# Heat Capacity Determination at High Temperatures by TGA/DSC. Part 1: DSC Standard Procedures

### Introduction

Several different standardized DSC measurement procedures are currently used for the determination of the specific heat capacity (cp). These have been described in earlier publications [1, 2]. The introduction of the TOPEM® technique [3, 4] provides another interesting new method.

In DSC, the measured heat flow is directly proportional to the specific heat capacity. This allows cp to be calculated directly from the DSC signal (Fmeas). To do this, the DSC curve must be corrected by subtracting a blank curve and the masses of the crucibles should be as close as possible.

The isothermal baselines measured before and after the temperature increase should be long enough for the system to stabilize and reach stationary conditions. The results are evaluated according to standards such as ISO 11357, DIN 53765, DIN 51007 or ASTM E1269 [5–8].

dH/dT: change in enthalpy with temperature,

Cp:     heat capacity,

cp:     specific heat capacity,

m:     mass, which should remain constant during the measurement,

βs:     heating rate (change of the sample temperature with time),

Ф:     heat flow,

dH/dt is the change in enthalpy with time and in this case is called the sensible heat flow (Фsens). The measured heat flow (Фmeas) is the sum of the sensible and latent heat flows plus the heat flow (Фbl) of the blank curve. The latent heat flow (Flat) is the sum of thermal events such as transitions or reactions.

The measured heat flow (Фmeas) is the sum of the sensible and latent heat flows plus the heat flow (Фbl) of the blank curve. The latent heat flow (Фlat) is the sum of thermal events such as transitions or reactions.

Measurement of Фsens to calculate the heat capacity assumes that Фlat and Фbl are known. In cp determination, this means that other overlapping thermal events must not occur. Usually, the following two methods are employed:

The Direct method uses eq 3 to calculate the specific heat capacity.

The Sapphire method is carried out according to the standard methods given above and eq 4:

cp=

where msap, cp,sap and Фsap are obtained from the sapphire measurement. Both methods take the influence of different crucible masses into account. Details and information on the use of the different methods are given in UserCom 7 [1]. This present article discusses methods for the determination of the specific heat capacity at temperatures above 500 °C and shows suitable examples. Table 1 summarizes different cp reference values taken from the literature to check the results. The values for quartz are relatively uncertain because the literature values differ by up to 40%.

### Experimental Details

The experiments to determine specific heat capacity at high temperatures were carried out using stable materials that could be repeatedly measured and that differed in cp, thermal conductivity, and color.

### Conclusions

Two standard DSC methods were used to determine cp at temperatures up to 1600 °C. In general, results from the direct method show that repeatability and absolute accuracy are strongly temperature dependent. The method cannot therefore be recommended. In contrast, the sapphire method has the great advantage that no additional calibrations are needed for special crucibles or gases. The best way to minimize the influence of the thermal conductivity of the sample and other effects is to use platinum crucibles with lids. Depending on the temperature range, measurements of pure substances are accurate to ± 5% to ± 10% in comparison with literature values. To achieve high reproducibility and accuracy, measurements of a series should be performed directly one after the other at constant time intervals. This is most easily done using the sample robot. Furthermore, one or two blank measurements should be performed at the beginning of a series but not used for subtraction.

Heat Capacity Determination at High Temperatures by TGA/DSC. Part 1: DSC Standard Procedures | Thermal Analysis Application No. UC 271 | Application published in METTLER TOLEDO Thermal Analysis UserCom 27