1、Designation: E 2113 04Standard Test Method forLength Change Calibration of Thermomechanical Analyzers1This standard is issued under the fixed designation E 2113; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revi
2、sion. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This method describes calibration of the length change(deflection) measurement or thermal expansion of thermome-chanical analy
3、zers (TMA) within the temperature range from-150 to 1000 C using the thermal expansion of a suitablereference material.1.2 SI values are the standard.1.3 This method differs from ISO standard 11359-1 byproviding an alternative calibration procedure.1.4 This standard does not purport to address all o
4、f thesafety concerns, if any, associated with its use. It is theresponsibility of whoever uses this standard to consult andestablish appropriate safety and health practices and deter-mine the applicability of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:E 473 Termino
5、logy Relating to Thermal Analysis2E 831 Test Method for Linear Thermal Expansion of SolidMaterials by Thermomechanical Analysis2E 1142 Terminology Relating to Thermophysical Proper-ties2E 1363 Test Method for Temperature Calibration of Ther-momechanical Analyzers22.2 Other Standards:ISO 11359-1 Plas
6、ticsThermomechanical analysis(TMA)Part 1: General principles33. Terminology3.1 Specific technical terms used in this method are de-scribed in Terminologies E 473 and E 1142.4. Summary of Test Method4.1 Thermomechanical analyzers (TMAs) or related devicesare commonly used to determine coefficient of
7、linear thermalexpansion of solid materials (e.g., Test Method E 831). The testspecimen is heated at a linear rate over the temperature rangeof interest and the change in length (dimension) is electroni-cally recorded.4.2 Performance verification or calibration of the lengthchange measurement is need
8、ed to obtain accurate coefficient ofthermal expansion data.4.3 The thermal expansion of a reference material is re-corded using a thermomechanical analyzer. The recordedthermal expansion is compared to the known value of thereference material. The resultant ratio, a calibration coefficient,may then
9、be applied to the determination of unknown speci-mens to obtain accurate results.5. Significance and Use5.1 Performance verification or calibration is essential to theaccurate determination of quantitative dimension change mea-surements.5.2 This method may be used for instrument performancevalidatio
10、n, regulatory compliance, research and developmentand quality assurance purposes.6. Apparatus6.1 Thermomechanical Analyzer (TMA) The essentialinstrumentation required to provide the minimum thermome-chanical analytical or thermodilatometric capability for thismethod includes:6.1.1 A rigid specimen h
11、older of inert, low expansivitymaterial 0.5 m m-1K-1 to center the specimen in thefurnace and to fix the specimen to mechanical ground.6.1.2 A rigid expansion probe of inert, low expansivitymaterial 0.5 m m-1K1 which contacts the specimen withan applicable compressive or tensile force.6.1.3 A sensin
12、g element, linear over a minimum of 2 mm, tomeasure the displacement of the rigid probe to within 6 10 nmresulting from changes in length/height of the specimen.6.1.4 A weight or force transducer to generate a constantforce between 1 and 100 mN (0.1 and 10 g) applied through therigid probe to the sp
13、ecimen.6.1.5 A furnace capable of providing uniform controlledheating (cooling) of a specimen to a constant temperature or ata constant rate within the applicable temperature range of thismethod.1This test method is under the jurisdiction of ASTM Committee E37 on ThermalMeasurements and is the direc
14、t responsibility of Subcommittee E37.01 on Thermal.Current edition approved Oct. 1, 2004. Published November 2004. Originallyapproved in 2000. Last previous edition approved in 2002 as E 211302.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at s
15、erviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.3Available from American National Standards Institute, 11 W 42nd Street, 13thFloor, New York, NY 10036.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C70
16、0, West Conshohocken, PA 19428-2959, United States.6.1.6 A temperature controller capable of executing a spe-cific temperature program by operating the furnace over anysuitable temperature range between -150 and 1000 C at a rateof temperature change of 5 K/min constant to within 6 0.1K/min.6.1.7 A t
17、emperature sensor that can be attached to, incontact with, or reproducibly positioned in close proximity tothe specimen to provide an indication of the specimen/furnacetemperature to within 6 0.1 K.6.1.8 A means of sustaining an environment around thespecimen of an inert purge gas at a rate of 10 to
18、 50 6 5mL/min.NOTE 1Typically, 99.9+% pure nitrogen, helium or argon is em-ployed, when oxidation in air is a concern. Unless effects of moisture areto be studied, use of dry purge gas is recommended and is essential foroperation at subambient temperatures.6.1.9 A recording device, capable of record
19、ing and display-ing any fraction of the specimen dimension change signal(TMA curve) including the signal noise on the ordinate(Y-axis) versus temperature on the abscissa (X-axis).6.2 Micrometer, calipers or other length measurement de-vice capable of measuring linear dimensions up to 10 mm withreada
20、bility of 6 25 m.6.3 While not required, the user may find useful softwarethat performs the calculations described in this method.6.4 Thermal expansion reference material of 8 6 2mmlength, the linear coefficient of expansion of which is known to6 0.1 m m-1K-1. The coefficient of thermal expansion sh
21、ouldbe between 9 and 40 m m-1K-1.6.4.1 Reference materials of known value traceable to aNational Reference laboratory are available from a number ofsuppliers. Contact ASTM Headquarters for list of such poten-tial suppliers4.6.4.2 In the absence of primary or secondary referencematerials, high purity
22、 aluminum or platinum may be usedalong with the values for coefficient of thermal expansionpresented in Table 1.NOTE 2The linear expansion of high purity aluminum, commonlysupplied by instrument manufactures, is useful as a working referencematerial. Coefficient of thermal expansion values for pure
23、aluminum arepresented in Table 1 along with those for platinum.7. Test Specimen7.1 Specimens shall be between 6 and 10 mm in length andhave flat and parallel ends to within 6 25 m. Lateraldimensions shall be between 3 and 9 mm. Other lengths andwidths may be used but shall be noted in the report.8.
24、Calibration8.1 Perform any calibration procedures described in themanufacturers operations manual.8.2 Calibrate the temperature sensor using Method E 1363.9. Procedure9.1 Measure the initial specimen length in the direction ofthe expansion test to within 6 25 m at 23 6 2 C.4A Research Report is avai
25、lable from ASTM Headquarters. RequestRR:E371033.TABLE 1 Thermal Expansion CoefficientsAAluminumBCDEFPlatinumGHI,JTemperature, CMean Coefficient of Linear Thermal Expansion, m/(m C)Mean Coefficient of Linear Thermal Expansion, m/(m C)1100 12.331000 11.87900 11.26800 11.08700 10.75600 10.45550 35.3 10
26、.31500 33.2 10.18450 31.8 10.05400 30.5 9.92350 29.2 9.80300 27.8 9.67250 26.8 9.64200 26.2 9.45150 25.5 9.38100 24.5 9.1850 23.6 9.010 22.6 8.8550 20.9 8.59100 18.8 8.19150 7.37AMean coefficient of linear thermal expansion values are calculated for 6 50 C from the indicated temperature except in th
27、e case of platinum where values are for 6100 C of the indicated temperature for the range of 200 to 700 C.BNix, F. C., and MacNair D., Physical Review, Vol 60, 1941, p. 597.CSimmons, R. O., and Balluffi R. W., Physical Review, Vol 117, 1960, p. 52.DFraser, D. B., and Hollis Hallet, A. C., 7th Intern
28、ational Conference on Low-Temperature Physics, 1961, p. 689.EAltman, H. W., Rubin, T., and Johnson, H. L., Ohio State University, Cryogenic Laboratory Report OSU-TR-26427 (1954) AD 26970.FHidnert, P., and Krider, H. S., Journal of Research National Bureau of Standards, Vol 48, 1952, p. 209.GNix, F.
29、C., and MacNair, D., Physical Review, Vol 61, 1942, p. 74.HWhite, G. K., Journal of Physics, Vol 2F, 1972, p. 130.IHahn, T. A., and Kirby, R. K., AIP Conference Proceedings, No. 3, Vol 87, 1972.JKirby, R. K., Thermal Conductivity 24/Thermal Expansion 12, Technomic Publishing, Lancaster, PA 1997, pp.
30、 655661.E21130429.2 Place the specimen on the specimen holder under theprobe. Place the specimen temperature sensor within 2 mm butnot touching the test specimen.9.3 Move the furnace to enclose the specimen holder. Ifmeasurements at subambient temperatures are to be made, coolthe test specimen to at
31、 least 20 C below the lowest tempera-ture of interest. The refrigerant used for cooling shall not comeinto direct contact with the specimen.9.4 Apply an appropriate load force to the sensing probe toensure that it is in contact with the specimen. A force between1 and 50 mN (0.1 and 5 g) is adequate.
32、 The actual incrementalforce, mass or stress above that required to make contact withthe zero force shall be noted in the report.9.5 Heat the specimen at a rate of 5 6 0.1 C/min over thedesired temperature range and record the change in specimenlength and temperature to all available decimal places.
33、 Otherheating rates may be used but shall be noted in the report.NOTE 3For best results, specimen temperature gradients should besmall. High heating rates, large specimen size and low specimen thermalconductivity may lead to large specimen temperature gradients.NOTE 4Intralaboratory testing indicate
34、s that no detectable increase inimprecision is observed for specimens size 2 to 20 mm in length, forheating rates between 2 and 10 C min-1and for thermal conductivitiesbetween 0.2 and 400 Wm-1K1, if only one parameter is changed.9.6 Determine the measurement instrument baseline byrepeating steps 9.2
35、-9.5 using the same test parameters butwithout a test specimen. The measured change of length (DL)of the specimen should normally be corrected by curvesubtraction for this baseline (that is, the probe is placed on theempty specimen holder) especially for low expansion materi-als.9.7 Select a DT from
36、 a smooth portion of the thermal curvein the desired temperature range. Then obtain the DL for thistemperature range as depicted in Fig. 1.9.8 Record the change in length (DL) for the test specimenover a corresponding change in temperature (DT). See Fig. 1.NOTE 5For the best calibration results, val
37、ues for DT should rangebetween 50 and 100 C.FIG. 1 Specimen Expansion Versus TemperatureE211304310. Calculation10.1 Calculate the mean coefficient of linear thermal expan-sion for the desired temperature range and calibration coeffi-cient retaining all available significant figures.k 5a L DT / DL (1
38、)where:a = mean coefficient of linear thermal expansion for thereference material at the midpoint of the DT range, inm m-1C-1.k = calibration coefficient, dimensionlessL = length of the reference material at room temperature,in mDL = change in length of the reference material due toheating, in mDT =
39、 temperature difference over which the change inspecimen length is measured, in C.NOTE 6The mean coefficient of linear thermal expansion describedhere is an approximation to the traditional coefficient of linear thermalexpansion where the reference length is taken at the test temperature ofinterest.
40、 This approximation creates a bias on the order of about 0.015%.10.2 The true length change (DLt) of an unknown may bederived by multiplication of the observed length change (DLo)by the calculation coefficient (k).DLt5 k DLo(2).11. Report11.1 Designation of the Reference Material for coefficient ofl
41、inear thermal expansion including its source, lot number andchemical composition.11.2 Dimensions of the specimen and any physical, me-chanical or thermal pre-treatment and orientation with respectto the original part (if cut to size).11.3 Designation of the thermomechanical analyzer bymodel number,
42、serial number and specimen holder stage andprobe type.11.4 Experimental conditions including temperature rangeof test, heating rate, purge gas type and flow rate.11.5 The calibration coefficient value determined the mid-point of the temperature range of calibration. For example:k = 1.001 at 100 C.11
43、.6 The specific dated version of this method used.12. Precision and Bias12.1 Precision12.1.1 Precision of the calibration constant value may beestimated by the propagation of uncertainties method fromestimates of the precision of the respective components of thecalculation using:dkk5FSdDLDLD21SdLLD2
44、1SdDTDTD2G12(3)where:k = calibration coefficient, dimensionlessdk = imprecision in the measurement of k, dimensionlessL = length of the reference material, in mmdL = imprecision in the measurement of L, in mmDL = change in specimen length due to heating, in mdDL = imprecision of the measurement of L
45、, in mDT = temperature difference over which the change inspecimen length is measured, in CdDT = imprecision of the measurement of DT, in C.12.1.2 For example, if:L = 8.00 mmdL = 25 m = 0.025 mmDL = 18.8 mdDL = 0.10 mDT = 100.0CdDT = 0.10Cdkk5FS0.10 m18.8 mD21S0.025 mm8.00 mmD21S0.10 C100.0 CD2G12(4
46、)dk/k 5 0.005319!21 0.003125!21 0.001000!2#12 (5)dk/k 5 0.00002829! 1 0.000009766! 1 0.000001000!#125 0.00003905612 (6)dk/k 5 0.006249 (7)or expressed as percentdk/k 5 0.6249 % (8)12.1.3 Intralaboratory precision measurements confirm therelationship in section 12.1.1.12.1.4 An interlaboratory test i
47、nvolving eight laboratoriesand six instrument models was conducted in 19854.Analuminum calibration material, 8.0 mm in length was testedover a 100C temperature range.12.1.5 Repeatability The standard deviation of resultsobtained by a single instrument and laboratory was 6 2.6%.Two results, each the
48、mean value of duplicate determinations,should be considered suspect (95% confidence limit) if theydiffer by more than 7.3%.12.1.6 Since the determination of the calibration coefficientis specific to a single instrument or laboratory, interlaboratoryreproducibility has no meaning and is not reported.
49、12.2 Bias12.2.1 The calibration constant determined by this method(i.e., its difference from unity) is, in itself, an estimation ofbias. No further estimation is necessary.13. Keywords13.1 calibration; coefficient of thermal expansion; deflec-tion; expansion; expansivity; thermal analysis; thermal expan-sion; thermomechanical analyzer (TMA)E2113044ASTM International takes no position respecting the validity of any patent rights asserted in connection with any item mentionedin this standard. Users of this
