Linear Thermal Expansion of Solid Materials With A Vitreous Silica Dilatometer [PDF]

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Designation: E 228 – 95 AMERICAN SOCIETY FOR TESTING AND MATERIALS 100 Barr Harbor Dr., West Conshohocken, PA 19428 Reprinted from the Annual Book of ASTM Standards. Copyright ASTM

Standard Test Method for

Linear Thermal Expansion of Solid Materials With a Vitreous Silica Dilatometer1 This standard is issued under the fixed designation E 228; 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 (e) indicates an editorial change since the last revision or reapproval.

all such instruments or techniques may not be equivalent. It is the responsibility of the user to determine the necessary equivalency prior to use. In the case of dispute only, the manual procedures described herein are to be considered valid. 1.6 The values stated in SI units are to be regarded as the standard. 1.7 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 and health practices and determine the applicability of regulatory limitations prior to use.

1. Scope 1.1 This test method covers the determination of the linear thermal expansion of rigid solid materials over the temperature range of −180 to 900°C using vitreous silica push-rod or tube dilatometers. NOTE 1—The temperature range for push-rod dilatometers can be extended to 1600°C by using high-purity alumina push-rod systems and up to over 2500°C using isotropic graphite systems. 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.

2. Referenced Documents 2.1 ASTM Standards: D 696 Test Method for Coefficient of Linear Thermal Expansion of Plastics2 E 220 Test Method for Calibration of Thermocouples by Comparison Techniques3 E 289 Test Method for Linear Thermal Expansion of Rigid Solids with Interferometry4 E 473 Terminology Relating to Thermal Analysis4 E 644 Test Methods for Industrial Resistance Thermometers3 E 831 Test Method for Linear Thermal Expansion of Solid Materials by Thermomechanical Analysis4 E 1142 Terminology Relating to Thermophysical Properties4

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, regarding significantly affecting the precision of thermallength change measurements. This includes metals, ceramics, refractories, glasses, rocks and minerals, graphites, plastics, cements, mortars, woods, and fiber, and other reinforced matrix composites. 1.3 Many materials and certain material applications require that detailed preconditioning and specific thermal test schedules be followed for the correct evaluation of thermal expansion. Since a general test method cannot cover all specific requirements, details of this nature should be contained in the relevant material specification. 1.4 The precision of this comparative test method is greater than that of other push-rod dilatometery (for example, Test Method D 696) and thermomechanical analysis (for example, Test Method E 831) techniques but is significantly lower than that of absolute methods such as interferometry (for example, Test Method E 289). It is generally applicable to materials having linear expansion coefficients above 5 µm/m·K and can be used for lower expansion coefficient materials for which a sufficient length of specimen is available. 1.5 Computer- or electronic-based instrumentation, techniques, and data analysis systems equivalent to this test method can be used. Users of the test method are expressly advised that

3. Terminology 3.1 Definitions—The following terms are applicable to this test method and are listed in Terminologies E 473 and E 1142: coeffıcient of linear thermal expansion, thermodilatometry, and thermomechanical analysis. 3.2 Definitions of Terms Specific to This Standard: 3.2.1 mean coeffıcient of linear thermal expansion, am—the average change in length relative to the length of the specimen accompanying a change in temperature, between temperatures T1 and T2 , expressed as follows: am 5 @~L2 2 L1!/L0 ~T2 2 T1!# 5 ~DL/L0!/DT

(1)

am is, therefore, obtained by dividing the linear thermal 1

This test method is under the jurisdiction of ASTM Committee E-37 on Thermal Measurements and is the direct responsibility of Subcommittee E37.05 on Thermophysical Properties. Current edition approved Sept. 10, 1995. Published December 1995. Originally published as E 228 – 63 T. Last previous edition E 228 – 85 (1989).

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Annual Book of ASTM Standards, Vol 08.01. Annual Book of ASTM Standards, Vol 14.03. 4 Annual Book of ASTM Standards, Vol 14.02. 3

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E 228 temperature excursion(s). 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 vitreous silica dilatometer be calibrated by using a reference material that has a known reproducible thermal expansion. Table 1 and Table 2 contain information on the current thermal expansion standard reference materials available for such purposes. Table 3 contains information relating to other reference materials in current general use. 5.4 The measurement of thermal expansion involves two parameters: change of length and change of temperature. Since measurements of the first parameter can be made by this test method with good precision, it is essential that great attention also be paid to the second. In order to ensure the necessary uniformity in temperature of the specimen, it is essential that the uniform temperature zone of the surrounding furnace or environmental chamber be made significantly longer than the length of the specimen. Temperature gradients depend on the length/diameter ratio and insulation quality of the furnace. They can be reduced by adjusting the furnace heater windings such that they are closer at the ends than at the center. In addition, for high-temperature operations, it is recommended that a heavy metal liner and radiation shields be used. Temperature control is best attained when the sensing element of the controller is either the same as that for measuring the specimen temperature (radiant heating furnace) or very close to the heating element (resistive heated furnace). 5.5 This test method contains essential details of the design principles, specimen configurations, and procedures for providing precise values of thermal expansion. It is not practical in a test method of this type to try to establish specific details of design, construction, and procedures to cover all contingencies that might present difficulties to an individual not having the technical knowledge relating to the thermal measurements and general testing practice. Standardization of the test method is not intended to restrict further development of improved methodology in any way. 5.6 The test method can be used for research, development, specification acceptance, and quality control (QC) and quality assurance (QA).

expansion (DL/L0) by the change of temperature (DT). It is normally expressed as µm/m·K. 3.2.2 thermal expansivity, aT—at temperature T, this is calculated as follows: 1 limit ~L2 2 L1! aT 5 L T2 →T1 5 ~dL/dT!/Li ~T1 , T1 , T2! ~ T2 2 T1 ! i

(2)

and expressed as µm/m·K. NOTE 2—Thermal expansivity is sometimes referred to as the instantaneous coefficient of linear expansion.

3.2.3 vitreous silica dilatometer—a device that measures the difference in linear thermal expansion between a test specimen and the vitreous silica parts of the dilatometer. 3.3 Symbols:Symbols: am aT L0 L1 L2 Li DL (DL/L0)a T0 T1, T2 Ti DT m t s A,B

5 mean coefficient of linear thermal expansion, (see 3.2.1), µm/m·K 5 expansivity at temperature T (see 3.2.2), µm/ m·K 5 original length of specimen at temperature T0, mm 5 length at temperature T1, mm 5 length at temperature T2, mm 5 length at a particular temperature Ti, mm 5 change in length of specimen between temperature T1 and T2, µm 5 expansion indicated by the measurement transducer, µm 5 temperature at which initial length is L0, °K 5 two temperatures at which measurements are made, °K 5 temperature at which length is Ti, °K 5 temperature difference between T2 and T1, °K 5 measured expansion of the reference material, µm 5 true or certified expansion of the reference material, µm 5 assumed or known expansion of the vitreous silica parts of the dilatometer, µm 5 numerical constants (see 9.3.1).

4. Summary of Test Method 4.1 This test method uses a vitreous silica dilatometer of the single push-rod or tube type 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 is sometimes used. This form is described briefly in Appendix X1. 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.

6. Interferences 6.1 Heating unannealed vitreous silica above 800°C may cause viscous flow and a time-dependent change in its thermal expansion. The magnitude of these effects will depend on the particular type of vitreous silica. 6.1.1 Recommended Annealing Procedure—Annealing the vitreous silica specimen and dilatometer parts in the following steps may reduce any excessive lot-to-lot differences in linear thermal expansion: 6.1.1.1 Heat at 100°C/h to 1200°C, 6.1.1.2 Hold at 1200°C for 2 h, 6.1.1.3 Cool at 60°C/h to 1000°C, 6.1.1.4 Cool at 120°C/h to 600°C, and 6.1.1.5 Cool at 200°C/h to room temperature. 6.2 Heating vitreous silica that is contaminated with alkali compounds above 500°C may cause it to crystallize. To prevent

5. Significance and Use 5.1 Coefficients of linear expansion are required for design purposes and are used, for example, to determine thermal stresses that can occur and cause failure of a solid artifact composed of different materials when it is subjected to a 2

E 228 TABLE 1 Thermal Expansion of Various Standard Reference Materials SRM 731 (Borosilicate Glass)A

A

Temperature,° K

Expansion, 10 DL/L293

80 100 120 140 160 180 200 220 240 260 280 293 300 320 340 380 420 460 500 540 560 580 600 620 640 660 680 700 720 740 760 780 800 840 880 920 960 1000

−819 −771 −714 −649 −578 −501 −419 −334 −246 −155 −62 0 34 131 230 432 638 847 1057 1267 1372 1478 1583 1689 1794 1900 2007 ... ... ... ... ... ... ... ... ... ... ...

6

SRM 738 (Stainless Steel)A 6

SRM 739 (Fused Silica)A

106 Expansivity

Expansion, 10 DL/L292

106 Expansivity

Expansion, 106 DL/L293

106 Expansivity

... 2.64 3.07 3.43 3.72 3.97 4.17 4.34 4.48 4.60 4.71 4.78 4.82 4.91 4.99 5.11 5.19 5.23 5.26 5.27 5.27 5.27 5.27 5.28 5.29 ... ... ... ... ... ... ... ... ... ... ... ... ...

... ... ... ... ... ... ... ... ... ... ... 0 69 ... 466 872 1288 1714 2149 2593 ... 3048 ... 3511 ... 3984 ... 4467 ... 4959 ... 5461 ... ... ... ... ... ...

... ... ... ... ... ... ... ... ... ... ... 9.76 9.81 ... 10.04 10.28 10.52 10.76 11.00 11.23 ... 11.47 ... 11.71 ... 11.95 ... 12.19 ... 12.42 ... 12.66 ... ... ... ... ... ...

−1 −13 −22.5 −28.5 −32 −32.5 −31 −27.5 −22 −14 −6 0 ... 13.5 24.5 47.5 72 97 122 ... 159 ... 183 ... 206 ... 228 ... 249 ... 269 ... 228 307 324 340 356 371

−0.07 −0.53 −0.38 −0.24 −0.10 0.02 0.13 0.23 0.32 0.39 0.45 0.48 ... 0.53 0.56 0.60 0.62 0.63 0.63 ... 0.61 ... 0.59 ... 0.56 ... 0.54 ... 0.51 ... 0.49 ... 0.47 0.44 0.42 0.40 0.38 0.37

Available from NIST, Gaithersburg, MD. Values in table from relevant certificate for the reference material.

percent uncertainty in the coefficient, a larger temperature range must be used for low-expansion materials than that for high expansion materials. Conversely, the percent uncertainty of the coefficient will be much larger for the low-expansion material if the same temperature range is used. 6.10 Conditioning of specimens is often necessary before reproducible expansion data can be obtained. For example, heat treatments are frequently necessary to eliminate certain effects (strain, moisture, etc.) that may introduce length changes not associated with thermal expansion.

this, clean the component by immersion in an aqueous solution containing 10 % hydrofluoric acid for 1 min followed by a thorough rinse with distilled water. To prevent contamination with alkali compounds do not touch the vitreous silica with the hands after cleaning. 6.3 Inelastic creep of a specimen at elevated temperatures can often be prevented by making its cross section sufficiently large. 6.4 Care is necessary to control the temperature gradient in long specimens. 6.5 Avoid moisture in the dilatometer, especially when used at cryogenic temperatures. 6.6 A closed specimen holder is required when the dilatometer is immersed in a liquid bath. 6.7 Support or hold the specimen in a position so that it is stable during the test. 6.8 The specimen holder and push-rod shall consist of the same type of vitreous silica. 6.8.1 When applying the system calibration outlined in Section 9, a test run with a vitreous silica specimen should not result in an apparent mean coefficient of linear thermal expansion greater than 6 0.3 µm/m·K. 6.9 Since the precision and accuracy of the length measurements are fixed for a specific apparatus, to obtain the same

7. Apparatus 7.1 Push-Rod Dilatometer System, consisting of the following: 7.1.1 Specimen Holder and Push-Rod or Tube, both made of annealed vitreous silica. Illustrations of typical tube and rod-type configurations are given in Fig. 1. Paragraph 6.1.1 contains a recommended annealing procedure for vitreous silica. 7.1.2 Furnace, Cryostat, and Bath, used for heating or cooling the specimen uniformly at a controlled rate over the temperature range of interest but not below −180°C or above 900°C. 7.1.3 Transducer, for example, a digital encoder, differential 3

E 228 TABLE 2 Thermal Expansion of Standard Reference Material Kieselglas K001A Temperature, °C −170 −160 −140 −120 −100 −80 −60 −40 −20 −10 0 10 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300

Expansion, 106DL/L0 −2.16 −7.35 −15.15 −19.80 −21.67 −21.09 −18.36 −13.76 −7.57 −3.94 0.00 4.23 8.71 18.38 28.81 39.86 51.37 63.22 75.31 87.52 99.78 112.01 124.16 136.18 148.03 159.68 171.10

106a, K−1

Expansivity, 106a (t)

60.67 60.55 60.44 60.43 60.43 60.43 60.41 60.38 60.36 60.34 60.34 60.33 60.33 60.35 60.37 60.39 60.41 60.43 60.44 60.44 60.45 60.45 60.45 60.46 60.47 60.48 0.50

−0.565 −0.475 −0.300 −0.160 −0.030 0.085 0.185 0.272 0.346 0.379 0.409 0.436 0.46 0.504 0.538 0.565 0.585 0.599 0.608 0.612 0.613 0.610 0.605 0.567 0.588 0.577 0.565

60.019 60.016 60.011 60.007 60.005 60.004 60.004 60.004 60.005 60.005 60.005 60.005 60.004 60.004 60.004 60.003 60.003 60.003 60.003 60.003 60.003 60.004 60.004 60.004 60.004 60.004 0.004

0.013 0.046 0.108 0.165 0.217 0.264 0.306 0.344 0.378 0.394 ... 0.423 0.436 0.459 0.480 0.498 0.514 0.527 0.538 0.547 0.554 0.560 0.564 0.567 0.569 0.570 0.570

60.004 60.003 60.003 60.004 60.004 60.006 60.007 60.010 60.019 60.038 ... 60.038 60.019 60.010 60.007 60.006 60.005 60.004 60.004 60.003 60.003 60.003 60.002 60.002 60.002 60.002 60.002

FIG. 1 Common Forms of Tube Types

accordance with Test Method E 220 or fine-gage resistance thermometers calibrated according to Test Methods E 644. 7.1.4.2 Type E and T are recommended for the temperature range of 190 to 350°C, and Types K, S, and N are recommended for temperatures of 0 to 900°C. If Type K is used continuously, regular checking of the calibration should be undertaken to ensure that contamination or phase change phenomena due to alloy component migration from the junction has not occurred during testing. 7.1.4.3 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 reference system insulated from the effects of temperature variations in the immediate surrounding ambient environment. 7.1.4.4 Additional information relating to the precise determination of temperature in dilatometry is contained in Appendix X2. 7.2 Measurement Instrument, such as an index micrometer or calipers capable of reading to at least6 25 µm in order to determine the initial and final lengths of the test specimen (and other relevant components, where required).

A Fused silica available from Physikalisch Technische Bundesanstalt, Braunschweig, Germany. Values in table from relevant certificate for the reference material.

TABLE 3 Linear Thermal Expansion

A B

Temperature, °C

Platinum,A 106DL/L0

Aluminum,B 106DL/L0

−195 −150 −100 −50 0 20 50 100 200 300 400 500 600 700 800

−1756.66 −1420.6 −1024.09 −607.96 −176.2 0 268.06 722.38 1654.6 2612.01 3692.18 4596.55 5628.65 6692.81 7793.27

... −3430 −2550 −1550 −460 0 710 1900 4450 7130 10 050 13 230 16 760 ... ...

8. Test Specimens 8.1 The specimen length shall be such that the accuracy of determining DL/L0 is at least6 20 µm/m. Where possible, the specimen should be at least 256 0.1-mm long and between 5 and 10 mm in diameter.

See Refs (1-3). See Refs (4-8).

NOTE 3—For example, if the transducer is accurate to 62 µm, the length must be at least 0.1 m.

or dial-gage transformer for measuring the difference in length between the specimen and specimen holder or probe with a precision of at least 6 1.3 µm. The transducer shall be protected or mounted so that the maximum temperature change observed in the transducer during a test will affect the transducer readings by not more than 1.0 µm. 7.1.4 Temperature Measurement System, consisting of a calibrated sensor or sensors, together with manual, electronic, or equivalent readout such that the indicated temperature can be determined to better than 60.5°C. 7.1.4.1 Since this test method is used over a broad temperature range, different types of sensors may have to cover the complete range. The common sensors are fine gage (32 AWG or smaller wire) or thin foil thermocouples calibrated in

8.2 The end surfaces of the specimen (as well as the contacting surface of the specimen holder or rods, or both) should not be rougher than approximately 10 µm rms and shall be uniform in shape, as shown in Fig. 2. Avoid pointed specimen ends that may deform during a test. 9. Calibration 9.1 Calibrate the transducer by imposing a series of known displacements with a precision screw micrometer, end-gage blocks, or equally accurate device. This step can be omitted for absolute transducers such as a digital encoder. 9.2 Calibrate the temperature sensor according to Test Methods E 220 and E 644 or the procedure recommended by 4

E 228 10.8 Measure the expansion (contraction) of the specimen over the desired range of temperature to the highest temperature level required. 10.8.1 The most precise measurement is achieved by heating (or cooling) the specimen successively to a number of regular incremental constant temperatures and allowing the system to equilibrate until the transducer reading attains a constant value (variation less than 62.6 µm). At that point, the indicated temperature of the specimen shall not vary by more than 62°C, and the temperature gradient in the specimen shall not exceed 0.5°C/cm. The hold time is a function of the total thermal mass (thermal capacity) of the dilatometer and specimens and will vary for different temperatures. Readings of temperature Ti and changed specimen length Li need to be recorded at each constant temperature Ti. 10.8.2 Alternatively, heat or cool at some constant rate less than 3°C/min. When using this procedure, the mean temperature of the specimen will probably differ from the measured temperature (lower on heating and higher on cooling), but the measured expansion of the test specimen will be accurate if the system is calibrated correctly with a reference material. Readings of temperature and change of length should be recorded continuously. 10.9 A retest should be considered if the length of the specimen at the end of the test differs from that at the beginning by more than 20 µm/m, or this permanent deformation should be taken into account when reporting the expansion values.

FIG. 2 Suggested Shapes of Specimens and Push-Rod Ends

the National Institute of Standards and Technology (NIST) (1).5 9.3 As a total system, calibrate the dilatometer by measuring at least one reference material of known thermal expansion. Select a reference material with expansion as close as possible to that of the sample material. Refer to Tables 1-3 regarding available materials. 9.3.1 Either one of the following two calibration constants indicated in Section 1 may be used: A 5 1DL/L0!m @~DL/L0!t 2 ~DL/L0!s #

(3)

B 5 ~DL/L0!t 2 ~DL/L0!m

(4)

or

11. Calculation 11.1 Depending on the calibration constant used, calculate the linear thermal expansion of the test specimen as follows:

9.3.2 Calibrate the dilatometer using the same test conditions and procedures as those used for the test specimen, for example, the same specimen length, temperature program, and gaseous environment.

~DL/L0! 5 A~DL/L0!a 1 ~DL/L0!s

(5)

~DL/L0! 5 ~DL/L0!a 1 B

(6)

or

10. Procedure 10.1 Each step may not need to be followed in the sequence given and, depending on the apparatus, all steps may not be needed. 10.2 Measure the initial (room temperature) length of the specimen. 10.3 Place the specimen in the dilatometer after making certain that all contacting surfaces are free of foreign material. Ensure good seating of the specimen in a stable position. 10.4 Place the temperature sensor at the mid-length of the specimen. It should preferably be in intimate contact with the specimen, but it shall be as close to the specimen as possible. The temperature sensor shall not restrict movement of the specimen in the dilatometer. 10.5 Ensure that the transducer is in stable contact with the probe(s) and specimen. 10.6 Place the assembled dilatometer into the furnace, cryostat, or bath, and allow the temperature of the specimen to reach equilibrium. 10.7 Record the initial readings of the temperature sensor, T0, and the transducer, L0.

11.2 Using the calculated values of the linear thermal expansion, calculate the mean coefficients by dividing by the appropriate temperature range T1 − T2. am 5 ~DL/L0!DT

(7)

11.3 The following instantaneous coefficients are determined from the slopes, dL/dT, of the length versus temperature curve at each appropriate temperature. The slope may be determined either graphically from a plot or numerically from an equation fit to the data. aT 5 ~1/Li !dL/dT

(8)

11.4 In calculation of the relevant quantities, use all available decimal places for each input parameter, measured to its actual level of precision, through to the final result, and report the data to three significant figures. 12. Report 12.1 Report the following information: 12.1.1 Description of the material, manufacturer, chemical composition, and thermal and mechanical history; 12.1.2 Method of test specimen preparation, and axis orientation, if material is anisotropic, together with details of any subsequent thermal, mechanical, moisture, or other conditioning;

5 The boldface numbers in parentheses refer to the list of references at the end of this test method.

5

E 228 12.1.3 Form and dimensions of the test specimen, including initial length, L0, and reference temperature, T0; 12.1.4 Brief description of the apparatus, including displacement and temperature measuring systems, estimation of precision, heating and cooling rates, temperature controls, and atmosphere; 12.1.5 Listing of the reference material(s) and procedure used to calibrate the dilatometer system, including the transducer and temperature sensor; 12.1.6 Tabulation of the data, showing linear thermal expansion, test temperatures, and values for mean coefficient of linear thermal expansion for selected temperature intervals; 12.1.7 Curves plotted as:

between the assumed or measured value of expansion of the vitreous silica; and, effect of additional surface contacts between the specimen and the transducer. Little can be done to improve the random errors once the transducer and temperature sensor have been selected except to follow good experimental practice. However, systematic errors can be reduced by careful calibration of the individual components and the total system. 13.2 Repeat measurements on many different materials have confirmed that the precision with which linear thermal expansion (DL/L0) is measured with a vitreous silica dilatometer can be estimated from the precision of the length and temperature measurements. This estimate is determined from the following:

~DL/L0 versus T, am versus T, aT versus T

d~~DL/L0! 5 62/L0 @~dE!2 1 ~aT L0 d T!2#2

where: am is computed from a common reference temperature to T; 12.1.8 Complete description of any unusual behavior of the specimen, such as a permanent change in specimen length at the reference temperature following testing, excessive oxidation, scaling, discoloration, deformation, cracking, spalling, etc., all of which may be of value in interpreting the test results; and, 12.1.9 Any additional information required by a particular material specification.

where: dE and dT 5 precisions of the single measurements of length and temperature. The error in measuring L0 is usually so small that it does not contribute to this estimate. For example,

1

(9)

L0 5 0.1 m, dE 5 61 µm, dT 5 20 µm/m°C and dT 5 60.5°C

The precision in determining (L/L0 ) is estimated to be as follows: 2 d~DL/L0! 5 6 0.1 @~1!2 1 ~20 3 0.1 3 0.5!2#1/2 5 28 µm/m

13. Precision and Bias 13.1 The precision and bias of determining both thermal expansion and the mean coefficient of thermal expansion depend on the simultaneous measurement of temperature and relative length. 13.1.1 Random error is usually associated with the precision and bias of repeated length and temperature measurements, but other variables may also intrude on the measurements. For instance, a specimen may change position repeatably or the voltage applied to the measurement transducer may fluctuate. 13.1.2 Systematic error is usually larger and can result from many sources. These include the following: accuracy of the length and temperature measurements; deviation of the specimen mean temperature from that indicated by the sensor; deviation from linearity of the transducer; temperature gradients between the specimen holder or probes, or both; difference

(10)

It has been shown that the maximum difference to be expected from repeated tests is estimated by the following: 2 d~DL/L0!max 5 6 L @dE 1 aT L0 dT#

(11)

0

13.3 Tests of linear thermal expansion of borosilicate glass, copper, and tungsten over the range of 25 to 400°C have indicated that a vitreous silica dilatometer can be accurate to 4 % at the 95 % confidence level when carefully calibrated. This corresponds to a precision of approximately 0.8 % as calculated from the example in 13.2. 14. Keywords 14.1 contraction; dilatometer; dilatometry; expansion; linear thermal expansion; thermal expansivity; vitreous silica

APPENDIXES (Nonmandatory Information) X1. DIFFERENTIAL DILATOMETER

X1.1 This variation of the basic configuration is undertaken by the introduction of a second push-rod and a separate reference specimen next to the test specimen. The transducer is coupled to both push-rods such that it measures the differential movement between them and not between one and the holder, as in the regular configuration.

contacting the lower surface in contact (or end plug, in a horizontally oriented device) with the tube. Each has one push-rod resting at the other end. The reference is usually chosen to have expansion characteristics similar to those of the test material so that the displacement difference between the two push-rods is very small.

X1.2 The specimen and reference are made the same length and are placed adjacent to each other, with one end of each

X1.3 Historically, the latter feature popularized this type of configuration when transducers and recording means were 6

E 228 limited. However, the advantages became limited to special applications with the advent of improved transducers. For example, when it is difficult to replicate thermal cycles with high accuracy and good reproducibility, it is a major advantage of the calibration of the device not to be undertaken during one cycle with the test itself during another. By having the reference adjacent to the test specimen, both will experience identical thermal excursions, and this will eliminate cycle-tocycle uncertainty. Modern temperature controls greatly diminish the value of this feature. However, it still offers desirable

characteristics in some instances, most notably in cases in which a large number of specimens of closely similar materials are compared (such as in production control, screening studies, etc.). X1.4 The disadvantages are the strict and limited specimen requirements (which must be equal to that of the reference), continued cycling of the reference, larger space needed, and a greater difficulty in detecting faulty operation.

X2. TEMPERATURE DETERMINATION

X2.1 Special care must be taken when the sensor(s) is not in direct contact with the specimen, for the measured temperature can still be in error even when it is in good thermal contact. This is caused by heat being conducted away from or toward the specimen or the thermocouple junction, or both, by the thermocouple wires. This heat flow can be minimized by reducing the temperature gradient along the thermocouple wires near the junction. For example, some of the wire is looped once or twice within an area that has a temperature very close to that of the specimen. The temperature gradient is thereby shifted to an area between an intermediate point on the wire and the outside of the furnace.

X2.3 However, the sensor lead and lag can be determined in the following manner: X2.3.1 Where the specimen to be measured is known or shown to be reversible in its thermal expansion behavior, heat the interferometer at a constant rate over the temperature range of interest, and then cool through this region at the same rate. A plot of the expansion versus apparent temperature will exhibit a temperature displacement between the heating and cooling data. One half of this displacement parallel with the temperature axis is the lead and lag correction. Subtract this correction from the apparent temperature on heating and add on cooling. If the specimen is not reversible in thermal expansion behavior, another material of similar emittance and thermal diffusivity and known to be reversible may be substituted to determine the approximate lead and lag.

X2.2 When the junction is not in direct contact with the specimen, the temperature measurements may also be in error when heating or cooling. The magnitude of this sensor lead or lag is usually not great, but it will be dependent on its distance from the specimen, the specimen size, the emittance and thermal diffusivity of the material, and the heating or cooling rate.

REFERENCES (1) Hahn, T. A., and Kirby, R. K., “Thermal Expansion of Platinum 293 to 1900 K,” AIP Conference Proceedings, No. 3, 1972. (2) Nix, F. C., and MacNair, D., “Thermal Expansion of Pure Metals,” Physical Review, Vol 61, 1942, p. 74. (3) White, G. K., “Expansion Coefficients of Coppers at 283K and Oxygen Atmospheres,” Journal of Physics, Vol 26, 1972, p. 30. (4) Nix, F. C., and MacNair, D., “Thermal Expansion of Pure Metals,” Physical Review, Vol 60, 1941, p. 597. (5) Simmons, R. D., and Bullutfi, R. W., “Measurements of Equilibrium Vacancy Concentrations in Aluminum,” Physical Review, Vol 117, 1960, p. 52.

(6) Fraser, D. B., and Hollis-Hallet, A. C., Proceedings of the 7th International Conference on Low Temperature Physics, 1961, p. 689. (7) Altman, H. W., Rubin, T., and Johnson, H. L., “Coefficients of Thermal Expansion of Solids at Low Temperatures,” Ohio State University Cryogenic Laboratory Report OSU-TR-264-27, 1954. (8) Hidnert, P., and Krider, H. S., “Thermal Expansion Measurements,” Journal of Research National Bureau of Standards, Vol 48, 1952, p. 209.

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