ASTM E289-04(2010)
(Test Method)Standard Test Method for Linear Thermal Expansion of Rigid Solids with Interferometry
Standard Test Method for Linear Thermal Expansion of Rigid Solids with Interferometry
SIGNIFICANCE AND USE
Coefficients of linear expansion are required for design purposes and are used particularly to determine thermal stresses that can occur when a solid artifact composed of different materials may fail when it is subjected to a temperature excursion(s).
Many new composites are being produced that have very low thermal expansion coefficients for use in applications where very precise and critical alignment of components is necessary. Push rod dilatometry such as Test Methods D696, E228, and TMA methods such as Test Methods E831 are not sufficiently precise for reliable measurements either on such material and systems, or on very short specimens of materials having higher coefficients.
The precision of the absolute method allows for its use to:
Measure very small changes in length;
Develop reference materials and transfer standards for calibration of other less precise techniques;
Measure and compare precisely the differences in coefficient of “matched” materials.
The precise measurement of thermal expansion involves two parameters; change of length and change of temperature. Since precise measurements of the first parameter can be made by this test method, it is essential that great attention is also paid to the second, in order to ensure that calculated expansion coefficients are based on the required temperature difference. Thus in order to ensure the necessary uniformity in temperature of the specimen, it is essential that the uniform temperature zone of the surrounding furnace or environmental chamber shall be made significantly longer than the combined length of specimen and mirrors.
This test method contains essential details of the design principles, specimen configurations, and procedures to provide precise values of thermal expansion. It is not practical in a method of this type to try to establish specific details of design, construction, and procedures to cover all contingencies that might present difficulties to a person not having the technic...
SCOPE
1.1 This test method covers the determination of linear thermal expansion of rigid solids using either a Michelson or Fizeau interferometer.
1.2 For this purpose, a rigid solid is defined as a material which, at test temperature and under the stresses imposed by instrumentation, has a negligible creep, insofar as significantly affecting the precision of thermal length change measurements.
1.3 It is recognized that many rigid solids require detailed preconditioning and specific thermal test schedules for correct evaluation of linear thermal expansion behavior for certain material applications. Since a general method of test cannot cover all specific requirements, details of this nature should be discussed in the particular material specifications.
1.4 This test method is applicable to the approximate temperature range −150 to 700°C. The temperature range may be extended depending on the instrumentation and calibration materials used.
1.5 The precision of measurement of this absolute method (better than ±40 nm/(m·K)) is significantly higher than that of comparative methods such as push rod dilatometry (for example, Test Methods D696 and E228) and thermomechanical analysis (for example, Test Method E831) techniques. It is applicable to materials having low and either positive or negative coefficients of expansion (below 5 μ m/(m·K)) and where only very limited lengths or thickness of other higher expansion coefficient materials are available.
1.6 Computer or electronic based instrumentation, techniques and data analysis systems equivalent to this test method can be used. Users of the test method are expressly advised that all such instruments or techniques may not be equivalent. It is the responsibility of the user to determine the necessary equivalency prior to use.
1.7 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.
1.8 This standard...
General Information
Relations
Standards Content (Sample)
NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
Designation:E289 −04(Reapproved 2010)
Standard Test Method for
Linear Thermal Expansion of Rigid Solids with
Interferometry
This standard is issued under the fixed designation E289; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope 1.7 The values stated in SI units are to be regarded as
standard. No other units of measurement are included in this
1.1 This test method covers the determination of linear
standard.
thermal expansion of rigid solids using either a Michelson or
1.8 This standard does not purport to address all of the
Fizeau interferometer.
safety concerns, if any, associated with its use. It is the
1.2 For this purpose, a rigid solid is defined as a material
responsibility of the user of this standard to establish appro-
which, at test temperature and under the stresses imposed by
priate safety and health practices and determine the applica-
instrumentation, has a negligible creep, insofar as significantly
bility of regulatory limitations prior to use.
affectingtheprecisionofthermallengthchangemeasurements.
2. Referenced Documents
1.3 It is recognized that many rigid solids require detailed
preconditioning and specific thermal test schedules for correct
2.1 ASTM Standards:
evaluation of linear thermal expansion behavior for certain
D696TestMethodforCoefficientofLinearThermalExpan-
material applications. Since a general method of test cannot
sion of Plastics Between −30°C and 30°C with a Vitreous
cover all specific requirements, details of this nature should be
Silica Dilatometer
discussed in the particular material specifications.
E220Test Method for Calibration of Thermocouples By
Comparison Techniques
1.4 This test method is applicable to the approximate
E228Test Method for Linear Thermal Expansion of Solid
temperature range −150 to 700°C. The temperature range may
Materials With a Push-Rod Dilatometer
be extended depending on the instrumentation and calibration
E473Terminology Relating to Thermal Analysis and Rhe-
materials used.
ology
1.5 The precision of measurement of this absolute method
E831Test Method for Linear Thermal Expansion of Solid
(better than 640 nm/(m·K)) is significantly higher than that of
Materials by Thermomechanical Analysis
comparative methods such as push rod dilatometry (for
E1142Terminology Relating to Thermophysical Properties
example, Test Methods D696 and E228) and thermomechani-
cal analysis (for example, Test Method E831) techniques. It is 3. Terminology
applicable to materials having low and either positive or
3.1 Definitions:
negative coefficients of expansion (below 5 µ m/(m·K)) and
3.1.1 The following terms are applicable to this document
where only very limited lengths or thickness of other higher
and are listed in Terminology E473 and E1142: coefficient of
expansion coefficient materials are available.
linear thermal expansion, thermodilatometry, thermomechani-
cal analysis.
1.6 Computer or electronic based instrumentation, tech-
3.2 Definitions of Terms Specific to This Standard:
niquesanddataanalysissystemsequivalenttothistestmethod
3.2.1 mean coeffıcient of linear thermal expansion, α , the
canbeused.Usersofthetestmethodareexpresslyadvisedthat
m
all such instruments or techniques may not be equivalent. It is average change in length relative to the length of the specimen
accompanying a change in temperature between temperatures
the responsibility of the user to determine the necessary
equivalency prior to use. T and T , expressed as follows:
1 2
1 L 2 L 1 ∆L
2 1
αm 5 · 5 · (1)
L T 2 T L ∆T
0 2 1 o
This test method is under jurisdiction of ASTM Committee E37 on Thermal
Measurements and is the direct responsibility of Subcommittee E37.05 on Thermo-
physical Properties. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Current edition approved March 1, 2010. Published May 2010. Originally contact ASTM Customer service at service@astm.org. For Annual Book of ASTM
approved in 1965. Last previous edition approved in 2004 as E289–04. DOI: Standards volume information, refer to the standard’s Document Summary page on
10.1520/E0289-04R10. the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E289−04 (2010)
where:
α isobtainedbydividingthelinearthermalexpansion(∆L/L )
m 0
by the change of temperature (∆T). It is normally expressed as
µm/m·K. Dimensions (L) are normally expressed in mm and
wavelength (λ)innm.
3.2.2 thermalexpansivity,α ,attemperatureT,iscalculated
T
as follows from slope of length v temperature curve:
1 L 2 L 1 dL
2 1
limit
α 5 5 withT ,T ,T (2)
T T →T 1 i 2
2 1
L T 2 T L dT
i 2 1 i
and expressed as µm/m·K.
NOTE1—Thermalexpansivityissometimesreferredtoasinstantaneous
coefficient of linear expansion.
3.3 Symbols:
3.3.1 α =mean coefficient of linear thermal expansion, see
m
3.2.2,/K .
3.3.2 α =expansivity at temperature T, see 3.2.1,/ K .
T FIG. 1 Typical Specimen Configurations (a) Michelson Type,
(b–d) Fizeau Type
3.3.3 L =original length of specimen at temperature T ,
0 0
mm.
3.3.4 L =length at temperature T , mm.
1 1
length change from which the expansion and expansion coef-
3.3.5 L =length at temperature T , mm.
2 2
ficient can be determined (1-5).
3.3.6 ∆L=change in length of specimen between tempera-
tures T and T , nm.
1 2 5. Significance and Use
3.3.7 ∆L =changeinlengthofreferencespecimenbetween
s
5.1 Coefficients of linear expansion are required for design
T and T , mm.
1 2
purposes and are used particularly to determine thermal
3.3.8 T =temperature at which initial length is L , K.
0 0 stresses that can occur when a solid artifact composed of
3.3.9 N=number of fringes including fractional parts that
different materials may fail when it is subjected to a tempera-
are measured on changing temperature from T to T .
ture excursion(s).
1 2
3.3.10 n=index of refraction of gas at temperature T and
5.2 Many new composites are being produced that have
pressure, P.
very low thermal expansion coefficients for use in applications
3.3.11 n =index of refraction of gas at reference condition
where very precise and critical alignment of components is
r
of temperature 288K and pressure of 100 kPa.
necessary. Push rod dilatometry such as Test Methods D696,
E228, and TMA methods such as Test Methods E831 are not
3.3.12 n , n =index of refractive of gas at temperature T
1 2 1
sufficiently precise for reliable measurements either on such
and T , and pressure, P.
material and systems, or on very short specimens of materials
3.3.13 P=average pressure of gas during test, torr.
having higher coefficients.
3.3.14 T , T =two temperatures at which measurements
1 2
5.3 The precision of the absolute method allows for its use
are made, K.
to:
3.3.15 ∆T=temperature difference between T and T , K.
2 1
5.3.1 Measure very small changes in length;
3.3.16 λ =wavelengthoflightusedtoproducefringes,nm.
v
5.3.2 Developreferencematerialsandtransferstandardsfor
calibration of other less precise techniques;
4. Summary of Test Method
5.3.3 Measure and compare precisely the differences in
4.1 A specimen of known geometry can be given polished
coefficient of “matched” materials.
reflective ends or placed between two flat reflecting surfaces
5.4 Theprecisemeasurementofthermalexpansioninvolves
(mirrors). Typical configurations, as shown in Fig. 1, are a
two parameters; change of length and change of temperature.
cylindricaltubeorarodwithhemisphericalorflatparallelends
Sinceprecisemeasurementsofthefirstparametercanbemade
or machined to provide a 3-point support. The mirrors consist
by this test method, it is essential that great attention is also
of flat-uniform thickness pieces of silica or sapphire with the
paidtothesecond,inordertoensurethatcalculatedexpansion
surfaces partially coated with gold or other high reflectance
coefficients are based on the required temperature difference.
metal. Light, either parallel laser beam (Michelson, see Fig. 2
Thusinordertoensurethenecessaryuniformityintemperature
and Fig. 3) or from a point monochromatic source (Fizeau, see
of the specimen, it is essential that the uniform temperature
Fig. 4) illuminates each surface simultaneously to produce a
zone of the surrounding furnace or environmental chamber
fringe pattern.As the specimen is heated or cooled, expansion
or contraction of the specimen causes a change in the fringe
pattern due to the optical pathlength difference between the
The boldface numbers in parentheses refer to a list of references at the end of
reflecting surfaces. This change is detected and converted into this standard.
E289−04 (2010)
FIG. 2 (a) Principle of the Single Pass Michelson Interferometer, (b) Typical Single Pass System
FIG. 3 Typical Double Pass Michelson Interferometer System
FIG. 4 Principle of the Fizeau Interferometer
shall be made significantly longer than the combined length of
specimen and mirrors.
refractive index of air or other gases at normal pressures.
5.5 This test method contains essential details of the design
However, due to the reduced heat transfer coefficient from the
principles, specimen configurations, and procedures to provide
surrounding environment, measurement in vacuum or low
precise values of thermal expansion. It is not practical in a
pressure can make actual specimen temperature measurement
methodofthistypetotrytoestablishspecificdetailsofdesign,
construction, and procedures to cover all contingencies that more difficult. Additional care and longer equilibrium time to
ensure that the specimen is at a uniform temperature are
might present difficulties to a person not having the technical
knowledge relating to the thermal measurements and general necessary.
testing practice. Standardization of the method is not intended
6.2 If vitreous silica flats are used, continuous heating to
to restrict in any way further development of improved
high temperatures may cause them to distort and become
methodology.
cloudy resulting in poor fringe definition.
5.6 The test method can be used for research, development,
7. Apparatus
specification acceptance and quality control and assurance.
7.1 Interferometer, Michelson Type:
6. Interferences
7.1.1 The principle of the single pass absolute system is
6.1 Measurements should normally be undertaken with the shown in Fig. 2a.Aparallel light beam usually generated from
specimeninvacuumorinheliumatalowgaspressureinorder a laser through a beam expander is split by a beam splitter B.
to off-set optical drifts resulting from instabilities of the The resulting beams are reflected by mirrors M and M and
1 2
E289−04 (2010)
recombinedonB.IfM' isinclinedslightlyoverthelight-beam
its mirror image M' forms a small angle with M producing
2 1
fringes of equal thickness located on the virtual face M' .
7.1.2 One example of a single contact type is shown in Fig.
2b.Aprism or a polished very flat faced cylindrical specimen
is placed on one mirror with one face also offered to the
incident light. An interference pattern is generated and this is
divided into two fields corresponding to each end of the
specimen.The lens, L, projects the image of the fringes onto a
plane where two detectors are placed one on the specimen and
the other on the baseplate fields.As the specimen is heated or
cooled,boththespecimenandsupportchangeoflengthscause
the surface S and M to move relative to M at different rates.
2 1
Thedifferenceinthefringecountprovidesameasureofthenet
absolute expansion.
7.1.3 The principle of the double pass system is essentially
similartothesinglepasswiththreeimportantdistinctions.The
specimen can be a relatively simple cylinder with hemispheri-
cal or flat ends and requiring less precise machining, the
interfering beams are reflected twice from each face to the
specimen thus giving twice the sensitivity of the single pass,
and no reference arm is required. One example of the double
pass form is shown in Fig. 3.
FIG. 5 Typical Furnace
7.1.4 It is common practice to use polarized laser light and
quarter wave plates to generate circularly polarized light. In
this way detectors combined with appropriate analyzers gen-
eratesignalseitherwithinformationonfringenumber,fraction
and motion sense for each beam or linear array data of light
intensity, which indicate the profile of the instantaneous whole
fringe pattern. The array data provides complete information
(position of fringe and distance between fringes) to determine
theabsolutelengthchangeofthespecimendependinguponthe
system. These signals are normally processed electronically.
7.2 Fizeau Type:
7.2.1 This type is available in both absolute and compara-
tive versions.
7.2.2 The principle of the absolute method is illustrated in
Fig. 4. The specimen is retained between two parallel plates
and illuminated by the point source. Expansion or contraction
ofthespecimencausesspatialvariationbetweentheplatesand
radial motion of the circular fringe pattern.
7.2.3 The difference in the fringe counts yields the net
absolute expansion of the specimen.
7.2.4 In practice, P is wedge shaped (less than 30 min of
arc) such that light reflected by the upper face is diverted from
the viewing field, while the lower face of P is made to absorb
the incident light, depending upon the total separation of the
FIG. 6 Typical Low-Temperature Cryostat
flats.
7.2.5 For use in the comparative mode, two forms are
7.4 Temperature Measurement System:
available. These are described in detailed in Annex A1.
7.4.1 The temperature measurement system shall consist of
7.3 Furnace/Cryostat:
a calibrated sensor or sensors together with manual, electronic
7.3.1 Fig.5andFig.6illustratetheconstructionofatypical
or equivalent read-out such that the indicated temperature can
vertical type of furnace and cryostat that are suitable for use in
be determined better than 6 0.5°C.
undertaking these measurements. For the double pass Michel-
7.4.1.1 Since this method is used over a broad temperature
son system, horizontal forms of furnace and cryostat can be
range, different types of sensors may have to be used to cover
used.
the complete range. The common sensor(s) is a fine gage (32
AWG or smaller wire) or thin foil thermocouples calibrated in
accordance with Test Method E220.
E289−04 (2010)
7.4.1.2 TypesEandTarerecommendedforthetemperature 9. Verification
range −190 to 350°C and Types K and S and Nicrosil for the
9.1 The Michelson and Fizeau interferom
...
Questions, Comments and Discussion
Ask us and Technical Secretary will try to provide an answer. You can facilitate discussion about the standard in here.