Calibration of the Horizontal Pushrod Dilatometer

Transcription

1 Caibration of the Horizonta Pushrod Diatometer Štefan Vaovič, Igor Štubňa Physics Dpt., Constantine the Phiosopher Univ., A. Hinku 1, Nitra, Sovakia E-mai: Abstract In this paper we present caibration of a horizonta pushrod aumina diatometer and expain the principe of the diatometer. We performed caibration of the inear expansions sensor using etaon materias patinum, stee and sapphire and estimated the correction function for aumina and zero. We aso performed caibration of the temperature-measuring sensor and estimated the corresponding correction function for temperature. Therma fied homogeneity was measured using a thermocoupe. The measurement uncertainty was estimated for the case of inhomogeneous heating of the sampe. We conducted the exampe measurement using the correction functions mentioned above. Key words: inear therma expansion coefficient, pushrod diatometer, caibration 1 Introduction The therma expansion coefficient is a very important materia property. Tracking of the materias expansion in the dependence of temperature provides us with important information for praxis and research. (for exampe [1, ]). An expansion of a materia is measured by an apparatus caed a diatometer. The principe of differentia diatometers ies in a parae measurement of the expansion of an unknown sampe and of a known sampe for which we have known vaues of the therma expansion coefficient. By comparing the expansion of these two sampes we are abe to estimate the therma expansion coefficient of an unknown sampe. The most commony used comparison materia is the aumina A O 3 (up to 15 C) [3]. Diatometers differ in their geometry of the imposition of the sampe (horizonta or vertica) and in the manner of measuring the geometrica changes of the sampe and its recording. In this paper we present the caibration of the horizonta pushrod diatometer. Principe of the apparatus The therma expansivity of materias depends on their chemica composition, structure of the materia and temperature. Therma expansion of materias is characterized by the inear therma expansion coefficient (LTEC) α, which is defined as [3, 4, 5] 1 d α =, (1) dt where is the ength of the sampe at the beginning of measurement, d is the change of the sampes ength resuting from the temperature change dt. In the praxis, the 16

2 temperature change dt is reaized by a sufficienty sma temperature change t = t t 1. We show the principe of our diatometer on the figure 1. d A B Differentia transformer with pushrod Fixed hoder Aumina rods and aumina pushrod Sampe Supporting aumina rod Free hoder c Fig.1 - Scheme of the diatometer The diatometric system consists of aumina rods (Degussa, Germany) that are fastened to the fixed hoder (auminium). A free hoder (auminium) is at the opposite end of these rods. A supporting aumina rod is fastened into the free hoder with a zeroing screw. In the centra part of the diatometric system, the sampe is being hed between the supporting aumina rod and the other aumina rod that acts as a piston pushing to the pushrod of a differentia transformer (INPOS, ZPA Jinonice Nová Paka, Bohemia [6]). The differentia transformer measures the defection d of the centra rods and the sampe. The midde part is hed in the furnace. The siicium carbide rods are used as the heating eement, and the working temperature range is from C up to 1 C. Temperature is measured by a thermocoupe that touches the sampe. A data is stored by a PC that aso operates the power of furnace by a reguator. Using the differentia measurement method we measure the expansion of a known materia (aumina) and an unknown materia (sampe). In the parts and a aumina rods expand to the right direction (because the eft hoder is fixed), and ony the centra part is important. The ength of the sampe is equay ong as the aumina ength at the beginning of a measurement. At higher temperatures the aumina expands to the right and aso the unknown sampe, but the sampe has a different LTEC, so it expands (or contracts) aso to the eft. This movement is measured by the differentia transformer as defection d. Then the defection d = c, where means the expansion of the sampe and c the expansion of aumina, can be easiy cacuated. The expansion of the aumina is we known for the whoe temperature range of our furnace, so we can estimate the expansion of the sampe from the known and the measured d. Finay, for the reative expansion ε = we obtain the equation: 17 A c B

3 d = + c. () 3 Caibration of the apparatus We have caibrated the induction detector using three reference materias. Homogeneity of the therma fied in the furnace was measured, and considerations about the impact of the inhomogeneity of the therma fied were cacuated. Caibration of the thermocoupe was aso performed. 3.1 Caibration of the induction detector Caibration was performed using the reference materias stee X1NiCrMoTiB 1515, sapphire 59 Sehnit SA5 and the pure patinum. We measured these materias and obtained their defections d. From the known vaues of the reative expansion of these materias we were abe to get the reative expansion of the reference aumina. However, these vaues incuded not ony the correction for aumina but aso hidden systematic errors of our apparatus. So, using the poynomia fitting with the hep of a program Mathcad 1 we obtained the corrections as a function of the temperature T for these materias and then cacuated the vaues for the mean correction function for our apparatus. The fina equation for the correction function is: c c d ( T) corr. = ( T) etaon ( T) measured. (3) Such correction functions were made four times for the stee, two times for the patinum and two times for the sapphire. The exampe for the stee in Figure shows the difference between the etaon data and the measured data: Fig. Caibration for the stee X1NiCrMoTiB 1515 The correction is the difference between the soid and the dashed curve. A caibration functions and the mean caibration function are drawn in Figure 3. We used the third 18

4 order poynomia fitting for obtaining these caibration functions. The fina mean caibration function has the foowing form: c ( T) = 4,16.1. T + 1, T + 6, T 1,4.1 corr. Equation () changes finay into: d sampe measured c ( T) = ( T) ( T). (4) corr.. (5) reative expansion / % temperature / C Fig 3 Correction functions and the mean correction function 3. Homogeneity of the therma fied In accordance with the norms [7, 8] the temperature deviations in the furnace near the sampe have to be ess then 5 C. Therefore the measurement of the temperature aong the diatometric system was performed. We used a thermocoupe to measure it aong the paces where the sampe usuay ies. We performed the measurements at constant temperatures 3, 6 and 9 C. At these constant temperatures, the thermocoupe was moved through the whoe part of the diatometric system that is paced in the furnace. At the edges of the furnace the deviations were greater than 5 C, but in the centra part, where the sampe is usuay paced, the temperature deviations were in the permitted range. With the higher temperatures the temperature deviations were higher too. Nevertheess, we performed an additiona cacuation of the systematic error of the measurement resuting from the temperature fied inhomogeneity. Let the temperature in the midde of the sampe be T m. Suppose that temperature T sinks towards the edges of the sampe in accordance with the function T( x) Tm x = η, (6) 19

5 where x is a position aong the sampes ength and η ([ η] K.m = ) is the coefficient of inhomogeneity of the therma fied. Let the initia temperature be T (for exampe C). Then the temperature difference T = T T in the pace x is T = ( T T) = ( Tm η x ) T. We suppose that LTEC α is in the segment dx constant. Segment dx wi expand by α. dx. T = α. ( Tm T ) ηx dx. Summation of such expansions wi be the tota expansion of the sampe. We obtain it by integrating the ast formua in the boundaries from to, where is the ength of a one haf of the sampe 3 = α ( Tm T ) αη, (7) 3 where mutipication by two takes note of the two sampe haves, but is aready the expansion of the whoe sampe. When the therma fied is homogeneous, η =, and we obtain the we-known expression = α ( T m T ). Then the cacuation of the reative systematic error of the expansion of the sampe is γ 3 αη ( ) ( ) homog ( ) α T α T nehomog 3 η = = =. (8) ( ) α T 3 T homog Let us estimate the systematic error induced by inhomogeneity of the therma fied. If T = C (sampe temperature C), the ength of one haf of the sampe is = 5 mm and the temperature of the edges of the sampe differs by 5 C from the temperature of the midde of the sampe, then we can obtain the coefficient η = K.m from the equation (6) and the reative systematic error from the equation (8), which then is γ =,83 %. According to the equation (8) this error reduces with higher temperatures, at the sampes temperature of 1 C ( T 98 C) it is γ =,17 %. In the rea experimenta conditions the temperature fied inhomogeneity has an increasing tendency, which means that the coefficient η aso increases. These two infuences partiay compensate each other. The true vaue of γ is a function of the temperature and shoud be cacuated after the experimenta estimation of the coefficient η using the equation (6). 3.3 Caibration of the thermocoupe We use the thermocoupe NiCr/Ni for the temperature measurement. It is paced cosey to the sampe. It measures the temperature of the furnace, not the temperature in the sampe. According to [9], the difference between the temperature measured in the furnace and the rea temperature in the kern of the sampe can be up to hundreds of degrees of Cesius for metas, and at most 1 C for other materias. The reason is the radiation from the sampe. Hence it is materia dependent. According to [4, p.171] we shoud take the furnace temperature as the sampe temperature because the properties of most materias are not so much temperature dependent that this coud be a probem. 13

6 But it is possibe to partiay improve the temperature measurement. We measured the temperature of the meting point of the auminium. According to the we-known vaue 66,3 C we were abe to cacuate a primitive inear correction function for the temperature from two points. One was the temperature of C, which is the starting temperature of our measurements when the furnace temperature is equa to the sampe temperature. The second point is the temperature of meting of the auminium measured by the thermocoupe. Thermocoupe showed us approximatey 669,3 C, when the auminum was meting in the furnace. From this, we obtained this temperature correction: t = 1, 14. t, 81. (9) corrected measured This correction shoud be refined in the future by measurements of other we-known temperature dependent effects. 4 Concusions The resuts of caibration of the diatometer are formuae (4), (5) for cacuating the reative expansion from measured inear dispacement and formua (9) for cacuating the temperature from thermo-emf measured by thermocoupe. The corrections we presented in this paper enabe us to precisey measure the LTEC of various materias with measurement uncertainty ess than 3 % (cacuated in accordance to norm [7]). Acknowedgement Authors wish to thank the Sovak-Czech joined committee for science-technica cooperation project No. 141/5 and the Sovakian Science Grant Agency project No. VEGA 1/79/3 for the financia support. References [1] Štubňa, I. Trnovcová, V.: The Effect of Texture on Therma Expansion of Extruded Ceramics. Ceramics - Siikáty, 4, 1998, p. 1-4 [] Le Parouer, P. Chan, I.: Caorimetry, Diatometry at High Temperature: Recent Deveopments in Instrumentation and Appications. Amer. Cer. Soc. Bu. 8, 1, p. 31 [3] Šašek, L. et a.: Laboratorní metody v siikátech. Praha Bratisava : SNTL Afa, (in sovak) [4] Tayor, R. E. et a.: Therma expansion of soids (Ed. C. Y. Ho). Materias Park, OH : ASM Int., ISBN [5] Karafa, B. Štubňa, I. Vozár, L.: Proceedings of the workshop Kaorimetrický seminář. Ostrava : ES OU,, s ISBN (in sovak) [6] Indukční snímač INPOS. Booket ZPA Jinonice (in czech) [7] German norm DIN [8] European norm EN 81-1 [9] Hahnekamp, G. Krojer, P.: Evauation of Reference Materias for Thermophysica Charakterisation. Seibersdorf : Austrian Research Centers,. p.19 (in german) 131