Variation of Peak Temperature With Heating Rate in Differential Thermal Analysis

Variation of Peak Temperature With Heating Rate in Differential Thermal Analysis

October 1956 | Homer E. Kissinger
In differential thermal analysis (DTA), the peak temperature varies with heating rate for certain reactions. An expression relating this variation to reaction kinetics was derived. By analyzing DTA patterns at different heating rates, kinetic constants can be obtained directly. Measurements were made on kaolin group minerals, and kinetic constants were compared with those from isothermal techniques. Factors affecting results were discussed. DTA records thermal effects as a sample is heated, with deflections indicating heat changes. Endothermic effects show negative deflections, exothermic positive. Peak temperatures often differ from known transition temperatures and are influenced by technique. Only crystalline inversions have satisfactory explanations for DTA peaks. Murray and White's work on clay mineral decomposition applies to DTA interpretation. They measured isothermal dehydration rates, calculated kinetic constants, and constructed reaction rate curves. These curves matched DTA patterns, with peak temperatures close to observed DTA peaks. Sewell later found that DTA peak temperatures could be predicted by Murray and White's equation. The equation derived by Murray and White defines peak temperature by kinetic constants and heating rate. The assumption that peak temperature occurs at maximum reaction rate is supported by experiments. It should be possible to calculate kinetic constants from DTA data by making patterns at different heating rates. Murray and White reported that clay decomposition follows a first-order law. At constant temperature, the rate is given by a differential equation. The rate constant is determined by the Arrhenius equation. When temperature changes, the reaction rate is modified. The maximum reaction rate occurs at a specific temperature, defined by an equation derived by Murray and White. The experimental procedure involved kaolinite and halloysite samples. DTA was performed at various heating rates, and isothermal weight-loss measurements were made. Activation energies and frequency factors were calculated. Results showed that kaolinites followed the first-order law, while halloysite did not at higher temperatures. Activation energies and frequency factors were calculated for kaolinites. Values varied between samples. Well-crystallized kaolinites had higher activation energies. Halloysite had slightly lower activation energies. DTA peak temperatures were influenced by heating rate and activation energy. Plotting ln(φ/Tm²) vs 1/Tm gave a straight line with slope -E/R. Results showed that peak temperatures were reproducible, with standard deviations within acceptable limits. Activation energies determined by DTA were slightly lower than isothermal values. The discrepancy may be due to temperature gradients in the sample. Diluting samples with α-Al2O3 reduced temperature differences but increased activation energy values. Experiments with smaller specimen holders showed lower peak temperatures. Standard deviations were similar to larger holders. Activation energies were slightly lower with smaller holders. The DTA method's precision was calculated, showing it is not more precise than isothermal methods. Agreement between DTA and isothermal results confirms the validity of the equation for reactions varying with temperature. Discrepancies inIn differential thermal analysis (DTA), the peak temperature varies with heating rate for certain reactions. An expression relating this variation to reaction kinetics was derived. By analyzing DTA patterns at different heating rates, kinetic constants can be obtained directly. Measurements were made on kaolin group minerals, and kinetic constants were compared with those from isothermal techniques. Factors affecting results were discussed. DTA records thermal effects as a sample is heated, with deflections indicating heat changes. Endothermic effects show negative deflections, exothermic positive. Peak temperatures often differ from known transition temperatures and are influenced by technique. Only crystalline inversions have satisfactory explanations for DTA peaks. Murray and White's work on clay mineral decomposition applies to DTA interpretation. They measured isothermal dehydration rates, calculated kinetic constants, and constructed reaction rate curves. These curves matched DTA patterns, with peak temperatures close to observed DTA peaks. Sewell later found that DTA peak temperatures could be predicted by Murray and White's equation. The equation derived by Murray and White defines peak temperature by kinetic constants and heating rate. The assumption that peak temperature occurs at maximum reaction rate is supported by experiments. It should be possible to calculate kinetic constants from DTA data by making patterns at different heating rates. Murray and White reported that clay decomposition follows a first-order law. At constant temperature, the rate is given by a differential equation. The rate constant is determined by the Arrhenius equation. When temperature changes, the reaction rate is modified. The maximum reaction rate occurs at a specific temperature, defined by an equation derived by Murray and White. The experimental procedure involved kaolinite and halloysite samples. DTA was performed at various heating rates, and isothermal weight-loss measurements were made. Activation energies and frequency factors were calculated. Results showed that kaolinites followed the first-order law, while halloysite did not at higher temperatures. Activation energies and frequency factors were calculated for kaolinites. Values varied between samples. Well-crystallized kaolinites had higher activation energies. Halloysite had slightly lower activation energies. DTA peak temperatures were influenced by heating rate and activation energy. Plotting ln(φ/Tm²) vs 1/Tm gave a straight line with slope -E/R. Results showed that peak temperatures were reproducible, with standard deviations within acceptable limits. Activation energies determined by DTA were slightly lower than isothermal values. The discrepancy may be due to temperature gradients in the sample. Diluting samples with α-Al2O3 reduced temperature differences but increased activation energy values. Experiments with smaller specimen holders showed lower peak temperatures. Standard deviations were similar to larger holders. Activation energies were slightly lower with smaller holders. The DTA method's precision was calculated, showing it is not more precise than isothermal methods. Agreement between DTA and isothermal results confirms the validity of the equation for reactions varying with temperature. Discrepancies in
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