1、Designation: E289 04 (Reapproved 2010)Standard Test Method forLinear Thermal Expansion of Rigid Solids withInterferometry1This standard is issued under the fixed designation E289; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the
2、 year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1. Scope1.1 This test method covers the determination of linearthermal expansion of rigid solids using either a Michelson
3、 orFizeau interferometer.1.2 For this purpose, a rigid solid is defined as a materialwhich, at test temperature and under the stresses imposed byinstrumentation, has a negligible creep, insofar as significantlyaffecting the precision of thermal length change measurements.1.3 It is recognized that ma
4、ny rigid solids require detailedpreconditioning and specific thermal test schedules for correctevaluation of linear thermal expansion behavior for certainmaterial applications. Since a general method of test cannotcover all specific requirements, details of this nature should bediscussed in the part
5、icular material specifications.1.4 This test method is applicable to the approximatetemperature range 150 to 700C. The temperature range maybe extended depending on the instrumentation and calibrationmaterials used.1.5 The precision of measurement of this absolute method(better than 640 nm/(mK) is s
6、ignificantly higher than that ofcomparative methods such as push rod dilatometry (for ex-ample, Test Methods D696 and E228) and thermomechanicalanalysis (for example, Test Method E831) techniques. It isapplicable to materials having low and either positive ornegative coefficients of expansion (below
7、 5 m/(mK) andwhere only very limited lengths or thickness of other higherexpansion coefficient materials are available.1.6 Computer or electronic based instrumentation, tech-niques and data analysis systems equivalent to this test methodcan be used. Users of the test method are expressly advised tha
8、tall such instruments or techniques may not be equivalent. It isthe responsibility of the user to determine the necessaryequivalency prior to use.1.7 The values stated in SI units are to be regarded asstandard. No other units of measurement are included in thisstandard.1.8 This standard does not pur
9、port to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2D6
10、96 Test Method for Coefficient of Linear Thermal Ex-pansion of Plastics Between 30C and 30C with aVitreous Silica DilatometerE220 Test Method for Calibration of Thermocouples ByComparison TechniquesE228 Test Method for Linear Thermal Expansion of SolidMaterials With a Push-Rod DilatometerE473 Termin
11、ology Relating to Thermal Analysis and Rhe-ologyE831 Test Method for Linear Thermal Expansion of SolidMaterials by Thermomechanical AnalysisE1142 Terminology Relating to Thermophysical Properties3. Terminology3.1 Definitions:3.1.1 The following terms are applicable to this documentand are listed in
12、Terminology E473 and E1142: coefficient oflinear thermal expansion, thermodilatometry, thermomechani-cal analysis.3.2 Definitions of Terms Specific to This Standard:3.2.1 mean coeffcient of linear thermal expansion, am, theaverage change in length relative to the length of the specimenaccompanying a
13、 change in temperature between temperaturesT1and T2, expressed as follows:am 51L0L22 L1T22 T151LoDLDT(1)where:amis obtained by dividing the linear thermal expansion(DL/L0) by the change of temperature (DT). It is normally1This test method is under jurisdiction of ASTM Committee E37 on ThermalMeasure
14、ments and is the direct responsibility of Subcommittee E37.05 on Thermo-physical Properties.Current edition approved March 1, 2010. Published May 2010. Originallyapproved in 1965. Last previous edition approved in 2004 as E289 04. DOI:10.1520/E0289-04R10.2For referenced ASTM standards, visit the AST
15、M website, www.astm.org, orcontact ASTM Customer service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, Unite
16、d States.expressed as m/mK. Dimensions (L) are normally expressedin mm and wavelength (l)in nm.3.2.2 thermal expansivity, aT, at temperature T, is calculatedas follows from slope of length v temperature curve:aT51LiT2T1limitL22 L1T22 T151LidLdTwith T1, Ti, T2(2)and expressed as m/mK.NOTE 1Thermal ex
17、pansivity is sometimes referred to as instanta-neous coefficient of linear expansion.3.3 Symbols:3.3.1 am= mean coefficient of linear thermal expansion, see3.2.2,/K1.3.3.2 aT= expansivity at temperature T, see 3.2.1,/K1.3.3.3 L0= original length of specimen at temperature T0,mm.3.3.4 L1= length at t
18、emperature T1, mm.3.3.5 L2= length at temperature T2, mm.3.3.6 DL = change in length of specimen between tempera-tures T1and T2, nm.3.3.7 DLs= change in length of reference specimen betweenT1and T2, mm.3.3.8 T0= temperature at which initial length is L0, K.3.3.9 N = number of fringes including fract
19、ional parts thatare measured on changing temperature from T1to T2.3.3.10 n = index of refraction of gas at temperature T andpressure, P.3.3.11 nr= index of refraction of gas at reference conditionof temperature 288K and pressure of 100 kPa.3.3.12 n1, n2= index of refractive of gas at temperature T1a
20、nd T2, and pressure, P.3.3.13 P = average pressure of gas during test, torr.3.3.14 T1, T2= two temperatures at which measurementsare made, K.3.3.15 DT = temperature difference between T2and T1, K.3.3.16 lv= wavelength of light used to produce fringes, nm.4. Summary of Test Method4.1 A specimen of kn
21、own geometry can be given polishedreflective ends or placed between two flat reflecting surfaces(mirrors). Typical configurations, as shown in Fig. 1, are acylindrical tube or a rod with hemispherical or flat parallel endsor machined to provide a 3-point support. The mirrors consistof flat-uniform t
22、hickness pieces of silica or sapphire with thesurfaces partially coated with gold or other high reflectancemetal. Light, either parallel laser beam (Michelson, see Fig. 2and Fig. 3) or from a point monochromatic source (Fizeau, seeFig. 4) illuminates each surface simultaneously to produce afringe pa
23、ttern. As the specimen is heated or cooled, expansionor contraction of the specimen causes a change in the fringepattern due to the optical pathlength difference between thereflecting surfaces. This change is detected and converted intolength change from which the expansion and expansion coef-ficien
24、t can be determined (1-5).35. Significance and Use5.1 Coefficients of linear expansion are required for designpurposes and are used particularly to determine thermalstresses that can occur when a solid artifact composed ofdifferent materials may fail when it is subjected to a tempera-ture excursion(
25、s).5.2 Many new composites are being produced that havevery low thermal expansion coefficients for use in applicationswhere very precise and critical alignment of components isnecessary. Push rod dilatometry such as Test Methods D696,E228, and TMA methods such as Test Methods E831 are notsufficientl
26、y precise for reliable measurements either on suchmaterial and systems, or on very short specimens of materialshaving higher coefficients.5.3 The precision of the absolute method allows for its useto:5.3.1 Measure very small changes in length;5.3.2 Develop reference materials and transfer standards
27、forcalibration of other less precise techniques;5.3.3 Measure and compare precisely the differences incoefficient of “matched” materials.5.4 The precise measurement of thermal expansion involvestwo parameters; change of length and change of temperature.Since precise measurements of the first paramet
28、er can be madeby this test method, it is essential that great attention is alsopaid to the second, in order to ensure that calculated expansioncoefficients are based on the required temperature difference.Thus in order to ensure the necessary uniformity in temperatureof the specimen, it is essential
29、 that the uniform temperaturezone of the surrounding furnace or environmental chambershall be made significantly longer than the combined length ofspecimen and mirrors.5.5 This test method contains essential details of the designprinciples, specimen configurations, and procedures to provideprecise v
30、alues of thermal expansion. It is not practical in amethod of this type to try to establish specific details of design,construction, and procedures to cover all contingencies thatmight present difficulties to a person not having the technical3The boldface numbers in parentheses refer to a list of re
31、ferences at the end ofthis standard.FIG. 1 Typical Specimen Configurations (a) Michelson Type, (bd)Fizeau TypeE289 04 (2010)2knowledge relating to the thermal measurements and generaltesting practice. Standardization of the method is not intendedto restrict in any way further development of improved
32、methodology.5.6 The test method can be used for research, development,specification acceptance and quality control and assurance.6. Interferences6.1 Measurements should normally be undertaken with thespecimen in vacuum or in helium at a low gas pressure in orderto off-set optical drifts resulting fr
33、om instabilities of therefractive index of air or other gases at normal pressures.However, due to the reduced heat transfer coefficient from thesurrounding environment, measurement in vacuum or lowpressure can make actual specimen temperature measurementmore difficult. Additional care and longer equ
34、ilibrium time toensure that the specimen is at a uniform temperature arenecessary.6.2 If vitreous silica flats are used, continuous heating tohigh temperatures may cause them to distort and becomecloudy resulting in poor fringe definition.7. Apparatus7.1 Interferometer, Michelson Type:7.1.1 The prin
35、ciple of the single pass absolute system isshown in Fig. 2a. A parallel light beam usually generated froma laser through a beam expander is split by a beam splitter B.The resulting beams are reflected by mirrors M1and M2andrecombined on B. If M82is inclined slightly over the light-beam its mirror im
36、age M82forms a small angle with M1producing fringes of equal thickness located on the virtual faceM82.7.1.2 One example of a single contact type is shown in Fig.2b. A prism or a polished very flat faced cylindrical specimenis placed on one mirror with one face also offered to theincident light. An i
37、nterference pattern is generated and this isdivided into two fields corresponding to each end of thespecimen. The lens, L, projects the image of the fringes onto aplane where two detectors are placed one on the specimen andthe other on the baseplate fields. As the specimen is heated orFIG. 2 (a) Pri
38、nciple of the Single Pass Michelson Interferometer, (b) Typical Single Pass SystemFIG. 3 Typical Double Pass Michelson Interferometer SystemFIG. 4 Principle of the Fizeau InterferometerE289 04 (2010)3cooled, both the specimen and support change of lengths causethe surface S and M2to move relative to
39、 M1at different rates.The difference in the fringe count provides a measure of the netabsolute expansion.7.1.3 The principle of the double pass system is essentiallysimilar to the single pass with three important distinctions. Thespecimen can be a relatively simple cylinder with hemispheri-cal or fl
40、at ends and requiring less precise machining, theinterfering beams are reflected twice from each face to thespecimen thus giving twice the sensitivity of the single pass,and no reference arm is required. One example of the doublepass form is shown in Fig. 3.7.1.4 It is common practice to use polariz
41、ed laser light andquarter wave plates to generate circularly polarized light. Inthis way detectors combined with appropriate analyzers gen-erate signals either with information on fringe number, fractionand motion sense for each beam or linear array data of lightintensity, which indicate the profile
42、 of the instantaneous wholefringe pattern. The array data provides complete information(position of fringe and distance between fringes) to determinethe absolute length change of the specimen depending upon thesystem. These signals are normally processed electronically.7.2 Fizeau Type:7.2.1 This typ
43、e is available in both absolute and compara-tive versions.7.2.2 The principle of the absolute method is illustrated inFig. 4. The specimen is retained between two parallel platesand illuminated by the point source. Expansion or contractionof the specimen causes spatial variation between the plates a
44、ndradial motion of the circular fringe pattern.7.2.3 The difference in the fringe counts yields the netabsolute expansion of the specimen.7.2.4 In practice, P1is wedge shaped (less than 30 min ofarc) such that light reflected by the upper face is diverted fromthe viewing field, while the lower face
45、of P2is made to absorbthe incident light, depending upon the total separation of theflats.7.2.5 For use in the comparative mode, two forms areavailable. These are described in detailed in Annex A1.7.3 Furnace/Cryostat:7.3.1 Fig. 5 and Fig. 6 illustrate the construction of a typicalvertical type of f
46、urnace and cryostat that are suitable for use inundertaking these measurements. For the double pass Michel-son system, horizontal forms of furnace and cryostat can beused.7.4 Temperature Measurement System:7.4.1 The temperature measurement system shall consist ofa calibrated sensor or sensors togeth
47、er with manual, electronicor equivalent read-out such that the indicated temperature canbe determined better than 6 0.5C.7.4.1.1 Since this method is used over a broad temperaturerange, different types of sensors may have to be used to coverthe complete range. The common sensor(s) is a fine gage (32
48、AWG or smaller wire) or thin foil thermocouples calibrated inaccordance with Test Method E220.7.4.1.2 Types E and T are recommended for the temperaturerange 190 to 350C and Types K and S and Nicrosil for thetemperature range from 0 to 800C. If Type K is usedcontinuously, regular checking of the cali
49、bration should beundertaken to ensure that contamination or phase changephenomena due to alloy component migration from the junc-tion has not taken place during testing.7.4.1.3 In all cases where thermocouples are used they shallbe referenced to 0C by means of an ice water bath orequivalent electronic reference system, insulated from theeffects of temperature variations in the immediate surroundingambient.7.4.1.4 For temperatures below 190C a calibrated carbonor germanium resistance thermometer is used.FIG. 5 Typical FurnaceFIG. 6 Typical Low-Temperatur
