heat
pulse) method

The European Standard EN 821-2:1997 has the status of a
British Standard

ICS 81.060.99

BS EN
821-2:1997


BS EN 821-2:1997

National foreword
This British Standard is the English language version of EN 821-2:1997. It
supersedes BS 7134-4.2:1990.
The UK participation in its preparation was entrusted to Technical Committee
RPI/13, Advanced technical ceramics, which has the responsibility to:
— aid enquirers to understand the text;
— present to the responsible European committee any enquiries on the
interpretation, or proposals for change, and keep the UK interests informed;
— monitor related international and European developments and

promulgate them in the UK.
A list of organizations represented on this committee can be obtained on
request to its secretary.
Cross-references
The British Standards which implement international or European
publications referred to in this document may be found in the BSI Standards
Catalogue under the section entitled “International Standards Correspondence
Index”, or by using the “Find” facility of the BSI Standards Electronic
Catalogue.
A British Standard does not purport to include all the necessary provisions of
a contract. Users of British Standards are responsible for their correct
application.
Compliance with a British Standard does not of itself confer immunity
from legal obligations.

Summary of pages
This document comprises a front cover, an inside front cover, pages i and ii,
the EN title page, pages 2 to 15 and a back cover.
This standard has been updated (see copyright date) and may have had
amendments incorporated. This will be indicated in the amendment table on
the inside front cover.

This British Standard, having
been prepared under the
direction of the Sector Board for
Materials and Chemicals, was
published under the authority of
the Standards Board and comes
into effect on
15 November 1997

© BSI 04-2000

ISBN 0 580 28389 5

Amendments issued since publication
Amd. No.

Date

Comments


BS EN 821-2:1997

Contents
National foreword
Foreword
Text of EN 821-2

© BSI 04-2000

Page
Inside front cover
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ii

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EUROPEAN STANDARD

EN 821-2

NORME EUROPÉENNE
June 1997

EUROPÄISCHE NORM
ICS 81.060.99

Descriptors: Ceramics, powdery materials, thermodynamic properties, tests, determination, diffusion, thermal conductivity

English version

Advanced technical ceramics — Monolithic ceramics —
Thermo-physical properties
Part 2: Determination of thermal diffusivity by the laser
flash (or heat pulse) method
Céramiques techniques avancées —
Céramiques monolithiques — Propriétés
thermo-physiques —
Partie 2: Détermination de la diffusivité
thermique par la méthode Flash laser
(ou impulsion de chaleur)

Hochleistungskeramik — Monolithischer

Keramik — Thermophysikalische
Eigenschaften —
Teil 2: Messung der Temperaturleitfähigkeit
mit dem Laserflash- (oder Wärmeimpuls-)
Verfahren

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This European Standard was approved by CEN on 1997-05-24. CEN members
are bound to comply with the CEN/CENELEC Internal Regulations which
stipulate the conditions for giving this European Standard the status of a
national standard without any alteration.
Up-to-date lists and bibliographical references concerning such national
standards may be obtained on application to the Central Secretariat or to any
CEN member.
This European Standard exists in three official versions (English, French,
German). A version in any other language made by translation under the
responsibility of a CEN member into its own language and notified to the
Central Secretariat has the same status as the official versions.
CEN members are the national standards bodies of Austria, Belgium,
Czech Republic, Denmark, Finland, France, Germany, Greece, Iceland,
Ireland, Italy, Luxembourg, Netherlands, Norway, Portugal, Spain, Sweden,
Switzerland and United Kingdom.

CEN
European Committee for Standardization
Comité Européen de Normalisation
Europäisches Komitee für Normung
Central Secretariat: rue de Stassart 36, B-1050 Brussels
© 1997 CEN — All rights of exploitation in any form and by any means reserved worldwide for CEN

national Members.
Ref. No. EN 821-2:1997 E


EN 821-2:1997

Foreword
This European Standard has been prepared by
Technical Committee CEN/TC 184, Advanced
technical ceramics, the secretariat of which is held
by BSI.
This European Standard shall be given the status of
a national standard, either by publication of an
identical text or by endorsement, at the latest by
December 1997, and conflicting national standards
shall be withdrawn at the latest by December 1997.
EN 821 consists of three Parts:
— Part 1: Determination of thermal expansion;
— Part 2: Determination of thermal diffusivit;
— Part 3: Determination of specific heat capacity
(ENV).
According to the CEN/CENELEC Internal
Regulations, the national standards organizations
of the following countries are bound to implement
this European Standard: Austria, Belgium,
Czech Republic, Denmark, Finland, France,
Germany, Greece, Iceland, Ireland, Italy,
Luxembourg, Netherlands, Norway, Portugal,
Spain, Sweden, Switzerland and the
United Kingdom.

2

Contents
Foreword
1 Scope
2 Normative references
3 Definitions
4 Principle
5 Apparatus
6 Test pieces
7 Calibration
8 Test procedure
9 Results
10 Test report
Annex A (informative) Fundamental
equations for calculation
Annex B (informative) Deviations from
ideal behaviour
Annex C (informative) Bibliography
Figure 1 — Schematic representation of
transient at rear face of test piece
Figure 2 — Schematic diagram of
thermal diffusivity apparatus
Figure 3 — Schematic diagram of a typical
ambient and low temperature test piece
holder
Figure 4 — Heat loss correction curves
Table 1 — Values of constant Wx for a
range of transient times

Table B.1 — Coefficients for the decay time
heat loss correction
Table B.2 — Finite pulse time correction
constants

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EN 821-2:1997

1 Scope
This Part of EN 821 specifies a method for the
determination of thermal diffusivity of advanced
monolithic technical ceramics, to an accuracy of
approximately ± 5 %. It is suitable for the
measurement of thermal diffusivity values in the
range 0,1 mm2/s to 1 000 mm2/s at temperatures
greater than – 180 °C.
Annex A gives the mathematical derivation of the
calculations, and Annex B contains instruction on
actions necessary when the calculations cannot be
made in the usual way.
NOTE 1 It is not advisable to exceed the temperature at which
the test piece was manufactured.
NOTE 2 This method involves the use of a high powered pulsed
laser system or high energy photoflash equipment as well as high
vacuum and high temperature furnace capability. Such
equipment therefore should be operated within established
safety procedures. (See EN 60825).

2 Normative references
This European Standard incorporates, by dated or
undated reference, provisions from other
publications. These normative references are cited

at the appropriate places in the text and the
publications are listed hereafter. For dated
references, subsequent amendments to or revisions
of any of these publications apply to this European
Standard only when incorporated in it by
amendment or revision. For undated references the
latest edition of the publication referred to applies.
EN 45001, General criteria for the operation of
testing laboratories.
EN 60584-1, Thermocouples — Part 1: Reference
tables.
EN 60584-2, Thermocouples — Part 2: Tolerances.

3.4
transient half time
the time required for the temperature to rise to half
of its peak or maximum

4 Principle
Thermal diffusivity is a measure of the heat flow in
a material under non-steady state conditions. It can
also be related to thermal conductivity via the
specific heat of the material using the relationship:
(1)
where
a
Ỉ
Ơ
cp

is the thermal diffusivity in
is the thermal conductivity in
is the density in
is the specific heat in

m2/s
Wm–1K–1
kg/m3
J/(kg·K)

Thermal diffusivity is measured by applying a high
intensity short duration heat pulse to one face of a
parallel sided homogeneous test piece, monitoring
the temperature rise at the opposite face as a
function of time, and determining the transient half
time (t0,5). The transient temperature rise
(see Annex A) is shown schematically in Figure 1.
The signal from the temperature detector is
recorded with an appropriate data acquisition
system.
The experimental data are subject to both
systematic and random errors e.g. those associated
with
a) test piece thickness determination;
b) time measurement on transient curve;
c) response time of detectors;
d) response time of recording and analysis
equipment;
e) trigger delays;
f) non-uniform heating of the test piece.

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3 Definitions
For the purposes of this Part of EN 821, the
following definitions apply.
3.1
thermal diffusivity
thermal conductivity divided by heat capacity per
unit volume

NOTE Improvement in the accuracy can be obtained by
increasing the sophistication of the data collection and analysis
systems.

3.2
thermal conductivity
density of heat flow rate divided by temperature
gradient under steady state conditions
3.3
specific heat
the heat capacity per unit mass

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EN 821-2:1997

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© BSI 04-2000

Figure 1 — Schematic representation of transient at rear face of test piece


© BSI 04-2000

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5

EN 821-2:1997

Figure 2 — Schematic diagram of thermal diffusivity apparatus


EN 821-2:1997

5 Apparatus
NOTE 1 The essential features of the apparatus are shown
in Figure 2.

5.1 Heat pulse source
The heat pulse source may be a pulsed laser, a flash
tube or an electron beam. The pulse energy shall be
uniform over the face of the test piece.

NOTE 2 This is reasonably simple to achieve in the case of the
flash lamp, which should be housed in a totally reflecting box
with a hole, and a light guide of approximately 25 mm diameter
abutting the sample.
NOTE 3 Significant errors in derived data can arise if the
temperature rise exceeds 5 K, especially in materials where the
thermal diffusivity is strongly temperature dependent.

The pulse source shall produce a rise in temperature
not exceeding 10 K (preferably not exceeding 5 K)
on the rear face of the test piece.
For measurement at high temperature, the use of a
laser is recommended; flash tubes are usually
restricted to a maximum of 400 °C.
NOTE 4 Where a laser is used, it is recommended that a
neodymium-glass laser system is utilized because of its excellent
beam uniformity over the whole diameter. “Footprint” paper or
photographic film can be used to monitor this uniformity and also
to align the beam centrally on the sample front face.

5.2 Environmental control chamber
5.2.1 General
The environmental control chamber shall be either
a furnace (see 5.2.2), a cryostat (see 5.2.3), or a
draught-proof enclosure (for ambient temperature
measurements).
5.2.2 Furnace, capable of operation within the
temperature range required, and of sufficient size to
contain the specimen holder (see 5.6).
The heating elements for the furnace may be

constructed from either:
a) nickel-chrome alloy, for temperatures up
to 1 000 °C; or
b) platinum or silicon carbide, for temperatures
up to 1 500 °C; or
c) graphite, tantalum or tungsten, for
temperatures above 1 500 °C.
In steady state conditions the drift in temperature
shall be less than 0,01 K/s. The temperature of the
test piece shall be monitored either by a
thermocouple in accordance with EN 60584-1 or by
an optical pyrometer (preferably two-colour).
An appropriate inert atmosphere or vacuum shall be
used when necessary to protect furnace parts and
test piece holder (see 5.6) from oxidation, and to
protect the test piece and its coating (see 6.3) from
structure/phase changes, stoichiometric changes
and compatibility problems.

6

NOTE 1 Care should be taken to avoid decomposition of
materials at high temperatures and under reducing conditions.
At high temperatures some types of ceramics may vaporize
(e.g. nitrides and silicates) or otherwise react with the
environment or the applied coating.

The furnace shall either be fitted with a window,
transparent to the incident heat pulse radiation, or
else the heat pulse source may be placed inside the

furnace, for example at temperatures where a flash
lamp may be employed. The furnace shall also be
fitted with a window, transparent to the emitted
thermal radiation opposite the rear face of the test
piece, for measurement of temperature using a
pyrometer and for transmission of the transient
pulse to a remote detector.
5.2.3 Cryostat, capable of temperature control
to 0,01 K
NOTE 2 Various liquids can be used (in a vacuum flask) to
provide the low temperature environment e.g. liquid nitrogen,
liquid oxygen, solid carbon dioxide-acetone mixture, iced water
etc., or a slow flow of boiled and pre-heated liquid nitrogen.

5.3 Transient detector
5.3.1 General
The transient detector shall be either an infra-red
detector (see 5.3.2) or a thermocouple (see 5.3.3). It
shall be capable of detecting changes of < 1 % of the
total rear face temperature rise of the test piece with
a rapid linear time response, which shall
discriminate to 1 % of the half rise time of the
transient (t0,5).
5.3.2 Infra-red detector, of type appropriate to the
minimum test piece temperature required
e.g. a liquid nitrogen cooled indium antimonide
(InSb) cell (for test piece temperatures down
to 40 °C) or a lead sulphide (PbS) cell (for test piece
temperatures down to 250 °C).
The detector shall be kept at some distance from the

test piece (remote from the high temperature
environment) and hence a lens shall be used to focus
the radiation from the centre of the rear face on to
the detector. Therefore all viewing windows and
lenses shall transmit radiation in the appropriate
wavelength band. The sensor shall always be
protected against damage or saturation from the
direct laser beam energy.
5.3.3 Thermocouple, of appropriate type for the
required temperature range, manufactured in
accordance with the tolerances given in
EN 60584-2, allowing use of the reference tables
given in EN 60584-1. The wire diameter shall
be 0,15 mm.

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NOTE 1 The thermocouple may serve a secondary purpose of
monitoring the test piece temperature by switching into a digital
thermometer.

© BSI 04-2000


EN 821-2:1997

The wire ends of the thermocouple shall be prepared
to minimize heat losses from the test piece into the
wires, and are pressed against the test piece by
using fine (1 mm to 2 mm diameter) twin bore

alumina tube and springs.
NOTE 2 Figure 3 shows an example of a test piece and
thermocouple holder suitable for use at ambient temperature and
below.

Non-conducting test pieces shall be coated on the
rear face (see 6.3) in order to effect the
thermocouple junction, where the wires are open
ended and separated by approximately 1 mm. The
extra thickness of the high conductivity coating
shall not increase the transient at t0,5 by more
than 1 % and this shall be checked by calculation.

NOTE 3 The use of a number of thermocouple junctions in
differential mode may be used to increase the sensitivity of
measurement of the transient.

5.4 Signal amplifiers
Signal amplifiers, including spike protections,
analogue-digital converters, high temperature bias
circuitry. They shall have low noise and fast
response so as not to introduce errors into the
transient measurements. None of the electronic
components shall become saturated or the signals
distorted. The integration time shall be less
than 0,3 ms.

1 Brass screw
2 Thermocouple wires
3 Spring

4 Pin-vice chuck
5 Insulating plastic
6 Alumina twin bore tube
7 Polished nickel reflector
8 Transparent plastic
9 Test piece

Figure 3 — Schematic diagram of a typical ambient and low temperature test piece holder

© BSI 04-2000

7


EN 821-2:1997

5.5 Data acquisition system

6 Test pieces

The system for acquiring and storing data may be
either a computer data processor (preferred) or a
storage oscilloscope. The system shall be equipped
with an accurate means of recording the energy
pulse to initiate the recording system, for example a
triggering photocell.

6.1 Sampling

NOTE The computer data processor is able to analyse several

thousands of data points from the transient, and can be
programmed to drive the laser and trigger systems, collect data,
analyse for heat losses etc., print out results and produce plots of
thermal diffusivity against temperature. The oscilloscope is not
very accurate and does require a means to photograph the trace
for manual analysis.
It is important in both cases to verify the accuracy of time bases
and response times.

5.6 Test piece holder
For tests at near ambient temperature or below, the
test piece holder may be constructed from a material
of poor thermal conductivity (e.g. a plastics
material). An example is shown in Figure 3. At
higher temperatures, where plastics materials
become unsuitable, the test piece holder shall be
constructed of suitably refractory materials (metals,
graphite, etc.) in such a manner as to minimize heat
transfer between it and the test piece, e.g. by
allowing the test piece to be clamped at only three
points on or near its periphery. For use at
temperatures below room temperature, the test
piece holder shall be constructed in such a way that
it can be inserted into an evacuated stainless steel
vessel which can be placed inside the cryostat
(see 5.2.3).
When a thermocouple is employed as the transient
detector, the test piece holder shall incorporate a
device which pushes the two thermocouple leads
into contact with the conducting rear surface of the

test piece using a spring arrangement (e.g. as shown
in Figure 3).
The test piece holder shall also be of such design as
to minimize the amount of incident energy arriving
on the sides of the test piece, either directly or
scattered to the transient detector, especially when
an infra-red detector is employed. When using a
laser energy source, the specimen holder shall be
equipped with apertures to the front and rear of the
test piece, the diameters of which are not more
than 0,5 mm and not less than 0,2 mm smaller than
the diameter of the test pieces, such that only the
front face of the test piece receives the energy pulse.
When using a flash-lamp energy source and a
thermocouple as a transient detector, the use of
apertures is advisable to avoid spurious detector
level changes immediately after the heat pulse has
been fired (see clause 8).

8

Test pieces or components should be sampled
according to the guidance given in ENV 1006.
Whenever possible, six test pieces should be cut
(see 6.2) from the same bulk material to obtain a
level of the material variability. Where
measurements are required over a large
temperature range then the minimum number of
test pieces shall be prepared in each of two
thicknesses, one for high temperature and one for

low temperature measurement, with an overlap of
at least two measurement points (for comparison). A
separate test report (see clause 10) is issued for
each test piece.
6.2 Size
The test piece shall be of sufficient size to enable a
circular disc or a square plate of between 6 mm
and 15 mm diameter or side to be exposed to the
laser beam. The bulk material shall be as far as
possible homogeneous, and consist of a single rigid
layer with grain and pore sizes of less than a few
hundred microns, with the exception of single
crystals.
NOTE 1 The microstructure of the ceramic can influence the
results, especially if the material has a high level of porosity, or a
texture on the scale of the thickness of the test piece.

Test pieces for use on the laser system (see 5.1) shall
have a diameter less than the laser rod diameter, or
if a beam expander is used, the expanded spot
diameter, or sides short enough to allow coverage of
the test piece by the laser pulse.
The test piece thickness shall be chosen to be as
follows:
a) representative of the bulk material;
b) thick enough so that the t0,5 value
[see equation (3)] is > 50 times the heat pulse
width, thus reducing the finite pulse time effect,
and so that the transient half time is within the
range 0,025 s to 0,2 s;

NOTE 2 If experimental conditions do not fall within these
limits, then corrections for finite pulse time and/or heat losses
(see Annex B, B.3 and B.2 respectively) should be used.

c) thin enough to minimize the heat loss from the
test piece surface, taking account of b) above.
NOTE 3 Heat losses may also occur through the sample holder
and this can be reduced by holding the sample at three points
only.
NOTE 4 Normally the thickness of a test piece should be > 10
times the scale of any heterogeneities.

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EN 821-2:1997

NOTE 5 The optimum test piece thickness within the range
depends on the magnitude of the estimated thermal diffusivity.
Many ceramics possess a large negative temperature dependence
of thermal diffusivity and as measurement temperatures
increase, t0,5 values increase. Therefore in order to enable
accurate measurement of the rear face temperature rise, with
little or no correction, a second test piece should be used (see 6.1)
with reduced thickness as measurement temperatures increase,
whilst observing the thickness and homogeneity criteria above.

The thickness shall be measured, using a
transducer, to an accuracy of 0,5 %, and be uniform
within ± 1,0 % across a diameter or side of square.

NOTE 6 The diameter or side of square is not critical as the
aperture stop will adjust for any irregularities. However, the
outer diameter should not be in contact with more of the test
piece holder than necessary to give good support, and preferably
at only three points or studs, to minimize the heat loss to the
holder.

6.3 Coating
Test pieces with a highly polished surface shall be
initially roughened by abrasion where the scale of
the surface irregularities is < 0,1 % of the thickness.
NOTE 1 This gives better coating adhesion and more diffuse
absorption.

Test pieces which are transparent or translucent
shall be coated on the front face with a thin layer
designed to absorb the laser beam. The coating shall
be opaque and non-reflective and shall adhere to,
and not react with, the test piece over the
temperature range to be measured. It shall also not
melt or vaporize over this temperature range. All
surfaces shall be degreased before coating.
NOTE 2 Coatings such as platinum, nickel, copper, gold and
colloidal graphite are appropriate.

Test pieces shall also be coated on the rear face. If an
infra-red detector (see 5.3.2) is used, the coating
shall be of high emissivity. If a thermocouple
(see 5.3.3) is used as a transient detector, the
coating shall be electrically conducting. In such a

case, these coatings shall be either vacuum
sputtered metal (aluminium and copper are
suitable), colloidal silver, or other appropriate
highly conducting material. When used with a
thermocouple, the thickness of the coatings shall be
greater than 5 4m.

7 Calibration
7.1 Calibration of apparatus
All of the instruments used in the method or in the
analysis shall be calibrated against traceable
standards. The test piece thickness (L) and
transient half time (t0,5) are required in
equations (2) and (3). Hence it is required that the
calibration of the thickness measurement
transducer (see 6.2) and of the response times
(see clause 5) be known accurately.

© BSI 04-2000

7.2 Calibration of measurement
The measurement of thermal diffusivity by this
method is absolute and calibration of the method
itself is not essential.
NOTE There are no recognized standard reference materials
for thermal diffusivity measurements although several materials
are used as such. The use of such standards is recommended to
check the operation of the equipment. Only alumina has been
used to identify a ceramic standard, but there are recognized
ceramic thermal conductivity standards and these could be used

as reference materials if the specific heat of the material is
accurately known in equation (1). Care should be taken in the use
of these references or standards to ensure that the transient half
time and diffusivity values match closely that of the unknown
materials and that the transient half times are established in
identical ways.

8 Test procedure
Prepare the test piece in accordance with clause 6.
Measure its thickness to the nearest 0,01 mm with
a micrometer.
Place the test piece in the test piece holder (see 5.6),
which is appropriately constructed for the
temperature conditions of measurement.
Assemble the apparatus in an appropriate manner,
ensuring that the trigger photocell can receive
incident radiation, that the temperature
measurement thermocouple is correctly positioned
to record the test piece temperature, and that if
appropriate, the thermocouple used as a rear-face
transient detector is making good electrical contact
through the test piece or its coating.
Allow the test piece to heat or cool to the required
measurement temperature and maintain this
temperature for at least 10 min, or until the
temperature drift recorded is less than 0,01 K/s,
whichever takes the greater time. Record the test
piece temperature.
Adjust the amplification of the transient detector
circuit, and offset any detector voltage to zero such

that a transient with low noise covers at least 75 %
of the monitor screen. Energize the heat pulse
source, set all trigger circuits and arm the data
acquisition system. When the test piece
temperature is stable, fire the heat pulse source and
collect data for up to 10 times the recorded half rise
time value, including 5 % pre-flash and 95 %
post-flash information.
NOTE If a significant change in detector voltage occurs
between the pre-flash and immediate post-flash levels, the
assembly of the systems is examined for evidence of heat pulse
energy directly affecting the detector, e.g. if the test piece has
cracked due to thermal damage.

Perform at least three determinations at each test
piece temperature.

9


EN 821-2:1997

9 Results
9.1 Principle of calculation
In theory, any point on the rise curve can be
analysed to yield the thermal diffusivity, a. This will
be given by equation (2) as follows:
(2)
where
L

tx
x
Wx

is the test piece thickness in millimetres;
is the time for the test piece rear face to
reach a fraction of the maximum
temperature, in seconds (see Table 1);
is the percentage of the maximum rise in
temperature;
is a constant relating a to L and tx in the
absence of radiation loss and finite pulse
corrections.

Table 1 gives a few of the Wx values with
corresponding tx values for an ideal curve (i.e. no
corrections).
Table 1 — Values of constant Wx for a range of
transient times
x

Wx (equation 2)

tx

10

0,653

t0,1

20

0,832

t0,2

30

0,999

t0,3

40

1,174

t0,4

50

1,370

t0,5

60

1,601

t0,6

70

1,894

t0,7

80

2,302

t0,8

90

2,996

t0,9

To evaluate the thermal diffusivity, a, proceed using
the calculation methods given in 9.2 or 9.3.
NOTE 1 It is recommended that more than one evaluation
technique is used to ensure the reproducibility of the result.

t0,5 is the time from the initiation of the pulse
until the rear face of the piece reaches one
half of its maximum temperature, in
seconds.
Check the thermal diffusivity values at fractional
temperature rises other than t0,5. If the values at t0,3,

t0,5 and t0,7 calculated using the relevant values of Wx
in Table 1 are all within ± 2 % then it can be
assumed that no corrections apply and the accuracy
of the measurements lie within the range ± 5 %.
If the spread of thermal diffusivity values so
calculated is greater than ± 2 %, analyse the
response curve for radiation heat loss, finite pulse
time effects, or non-uniform heating effects.
NOTE 1 Examples of such analyses are given in Annex B, and
references to further methods are given in Annex C.

Use two different methods to analyse the rising and
declining parts of the thermal transient. If results
from two different methods differ by more than 5 %
the original data are suspect, and the experimental
set-up shall be re-examined to check for the
electronic drift or for heat reaching the test piece
through the test piece holder.
If it is not possible to adjust the sample thickness to
achieve t0,5 greater than 50 times the heat pulse
width [see b) of 6.2], then apply a finite pulse time
correction.
NOTE 2

Annex B gives an example of such a correction method.

Make regular inspection procedures of the energy
beam profile and any system optics, since
non-uniform heating effects can seriously distort the
curve.

At temperatures differing considerably from room
temperature, consideration shall be given as to
whether a correction is applicable to the thickness L
because of thermal expansion changes with
temperature. For example, a material with a linear
thermal expansion coefficient of 10 × 10–6 K–1 will
increase L by 1 % at 1 000 °C and the true value will
be 2 % larger than the measured or calculated value
to which a correction is not applied.
9.3 Alternative methods of calculation

Methods of calculation other than that given in 9.2
and corrections other than those in Annex B are
Calculate the thermal diffusivity, a, from equation 3 permitted. If such alternative methods are used,
these shall be mentioned in the test report
(3) [see 10 l)] giving full details and/or references.
9.2 Calculation based on t0,5

NOTE References citing some alternative methods are given in
Annex C.

where:
L

10

is the test piece thickness, in millimetres;

© BSI 04-2000

EN 821-2:1997

10 Test report
The test report shall include the following
information:
a) the name and address of the testing
establishment;
b) the date of the test; unique identification of
report and each page, customer name and
address and signatory;
c) a reference to this standard, i.e. “Determined
in accordance with EN 821-2”;
d) the description of the test material; (material
type, manufacturing code, batch number, date of
receipt);
e) method of production of test pieces from
supplied material;
f) test piece thicknesses, and thickness and type
of coatings;
g) measurement temperature(s);
h) heat pulse source and pulse width;
i) transient detector employed;

j) environmental conditions, i.e. vacuum, inert
gas, etc.;
k) measured values of transient half time t0,5, in
seconds;
l) the method of calculation employed, giving full
details if not that in 9.2;

m) the thermal diffusivity value(s) in m2/s;
n) calculated values of heat loss corrections, if
any, giving full details if not the methods given in
Annex B;
o) calculated value of finite pulse time correction,
if any, giving full details if not the methods given
in Annex B;
p) a statement regarding the thermal expansion
of the test piece and whether or not a correction
to the thickness was applied;
q) a statement regarding the use or otherwise of
a reference material for checking purposes;
r) discussion of errors and correction procedures;
s) comments about the test or test results.

Figure 4 — Heat loss correction curves

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11


EN 821-2:1997

Annex A (informative)
Fundamental equations for calculation
Following Parker’s method (reference 1, Annex C) and using an assumption of no heat losses, the general
heat transmission equation for linear flow of heat between two parallel planes is given by:

It can be shown that the temperature rise %T at the rear face of a parallel sided test piece of thickness L

subjected to a heat pulse of short duration absorbed in a finite element of the front surface is given by:

and:

At any time t, the rear surface will rise to a fraction of Tmax:

When V = 0,5:

hence:
[equation (3), in 9.2]
where t0,5 is the time, in seconds, taken for the sample rear face to reach one half of its maximum
temperature. Hence for unidirectional heat flow, uniform irradiation of the sample front surface and no
corrections for heat losses and finite pulse time effects, the thermal diffusivity a of a material is calculated
from equation (3).
However, any point on the transient curve can be measured, e.g. t0,1 to t0,9, and the more general
equation (2) can be used:
[equation (2), in 9.1]
where Wx is a function of tx. Table 1 shows the values of Wx applicable to values of tx when no heat losses or
other corrections apply When corrections are applied, these alter the value of Wx in equation (2)
(see Annex B).

Annex B (informative)
Deviations from ideal behaviour
B.1 General
The calculation of thermal diffusivity using equations (2) or (3) is modified if heat is lost from the sample
or if the pulse transit time is less than 25 times the duration of the heat pulse. Example modifications
applying to the calculation method given in 9.2 are described in B.2 to B.3.

12

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EN 821-2:1997

B.2 Heat loss correction
B.2.1 General
The mathematical derivation given in Annex A assumes that no heat is lost from the test piece during the
time taken for the heat pulse to pass through it. For good conductors at temperatures close to ambient, this
is a reasonable approximation, but for poor conductors and for most samples at high temperatures,
corrections for heat losses will almost certainly be applicable. Provided that use of a suitable holder design
has minimized heat lost from the test piece by conduction and that the duration of the transient is short
enough for heat lost by convection to be neglected (there are no convective losses if the measurement is
performed in vacuum), the main source of heat loss is by radiation from the test piece surfaces.
The best way to analyse heat loss is to compare the entire experimental curve with one or more of the many
theoretical models available.
Examples of analytical methods are given in the references in Annex C. Two suitable techniques that
modify the W0,5/;2 parameter in the thermal diffusivity evaluation in equation (3) are described below.
B.2.2 Example procedure
Two heat loss correction techniques are used, one based on the rising portion of the temperature/time
curve, and one based on the decaying portion.
Data capture of the rear surface temperature/time transient can continue out to 5t0,5 or 10t0,5
(see Figure 1). This choice will depend on the type of recording equipment used. The use of 10t0,5 will
provide the most reliable heat loss correction and is best suited to a computer data acquisition system. The
use of 5t0,5 is best suited for use with an oscilloscope where the amount of data recorded is limited.
NOTE

The original sources of these methods are given in Annex C.

a) Rise time correction (Clark and Taylor’s method; reference 8 in Annex C).

From the data recorded, calculate the ratio t0,75/t0,25 (see Figure 1), then a value for W0,5/;2 for use in
equation (3) can be calculated:
W0,5/;2 = – 0,3461467 + 0,361578(t0,75/t0,25) – 0,06520543(t0,75/t0,25)2

(B.1)

Corrections based on other ratios (e.g. t0,7/t0,3 or t0,8/t0,2) are possible, but should be stated in the report.
b) Decay time correction (Cowan’s method; reference 9 in Annex C).
From the data recorded, calculate the ratio %T(10t0,5)/%T(t0,5) or %T(5t0,5)/%T(t0,5), where %T(10t0,5)
and %T(5t0,5) are the rises in rear surface temperature at times of 10t0,5and 5t0,5respectively, and %T(t0,5) is
the temperature rise at t0,5. The new value of W0,5/;2 (allowing for heat loss) is then read from the graph in
Figure 4 and can be used in equation (3) to calculate the thermal diffusivity at t0,5.
Alternatively, it can be found from the following polynomial equation:
W0,5/;2 = A + BỴ + CỴ2 + DỴ3 + 4 + FỴ5 + GỴ6 + HỴ7

(B.2)

where Î = %T(10t0,5)/%T(t0,5) or %T(5t0,5)/%T(t0,5), and the coefficients A to H are given in Table B.1. These
data in Table B.1 were prepared by reference 10 in Annex C by digitising the curves in the original
reference 9 in Annex C (see Figure 4).
Table B.1 — Coefficients for the decay
time heat loss correction
Coefficient

ẻ = %T(5t0,5)/%T(t0,5)

ẻ = %T(10t0,5)/%T(t0,5)

A

1,37197

B

6,60729

0,225519

C

13,4875

0,608794

D

14,2789

1,09003

E

8,33319

1,14911

F

2,54624

G

0,318889

H

0

â BSI 04-2000

0,0512553

0,694679
– 0,222146
0,0291019

13


EN 821-2:1997

B.3 Finite pulse time effect (reference 13 in Annex C)
When t0,5 is less than 50 times the heat pulse duration, the shape of the heat pulse influences the shape of
the temperature transient at the rear surface of the test piece. The shape of the heat pulse from a
neodymium-glass laser and a flash-lamp can be approximated by a triangular pulse of duration Ù with a
maximum occurring at ¶.Ù where ¶ is a fraction between zero and one. To apply the finite pulse correction
it is necessary to know Ù and ¶ for the equipment being used.
This is most easily achieved by using a fast response photodiode (as used in several laser calorimeters) or
by measuring the change in resistance of a thin (approximately 25 4m) tantalum foil strip when subjected
to the heat pulse. The parameters Ù and ¶ usually change with the heat pulse power and so should be

determined at the power to be used.
Once Ù and ¶ are known, the thermal diffusivity a is given by the equation:
(B.3)
where the constants C1 and C2 are given in Table B.2 for values of ¶ (see also reference 4 in Annex C).
Table B.2 — Finite pulse time correction
constants
¶

C1

C2

0,15

0,34844

2,5106

0,28

0,31550

2,2730

0,29

0,31110

2,2454

0,30

0,30648

2,2375

0,50

0,27057

1,9496

The finite pulse time correction given in equation (B.3) should not be used for t0,5 less than 10Ù: thicker
samples should be used or the pulse width reduced.

Annex C (informative)
Bibliography
General references and calculation methods
1 Parker, W J, Jenkins, R J, Butler, C P, Abbot, G L, Flash method for determination of thermal diffusivity,
heat capacity and thermal conductivity, J Appl. Phys., 32, 1679-84, 1961.
2 Taylor, R, An investigation of the heat pulse method for measuring thermal diffusivity, Brit J Appl.
Phys, 16, 509-15, 1965.
3 Beedham, K, Dalrymple P, The measurement of thermal diffusivity by the flash method. An investigation
into errors arising from the boundary conditions, Rev. Hautes Temp. Refr. 7, 278-83, 1970.
4 Righini, F, Cesairliyan, A, Pulse method of thermal diffusivity measurements (a review), High temps.
High Press. 5, 481–501, 1973.
5 Degiovanni, A, Diffusivité et méthode flash. Conférence de la SFT (1976), Rev Génerale de
Thermique, 1977.
6 Degiovanni, A, Identification de la diffusivite thermique pour l’utilisation des moments temporals partiels,
High Temperature — High Pressure, 17, 683-9, 1985.

7 Takahashi, Y, Yamamoto, K, Ohsato, T, Advantages of logarithmic method — a new method for
determining thermal diffusivity in the laser flash technique, Netsu Sokutei 15, 103-9, 1988 (In Japanese).
Radiation losses
8 Clark, L M III, and Taylor, R E, Radiation loss in the flash method for thermal diffusivity, J Appl.
Phys. 34, 714-9, 1963.
9 Cowan, R D, Pulse method of measuring thermal diffusivity at high temperatures, J Appl.
Phys. 34, 926-7, 1963.
10 Preston, S D, AEA Technology Ltd, Risley, UK, 1993.

14

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EN 821-2:1997

Finite pulse time effects
11 Cape, J A, Lehmann, G W, Temperature and finite pulse time effects in the flash method for measuring
thermal diffusivity, J Appl. Phys. 34, 1909-13, 1963.
12 Heckman, R C, Finite pulse time and heat loss effects in pulse thermal diffusivity measurement, J Appl.
Phys. 44, 1455-60, 1973.
13 Taylor, R E, Clark III, L M, Finite pulse time effects in flash diffusivity method, High Temperatures —
High Pressures, 6, 65–72, 1974.
14 Larsen, K B, Koyama, K, Correction for finite pulse time effects in very thin samples using the flash
method of measuring thermal diffusivity, J Appl. Phys. 39, 4408-16, 1968.
Non-uniform heating effects
15 Mackay, J A. Schriempf, P, Corrections for non-uniform surface heating errors in flash-method
thermal-diffusivity measurements, J Appl. Phys. 47, 1668-71, 1976
European Standards and Prestandards
16 EN 60825 Safety of laser products — Equipment classification, requirements and user’s guide

17 ENV 1006 Advanced technical ceramics — Methods of testing monolithic ceramics — Guidance on the
sampling and selection of test pieces

© BSI 04-2000

15


BS EN
821-2:1997

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