A comparison of a novel single-pan calorimeter with a conventional heat-flux differential scanning calorimeter

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1 High Temperatures ^ High Pressures, 2, volume 32, pages 311 ^ ECTP Proceedings pages 297 ^ 35 DOI:1.168/htwu26 A comparison of a novel single-pan calorimeter with a conventional heat-flux differential scanning calorimeter Hongbiao Dong, John D Hunt Department of Materials, University of Oxford, Oxford OX1 3PH, UK; fax: ; john.hunt@materials.ox.ac.uk Presented at the 15th European Conference on Thermophysical Properties, Wu«rzburg, Germany, 5 ^ 9 September 1999 Abstract. There are a number of problems associated with a conventional heat-flux differential scanning calorimeter. When latent heat is absorbed or evolved, large temperature differences arise in the calorimeter and heat can flow between the reference and sample leading to rate sensitive enthalpy changes. In addition the heat appears to be smeared over a large range of temperatures. The reason for the smearing is discussed and a simple scanning calorimeter has been designed which eliminates the need for de-smearing. The present apparatus uses samples of about 1 cm 3 and can be used from about 3 to 13 8C. The temperature can be scanned at a constant rate or alternatively the heat flux can be fixed and the thermal response recorded. A heat flow analysis is presented which allows enthalpy changes to be calculated. The results for pure aluminium and an aluminium alloy (LM25) are reported. It is concluded that the new calorimeter has a number of advantages. In a pure material, the latent heat appears over a very narrow range of temperature giving an indication of the improved temperature discrimination: the apparent latent heat per unit mass does not depend on specimen size or significantly on rate of heating. In alloys, the calorimeter is more sensitive to the onset of a phase transition because of the better temperature discrimination. 1 Introduction The differential scanning calorimeter (DSC) is used to measure thermal properties as a function of temperature or to measure the onset of phase transformations. Traditionally the heat-flux DSC is used at high temperatures and consists of a reference pan and a sample pan contained in a constant temperature enclosure (see figure 1). Typically the enclosure temperature is increased or decreased at a constant rate. The lag in temperature of the reference and sample represent a heat flux to or from the surroundings. In figure 2a, the enclosure temperature, T F, reference temperature, T R, and sample temperature, T S, are plotted schematically against time. As the enclosure temperature rises at a constant rate, the sample and reference temperature soon rise at the same rate; when the pure metal sample begins to melt, T S remains constant until the sample is completely melted. When it has melted, T S rises rapidly and again eventually reaches a steady state difference. The temperature differences, DT FS ˆ T F T S, and DT FR ˆ T F T R, are plotted against time, t, in figure 2b. If we assume heat fluxes are proportional to the temperature difference between the sample and the surroundings, then the product of the temperature difference and time is proportional to the enthalpy change. The hatched areas in figure 2b are proportional to the enthalpy changes from t 1 to t 2 in the sample and reference. The difference in temperature between the sample and reference, DT RS ˆ T R T S, thus gives a measure of the difference in enthalpy change of the sample and reference over the time interval. A calibrant of known enthalpy as a function of temperature allows absolute enthalpy changes to be calculated. It is often assumed that the difference DT RS is proportional to the difference in effective specific heat between the sample and reference. This is true when the sample and reference temperature change at the same rate, but is not true when the changes are different.

2 312 H B Dong, J D Hunt 15 ECTP Proceedings page 298 T F T S T R Figure 1. Schematic diagram of a conventional heat-flux DSC. This is apparent from figure 2c where the temperature differences are plotted against temperature. Immediately after melting DT RS is large because the sample temperature is rising more rapidly than the reference. Neglect of this effect leads to smearing of the temperature over which latent heat is apparently evolved (Richardson 1992). If effective specific heat (specific heat plus latent heat) is to be measured as a function of temperature, great care must be taken to ensure that the de-smearing calculations are rigorous (Ho«hne et al 1996). Although the difference in enthalpy of the reference and sample between time t 1 and t 2 is defined in figure 2b, the temperature changes in the sample and reference are very different. Other problems arise with a heat-flux DSC. When heat fluxes are present the thermocouples do not measure the temperature of the sample or reference. This is because the thermal resistance between the sample (or reference) and its thermocouple is significant when compared with the thermal resistance between the thermocouple and the surroundings. To a first approximation the two temperature drops might be expected to be proportional to one another. This would result in a sample thermocouple temperature, T T, plot against time similar to that shown by the dashed line in figure 2a. The plot of apparent temperature differences would appear as the dashed line in figure 2c. The important feature is that even though the sample melts at one temperature, heat appears to be absorbed over a range of temperatures. An experimental plot of DT RS against temperature for melting and freezing of pure aluminium is shown in section 4. It is seen that this can be as large as 25 K. Another potentially serious problem for measuring real changes in enthalpy is that for large temperature differences between sample and reference, heat flows from the reference to the sample (or vice versa) thus giving erroneous enthalpy changes. These three effects explain why it is generally recognised that small samples must be used in a two-pan calorimeter when a significant amount of latent heat is evolved. The problem is deciding how small the sample should be for accurate results. It is difficult to see the reason for using a reference pan. The difference in temperature between the sample and the enclosure contains similar information to that

3 A comparison of a novel single-pan calorimeter ECTP Proceedings page 299 T F T R Temperature Temperature T T DT FS DT FR T S DT SR Time (c) DT DT DT SR DT FR DT FS t 1 t 2 Time (b) Figure 2. A combined schematic plot of temperature against time, (b) temperature difference against time, (c) temperature difference against temperature for a heat-flux DSC. of the temperature difference between sample and reference (see figure 2b). These considerations led us to develop a simple single-pan calorimeter that appears to eliminate many of the problems in a conventional heat-flux DSC. 2 The new scanning calorimeter The essential feature of the calorimeter is that the sample is in a uniform temperature enclosure and that it has the largest possible thermal resistance between the sample and its surroundings. A schematic diagram of the apparatus is shown in figure 3. To ensure a uniform temperature enclosure, the outer crucible is thermally isolated from the furnace, is thick walled, and made of a material with a high conductivity. The inner crucible is thermally isolated from the outer crucible to ensure the maximum temperature difference between the two crucibles. There appears to be no disadvantage in using large samples. Sheathed thermocouples of.5 mm outer diameter are placed in the walls of the inner and outer crucibles. During most runs an additional thermocouple was placed in the centre of the sample. The thermocouple and a piece of thermocouple sheath act as supports for the specimen. Computer programs have been written to log the temperature data and to control temperature or temperature difference. The temperature of each thermocouple is sampled about 1 s 1, averaged, then sorted at intervals of 1 s. The temperature

4 314 H B Dong, J D Hunt 15 ECTP Proceedings page 3 outer crucible sample inner crucible 1 mm 1 mm thermocouples supports Figure 3. Schematic diagram of the calorimeter described in the present work. control can operate with full proportional integral and derivative action (PID) but is normally used as a proportional and derivative (PD) controller. Special care has been taken to eliminate thermal drift in the pre-amplifiers and to minimise electrical noise. Typically the temperature of the outer crucible has stability of better than :2 K. The calorimeter can be operated in the normal DSC manner by changing the outer (or inner) crucible temperature at a programmed rate. Because the specimens are much larger than a conventional heat-flux DSC, the calorimeter can be operated in a constant heat-flux mode as was proposed by Smith (194). In this mode the temperature difference between the sample and the surroundings is kept constant. This means the temperature rises less rapidly when latent heat is absorbed. Because the specimens are large the calorimeter is ideally suited for slow heating or cooling rates. Significant results can be obtained with heating rates as low as.1 K min 1 ; heating and cooling rates of 3 K min 1 have been achieved in the present apparatus. 3 Enthalpy calculations Because of the simplicity of the single-pan calorimeter, equations are easily derived to relate temperature changes to enthalpy changes. As in a conventional DSC a run is carried out with an empty pan, then with the empty pan calibrant, and then with the empty pan sample. The temperature differences are first corrected with a standard zero line adjustment. These are measured during an isothermal anneal (eg Richardson 1992) before, during, and after a run. As the calorimeter is heated in the time interval dt, the temperature of the empty inner crucible rises by dt E, the temperature of the calibrant empty pan rises by dt C, and the temperature ofthe sample empty pan rises by dt S.The corresponding temperature differences between the inner and outer crucible for the three cases are DT DE, DT DC,and DT DS.LetC C be the change in heat content per degree (ie specific heat times mass) of the calibrant; this must be known as a function of temperature. Similarly C E and C S are

5 A comparison of a novel single-pan calorimeter ECTP Proceedings page 31 those of the empty crucible and sample. It should be noted that C S contains any latent heat and is thus an effective specific heat. The heat transfer coefficient between the inner and outer crucible is a and is expected to be a function of temperature. For the empty crucible: adt DE dt ˆ C E dt E. (1) For the calibrant empty pan: adt DC dt ˆ C C C E dt C. (2) For the sample empty pan: adt S dt ˆ C S C E dt S. (3) Use of equation (1) to eliminate C E gives: DTDC adt DT DE DTDS ˆ C dt C dt C and adt DT DE ˆ C E dt S dt S. (4) E Dividing the two equations (4) and multiplying by dt S gives a general expression for the rise in enthalpy of the sample dh S in dt S : DT DS DT 1 DE dt dt S C E C B A ˆ C SdT S ˆ dh S. (5) DT DC dt C DT DE dt E The equation is valid as dt S! and can thus handle the latent heat of a pure material. The ratios DT DE =dt E and DT DC =dt C are evaluated from the empty and calibrant empty run at the relevant temperature with the same time interval. The meaning of these terms is best visualised by noting that the first is the inverse of dt E dt 1 DT DE, which is the rate of rise of the empty pan divided by the difference in temperature between the inner and outer crucible. The general equation is valid for any mode of operation and that includes constant rate of temperature rise or constant heat flux. It should be emphasised that the equation and use of a central thermocouple automatically handle the de-smearing process. 4 Results and discussion In the present work copper has been used as the calibrant with the specific heat data from Hultgren et al (1973). A number of materials have been investigated with either graphite or machinable alumina for the inner crucible. The results for pure aluminium and an aluminium alloy (LM25) are reported. 4.1 Pure aluminium Figure 4 compares a plot of counts/temperature difference against temperature for a typical heat-flux DSC and for the new calorimeter. The line on the top of the diagrams represents heating. If the thermocouple measured the sample temperature the line AB should be vertical. Any change in the apparent melting temperature (A to B) indicates an increased difference in temperature between the sample and the sample thermocouple. For the heat-flux DSC with a.5 g sample, the change is about 25 K; for the one pan calorimeter with a 2.2 g sample it is about 3 K for the inner thermocouple and.3 K for the central thermocouple. With the constant heat-flux mode the temperature of the central thermocouple varied by.4 K.

6 316 H B Dong, J D Hunt 15 ECTP Proceedings page 32 8 B 4 Counts A B DT=K 12 centre A inner 12 (b) Figure 4. Experimental plots of counts/temperature difference against temperature for a conventional heat-flux DSC with a.5 g sample heated at 1 Kmin 1, (b) the present singlepan scanning calorimeter with a 2.2 g sample heated at 4 Kmin 1. Figure 5 shows temperature and temperature difference plotted against time for pure aluminium and illustrates the different operational modes. In figure 5a the outer temperature was increased at a constant rate; in figure 5b the temperature difference between the inner and outer thermocouples was kept constant (Smith mode); in figure 5c the outer crucible temperature was ramped and oscillated. Note the different behaviour in figures 5a and 5b as the metal melts. Enthalpy changes are calculated by using the experimental results to integrate equation (5). Figure 6a shows the enthalpy for pure aluminium plotted as a function of temperature. The melting and freezing lines almost coincide. Figure 6b shows the effective specific heat obtained with the use of the slope of figure 6a for the melting line. More than 98% of the latent heat was evolved over a temperature change of only.4 K. The important feature is the narrowness of the effective specific heat peak. It is not possible to obtain such a narrow peak with a conventional heat-flux DSC for the reasons discussed in the introduction. Very good reproducibility can be obtained. The average values and standard deviation for seven runs for specific heat and latent heat are compared with the results of Hultgren et al (1973) in table 1. Table 2 shows runs carried out with different heat fluxes. Less than 1% variation was obtained between samples and runs with the same sample. Table 1. Results for seven runs with pure aluminium. C p =JK 1 mol 1 L=J mol 1 at 6 8C at 65 8C at 67 8C heating cooling Average Standard deviation Hultgren et al (1973)

7 A comparison of a novel single-pan calorimeter ECTP Proceedings page centre outer outer 665 centre (b) DT=K DT=K DT=K (c) Time=s Figure 5. Plots of temperature versus time (ö), temperature difference versus time () for a 2.2 g pure aluminium sample: outer crucible heated at 4 Kmin 1, (b) with a constant temperature difference 3 K between sample and furnace (Smith mode), (c) outer crucible temperature ramped and oscillated. Table 2. Results for pure aluminium with different heating/cooling rates. Rate=K min 1 C p =JK 1 mol 1 L=J mol 1 at 6 8C at 65 8C at 67 8C heating cooling

8 318 HBDong,JDHunt 15 ECTP Proceedings page 34 Specific heat=j K 1 mol 1 Enthalpy change=j mol 1 (b) Figure 6. Plots with pure aluminium for enthalpy change versus temperature during melting (ö) and freezing (), (b) effective specific heat versus temperature for melting. Constant temperature difference 3 K. 4.2 Alloy LM25 The aluminium alloy LM25 is otherwise composed of 6.7 wt% Si,.44 wt% Fe,.3 wt% Mn, and.35 wt% Mg. Figure 7 shows the enthalpy change and effective specific heat for LM25 measured by the constant heat-flux mode. The enthalpy line is different for melting and freezing (see figure 7a) and this is consistent with a departure from equilibrium as freezing takes place. The effective specific heats for melting, figure 7b, and for freezing, figure 7c, show a number of transitions. On freezing aluminium is formed at about 62 8C and continues to be deposited until a eutectic comes out at about 57 8C; finally another solid phase is deposited at about 55 8C. On heating the lowest temperature peak splits into two separated by about 2 K. It is possible that the additional peak is the result of a solid state reaction. This reaction was not detected by Quested et al (1997) in a commercial heat-flux DSC, but is very apparent on all the specimens examined in the present work. Six runs were carried out to investigate reproducibility; the results, average and standard deviation, for the solidus, liquidus, specific heat, and latent heat are given in table 3. Table 3. Results for six runs with LM25. C p =JK 1 mol 1 L=J mol 1 solidus liquidus at 53 8C at 63 8C heating cooling Average Standard deviation 5 Conclusion It is concluded that the present single-pan calorimeter has significant advantages over a conventional heat-flux DSC. The analysis and setup automatically removes the need for de-smearing. Similar results are obtained in pure materials at large or small heating

9 A comparison of a novel single-pan calorimeter ECTP Proceedings page Enthalpy change=j mol cooling heating 5 Specific heat=j K 1 mol 1 (b) heating Specific heat=j K 1 mol cooling (c) Temperature/8C Figure 7. Plots with LM25 for enthalpy change versus temperature during melting (ö) and freezing (), (b) effective specific heat versus temperature for (b) melting, and (c) freezing. Constant temperature difference 3 K. rates or in large and small specimens. High resolution is obtained for the onset of phase transformations because temperature can be measured from within a specimen. Accurate heat fluxes can be measured because the heat flow path is well defined and the flux thermocouples measure temperature differences over the largest possible thermal resistance; reproducibility is better than 1%. Heat flow cannot occur between a sample and a reference pan. A constant heat-flux mode can be used thus minimising errors due to an increasing heat flux. References Ho«hne G W H, Hemminger W, Flammersheim H-J, 1996 Differential Scanning Calorimetry: an Introduction for Practitioners (Berlin: Springer) Hultgren R, Desai P D, Hawkins D T, 1973 Selected Values of the Thermodynamic Properties of the Elements (Metals Park, OH: American Society for Metals) Quested P N, Mills K C, Brookes R F, Day A P, Taylor R, Szelagowski H, 1997, in Proceedings of the International Conference on Solidification Processing (Sheffield: Sheffield University Press) pp 143 ^ 15 Richardson M J, 1992, in Compendium of Thermophysical Property Measurement Methods Eds K D Maglic, A Cezairliyan, V E Peletsky (New York: Plenum) pp 519 ^ 545 Smith C S, 194 Trans. Am. Inst. Met. Eng ^ 245