Specific heat sapphire

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]. 

The specific heat at constant pressure, Cpf of the HIP-treated sample with nominal composition LaVg 25 0,7504 was measured over the temperature range 4-400 K by the heat pulse method in a calorimeter that incorporates a feedback system to regulate the temperature of concentric radiation shields surrounding the sample (9). The Cp values are accurate to within 1%, as determined by calibration runs using a polycrystalline copper sample and a sapphire single crystal sample. 

Figure 5.42. Comparison of calibration constant K determined by heat of fusion (indium) and specific-heat (sapphire) standards (156).

The usual scanning techniques are differential thermal analysis (DTA) [78] and differential scanning calorimetry (DSC) [79-81], In these methods it is assumed that the heat loss from the calorimeter is a function of temperature only. By comparing the rate of heat input and temperature rise for a polymer sample with that of a standard, usually synthetic sapphire, the specific heat of the polymer can be obtained. 

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. 

Specific heat measurements using a DSC are based on the principle that the offset from the baseline which would be obtained for a curve using an empty sample pan, is directly proportional to the specific heat of the sample multiplied by the mass of that sample. Determination of the specific heat requires a series of three heating curve measurements. On the first measurement, an empty pan is used in the sample location in the instrument to establish the baseline for the measurement. A second measurement is made using a standard of known specific heat and mass, usually a small sapphire disk, in the sample pan. Finally, a third... 

Specific heat measurements were made using a Perkin-Elmer DSC-IB differential scanning calorimeter. The sample size was generally 15 mg. and the data was obtained for a sample surrounded by a dry nitrogen atmosphere. Synthetic sapphire was used as a reference. In each run, carried out at a rate of 8°/min, a temperature range of 20°K was explored. D.S.C. scans were obtained at scanning rates of 32°C/min. 

Figure 4.95 illustrates the evaluation of the constant x as the slope of a plot of the square of the reciprocal of the uncorrected specific heat capacity as a function of the square of the frequency as suggested by Eqs. (2) and (3) of Fig. 4.94. Note that the c bration run of the sapphire and the polystyrene have different values of x. In...

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. 

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.

Heat flow calibration of the apparatus is also required. This is obtained by running baseline and experimental traces for a material whose specific heat capacity is well known. Sapphire is the calibration material of choice since it is easily available and its specific heat capacity is accurately known. 

In the absence of enthalpy changes, an ideal DSC trace is a straight line the slope of which depends on the difference of specific heat capacity between sample and reference material. After calibration with a substance of reliably known specific heat (sapphire is sometimes used), the specific heat of the test material can be calculated. 

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 use of a standard such as synthetic sapphire simplifies the determination of specific heats. By measuring the standard, an empty cell, and the substance, the specific heat value C2 of the sample can be obtained directly by comparison. For a given temperature. 

With the DSC technique, a third test is needed using a standard reference material (sapphire) that has a known specific heat capacity. 

Figure 1. 2 (a) Temperature profile and measured heat flow rate for empty pans, sapphire calibration standard (34 mg), and initially amorphous PEEK (29 mg), Heating rate = 20 K/ min, Perkin Ehner Pyris Diamond DSC. (b) Specific heat capacity versus temp>erature. Reference data (straight fines) for the fuUy amorphous (liquid) and crystaUine (solid) PEEK from ATHAS-DB [124],... 

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%. 

---