ASTM E2113-23

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: E2113 − 18 E2113 − 23
Standard Test Method for
Length Change Calibration of Thermomechanical Analyzers
This standard is issued under the fixed designation E2113; 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.
1. Scope Scope*
1.1 This test method describes calibration of the length change (deflection) measurement or thermal expansion of thermome-
chanical analyzers (TMAs) within the temperature range from –150 °C to 1000 °C using the thermal expansion of a suitable
reference material.
1.2 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.
1.3 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.
1.4 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.
2. Referenced Documents
2.1 ASTM Standards:
E473 Terminology Relating to Thermal Analysis and Rheology
E831 Test Method for Linear Thermal Expansion of Solid Materials by Thermomechanical Analysis
E1142 Terminology Relating to Thermophysical Properties
E1363 Test Method for Temperature Calibration of Thermomechanical Analyzers
E2161 Terminology Relating to Performance Validation in Thermal Analysis and Rheology
E3142 Test Method for Thermal Lag of Thermal Analysis Apparatus
3. Terminology
3.1 Specific technical terms used in this test method are described in Terminologies E473, E1142, and E2161 including
calibration, Celsius, coeffıcient of linear thermal expansion, Kelvin, reference material, repeatability, reproducibility, and
thermomechanical analysis.
4. Summary of Test Method
4.1 Thermomechanical analyzers (TMAs) or related devices are commonly used to determine coefficient of linear thermal
This test method is under the jurisdiction of ASTM Committee E37 on Thermal Measurements and is the direct responsibility of Subcommittee E37.10 on Fundamental,
Statistical and Mechanical Properties.
Current edition approved June 1, 2018Aug. 1, 2023. Published June 2018August 2023. Originally approved in 2000. Last previous edition approved in 20132018 as
E2113 – 13.E2113 – 18. DOI: 10.1520/E2113-18.10.1520/E2113-23.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
*A Summary of Changes section appears at the end of this standard
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E2113 − 23
expansion of solid materials (for example, Test Method E831). The test specimen is heated at a linear rate over the temperature
range of interest and the change in length (dimension) is electronically recorded.
4.2 Performance verification or calibration of the length change measurement is needed to obtain accurate coefficient of thermal
expansion data.
4.3 The thermal expansion of a reference material is recorded using a thermomechanical analyzer. The recorded thermal expansion
is compared to the known value of the reference material. The resultant ratio, a calibration coefficient, may then be applied to the
determination of unknown specimens to obtain accurate results.
5. Significance and Use
5.1 Performance verification or calibration is essential to the accurate determination of quantitative dimension change
measurements.
5.2 This test method may be used for instrument performance validation, regulatory compliance, research and development and
quality assurance purposes.
6. Apparatus
6.1 Thermomechanical Analyzer (TMA)—(TMA)—The essential instrumentation required to provide the minimum thermome-
chanical analytical or thermodilatometric capability for this test method includes:
-1 -1
6.1.1 A Rigid Specimen Holder, of inert, low expansivity material [<0.5 μm m °C ] to center the specimen in the furnace and
to fix the specimen to mechanical ground.
-1 -1
6.1.2 A Rigid Expansion Probe, of inert, low expansivity material [<0.5 μm m °C ] which contacts the specimen with an
applicable compressive or tensile force.
6.1.3 A Sensing Element, linear over a minimum of 2 mm, to measure the displacement of the rigid probe to within 610 nm
610 nm resulting from changes in length/height of the specimen.
6.1.4 A Weight or Force Transducer, to generate a constant force between 1 mN and 100 mN (0.1 g and 10 g) applied through
the rigid probe to the specimen.
6.1.5 A Furnace, capable of providing uniform controlled heating (cooling) of a specimen to a constant temperature or at a
constant rate within the applicable temperature range of this test method.
6.1.6 A Temperature Controller, capable of executing a specific temperature program by operating the furnace over any suitable
temperature range between –150 °C and 1000 °C at a rate of temperature change of 5 °C/min constant to within 60.160.1 °C
°C/min. ⁄min.
6.1.7 A Temperature Sensor, that can be attached to, in contact with, or reproducibly positioned in close proximity to the specimen
to provide an indication of the specimen/furnace temperature readable to within 60.1 °C.
6.1.8 A means of sustaining an environment around the specimen of an inert purge gas at a rate of 10 mL/min to 5050 mL ⁄min
6 5 5 mL mL/min.⁄min.
NOTE 1—Typically, 99.9+ % 99.9+ % pure nitrogen, helium or argon is employed, when oxidation in air is a concern. Unless effects of moisture are to
be studied, use of dry purge gas is recommended and is essential for operation at subambient temperatures.
6.1.9 A Data Collection Device, to provide a means of acquiring, storing, and displaying measured or calculated signals, or both.
The minimum output signals required are dimension (length) change, temperature, and time.
6.2 Micrometer, calipers or other length measurement device capable of measuring linear dimensions up to 10 mm with readability
of 625 μm.
E2113 − 23
6.3 While not required, the user may find useful software that performs the calculations described in this test method.
6.4 Thermal expansion reference material of 8 mm 6 2 mm length, the linear coefficient of expansion of which is known to 60.1
-1 -1 -1 -1 -1 -1
μm m °C . The coefficient of thermal expansion should be between 9 μm m °C and 40 μm m °C .
6.4.1 In the absence of primary or secondary reference materials, high purity aluminum or platinum may be used along with the
values for coefficient of thermal expansion presented in Table 1.
NOTE 2—The linear expansion of high purity aluminum, commonly supplied by instrument manufactures, is useful as a working reference material.
Coefficient of thermal expansion values for pure aluminum are presented in Table 1 along with those for platinum.
7. Test Specimen
7.1 Specimens shall be between 6 mm and 10 mm in length and have flat and parallel ends to within 625 μm. Lateral dimensions
shall be between 3 mm and 9 mm. Other lengths and widths may be used but shall be noted in the report.
8. Calibration
8.1 Perform any calibration procedures described in the manufacturer’s operations manual.
8.2 Calibrate the temperature sensor using Test Method E1363. at the same heating rate to be used for the test specimen (see Test
Method E3142 and Appendix X1).
A
TABLE 1 Thermal Expansion Coefficients
BCDEF GHIJ
Aluminum Platinum
Mean Coefficient of Linear Thermal Expansion, Mean Coefficient of Linear Thermal Expansion,
Temperature, °C
μm/(m · °C) μm/(m · °C)
1100 12.33
1000 11.87
900 11.26
800 11.08
700 10.75
600 10.45
550 35.3 10.31
500 33.2 10.18
450 31.8 10.05
400 30.5 9.92
350 29.2 9.80
300 27.8 9.67
250 26.8 9.64
200 26.2 9.45
150 25.5 9.38
100 24.5 9.18
50 23.6 9.01
0 22.6 8.85
–50 20.9 8.59
–100 18.8 8.19
–150 7.37
A
Mean coefficient of linear thermal expansion values are calculated for ±50 °C from the indicated temperature except in the case of platinum where values are for ±100
°C of the indicated temperature for the range of 200200 °C to 700 °C.
B
Nix, F. C., and MacNair, D., “The Thermal Expansion of Pure Metals: Copper, Gold, Aluminum, Nickel, and Iron,” Physical Review, Vol 60, 1941, pp. 597–605.
C
Simmons, R. O., and Balluffi, R. W., “Measurements of Equilibrium Vacancy Concentrations in Aluminum,” Physical Review, Vol 117, 1960, pp. 52–31.
D
Fraser, D. B., and Hollis Hallet, A. C., “The Coefficient of Linear Expansion and Gruneisen γ of Cu, Ag, Au, Fe, Ni, and Al from 4°K to 300°K,” Proceedings of the 7th
International Conference on Low-Temperature Physics, 1961, pp. 689–692.
E
Altman, H. W., Rubin, T., and Johnson, H. L., Ohio State University, Cryogenic Laboratory Report OSU-TR-264–27 (1954) AD 26970.
F
Hidnert, P., and Krider, H. S., “Thermal Expansion of Aluminum and Some Aluminum Alloys,” Journal of Research National Bureau of Standards, Vol 48, 1952, pp.
209–220
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