Measurement Uncertainty in the DTA Temperature Calibration

Transcription

1 International Journal of Pure and Applied Physics ISSN Volume 6, Number 4 (2010), pp Research India Publications Measurement Uncertainty in the DTA Temperature Calibration Yasser A. Abdelaziz, Essam M. Ibrahim and Mostafa M. Mekawy National Institute for Standards, Giza, Egypt Abstract In order to make good use of the Differential Thermal Analysis (DTA) and to obtain reliable results with good reproducibility and accuracy, it is necessary to carefully calibrate temperature measuring system of the apparatuses using standard reference materials with (99.999%) purity. The uncertainties in temperature calibration of the DTA were estimated according to the Guide to the Expression of Uncertainty in Measurement, GUM. Repeatability test was performed to access the accuracy of the instrument experimentally. The results demonstrate that the DTA temperature calibration uncertainty between 0.2 and 1 K by calibration at fixed melting points (zinc, aluminum and gold). The measurements traceability of DTA is also described in this paper. Keywords: DTA; Uncertainty; Reference Materials; Traceability. Introduction The determination of thermal properties of materials is a very important factor for a many applications at different temperatures. DTA has become one of today's routine techniques for the characterization of materials. The accuracy of the DTA measurements is affected by its temperature measurements within the DTA measurement cell to obtain reliable results with good reproducibility and accuracy, it is necessary to carefully calibrate the apparatuses using standard reference materials as described before in ASTM Standards, E793-85, standard methods [1]. DTA temperature calibration is necessary; to give a confidence in the accuracy of its data, to establish the traceability of the measured values to SI units; and to assess the uncertainty of measurement. Ultra pure reference material is the mostly wide method for the temperature calibration of DTA. The International Temperature Scale of 1990 (ITS-90) reported defined melting points of many substances [2], which can be used as reference material for DTA temperature calibration. Some papers were published, dealing with temperature calibration of DTA [3-5],

2 430 Yasser A. Abdelaziz et al but not deeply described the uncertainty calculations. In this work we use ISO-GUM [6] for determination of the uncertainty due to the systematic errors, when calibration of temperature measurements of the DTA using standard reference materials. Also we present a brief description of the DTA calibration and traceability chain. In the mathematical analysis of DTA temperature calibration, there are several factors to be considered. Those factors include measurement uncertainty, measurement resolution and purity of reference materials. These calculations can be helpful for the calibration laboratories, as one of the most important requirement for laboratory accreditation according to ISO/ IEC [7]. Experimental Sample preparation; High purity metal samples of at least % purity were obtained from Johnson Matthy Co, UK and certified to confirm their values with ITS-90 [2]. The sample was prepared by weighing 15 mg metal into Platinum crucible. The tube was connected to a GAS system. The metal sample was heated to red heat and the system evacuated to 1 mm Hg. The fused silica tube was sealed as close as possible to the sample, and the fused silica rod severed as close as possible to the bottom of the metal sample. The severed side of the sample was ground to achieve a smooth surface. Apparatus DTA (SHIMADZU DTA-50) involves heating or cooling a test sample and a reference under identical conditions, while recording any temperature difference between the sample and reference. This differential temperature is then plotted against time, or against temperature. Changes in the sample which lead to the absorption or evolution of heat can be detected relative to the reference. Differential temperatures can also arise between two samples when their response to the applied heat treatment is not identical. DTA can therefore be used to study thermal properties and phase changes which do not lead to a change in enthalpy. The baseline of the DTA curve should then exhibit discontinuities at the transition temperatures and the slope of the curve at any point will depend on the microstructural constitution at that temperature. The area under the DTA peak is due to the enthalpy change and is not affected by the heat capacity of the sample. The design of the differential thermal analysis apparatus is shown in (Fig. 1) consists of the sample holder comprising thermocouples, sample containers, ceramic or metallic block and the heating furnace. This system is also provided with a temperature programmer and a recording system. The essential requirements of the furnace are that, it should provide a stable and sufficiently large hot zone and must be able to respond rapidly to commands from the temperature programmer.

3 Measurement Uncertainty in the DTA Temperature Calibration 431 Figure 1: Schematic diagram of the DTA system. The sample holder assembly consists of a thermocouple each for the sample and reference, surrounded by a block to ensure a uniform heat distribution. The sample is contained in a small platinum crucible designed with an indentation on the base to ensure a snug fit over the thermocouple bead. The thermocouples should not be placed in direct contact with the sample to avoid contamination and degradation, although sensitivity may be compromised. The sample assembly is isolated against electrical interference from the furnace wiring with an earthed sheath, often made of platinum coated ceramic material. The sheath can also be used to contain the sample region within a controlled atmosphere or a vacuum. Measurements The temperatures of the sample and reference substance, when heated at a constant rate, rise as indicated by the two broken lines in (Fig.2). The thermally inert reference substance keeps rising in temperature at a constant rate. When endothermic change (such as fusion) takes place in the sample, on the other hand, heat energy supplied from the exterior is consumed by the change so that the temperature stops rising. Therefore, when the change is complete, substantial difference will result between the sample and the reference temperatures. This causes a large amount of heat energy to be transferred to the sample, resulting in a sharp rise in the sample temperature signal. Consequently, the sample temperature rises as high as it would be if the temperature had not stopped rising by the endothermic change. The above temperature difference ΔT (called the DTA signal) is detected and amplified to be recorded as a peak which is shown by a solid line in (Fig. 2). Under test sample temperature is measured by thermocouple. The output from the thermocouple for the reference substance is amplified and A/D converted before being sent to the CPU circuit which compares the signal from the thermocouple with the temperature program. Voltage applied to the

4 432 Yasser A. Abdelaziz et al heater of the furnace is controlled according to the comparison result. The sample temperature is displayed in digital form on the front panel and simultaneously output to the recorder or data processor. Thus, to obtain a stable baseline, the DTA-50 uses the temperature signal from the reference substance for controlling temperature also the signal from sample is shown on the display and the recorder. To detect temperature, the DTA-50 uses a unique Dumbbell-shaped detector which uses a thermocouple of Pt and Pt-10% rhodium alloy. This detector provides high sensitivity and good response Figure 2: Typical DTA Curves. Temperature Calibration There are a certified number of materials which be used as temperature calibration. These standards used under the dynamic conditions of DTA experiment, will enabled us to calibrate our instrument. We can compare our temperature data with those obtained by other instruments. Calibration of the peak areas (A) : Peak area (A) = ± K. H. m Where; K is the calibration constant and m is the sample mass. To determine K, a standard of high purity and known enthalpy of fusion ( H) is required. The appearance of the fusion peak will be affected by sample configuration [4]. The area under the peak is then measured, so K is determined and we can determine the enthalpy values for other materials by reference to our calibration standard. Therefore in DTA measurements, we should calibrate peak areas using a standard which provides a reference peak in the same temperature range as the test sample. Factors affecting DTA curves The effect of sample factor: Amount of sample:- The peak areas are proportional to the mass of the sample involved in the thermal

5 Measurement Uncertainty in the DTA Temperature Calibration 433 transition. So, we prefer to use a few milligrams of powdered solid sample. The particle size:- Phase transitions tend to be less affected by particle size vibrations, fine powders are preferable. Sample packing:- When the sample interacts with the atmosphere surrounding it, some effects on thermal records may expected. The ease of escape of volatiles may be influenced by packing density, so a reproducible method of packing the sample is desirable. There are other sample characteristics, These include its heat capacity and its thermal conductivity, which will vary with physical state or chemical constitution. Diluents:- There are materials will not react with the sample. These are used for modifying some properties of the sample. For example: We may want to bulk up a small sample in order to fill the container to an acceptable degree. The effect of the variation of instrumental factors on DTA: The heating rate: An increase in heating rate increases the procedural peak temperature and increases peak areas to a small degree. Sample holder materials: Glass, ceramic or metal containers are used in DTA. Metal containers, e.g. Shallow aluminum pans are common in DSC. Thermocouple: The sample and reference containers are in direct contact with the thermocouples. Atmosphere around sample: A flowing gas is preferable to a static atmosphere which is liable to change as soon as sample degradation or decomposition occurs. Estimate and evaluating uncertainty components The Guide to the Expression of Uncertainty in Measurement, more known as ISO- GUM [6], was elaborated by the International Organization for Standardization in order to establish a harmonized methodology for uncertainty estimation. Type A evaluation of uncertainty "Repeatability of measurements" Repeatability tests were performed by making several measurements for each metal

6 434 Yasser A. Abdelaziz et al reference material- and determining the onset temperature of melting, the results obtained are given in Table 1. Table 1: measurement repeatability of DTA temperature calibration at zinc, aluminum and gold. Metal Zinc Aluminum Gold Reference value according to ITS- 90 o C Sample No Melting temperature Using DTA C Each metal was placed in the DTA cell and cycled at least five times at a heating rate of 1 o C min - 1, and the mean melting point temperature was calculated. Although the repeatability for a specific sample has a low associated standard deviation, of between 0.02 C and 0.44 C, there was up to a 0.3 C difference in melting point value between experiments and nominal values. This difference could be attributed to the differences in the placement of the bead in the sample crucible. All of the tests reported in Table 1 were carried out with the bead in a platinum crucible. The above data set in the DTA system are used as the correction coefficients during this correction. Q = (a+bt+ct 2 ) X Qm Where; T: Temperature o C Qm: Signal before correction Q: Signal after correction The ratios of the heat quantity between the reference values and measured values were found and plotted against the temperature. Coefficients a, b and c were then

7 Measurement Uncertainty in the DTA Temperature Calibration 435 found through quadratic regression of these plots with respect to temperature. Type B evaluation of uncertainty All the following uncertainty calculation carried out experimentally at temperature calibration C (melting point of gold) using the factors affecting DTA curves, which described in this paper item 2.4. Some of these factors are not effecting in the temperature calibration at C (melting point of gold). Uncertainty in Temperature Measurement Resolution Platinum-/Platinum-Rhodium (10%) thermocouples were employed and the recorder consisted of a digital voltmeter on special software. The analog to digital conversion process which transforms probe resistance into digital values resolves to 0.01 C. Based on a rectangular distribution of the halfinterval, the uncertainty component of temperature resolution is then u(tres) = 0.01 * 0.5/ 3 (= ) Uncertainty of the Temperature Reference material The reference material has an uncertainty of ± C according to their certificates. Assuming rectangular distribution of the half interval, the uncertainty of the temperature reference standard, is then u(tref) = / 3 (= C) Heating rate In most DTA apparatus the rate of heating determines directly the linear dimensions of the temperature scale. A change, therefore, in the rate of heating would alter the temperature scale. Maintenance of a characteristic rate of heating will insure usually a constant temperature scale. Occasionally, however, due to variation in line voltage, the rate of heating alters somewhat, and consequently the scale also alters, is then u(trat) = 0.01/ 3 (= C) The existence of temperature differences within the sample due to position with respect to the thermocouples For example, it was found that by placing the sample at a distance of about 1 to 2 mm from the thermocouple junction increased the required amount of indicator from 2 to 4 mgm, which can lead to 0.1 C, is then u(tpos) = 0.1/ 3 (= C) Uncertainty in sample weight The uncertainty in the balance used in weight of the sample can be calculated from the calibration certificate (±0.40 mg). This uncertainty value experimentally equivalent to about ± C, is then u(twegt) = 0.010/1 (= C) Combined Standard Uncertainty of DTA the Temperature Calibration The standard uncertainty components and the resulting combined standard uncertainty

8 436 Yasser A. Abdelaziz et al of the DTA Temperature Calibration temperature, uc(tc), are listed in the following table. The combined uncertainty was computed as the square root of the sum of the variances with the equation, uc(tc) = [u 2 (Trel) + u 2 (Tref) + u 2 (Trat) + u 2 (Tpos) + u 2 (Twegt)] Expanded Uncertainty Utilizing a coverage factor k=2, the expanded uncertainty, U, is listed in the following table at various temperatures using the following formula. U = k * uc(tc) Table 2: Expanded Uncertainty of DTA Temperature Calibration with Coverage Factor k=2. Source of uncertainty Value ± Probability distribution Divisor c i Value ± Reference material Normal Temperature Rectangular Measurement Resolution Heating rate Rectangular sample position Rectangular Sample weight Repeatability Normal Combined uncertainty Normal Expanded uncertainty Normal (k = 2) Then the expanded uncertainty is; ±0.89 C at the melting point of gold. The traceability concept In the DTA measurements the SI units are the joule, the mole, the kilogram and the Kelvin. The definition of measurements traceability according to the International Vocabulary of Basic and General Terms in Metrology (VIM) [8]; "property of a measurement result whereby the result can be related to a reference through a documented unbroken chain of calibrations, each contributing to the measurement uncertainty" Traceability to the SI in chemical measurements of any other quantity requires that the measurements be made using a primary method of measurement, which is correctly applied and stated with an evaluated uncertainty. Also it possible to use indirect methods, include combinations of non-primary methods with associated uncertainties where the evaluation requires a study of the links to national or international measurement standards of each SI unit and includes an estimate of the uncertainty of the method, or comparison with reference materials,

9 Measurement Uncertainty in the DTA Temperature Calibration 437 which themselves are linked to the SI through a chain of other comparisons, culminating in a measurement using a primary method. [9] The heat and temperature measurements of the DTA systems were achieved through the SI units of joule, the mole, the kilogram and the Kelvin. All the temperature measurements are traceable to the ITS-90 fixed points [2]. Also the intensive units, J/mol, J/kg and J/(mol/K) are traceable to the measurements of Joule effect probe using a certified reference materials. Conclusion DTA measurements with an uncertainty in terms of SI units of 0.2 and 1 K are a realistic goal when the rules outlined above and the advices on calibration are followed at three melting points of reference materials. It is important to determine the different calibration factors for temperature calibration. All obtained results are very close to reference value of reference materials which gives us confidence in our results. The traceability of DTA calibration is to ITS-90 fixed points. This paper show how the uncertainty evaluations in DTA calibration, in case, the previous papers were explained only the calibration process. Finally, we can say that our DTA is an excellent instrument that, if operated carefully and accordingly to its theory of operation, can produce very accurate results. References [1] Annual Book of ASTM Standards, vol , E793-85, p. 437 and E794-85, p. 440, American Society for Testing and Materials, Philadelphia (1985). [2] Preston-Thomas, H., The International Temperature Scale of 1990, Metrologia 27, 3-10 (1990). [3] E. Gmelin, S.M. Sarge, Thermochim. Acta 347 (2000) 9. [4] A.N. Sembira t, J.G. Dunn, "High temperature calibration of DTA and DSC apparatus using encapsulated samples", Thermochimica Acta 274 (1996) [5] E. Gmelina, S.M. Sarge, "Temperature, heat and heat tow rate calibration of differential scanning calorimeters", Thermochimica Acta 347 (2000) [6] Guide to the Expression of Uncertainty in Measurement, ISO, Switzerland, [7] R. Kaarls, T.J Quinn, The Comite Consulatif pour la Quantite' de Matie're: a brief review of its origin present activities Metrologia 34 (1997) 1. [8] The International Vocabulary of Basic and General Terms in Metrology, BIPM, France (VIM). [9] C.A. Nieto de Castro*, M.J.V. Lourenc,o, M.O. Sampaio, "Calibration of a DSC: its importance for the traceability and uncertainty of thermal measurements", Thermochimica Acta 347 (2000)

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