On differential thermal analyzer curves for the melting and freezing of alloys
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I. INTRODUCTION
DIFFERENTIAL thermal analysis (DTA) measurements are a standard method of determining transformation temperatures of materials.[1] Accurate interpretation of these measurements is essential when they are used to infer the location of equilibrium-phase diagram boundaries. The accuracy of the measurements is affected by the details of heat transfer within the measurement cell and by transformation kinetics. Simulations can provide understanding of how thermal events from transformations are reflected in the DTA signal and can enable more accurate interpretation of DTA results from samples with unknown characteristics. While theoretical treatments and analysis of measurements from DTA and other thermoanalytical methods are not new,[2–15] errors of interpretation continue to filter through the scientific literature and industrial technology. It is timely to reexamine these theoretical treatments and couple them with recent progress in alloy thermodynamic descriptions and solidification models. Many early theoretical treatments of DTA were focused on the optimization of the apparatus configuration. Heat exchange is analyzed between the various parts of the apparatus; viz., the sample, reference material, containers, thermocouples, and furnace. The major differences between the various analyses are the number of parts that are considered and whether radiation, conduction, and convection are distinguished for the heat exchange. The heat flow between various objects in the system is typically modeled using systems of ordinary differential equations (ODEs). These methods assume that a single temperature can represent each of the W.J. BOETTINGER, NIST Fellow, and U.R. KATTNER, Physical Scientist, are with the Metallurgy Division, National Institute of Standards and Technology, Gaithersburg, MD 20899. Contact e-mail: [email protected] Manuscript submitted September 4, 2001. METALLURGICAL AND MATERIALS TRANSACTIONS A
different parts of the system. One exception to this approach, used a finite-element method (FEM) analysis of the temperature distribution within the parts of a DTA, and included radiation view factors.[2] Cunningham and Wilburn[3] included heat loss along the thermocouple wires in their very detailed treatment. In addition to DTA, Gray[4] applied the analysis to power-compensation differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA). Heyroth[5] developed an apparatus function for DTA that included radiation and convection in order to explain the heating-rate dependence of the time constants. Shull[6] showed that heat flow between the sample/cup and cup/ wall resulted in an offset between the temperatures of the beginning of the deviation from the baseline in the DTA curve and the actual temperature of an invariant reaction. Within the sample, early work focused on deriving an expression for the heat of reaction[7] or determining the factors affecting the DTA peak shape, such as sample aspect ratio.[8] Kissinger[9] used homogeneous reaction kinetics for the analysis of
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