1、Designation: E 289 04Standard Test Method forLinear Thermal Expansion of Rigid Solids withInterferometry1This standard is issued under the fixed designation E 289; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last re
2、vision. 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 test method covers the determination of linearthermal expansion of rigid solids using either a Michelson orFizeau inter
3、ferometer.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 many rigid solids
4、 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 particular material
5、 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 significantly hi
6、gher than that ofcomparative methods such as push rod dilatometry (for ex-ample, Test Methods D 696 and E 228) and thermomechanicalanalysis (for example, Test Method E 831) techniques. It isapplicable to materials having low and either positive ornegative coefficients of expansion (below 5 m/(mK) an
7、dwhere 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 thatall such in
8、struments or techniques may not be equivalent. It isthe responsibility of the user to determine the necessaryequivalency prior to use.1.7 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to esta
9、blish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2D 696 Test Method for Coefficient of Linear Thermal Ex-pansion of PlasticsE 220 Test Method for Calibration of Thermocouples byComparison
10、TechniquesE 228 Test Method for Linear Thermal Expansion of SolidMaterials with a Vitreous Silica DilatometerE 473 Terminology Relating to Thermal AnalysisE 831 Test Method for Linear Thermal Expansion of SolidMaterials by Thermomechanical AnalysisE 1142 Terminology Relating to Thermophysical Proper
11、ties3. Terminology3.1 Definitions:3.1.1 The following terms are applicable to this documentand are listed in Terminology E 473 and E 1142: coefficient oflinear thermal expansion, thermodilatometry, thermomechani-cal analysis.3.2 Definitions of Terms Specific to This Standard:3.2.1 thermal expansivit
12、y, aT, at temperature T, is calculatedas follows from slope of length v temperature curve:aT51LiT2 T1limitL22 L1T22 T151LidLdTwith T1, Ti, T2(1)and expressed as m/mK.NOTE 1Thermal expansivity is sometimes referred to as instanta-neous coefficient of linear expansion.3.2.2 mean coeffcient of linear t
13、hermal expansion, am, theaverage change in length relative to the length of the specimenaccompanying a change in temperature between temperaturesT1and T2, expressed as follows:am 51L0L22 L1T22 T151LoDLDT(2)1This test method is under jurisdiction of ASTM Committee E37 on ThermalMeasurements and is th
14、e direct responsibility of Subcommittee E37.05 on Thermo-physical Properties.Current edition approved May 1, 2004. Published June 2004. Originallyapproved in 1965. Last previous edition approved in 1999 as E 289 99.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM
15、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, United States.where:amis obtained by dividing
16、 the linear thermal expansion(DL/L0) by the change of temperature (DT). It is normallyexpressed as m/mK. Dimensions (L) are normally expressedin mm and wavelength (l)in nm.3.3 Symbols:Symbols:3.3.1 am= mean coefficient of linear thermal expansion, see3.2.1, /K1.3.3.2 aT= expansivity at temperature T
17、, see 3.2.2, / K1.3.3.3 L0= original length of specimen at temperature T0,mm.3.3.4 L1= length at temperature 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 T0= temperature at which initial length is L0, K.3.3.8 T1, T2= t
18、wo temperatures at which measurements aremade, K.3.3.9 DT = temperature difference between T2and T1, K.3.3.10 N = number of fringes including fractional parts thatare measured on changing temperature from T1to T2.3.3.11 lv= wavelength of light used to produce fringes, nm.3.3.12 nr= index of refracti
19、on of gas at reference conditionof temperature 288K and pressure of 100 kPa.3.3.13 n = index of refraction of gas at temperature T andpressure, P.3.3.14 n1, n2= index of refractive of gas at temperature T1and T2, and pressure, P.3.3.15 P = average pressure of gas during test, torr.3.3.16 DLs= change
20、 in length of reference specimen be-tween T1and T2, mm.4. Summary of Test Method4.1 A specimen of known 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
21、 or flat parallel endsor machined to provide a 3-point support. The mirrors consistof flat-uniform thickness 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 mo
22、nochromatic source (Fizeau, seeFig. 4) illuminates each surface simultaneously to produce afringe pattern. 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 c
23、hange is detected and converted intolength change from which the expansion and expansion coef-ficient can be determined(1-5).5. 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
24、artifact composed ofdifferent materials may fail when it is subjected to a tempera-ture excursion(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 dilato
25、metry such as Test Methods D 696,E 228, and TMA methods such as Test Methods E 831 are notsufficiently 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
26、:5.3.1 Measure very small changes in length;5.3.2 Develop reference materials and transfer standards 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 p
27、arameters; change of length and change of temperature.Since precise measurements of the first parameter 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 diffe
28、rence.Thus in order to ensure the necessary uniformity in temperatureof the specimen, it is essential 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 e
29、ssential details of the designprinciples, specimen configurations, and procedures to provideprecise values 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 diffic
30、ulties to a person not having the technicalknowledge relating to the thermal measurements and generaltesting practice. Standardization of the method is not intendedto restrict in any way further development of improvedmethodology.5.6 The test method can be used for research, development,specificatio
31、n acceptance and quality control and assurance.FIG. 1 Typical Specimen Configurations (a) Michelson Type, (bd)Fizeau TypeE2890426. 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 fro
32、m 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 equi
33、librium 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 princ
34、iple 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 ima
35、ge 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 in
36、terference 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 orcooled, both th
37、e specimen and support change of lengths causethe surface S and M2to move relative to M1at different rates.The difference in the fringe count provides a measure of the netabsolute expansion.FIG. 2 (a) Principle of the Single Pass Michelson Interferometer, (b) Typical Single Pass SystemFIG. 3 Typical
38、 Double Pass Michelson Interferometer SystemFIG. 4 Principle of the Fizeau InterferometerE2890437.1.3 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 flat ends a
39、nd 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 polarized laser
40、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 of the i
41、nstantaneous 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 type is avai
42、lable 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 andradial
43、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 of P2is m
44、ade 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 furnace an
45、d 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 together with m
46、anual, 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 (32AWG or sm
47、aller wire) or thin foil thermocouples calibrated inaccordance with Test Method E 220.7.4.1.2 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 calibration
48、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 refer
49、ence 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.7.5 A measurement instrument such as an index micrometeror calipers capable of reading to 0.01 mm in order to determinethe initial and final lengths of the test specimen (and otherFIG. 5 Typical FurnaceFIG. 6 Typical Low-Temperature CryostatE289044relevant components where required, see Section 8.1) andadjusting the specimen length originally to obtain fringes
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