ASTM E1461-92

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Designation: E 1461 – 92
Standard Test Method for
Thermal Diffusivity of Solids by the Flash Method
This standard is issued under the fixed designation E 1461; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (e) indicates an editorial change since the last revision or reapproval.
,
2 3
1. Scope parison Techniques
E 230 Temperature-Electromotive Force (EMF) Tables for
1.1 This test method covers the determination of the thermal
Thermocouples
diffusivity of homogeneous solid materials. Thermal diffusivity
values ranging from 0.1 to 1000 mm /s are readily measurable
3. Terminology
by this test method and measurements can be made from about
3.1 Definitions:
100 to 2500 K normally in a vacuum or inert gas environment.
3.1.1 thermal conductivity, l, of a solid material—the time
1.2 This test method is a more detailed form of Test Method
rate of steady heat flow through unit thickness of an infinite
C 714 but has applicability to much wider ranges of materials,
slab of a homogeneous material in a direction perpendicular to
applications, and temperatures with improved accuracy of
the surface, induced by unit temperature difference.
measurement.
3.1.1.1 Discussion—Where other modes of heat transfer are
1.3 This test method is applicable to the measurement of a
present in addition to conduction, this property is often referred
wide variety of homogeneous opaque materials and, with
to as apparent or effective thermal conductivity, e or app.
special precautions, can be used on transparent and some
3.1.1.2 Discussion—For practical purposes, the lateral ex-
porous and composite materials.
tent of a slab is considered to be infinite when heat flow
1.4 This test method is intended to allow a wide variety of
laterally is less than 2 % of the transverse flow.
apparatus design and design accuracies to satisfy the require-
3.1.1.3 Discussion—The property must be identified with
ments of specific measurements problems. It is not practical in
both a specific mean temperature, since it varies with tempera-
a test method of this type to establish details of construction
ture, and for a direction and orientation of thermal transmission
and procedures to cover all contingencies that might offer
since some bodies are not isotropic with respect to the thermal
difficulties to a person without pertinent technical knowledge
conductivity.
or to stop or restrict research and development for improve-
3.1.2 thermal diffusivity, a, of a solid material—the prop-
ments in the basic technique.
erty given by the thermal conductivity divided by the product
1.5 This test method can be considered an absolute (or
of the density and heat capacity per unit mass.
primary) method of measurement since no heat flux reference
3.2 Definitions:
standards are required except for verification purposes and to
3.2.1 a—1/(1 + 0.667 l /l ).
T s
confirm accuracy statements.
3.2.2 D—diameter, meters.
1.6 The values stated in SI units are to be regarded as the
3.2.3 k—constants in solution to diffusion equation.
standard.
3.2.4 L—specimen thickness, meters.
1.7 This standard does not purport to address all of the
3.2.5 t—response time, seconds.
safety problems, if any, associated with its use. It is the
3.2.6 t*—dimensionless time ( t*=4a t/D T).
s
responsibility of the user of this standard to establish appro-
3.2.7 T—temperature, Kelvins.
priate safety and health practices and determine the applica-
3.2.8 a—thermal diffusivity, m /s.
bility of regulatory limitations prior to use.
3.2.9 l—thermal conductivity, W/m.K.
2. Referenced Documents 3.2.10 b—fraction of pulse duration required to reach
maximum intensity.
2.1 ASTM Standards:
3.2.11 Dt —T (5t ⁄2 /T (t ⁄2)).
C 714 Test Method for Thermal Diffusivity of Carbon and 5
1 1
3.2.12 Dt —T (10t ⁄2/T (t ⁄2 )).
Graphite by a Thermal Pulse Method
3.3 Definitions:
E 220 Method for Calibration of Thermocouples by Com-
3.3.1 o—ambient.
3.3.2 s—specimen.
3.3.3 T—thermocouple.
This test method is under the jurisdiction of ASTM Committee E-37 on
3.3.4 x—percent rise.
Thermal Measurements and is the direct responsibility of Subcommittee E37.05 on
Thermophysical Properties.
Current edition approved Feb. 15, 1992. Published April 1992.
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Annual Book of ASTM Standards, Vol 15.01. Annual Book of ASTM Standards, Vol 14.03.
Copyright © ASTM, 100 Barr Harbor Drive, West Conshohocken, PA 19428-2959, United States.
E 1461
3.3.5 C—Cowan. 6. Interferences
3.3.6 R—ratio.
6.1 Experimental results are subject to two general types of
3.3.7 m—maximum.
errors:
3.3.8 t—time.
6.1.1 Measurement errors associated with uncertainties that
exist in measured quantities used to compute the thermal
4. Summary of Test Method
diffusivity from experimental data. The units of thermal
4.1 A small, thin, disc specimen mounted horizontally or diffusivity are length and time. Because test specimens are
vertically is subjected to a high-intensity short duration thermal relatively thin (generally 1.5 to 4 mm) and the thickness enters
pulse. The energy of the pulse is absorbed on the front surface as a squared term, uncertainties in the determination of the
of a specimen and the resulting rear face temperature rise is thickness can be very significant. The time is that observed for
measured. The ambient temperature of the specimen is con- the rear face temperature to attain a certain percentage of the
trolled by a furnace or cryostat. Thermal diffusivity values are maximum rise. This latter measurement involves determining a
calculated from the specimen thickness and the time required base line, the maximum rise above the base line, and the time
for the rear face temperature rise to reach certain percentages of initiation of the heat pulse as an integral part of the time
of its maximum value. This test method is described in detail
determination. Response times of the detectors and amplifiers
in a number of publications (1, 2) and review articles (3, 4, 5) are extremely important. Response time effects are considered
and has been standardized in Test Method C 714 in a more
in detail in 7.1.3. Measurement errors have been discussed in
simple form for carbons and graphites. some detail (5, 14, 15).
6.1.2 Non-measurement errors associated with deviations of
NOTE 1—While this test method was developed for and applied
actual experimental conditions as they exist during the experi-
originally to homogeneous opaque solids, in which a large front face
ment from the boundary conditions assumed in the mathemati-
temperature excursion was not detrimental, it can be extended under
appropriate conditions to a wide variety of materials and situations. These cal model used to derive the equation for computing the
include heterogeneous specimens of dispersed composites (6), layered
thermal diffusivity. The major sources of non-measurement
structures (7, 8) translucent materials, liquids and coatings (9, 10) and the
errors are finite pulse time effect, heat losses or gains, and
measurement of contact conductance and resistance (11, 12).
non-uniform heating. The mathematical derivation assumes
that the energy pulse is delivered in times short compared to
4.2 The pulse raises the temperature of the specimen only a
the rise time. The case where this is not true is called the finite
few degrees above its initial ambient value. However, initially
pulse time effect and it becomes important when the duration
all of this energy is deposited on the front surface and this
of the energy pulse is greater than 2 % of the half rise time. It
temperature may rise many degrees. If this should damage the
should be noted that these three effects are not strictly classified
specimen, a layer of a material with known properties (thermal
as errors (may be determined experimentally) but are merely
diffusivity, specific heat and density) and measured thickness
deviations from an ideal situation in which these effects are
can be attached to the front surface and results on the
assumed to be negligible. It is assumed that the material is
composite specimen analyzed using a two-layer method. This
opaque, that is, radiation from the energy source heats only the
requires that the specific heat and density of the specimen also
specimen surface. Furthermore, it is assumed that the tempera-
be known (13).
ture sensor follows accurately the rear surface temperature
excursion. Thus, if an i.r. detector is used, it must not view into
5. Significance and Use
the specimen interior. Specimens of translucent/transparent
5.1 Thermal diffusivity is an important property required for
materials require special techniques similar to those used for
such purposes as design applications under transient heat flow
layered structures.
conditions, determination of safe operating temperature, pro-
cess control, and quality assurance.
7. Apparatus
5.2 The flash method is used to measure values of thermal
7.1 The essential features of the apparatus are shown in Fig.
diffusivity (a) of a wide range of solid materials. It is
1. These are the flash source, sample holder and environmental
particularly advantageous because of the simple specimen
geometry, small specimen size requirements, rapidity of mea-
surement, and ease of handling materials having a wide range
of thermal diffusivity values over a large temperature range
with a single apparatus. The short measurement times involved
reduce the chances of contamination and change of specimen
properties due to exposure to high temperature environments.
5.3 Thermal diffusivity results in many cases can be com-
bined with values for specific heat (C ) and density (r) and
p
used to derive thermal conductivity (l) from the relation l = a
C r.
p
The boldface numbers given in parentheses refer to a list of references at the
end of the text. FIG. 1 Flash Diffusivity Apparatus (Schematic)
E 1461
system, temperature response detector, and data collection and behavior is best represented by Eq 2:
analysis components.
T 2 T 2
t 0
a
5 1 2 ~1 2 a!e t* Erfc ~at*! (2)
7.1.1 The flash source may be a laser, a flash lamp, or an
Tv2 T
electron beam. The duration of the energy flash should be less
than 0.02 of the time required for the rear face temperature rise
where:
to reach one-half of its maximum values (see Fig. 1). If this
T and T are shown in Fig. 2, t* is dimensionless time
0 ‘
condition is not met, it is necessary to correct the data for the
(t*=4a t/D T), and a is approximated by 1/(1 + 0.667 l T/l ).
s s
finite pulse time effect (16, 17, 18, 19). The energy source shall
In order to obtain the fastest response, small diameter thermo-
have uniform intensity over the front surface of the specimen.
couple wire of an alloy having a low thermal conductivity
The rear face temperature rise shall be kept to a few Kelvin.
attached to a substrate of high thermal diffusivity should be
7.1.2 An environmental control chamber for vacuum or
used. For example, a 25 μm constantan wire on a copper
inert gas environment is required for measurements above and
substrate, requires 3 μg to reach 95 % of steady-state. How-
below room temperature. Unless the source is enclosed within
ever, for the converse of this example, for example 25μ m
the chamber, for example, as for the case of an electron beam
copper wire on a constantan substrate, it is found that 15 ms are
source, the enclosure shall be fitted with a window which is
required to reach 95 % of the steady-state. This is 5000 fold
transparent to the flash source. A second window is required if
slower than the first example. Thus, the proper selection of
optical detection of the temperature rise curve is used and the
materials, based upon their thermal properties and geometries,
optical detector must be shielded from direct exposure to the
is essential for accurate measurement of transient responses
energy beam.
using intrinsic thermocouples (21).
7.1.2.1 The furnace or cryostat should be loosely coupled
7.1.3.2 Eq 1 and Eq 2 relate to the minimum response time
(thermally) to the specimen support system and shall be
possible for a thermocouple. Proper attachment of the thermo-
capable of maintaining the specimen temperature constant
couple is important since if the thermocouple is attached poorly
within 4 % of the maximum temperature rise over a time
to the specimen, the effective response time can be much
period equal to five half rise times. The furnace may be
longer. The preferred method for electrical conducting materi-
horizontal or vertical. The specimen support shall also be
als is to spotweld intrinsic thermocouples, that is, non-beaded
loosely coupled thermally to the specimen point contacts or
couples where each leg is independently attached to the
equivalent supports. Depending on specimen orientation point
specimen about 1 mm apart. For electrical insulators where
contacts or equivalent supports, constructed with low thermal
spot welding is not feasible, it may be possible to spring-load
diffusivity materials, are the preferred means.
the thermocouple against the back surface. For materials with
7.1.3 The detector can be a calibrated thermocouple (see
low diffusivity values, it may be preferred to spot-weld
Method E 220 and Tables E 230), infrared detector or auto- thermocouples onto a thin high thermal conductivity metallic
matic optical pyrometer. It shall be capable of detecting 50 mK
sheet and spring-load or paste this sheet onto the specimen.
change above the ambient temperature. It is desirable that the Metal-epoxy and graphite pastes have been used successfully
detector response be linear with temperature over a few
to bond layers together. This eliminates the problem of using
degrees and that the rear face temperature rise be limited to this thermocouples of relatively high diffusivity to measure speci-
range. The time response of the detector and its associated
mens of materials of low thermal diffusivity, that can lead to
amplifier is extremely important. While the response time of very large response times (see Eq 1).
the detectors in optical instruments is often orders of magni-
7.1.3.3 When using remote temperature sensing, several
tude faster than required for the flash method, the detector precautions are required. The sensor must be focused on the
signal is fed into amplifiers and filters having response times
center of the back surface. The sensor must be protected from
which can be slow enough to effect transient readings. There- the energy beam to prevent damage or saturation. When the
fore, the response time of the total circuit must be checked
specimen is housed in a furnace, the energy
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