Heat capacity of sapphire

It is seen that the calibration constant disappears, which assumes that it is constant over the experimental conditions. The calculation is carried out using dedicated software. In some circumstances the crucible used for the sample may have to be different from that used for the calibrant. This means that a correction will be required to take into account the difference between the heat capacity of the two crucibles - readily calculated with sufficient accuracy. Measurements can be made at a series of temperatures but are meaningful only within the quasi-steady-state region of the experiment. The specific heat capacity of sapphire has been listed by ASTM in connection with the standard test method E 1269 (1999) for determining specific heat capacity by differential scanning calorimetry. 

The next calibration concerns the area of the DSC trace or the amplitude at any one temperature. The peak area below the baseline in Fig. 4.62 can be compared with the melting peaks of standard materials such as the benzoic acid, urea, indium, or anthracene, listed at the bottom of the figure. The amplitudes measured from the baseline established in the heat-capacity mode of measurement are usually compared with the heat capacity of standard aluminum oxide in the form of sapphire. The heat capacity of sapphire is free of transitions over a wide temperature range and has been... 

Square of the reciprocal, uncorrected specific heat capacity of sapphire and polystyrene as function of the square of the modulation frequency, as suggested by Eq.(3). Polystyrene data of Figure 4.94. Sapphire data In the literature citation. 

The heat capacities were measured with a computer controlled Perkin-Elmer Differential Scanning Calorimeter DSC-II [17]. Data were taken in 0.2K increments at 20K/minute, corrected for instrumental variations and temperature lag and calibrated point by point with the heat capacity of sapphire. Polymers investigated were Conoco 5425 (ijgp = 0.42) poly vinyl chloride anionic... 

PET AN-82, Heat Capacity of Sapphire using the Two Curve Method. PETAN-83, Measurement of the Temperature Dependent Crystallinity of Polyethylene. 

For the most direct link to the SI, it is advantageous to weigh the amount of liquid or gas. Some of the most precise calorimetric measurements have been performed with weighing of the fluid for example, the determination of the heat capacity of sapphire, a widely used calibration material, has been performed with a... 

The melting transition of ultra-pure metals is usually used for calibration of DSC instruments. Metals such as indium, lead, and zinc are useful and cover the usual temperature range of interest. Calibration of DSC instruments can be extended to temperatures other than the melting points of the standard materials applied through the recording of specific heat capacity of a standard material (e.g., sapphire) over the temperature range of interest. Several procedures for the performance of a DSC experiment and the calibration of the equipment are available [84-86]. A typical sensitivity of DSC apparatus is approximately 1 to 20 W/kg [15, 87]. 

Figure 3.27 Calculation of heat capacity of an unknown using a Netzsch DSC200 heat-flux DSC [7]. The distinct shift in heat capacity at 690°C corresponds to the glass transition temperature (see section 7.6). A 191 mg sapphire standard was used as calibrant for a 130 mg (laser special) glass sample. All heating ramps were at 20°C/min (faster heating rates permit greater temperature lags). The right hand scale, in the original units of the differential thermocouple, is inverted in exothermic and endothermic directions as compared to the usual convention in this book.

Accurate heat capacity, Cp, measurements may be obtained by DSC under strict experimental conditions, which include the use of calibration standards of known heat capacity, such as sapphire, slow accurate heating rates (0.5-2.0 K/min), and similar sample and reference pan weights. MDSC or DDSC also have been used to determine the heat capacity of several pharmaceutical materials. ... 

The proportional factors are determined by the heating rate ft) and by the calibration factor (.B). We can eliminate these factors if a DSC curve of a standard sample is recorded under exactly same experimental conditions. Sapphire is commonly used as the standard with known heat capacity. Figure 10.13b illustrates DSC curves with an empty sample holder (pan), with a sample, and with a standard sample recorded on the same chart. The heat capacity of the sample can be calculated with the heat capacity of the standard (Cps) and displacements measured from Figure 10.13b. 

This is a very thorough study of the heat capacity of monoclinic zirconium dioxide using the heat pulse method. However, the experimental data are not reported nor are the discrepancies between the measured data and temperature dependent heat capacity equations determined from the data. Additionally, uncertainty estimates are not reported, although measurements performed by the authors on samples of AI2O3 and sapphire indicate that published heat capacity results can be reproduced to better than 1.5%. The same degree of uncertainty is assumed for the results for zirconium dioxide. 

The use of the corrections B in Fig. A.l 1.2 needs two calibration runs of the DSC of Fig. 4.54. The heat capacities of the calorimeter platforms, C pi and C pi, and the resistances to the constantan body, R pi and R pi, must be evaluated as a function of temperature. First, the DSC is ran without the calorimeters, next a run is done with sapphire disks on the sample and reference platforms without calorimeter pans. From the empty run one sets a zero heat-flow rate for and This allows to calculate the temperature-dependent time constants of the DSC, written as = C piRspi and Tr = CrpiRrpi, and calculated from the equations in the lower part of Fig. A. 11.2. For the second run, the heat-flow rates are those into the sapphire disks, known to be mCpQ, as suggested in Figs. 4.54 and 4.70. The heat-capacity-correction terms are zero in this second calibration because no pans were used. From these four equations, all four platform constants can be evaluated and the DSC calibrated. 

An alternative method [2] of determining Mi uses the fact that in power compensation DSC the proportionality constant between the transition peak area and Mi is equivalent to the constant which relates the sample heat capacity and the sample baseline increment. By measuring the specific heat capacity of a standard sapphire sample, an empty sample vessel and the sample of interest, from the difference in the recorded DSC curves of the three experiments Mi for the sample transition can be calculated. The advantage of this method is that sapphire of high purity and stability, whose specific heat capacity is very accurately known, is readily available. Only one standard material (sapphire) is necessary irrespective of the sample transition temperature. The linear extrapolation of the sample baseline to determine Mi has no thermodynamic basis, whereas the method of extrapolation of the specific heat capacity in estimating Mi is thermodynamically reasonable. The major drawbacks of this method are that the instrument baseline must be very flat and the experimental conditions are more stringent than for the previous method. Also, additional computer software and hardware are required to perform the calculation. 

Figure 4.20. Corrected specific heat capacities of liquid PEcoO and the reference material sapphire. Analysed as shown in Figure 4.19 with values of t of 2.40 and 2.24 s rad respectively. All data of periods >10 s were used for the evaluation of r.

Multiple DSC runs were made to determine the heat capacity of compositions where x = 0.0, 0.1, 0.2, 0.3, 0.4, and 0.5. Samples were evaluated relative to an empty Pt pan and the system was calibrated with a sapphire standard. Because the variation in specific heat values between each NZP composition was not significant, the combined mean values of specific heat from all compositions are shown in Figure 2. It is believed that the specific heat values presented are representative of the range of compositions being studied. 

The heat capacity of a substance can be measured from the sample mass and difference in heat flow rate of DSC curves, which are determined by programmed constant temperature, rising temperature and constant temperature procedures, using sapphire as a standard reference material [1]. 

With such heat capacity determination it would take a long time to determine temperature dependence of the heat capacity. However, the curves from Ti to steady state and steady state to T2 have similar shape therefore the hs-u (for sample and baseline) amplitude differences are proportional to the heat capacity at every temperature and there is no need to determine the Ss-bi area (shaded area in Fig. 2.19a), but simply to measure the /ts-bi amplitude differences. So, if the instrument is calibrated with a standard for which the temperature dependence of the heat capacity is well known, the heat capacity of the sample can be measured at any temperature. For this, the /isap-w amplitude differences must be used (see Fig. 2.19a, curves Sapphire run and Baseline ). The standard is usually sapphire (crystalline AI2O3), which is readily available from the instrument companies. For low-temperature heat capacity... 

The final step is the calibration run. In trhis run the sample is replaced by the standard AI2O3, sapphire. The uncalibrated heat capacity of AI2O3 is... 

Heat capacities of adhesives can be measured by comparison with a reference material such as synthetic sapphire. 

Figure 1.1 Heat capacity of PET obtained using fast scanning techniques showing the three traces required for subtraction. The height of the sampie compared to the empty pan is divided by the scan rate and the mass of sampie to obtain a vaiue for Cp. This is referenced against a known standard such as sapphire for accuracy, if smaii heating steps of, for exampie, 1 °C are used the area under the curve can be used to caicuiate Cp. This caicuiation is empioyed as an option in stepwise heating methods.

In practice the heat capacity of a material can be found by DSC either by reference to known calibrants as sapphire or by the use of modulated methods of thermal analysis [91]. It should be remembered that the best results are for non-reacting systems where the observed calorimetric signal is not complicated by the enthalpy change associated with a chemical reaction. 

After calibration, the measurement technique of specific heat of sample fluids composed of a double experiment performing two nearly identical runs-one with the two cells without sample and the other with the sample in one of the cells. In this way, any differences between the two crucibles are eliminated from the final signal to be used in equation (1). The uncertainty of the heat capacity determinations is found to be better than 1.5% at a 95% confidence level. It is noted that according to the ISO definition, a coverage factor k=2 is used and in order to obtain the accuracy value it must be divided by 2 (Sampaio Nieto de Castro, 1998). We have checked the accuracy of the measurements by measuring the heat capacity of certified reference material sapphire (NIST SRM-707), between room temperature and 430 K, and found deviations of less than 1.5 % with an average absolute deviation (AAD) of 0.68%. 

Absolute heat capacities of the samples were measured on heating at 10 K/min after cooling at 10 K/min from above Tg. Three consecutive runs were made. First, a reference run is made with an empty sample pan and a matched reference pan. Then, a sample run and a sapphire calibration run were performed using the same sample and reference pans as used from the reference run. Absolute heat capacity was determined from these three runs. Baseline subtraction was not used for these runs. 

Examples are water for the calibration of viscometers, sapphire as a heat-capacity calibrant in calorimetry, and solutions used for calibration in chemical analysis... 

Heat capacities were determined by using a differential scanning calorimeter (DSC). A sapphire standard was used for DSC cell calibration. Samples were cut directly from the samples used in the thermal diffusivity measurements. Heat capacity was determined, as usual, from the heat requirement of the sample in response to a particular change in temperature. Multiple scans were performed to verify that sample degradation did not influence the results. Char samples could be heated up to 850 K in these experiments. The DSC cell was continuously purged with nitrogen, in order to avoid oxidation of the samples. 

Direct observations of Tm (P) and AV may be made in a sapphire optical cell with simple screw-press pump by measuring the offset in the pressure versus volume curve. AH can be measured at room pressure using a simple differential calorimeter comprised of two paper nut cups outfitted with kitchen thermistors and containing water in one and a standard solid material in the other for which the heat capacity curve is known. Direct observations of pressure-release freezing of water (as compared to pressure-release melting in silicates) may be observed in such an optical pressure cell by sudden release of pressure. 

Reaction calorimeters are frequently calibrated using a known heat of a chemical reaction. No standard reaction is internationally accepted. For the measurement of heat capacities, drop calorimeters are frequently used and the calibration is made using a substance, the temperature dependence of which on heat capacity is known. As substances, metals like Cu, Ag, Au, and aluminum oxide in the form of sapphire are used. Calorimeters... 

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