ASTM E228-22

Standard Test Method for Linear Thermal Expansion of Solid Materials With a Push-Rod Dilatometer

SIGNIFICANCE AND USE
5.1 Coefficients of linear thermal expansion are required for design purposes and are used, for example, to determine dimensional behavior of structures subject to temperature changes, or thermal stresses that can occur and cause failure of a solid artifact composed of different materials when it is subjected to a temperature excursion.  
5.2 This test method is a reliable method of determining the linear thermal expansion of solid materials.  
5.3 For accurate determinations of thermal expansion, it is absolutely necessary that the dilatometer be calibrated by using a reference material that has a known and reproducible thermal expansion. The appendix contains information relating to reference materials in current general use.  
5.4 The measurement of thermal expansion involves two parameters: change of length and change of temperature, both of them equally important. Neglecting proper and accurate temperature measurement will inevitably result in increased uncertainties in the final data.  
5.5 The test method can be used for research, development, specification acceptance, quality control (QC) and quality assurance (QA).
SCOPE
1.1 This test method covers the determination of the linear thermal expansion of rigid solid materials using push-rod dilatometers. This method is applicable over any practical temperature range where a device can be constructed to satisfy the performance requirements set forth in this standard.
Note 1: Initially, this method was developed for vitreous silica dilatometers operating over a temperature range of –180 °C to 900 °C. The concepts and principles have been amply documented in the literature to be equally applicable for operating at higher temperatures. The precision and bias of these systems is believed to be of the same order as that for silica systems up to 900 °C. However, their precision and bias have not yet been established over the relevant total range of temperature due to the lack of well-characterized reference materials and the need for interlaboratory comparisons.  
1.2 For this purpose, a rigid solid is defined as a material that, at test temperature and under the stresses imposed by instrumentation, has a negligible creep or elastic strain rate, or both, thus insignificantly affecting the precision of thermal-length change measurements. This includes, as examples, metals, ceramics, refractories, glasses, rocks and minerals, graphites, plastics, cements, cured mortars, woods, and a variety of composites.  
1.3 The precision of this comparative test method is higher than that of other push-rod dilatometry techniques (for example, Test Method D696) and thermomechanical analysis (for example, Test Method E831) but is significantly lower than that of absolute methods such as interferometry (for example, Test Method E289). It is generally applicable to materials having absolute linear expansion coefficients exceeding 0.5 μm/(m·°C) for a 1000 °C range, and under special circumstances can be used for lower expansion materials when special precautions are used to ensure that the produced expansion of the specimen falls within the capabilities of the measuring system. In such cases, a sufficiently long specimen was found to meet the specification.  
1.4 Units—The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.  
1.5 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.6 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Or...

General Information

• Status: Published
• Publication Date: 30-Nov-2022
• ICS: 77.040.99 - Other methods of testing of metals
• Technical Committee: E37 - Thermal Measurements
• Drafting Committee: E37.05 - Thermophysical Properties

Relations

• Refers: ASTM E230/E230M-23a - Standard Specification for Temperature-Electromotive Force (emf) Tables for Standardized Thermocouples
• Effective Date: 01-Nov-2023
• Refers: ASTM E473-23b - Standard Terminology Relating to Thermal Analysis and Rheology
• Effective Date: 01-Oct-2023
• Refers: ASTM E1142-23b - Standard Terminology Relating to Thermophysical Properties
• Effective Date: 01-Oct-2023
• Refers: ASTM E230/E230M-23 - Standard Specification for Temperature-Electromotive Force (emf) Tables for Standardized Thermocouples
• Effective Date: 01-May-2023
• Refers: ASTM E644-11(2019) - Standard Test Methods for Testing Industrial Resistance Thermometers
• Effective Date: 01-Nov-2019
• Refers: ASTM E831-19 - Standard Test Method for Linear Thermal Expansion of Solid Materials by Thermomechanical Analysis
• Effective Date: 01-Apr-2019
• Refers: ASTM E289-17 - Standard Test Method for Linear Thermal Expansion of Rigid Solids with Interferometry
• Effective Date: 01-Apr-2017
• Refers: ASTM E289-04(2016) - Standard Test Method for Linear Thermal Expansion of Rigid Solids with Interferometry
• Effective Date: 01-Sep-2016
• Refers: ASTM D696-16 - Standard Test Method for Coefficient of Linear Thermal Expansion of Plastics Between −30°C and 30°C with a Vitreous Silica Dilatometer
• Effective Date: 01-Apr-2016
• Refers: ASTM E1142-15 - Standard Terminology Relating to Thermophysical Properties
• Effective Date: 01-May-2015
• Refers: ASTM E473-14 - Standard Terminology Relating to Thermal Analysis and Rheology
• Effective Date: 15-Aug-2014
• Refers: ASTM E1142-14b - Standard Terminology Relating to Thermophysical Properties
• Effective Date: 15-Aug-2014
• Refers: ASTM E831-14 - Standard Test Method for Linear Thermal Expansion of Solid Materials by Thermomechanical Analysis
• Effective Date: 01-Aug-2014
• Refers: ASTM E1142-14a - Standard Terminology Relating to Thermophysical Properties
• Effective Date: 01-Apr-2014
• Refers: ASTM E1142-14 - Standard Terminology Relating to Thermophysical Properties
• Effective Date: 15-Feb-2014

Overview

ASTM E228-22: Standard Test Method for Linear Thermal Expansion of Solid Materials With a Push-Rod Dilatometer is a key international standard developed by ASTM International. This test method specifies procedures for accurately determining the linear thermal expansion of rigid solid materials, such as metals, ceramics, glasses, plastics, and composites, using a push-rod dilatometer. Understanding the coefficient of linear thermal expansion is critical for material designers, engineers, and quality control specialists as it enables assessment of how materials will behave when subjected to temperature fluctuations, thereby influencing structural integrity, performance, and lifespan.

Key Topics

• Linear Thermal Expansion: The change in length per unit length of a material as a result of a temperature change, typically expressed as the coefficient of linear thermal expansion (α), is a fundamental property determined by this method.
• Push-Rod Dilatometer: The method uses a single- or dual-rod configuration to measure dimensional changes in the test specimen relative to a reference or the specimen holder, as temperature is increased or decreased.
• Calibration and Accuracy: Proper calibration using reference materials with well-known expansion properties is essential for reliable results. Accurate temperature measurements and careful experimental design minimize uncertainties.
• Applicable Materials: The standard is broadly applicable to rigid solids, including but not limited to: metals, ceramics, refractories, glasses, rocks, minerals, plastics, cements, cured mortars, wood, and composites.
• Precision and Bias: The method achieves higher precision than alternative push-rod techniques and most thermomechanical analysis methods. However, absolute measurement techniques, such as interferometry, offer greater precision.

Applications

• Design and Engineering: Knowing the thermal expansion coefficients aids in designing materials or components for environments with significant temperature variation. It helps prevent dimensional failures or thermal stresses in multi-material structures.
• Material Selection and Specification: Manufacturers and materials engineers use this test to compare and select appropriate materials for products exposed to temperature changes.
• Quality Control (QC) and Quality Assurance (QA): ASTM E228-22 supports routine QC/QA, ensuring consistency in thermal performance, especially in industries like aerospace, automotive, electronics, and construction.
• Research and Development: The test method assists in the development of new materials and verification of their thermal expansion properties against design requirements.
• Acceptance Testing: It provides an authoritative, repeatable means to verify material properties for acceptance in specification contracts.

Related Standards

Compliance with ASTM E228-22 often intersects with these related standards for thermal analysis and material property measurement:

• ASTM D696: Coefficient of Linear Thermal Expansion of Plastics Between –30°C and 30°C with a Vitreous Silica Dilatometer
• ASTM E289: Test Method for Linear Thermal Expansion of Rigid Solids with Interferometry
• ASTM E831: Test Method for Linear Thermal Expansion of Solid Materials by Thermomechanical Analysis
• ASTM E220: Calibration of Thermocouples By Comparison Techniques
• ASTM E644: Testing Industrial Resistance Thermometers
• ASTM E230/E230M: Temperature-Electromotive Force Tables for Standardized Thermocouples

Practical Value

Implementing ASTM E228-22 ensures reliable, consistent measurement of linear thermal expansion, crucial for:

• Reducing failure risks due to thermal stresses or expansion mismatches
• Meeting regulatory and contractual requirements through standardized testing
• Improving product durability and performance in varying temperature conditions

Overall, adherence to ASTM E228-22 gives manufacturers, engineers, and researchers robust, internationally recognized guidance for evaluating the thermal dimensional stability of solid materials using push-rod dilatometry.

Standards Content (Sample)

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: E228 − 22
Standard Test Method for
Linear Thermal Expansion of Solid Materials With a Push-
Rod Dilatometer
This standard is issued under the fixed designation E228; 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.
This standard has been approved for use by agencies of the U.S. Department of Defense.
1. Scope 1.4 Units—The values stated in SI units are to be regarded
asstandard.Nootherunitsofmeasurementareincludedinthis
1.1 This test method covers the determination of the linear
standard.
thermal expansion of rigid solid materials using push-rod
1.5 This standard does not purport to address all of the
dilatometers. This method is applicable over any practical
safety concerns, if any, associated with its use. It is the
temperature range where a device can be constructed to satisfy
responsibility of the user of this standard to establish appro-
the performance requirements set forth in this standard.
NOTE 1—Initially, this method was developed for vitreous silica priate safety, health, and environmental practices and deter-
dilatometers operating over a temperature range of –180°C to 900°C.
mine the applicability of regulatory limitations prior to use.
Theconceptsandprincipleshavebeenamplydocumentedintheliterature
1.6 This international standard was developed in accor-
to be equally applicable for operating at higher temperatures. The
dance with internationally recognized principles on standard-
precision and bias of these systems is believed to be of the same order as
ization established in the Decision on Principles for the
that for silica systems up to 900°C. However, their precision and bias
have not yet been established over the relevant total range of temperature Development of International Standards, Guides and Recom-
due to the lack of well-characterized reference materials and the need for
mendations issued by the World Trade Organization Technical
interlaboratory comparisons.
Barriers to Trade (TBT) Committee.
1.2 For this purpose, a rigid solid is defined as a material
2. Referenced Documents
that, at test temperature and under the stresses imposed by
instrumentation, has a negligible creep or elastic strain rate, or
2.1 ASTM Standards:
both, thus insignificantly affecting the precision of thermal- D696TestMethodforCoefficientofLinearThermalExpan-
length change measurements. This includes, as examples,
sion of Plastics Between −30°C and 30°C with a Vitreous
metals, ceramics, refractories, glasses, rocks and minerals,
Silica Dilatometer
graphites, plastics, cements, cured mortars, woods, and a
E220Test Method for Calibration of Thermocouples By
variety of composites.
Comparison Techniques
E230/E230MSpecification for Temperature-Electromotive
1.3 The precision of this comparative test method is higher
Force (emf) Tables for Standardized Thermocouples
than that of other push-rod dilatometry techniques (for
E289Test Method for Linear Thermal Expansion of Rigid
example, Test Method D696) and thermomechanical analysis
Solids with Interferometry
(forexample,TestMethodE831)butissignificantlylowerthan
E473Terminology Relating to Thermal Analysis and Rhe-
that of absolute methods such as interferometry (for example,
ology
Test Method E289). It is generally applicable to materials
E644Test Methods for Testing Industrial Resistance Ther-
having absolute linear expansion coefficients exceeding 0.5
mometers
µm/(m·°C) for a 1000°C range, and under special circum-
E831Test Method for Linear Thermal Expansion of Solid
stancescanbeusedforlowerexpansionmaterialswhenspecial
Materials by Thermomechanical Analysis
precautions are used to ensure that the produced expansion of
E1142Terminology Relating to Thermophysical Properties
the specimen falls within the capabilities of the measuring
system. In such cases, a sufficiently long specimen was found
3. Terminology
to meet the specification.
3.1 Definitions—The following terms are applicable to this
test method and are listed in Terminologies E473 and E1142:
ThistestmethodisunderthejurisdictionofASTMCommitteeE37onThermal
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 Dec. 1, 2022. Published January 2023. Originally contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
approved in 1963. Last previous edition approved in 2017 as E228–17. DOI: Standards volume information, refer to the standard’s Document Summary page on
10.1520/E0228-22. the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E228 − 22
coeffıcient of linear thermal expansion, thermodilatometry,and 3.3 Symbols:
thermomechanical analysis.
α = mean or average coefficient of linear thermal
m
3.2 Definitions of Terms Specific to This Standard:
expansion over a temperature range, µm/(m·°C)
3.2.1 dilatometer, n—a device that measures the difference
α = expansivity or instantaneous coefficient of linear
T
in linear thermal expansion between a test specimen and its
thermal expansion at temperature T, µm/(m·°C)
own parts adjacent to the sample.
L = originallengthofspecimenattemperature T,mm
0 0
3.2.1.1 Discussion—Thermomechanical analyzers (TMA),
L = length of specimen at temperature T,mm
1 1
instruments used in thermal analysis, are often also character-
L = length of specimen at temperature T,mm
2 2
ized as dilatometers, due to their ability to determine linear L = length of specimen at a particular temperature T,
i i
thermal expansion characteristics. Typically, they employ mm
specimens much smaller than dilatometers; however, TMA ∆L = change in length of specimen between any two
temperatures T and T , T and T , etc., µm
systems with sufficiently large specimen size capability have
1 2 0 1
(∆L/L ) = expansion
been shown to measure thermal expansion accurately. When
T = temperature at which initial length is L,°C
using the small TMA specimen size, this utilization of TMA 0 0
T ,T = two temperatures at which measurements are
1 2
equipment should be limited to testing only very high expan-
made, °C
sion materials, such as polymers, otherwise the data obtained
T = temperature at which length is L,°C
i i
may be substantially in error. Conversely, some dilatometers
∆T = temperature difference between any two tempera-
can perform some of the TMA functions, but the two devices
tures T and T , T and T , etc., °C
2 1 1 0
should not be considered equivalent or interchangeable in all
m = measured expansion of the reference material
applications.
t = true or certified expansion of the reference mate-
3.2.2 linear thermal expansion, ∆L/L,n—the change in
rial
length relative to the initial length of the specimen accompa-
s = assumed or known expansion of the parts of the
nying a change in temperature, between temperatures T and
dilatometer
T , expressed as:
A = numerical calibration constant
∆L L 2 L
1 0
5 (1)
4. Summary of Test Method
L L
0 0
3.2.2.1 Discussion—It is a dimensionless quantity, but for
4.1 This test method uses a single push-rod tube type
practical reasons the units most often used are µm/m.
dilatometer to determine the change in length of a solid
material relative to that of the holder as a function of
3.2.3 mean (average) coeffıcient of linear thermal
temperature. A special variation of the basic configuration
expansion, α ,n—the ratio between the expansion and the
m
known as a differential dilatometer employs dual push rods,
temperature difference that is causing it. It is referred to as the
where a reference specimen is kept in the second placement at
average coefficient of thermal expansion for the temperature
all times and expansion of the unknown is determined relative
range between T and T .
0 1
to the reference material rather than to the specimen holder.
1 ∆L
α 5 (2)
m
4.2 The temperature is controlled either over a series of
L ∆T
steps or at a slow constant heating or cooling rate over the
3.2.3.1 Discussion—Most commonly, it is expressed in
entire range.
µm/(m °C), and it is determined for a sequence of temperature
ranges,startingwith20°Cbyconvention,beingpresentedasa
4.3 The linear thermal expansion and the coefficients of
function of temperature. In case the reference temperature
linearthermalexpansionarecalculatedfromtherecordeddata.
differs from 20°C, the specific temperature used for reference
has to be indicated in the report.
5. Significance and Use
3.2.4 thermal expansivity (instantaneous coeffıcient of ther-
5.1 Coefficientsoflinearthermalexpansionarerequiredfor
mal expansion), α ,n—identical to the above, except that the
T
design purposes and are used, for example, to determine
derivative replaces the finite differences of Eq 2. The thermal
dimensional behavior of structures subject to temperature
expansivityisrelatedtothelengthchangeforaninfinitesimally
changes,orthermalstressesthatcanoccurandcausefailureof
narrow temperature range, at any temperature T (essentially a
a solid artifact composed of different materials when it is
“tangent” point), and is defined as follows:
subjected to a temperature excursion.
1 dL
5.2 This test method is a reliable method of determining the
α 5 (3)
S D
T
L dT
T linear thermal expansion of solid materials.
3.2.4.1 Discussion—It is expressed in the same units as the
5.3 For accurate determinations of thermal expansion, it is
average coefficient of thermal expansion. In terms of physical
absolutelynecessarythatthedilatometerbecalibratedbyusing
meaning, the instantaneous coefficient of thermal expansion is
areferencematerialthathasaknownandreproduciblethermal
the derivative of the expansion curve when plotted versus
expansion. The appendix contains information relating to
temperature, at the temperature T. It has a rather limited utility
reference materials in current general use.
for engineering applications, and therefore it is more common
to use the average coefficient of thermal expansion, than the 5.4 The measurement of thermal expansion involves two
instantaneous one. parameters: change of length and change of temperature, both
E228 − 22
of them equally important. Neglecting proper and accurate
temperature measurement will inevitably result in increased
uncertainties in the final data.
5.5 The test method can be used for research, development,
specification acceptance, quality control (QC) and quality
assurance (QA).
6. Interferences
6.1 Materials Considerations:
6.1.1 The materials of construction may have substantial
impact on the performance of the dilatometer. It is imperative
thatregardlessofthematerialsused,stepsbetakentoascertain
that the expansion behavior is stabilized, so that repeated
thermal cycling (within the operating range of the device)
causes no measurable change.
FIG. 1 Common Forms Specimen Holders
6.2 General Considerations:
6.2.1 Inelastic creep of a specimen at elevated temperatures
can often be prevented by making its cross section sufficiently
large.
6.2.2 Avoid moisture in the dilatometer, especially when
used at cryogenic temperatures.
6.2.3 Means to separate the bath from the specimen are
required when the dilatometer is immersed in a liquid bath.
6.2.4 Support or hold the specimen in a position so that it is
stable during the test without unduly restricting its free
movement.
6.2.5 Thespecimenholderandpush-rodshallbemadefrom
the same material. The user must not practice uncontrolled
substitutions (such as when replacing broken parts), as serious
increase of the uncertainties in the measured expansion may
result.
FIG. 2 Suggested Shapes of Specimen’s and Push-Rod Ends
6.2.6 A general verification of a dilatometer is a test run
using a specimen cut from the same material as the push rod
stable and is not prone to reversible configurational changes
and specimen holder. The resultant mean coefficient of linear
(such as twisting, etc.) upon heating and cooling.
thermal expansion should be smaller than 60.3 µm/(m·°C) for
a properly constructed system (after applying the system’s
NOTE 2—The tube and the push-rod beyond the specimen, while
correction).
parallel to each other, are expected to have identical thermal gradients
6.2.7 Conditioning of specimens is often necessary before along them, thereby identical thermal expansion. This is a critical factor,
as differences in net expansion between the tube and the push-rod will
reproducible expansion data can be obtained. For example,
appear very much like expansion produced by the specimen. To a limited
heat treatments are frequently necessary to eliminate certain
extent, calibration (see Section 9) can be used to account for these
effects (stress caused by machining, moisture, etc.) that may
differences in the thermal expansion of the two parts, however, it is noted
introduce irreversible length changes that are not associated
that this is one of the most fundamental of all practical limitations for
dilatometers.Tominimizethiseffect,thetubeandthepush-rodshallbein
with thermal expansion.
close proximity of each other and heated slowly enough to prevent
substantial thermal gradients that occur radially.
7. Apparatus
7.1.2 Test Chamber, composed of:
7.1 Push-Rod Dilatometer System, consisting of the follow-
7.1.2.1 Furnace, Cryostat, or Bath, used for heating or
ing:
cooling the specimen uniformly at a controlled rate over the
7.1.1 Specimen Holder—A structure of thermally stable
temperature range of interest, and able to maintain the tem-
material constructed in a fashion such that when a specimen of
perature uniform along the sample during its heating, cooling,
the same material is placed into it for a test, the qualifications
or just equilibrating.
given in 6.2.7 are satisfied. In any push rod dilatometer, both
the sample holder and the push-rod(s) shall be made of the
NOTE 3—Extreme care must be exercised in using furnaces for high
same material, having been proven to exhibit thermal expan- temperatures, to prevent interaction with the dilatometer’s parts or with
the specimen. In many instances, it is necessary to protect the specimen
sion characteristics within 61% of each other. Illustrations of
and the dilatometer from oxidation and in some cases this may be
typical tube and rod-type configurations are given in Fig. 1.It
accomplished with the use of a muffle tube. If it is necessary, the furnace,
is often practiced to configure specimen holders that are not
in such cases, shall contain provisions to provide inert atmosphere or
shaped as a tube, but serve the same structural purpose.This is
vacuum environment, as well as provisions to protect against air back-
an acceptable practice, as long as the shape is mechanically streaming on cooling.
E228 − 22
NOTE 4—Unless it is absolutely necessary to have the specimen tested
7.1.4.2 Manual, Electronic, or Equivalent Readout, such
in vacuum, measurements of thermal expansion in vacuum are not
that the indicated temperature can be determined without
recommended due to extreme thermal gradients, thermal lags, etc.
additional degradation to the sensor’s performance.
betweenvariouscomponentsofthedilatometerandthespecimen,thatare
caused by the very poor heat transfer that occurs in the absence of a gas.
NOTE 5—In all cases in which thermocouples are used, they shall be
referenced to 0°C by means of an ice water bath or equivalent electronic
7.1.2.2 Temperature Controller(orcircuitrywithequivalent
reference.
function) capable of executing a specific temperature program
NOTE6—Specialattentionmustbepaidtopreventcontaminationofthe
byoperatingthefurnace(s)betweenselectedtemperaturelimits
thermocouple by the specimen or even by the dilatometer tube itself (for
atratesprogrammed,andsupportedbythefurnace(s)’sthermal
example, type C thermocouple in a graphitic environment). Interaction
between atmosphere and the thermocouple (for example, type S thermo-
performance. Temperature control of a constant rate shall be
couple in hydrogen atmosphere) can also be extremely detrimental (see
monotonous within 62°C (exclusive of the approximately
Specification E230/E230M).
5% of instrument’s maximum temperature of its operating
NOTE 7—Placement of thermocouples is important, and the user is
range).Thecontrolofequilibriumtemperaturesshallbewithin
frequently given a choice. It is often a practice to bring the bead of a
61°Cor 60.05% of maximum temperature of the dilatom-
thermocouple in contact with the specimen, or even embed it in a hole, as
opposed to having it laying on top of it or in its proximity. While the
eter’s operating range, whichever is larger.
former seems better, it is actually sometimes the cause of mechanical
7.1.2.3 Optional means to cool furnace(s) or optionally
interference with the specimen, source of contamination, and while it
cryostat for operation below ambient.
registers a more true specimen temperature, it neglects the temperature of
the specimen holder around it.Agood practice is to have the bead of the
7.1.2.4 Optional means to seal the space occupied by the
thermocouple reside equidistant between the specimen holder and the
dilatometer, contain pressurized gas, or evacuated, without
specimen itself, ensuring that it is shielded from direct view of the heater
collapse or gradual deformation with time and temperature, or
or muffle tube (if one is employed).
without bursting when pressure is applied within specified
NOTE 8—The thermocouple positioning during the test should be the
limits.
same as was used in the instrument’s calibration. Frequent verification of
thermocouple performance is highly recommended.
7.1.3 Transducer—A device to convert and magnify the
minute mechanical translation conveyed by the push-rod(s)
7.2 Measuring Tool, such as a vernier micrometer or cali-
resulting from the expansion of the specimen, into visually
pers capable of reading to at least 625 µm in order to
discernable or electrically measurable signals, with a constant determine the initial and final lengths of the test specimen.
and defined functionality.
8. Test Specimens
7.1.3.1 Visually readable devices, such as dial gauges,
optical levers, rulers, etc.
8.1 The specimen length shall be such that the accuracy of
7.1.3.2 Electromechanical devices with a defined electrical
determining ∆L/L is at least 620 µm/m. Where possible, the
output corresponding to a defined mechanical displacement
specimen should be between 25 mm and 60 mm long and
input. Example electromechanical devices may be but are not
between 5 mm and 10 mm in diameter (or equivalent, if not
limited to linear variable differential transformers, digital
cylindrical), however, there is no fundamental limitation on
absolute or incremental encoders, capacitive sensors, optical
either dimension, as long as the dilatometer can accommodate
displacement sensors.
the specimen with a maximum thermal gradient of 2°C, either
7.1.3.3 Thetransducermustbeselectedsuchastocoverthe determined in 50 mm intervals over the entire specimen, or
maintained uniformly within 62°C⁄50 mm.
expected displacement within its linear range.
7.1.3.4 Transducers employed in dilatometry must have a
8.2 The cross sectional shape of the specimen, the cross
resolution (visible or sensible) of not less than 0.1% of their
sectional uniformity along its length, or the condition of the
linear range, with an attendant proven linearity of at least
surface along its length, have no bearing on the test.The ends,
60.1% of their range.
however, must be smooth and parallel. The cross section must
7.1.3.5 The linearity band of a transducer limits the maxi- be robust enough to prevent buckling or creep.
mum resolution that can be assigned to the dilatometer. (Since
8.2.1 In the instances when limitations of the source mate-
the band bound by linearity is considered unresolvable, even
rial precludes the forming of a cylinder or slab, irregular
with special calibrations, resolution cannot be ensured much
shaped samples may be tested. However, care must be exer-
beyond the transducer’s range of linearity.) Adding empty
cised not to have the
...

This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: E228 − 17 E228 − 22
Standard Test Method for
Linear Thermal Expansion of Solid Materials With a Push-
Rod Dilatometer
This standard is issued under the fixed designation E228; 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 (´) indicates an editorial change since the last revision or reapproval.
This standard has been approved for use by agencies of the U.S. Department of Defense.
1. Scope
1.1 This test method covers the determination of the linear thermal expansion of rigid solid materials using push-rod dilatometers.
This method is applicable over any practical temperature range where a device can be constructed to satisfy the performance
requirements set forth in this standard.
NOTE 1—Initially, this method was developed for vitreous silica dilatometers operating over a temperature range of –180°C–180 °C to 900°C.900 °C. The
concepts and principles have been amply documented in the literature to be equally applicable for operating at higher temperatures. The precision and
bias of these systems is believed to be of the same order as that for silica systems up to 900°C.900 °C. However, their precision and bias have not yet
been established over the relevant total range of temperature due to the lack of well-characterized reference materials and the need for interlaboratory
comparisons.
1.2 For this purpose, a rigid solid is defined as a material that, at test temperature and under the stresses imposed by
instrumentation, has a negligible creep or elastic strain rate, or both, thus insignificantly affecting the precision of thermal-length
change measurements. This includes, as examples, metals, ceramics, refractories, glasses, rocks and minerals, graphites, plastics,
cements, cured mortars, woods, and a variety of composites.
1.3 The precision of this comparative test method is higher than that of other push-rod dilatometry techniques (for example, Test
Method D696) and thermomechanical analysis (for example, Test Method E831) but is significantly lower than that of absolute
methods such as interferometry (for example, Test Method E289). It is generally applicable to materials having absolute linear
expansion coefficients exceeding 0.5 μm/(m·°C) for a 1000°C1000 °C range, and under special circumstances can be used for lower
expansion materials when special precautions are used to ensure that the produced expansion of the specimen falls within the
capabilities of the measuring system. In such cases, a sufficiently long specimen was found to meet the specification.
1.4 Units—The values stated in SI units are to be regarded as standard. No other units of measurement are included in this
standard.
1.5 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility
of the user of this standard to establish appropriate safety safety, health, and healthenvironmental practices and determine the
applicability of regulatory limitations prior to use.
1.6 This international standard was developed in accordance with internationally recognized principles on standardization
established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued
by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
This test method is under the jurisdiction of ASTM Committee E37 on Thermal Measurements and is the direct responsibility of Subcommittee E37.05 on
Thermophysical Properties.
Current edition approved April 1, 2017Dec. 1, 2022. Published April 2017January 2023. Originally approved in 1963. Last previous edition approved in 20162017 as
E228 – 11 (2016).E228 – 17. DOI: 10.1520/E0228-17.10.1520/E0228-22.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
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2. Referenced Documents
2.1 ASTM Standards:
D696 Test Method for Coefficient of Linear Thermal Expansion of Plastics Between −30°C and 30°C with a Vitreous Silica
Dilatometer
E220 Test Method for Calibration of Thermocouples By Comparison Techniques
E230/E230M Specification for Temperature-Electromotive Force (emf) Tables for Standardized Thermocouples
E289 Test Method for Linear Thermal Expansion of Rigid Solids with Interferometry
E473 Terminology Relating to Thermal Analysis and Rheology
E644 Test Methods for Testing Industrial Resistance Thermometers
E831 Test Method for Linear Thermal Expansion of Solid Materials by Thermomechanical Analysis
E1142 Terminology Relating to Thermophysical Properties
3. Terminology
3.1 Definitions—The following terms are applicable to this test method and are listed in Terminologies E473 and E1142: coeffıcient
of linear thermal expansion,thermodilatometry, and thermomechanical analysis.
3.2 Definitions of Terms Specific to This Standard:
3.2.1 dilatometer—dilatometer, n—a device that measures the difference in linear thermal expansion between a test specimen and
its own parts adjacent to the sample.
3.2.1.1 Discussion—
Thermomechanical analyzers (TMA), instruments used in thermal analysis, are often also characterized as dilatometers, due to
their ability to determine linear thermal expansion characteristics. Typically, they employ specimens much smaller than
dilatometers; however, TMA systems with sufficiently large specimen size capability have been shown to measure thermal
expansion accurately. When using the small TMA specimen size, this utilization of TMA equipment should be limited to testing
only very high expansion materials, such as polymers, otherwise the data obtained may be substantially in error. Conversely, some
dilatometers can perform some of the TMA functions, but the two devices should not be considered equivalent or interchangeable
in all applications.
3.2.2 linear thermal expansion, ΔL/L ,—n—the change in length relative to the initial length of the specimen accompanying a
change in temperature, between temperatures T and T , expressed as:
0 1
ΔL L 2 L
1 0
5 (1)
L L
0 0
3.2.2.1 Discussion—
It is a dimensionless quantity, but for practical reasons the units most often used are μm/m.
3.2.3 mean (average) coeffıcient of linear thermal expansion, α ,—n—the ratio between the expansion and the temperature
m
difference that is causing it. It is referred to as the average coefficient of thermal expansion for the temperature range between T
and T .
1 ΔL
α 5 (2)
m
L ΔT
3.2.3.1 Discussion—
Most commonly, it is expressed in μm/(m °C), and it is determined for a sequence of temperature ranges, starting with 20°C20 °C
by convention, being presented as a function of temperature. In case the reference temperature differs from 20°C,20 °C, the specific
temperature used for reference has to be indicated in the report.
3.2.4 thermal expansivity (instantaneous coeffıcient of thermal expansion), α ,—n—identical to the above, except that the
T
derivative replaces the finite differences of Eq 2. The thermal expansivity is related to the length change for an infinitesimally
narrow temperature range, at any temperature T (essentially a “tangent” point), and is defined as follows:
1 dL
α 5 (3)
S D
T
L dT
0 T
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
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3.2.4.1 Discussion—
It is expressed in the same units as the average coefficient of thermal expansion. In terms of physical meaning, the instantaneous
coefficient of thermal expansion is the derivative of the expansion curve when plotted versus temperature, at the temperature T.
It has a rather limited utility for engineering applications, and therefore it is more common to use the average coefficient of thermal
expansion, than the instantaneous one.
3.3 Symbols:
α = mean or average coefficient of linear thermal expansion over a temperature range, μm/(m·°C)
m
α = expansivity or instantaneous coefficient of linear thermal expansion at temperature T, μm/(m·°C)
T
L = original length of specimen at temperature T , mm
0 0
L = length of specimen at temperature T , mm
1 1
L = length of specimen at temperature T , mm
2 2
L = length of specimen at a particular temperature T , mm
i i
ΔL = change in length of specimen between any two temperatures T and T , T and T , etc., μm
1 2 0 1
(ΔL/L ) = expansion
T = temperature at which initial length is L , °C
0 0
T , T = two temperatures at which measurements are made, °C
1 2
T = temperature at which length is L , °C
i i
ΔT = temperature difference between any two temperatures T and T , T and T , etc., °C
2 1 1 0
m = measured expansion of the reference material
t = true or certified expansion of the reference material
s = assumed or known expansion of the parts of the dilatometer
A = numerical calibration constant
4. Summary of Test Method
4.1 This test method uses a single push-rod tube type dilatometer to determine the change in length of a solid material relative
to that of the holder as a function of temperature. A special variation of the basic configuration known as a differential dilatometer
employs dual push rods, where a reference specimen is kept in the second placement at all times and expansion of the unknown
is determined relative to the reference material rather than to the specimen holder.
4.2 The temperature is controlled either over a series of steps or at a slow constant heating or cooling rate over the entire range.
4.3 The linear thermal expansion and the coefficients of linear thermal expansion are calculated from the recorded data.
5. Significance and Use
5.1 Coefficients of linear thermal expansion are required for design purposes and are used, for example, to determine dimensional
behavior of structures subject to temperature changes, or thermal stresses that can occur and cause failure of a solid artifact
composed of different materials when it is subjected to a temperature excursion.
5.2 This test method is a reliable method of determining the linear thermal expansion of solid materials.
5.3 For accurate determinations of thermal expansion, it is absolutely necessary that the dilatometer be calibrated by using a
reference material that has a known and reproducible thermal expansion. The appendix contains information relating to reference
materials in current general use.
5.4 The measurement of thermal expansion involves two parameters: change of length and change of temperature, both of them
equally important. Neglecting proper and accurate temperature measurement will inevitably result in increased uncertainties in the
final data.
5.5 The test method can be used for research, development, specification acceptance, quality control (QC) and quality assurance
(QA).
6. Interferences
6.1 Materials Considerations:
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6.1.1 The materials of construction may have substantial impact on the performance of the dilatometer. It is imperative that
regardless of the materials used, steps be taken to ascertain that the expansion behavior is stabilized, so that repeated thermal
cycling (within the operating range of the device) causes no measurable change.
6.2 General Considerations:
6.2.1 Inelastic creep of a specimen at elevated temperatures can often be prevented by making its cross section sufficiently large.
6.2.2 Avoid moisture in the dilatometer, especially when used at cryogenic temperatures.
6.2.3 Means to separate the bath from the specimen are required when the dilatometer is immersed in a liquid bath.
6.2.4 Support or hold the specimen in a position so that it is stable during the test without unduly restricting its free movement.
6.2.5 The specimen holder and push-rod shall be made from the same material. The user must not practice uncontrolled
substitutions (such as when replacing broken parts), as serious increase of the uncertainties in the measured expansion may result.
6.2.6 A general verification of a dilatometer is a test run using a specimen cut from the same material as the push rod and specimen
holder. The resultant mean coefficient of linear thermal expansion should be smaller than 60.3 μm/(m·°C) for a properly
constructed system (after applying the system’s correction).
6.2.7 Conditioning of specimens is often necessary before reproducible expansion data can be obtained. For example, heat
treatments are frequently necessary to eliminate certain effects (stress caused by machining, moisture, etc.) that may introduce
irreversible length changes that are not associated with thermal expansion.
7. Apparatus
7.1 Push-Rod Dilatometer System, consisting of the following:
7.1.1 Specimen Holder—A structure of thermally stable material constructed in a fashion such that when a specimen of the same
material is placed into it for a test, the qualifications given in 6.2.7 are satisfied. In any push rod dilatometer, both the sample holder
and the push-rod(s) shall be made of the same material, having been proven to exhibit thermal expansion characteristics within
61 % of each other. Illustrations of typical tube and rod-type configurations are given in Fig. 1. It is often practiced to configure
specimen holders that are not shaped as a tube, but serve the same structural purpose. This is an acceptable practice, as long as
the shape is mechanically stable and is not prone to reversible configurational changes (such as twisting, etc.) upon heating and
cooling.
NOTE 2—The tube and the push-rod beyond the specimen, while parallel to each other, are expected to have identical thermal gradients along them,
thereby identical thermal expansion. This is a critical factor, as differences in net expansion between the tube and the push-rod will appear very much
like expansion produced by the specimen. To a limited extent, calibration (see Section 9) can be used to account for these differences in the thermal
FIG. 1 Common Forms Specimen Holders
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FIG. 2 Suggested Shapes of Specimen’s and Push-Rod Ends
expansion of the two parts, however, it is noted that this is one of the most fundamental of all practical limitations for dilatometers. To minimize this
effect, the tube and the push-rod shall be in close proximity of each other and heated slowly enough to prevent substantial thermal gradients that occur
radially.
7.1.2 Test Chamber, composed of:
7.1.2.1 Furnace, Cryostat, or Bath, used for heating or cooling the specimen uniformly at a controlled rate over the temperature
range of interest, and able to maintain the temperature uniform along the sample during its heating, cooling, or just equilibrating.
NOTE 3—Extreme care must be exercised in using furnaces for high temperatures, to prevent interaction with the dilatometer’s parts or with the specimen.
In many instances, it is necessary to protect the specimen and the dilatometer from oxidation and in some cases this may be accomplished with the use
of a muffle tube. If it is necessary, the furnace, in such cases, shall contain provisions to provide inert atmosphere or vacuum environment, as well as
provisions to protect against air back-streaming on cooling.
NOTE 4—Unless it is absolutely necessary to have the specimen tested in vacuum, measurements of thermal expansion in vacuum are not recommended
due to extreme thermal gradients, thermal lags, etc. between various components of the dilatometer and the specimen, that are caused by the very poor
heat transfer that occurs in the absence of a gas.
7.1.2.2 Temperature Controller (or circuitry with equivalent function) capable of executing a specific temperature program by
operating the furnace(s) between selected temperature limits at rates programmed, and supported by the furnace(s)’s thermal
performance. Temperature control of a constant rate shall be monotonous within 62°C62 °C (exclusive of the approximately 5 %
of instrument’s maximum temperature of its operating range). The control of equilibrium temperatures shall be within 61°C61 °C
or 60.05 % of maximum temperature of the dilatometer’s operating range, whichever is larger.
7.1.2.3 Optional means to cool furnace(s) or optionally cryostat for operation below ambient.
7.1.2.4 Optional means to seal the space occupied by the dilatometer, contain pressurized gas, or evacuated, without collapse or
gradual deformation with time and temperature, or without bursting when pressure is applied within specified limits.
7.1.3 Transducer—A device to convert and magnify the minute mechanical translation conveyed by the push-rod(s) resulting from
the expansion of the specimen, into visually discernable or electrically measurable signals, with a constant and defined
functionality.
7.1.3.1 Visually readable devices, such as dial gauges, optical levers, rulers, etc.
7.1.3.2 Electromechanical devices with a defined electrical output corresponding to a defined mechanical displacement input.
Example electromechanical devices may be but are not limited to linear variable differential transformers, digital absolute or
incremental encoders, capacitive sensors, optical displacement sensors.
7.1.3.3 The transducer must be selected such as to cover the expected displacement within its linear range.
7.1.3.4 Transducers employed in dilatometry must have a resolution (visible or sensible) of not less than 0.1 % of their linear
range, with an attendant proven linearity of at least 60.1 % of their range.
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7.1.3.5 The linearity band of a transducer limits the maximum resolution that can be assigned to the dilatometer. (Since the band
bound by linearity is considered unresolvable, even with special calibrations, resolution cannot be ensured much beyond the
transducer’s range of linearity.) Adding empty amplification (extra digits to the readout), may give the impression of more
sensitivity, but in reality it does not. Nonlinearity errors cannot be effectively accounted for with calibration.
7.1.4 Temperature Measurement System, consisting of:
7.1.4.1 Calibrated Sensor or Sensors, to provide indication of the specimen temperature 60.5°C,60.5 °C, or 61 % of the overall
temperature range, whichever is larger. Temperature sensors may be, but are not limited to, thermocouples, pyrometers, resistance
thermometers, thermistors, mercury thermometers, etc.
7.1.4.2 Manual, Electronic, or Equivalent Readout, such that the indicated temperature can be determined without additional
degradation to the sensor’s performance.
NOTE 5—In all cases in which thermocouples are used, they shall be referenced to 0°C0 °C by means of an ice water bath or equivalent electronic
reference.
NOTE 6—Special attention must be paid to prevent contamination of the thermocouple by the specimen or even by the dilatometer tube itself (for example,
type C thermocouple in a graphitic environment). Interaction between atmosphere and the thermocouple (for example, type S thermocouple in hydrogen
atmosphere) can also be extremely detrimental (see Specification E230/E230M).
NOTE 7—Placement of thermocouples is important, and the user is frequently given a choice. It is often a practice to bring the bead of a thermocouple
in contact with the specimen, or even embed it in a hole, as opposed to having it laying on top of it or in its proximity. While the former seems better,
it is actually sometimes the cause of mechanical interference with the specimen, source of contamination, and while it registers a more true specimen
temperature, it neglects the temperature of the specimen holder around it. A good practice is to have the bead of the thermocouple reside equidistant
between the specimen holder and the specimen itself, ensuring that it is shielded from direct view of the heater or muffle tube (if one is employed).
NOTE 8—The thermocouple positioning during the test should be the same as was used in the instrument’s calibration. Frequent verification of
thermocouple performance is highly recommended.
7.2 Measuring Tool, such as a vernier micrometer or calipers capable of reading to at least 625 μm in order to determine the initial
and final lengths of the test specimen.
8. Test Specimens
8.1 The specimen length shall be such that the accuracy of determining ΔL/L is at least 620 μm/m. Where possible, the specimen
should be between 25 mm and 60 mm long and between 5 mm and 10 mm in diameter (or equivalent, if not cylindrical), however,
there is no fundamental limitation on either dimension, as long as the dilatometer can accommodate the specimen with
...