Cooling Curve Analysis to Determine Phase Fractions in Solid-State Precipitation Reactions
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INTRODUCTION
A new method of cooling curve analysis has been developed that allows for the measurement and quantification of the amounts of phases present during solidstate phase transformations. This method is based on the use of a heat-balance equation in which the enthalpy change of a metal sample is equated to heat lost from convection; this equation then is manipulated to relate phase fraction information to temperature data via fitted parameters and tabulated thermophysical properties. The thermal analysis technique presented here is designed to make in situ measurements of reactions that occur under a variety of cooling conditions; it is designed to require little in the way of specialized machinery or facilities. These attributes are useful when considering that these types of measurements currently are made using light or electron microscopy, differential thermal analysis (DTA), differential scanning calorimetry (DSC), synchrotron diffraction or dilatometry. All of these techniques require specialized and often expensive facilities, and many are limited with respect to their ability to make in situ measurements on full-scale samples. Established cooling curve analysis techniques can be broadly divided into two areas of focus—solid-state phase transformations and solidification. Techniques that are focused on solid-state transformations include DTA and single-sensor differential thermal analysis (SSDTA).[1] Although these techniques can be used to make in situ determinations of transformation start and finish JOHN W. GIBBS, Post Masters Student, and ROBERT E. HACKENBERG, Technical Staff Member, are with Los Alamos National Laboratory, Los Alamos, NM 87545. MICHAEL J. KAUFMAN, Professor, is with Colorado School of Mines, Golden, CO 80401. PATRICIO F. MENDEZ, Professor, is with the University of Alberta, Alberta, Canada, T6G 2R3. Contact e-mail: pmendez@ ualberta.ca Manuscript submitted June 3, 2009. Article published online June 4, 2010 2216—VOLUME 41A, SEPTEMBER 2010
temperatures of solid-state phase transformations, they cannot be used to make phase fraction measurements. DSC is one technique that can phase fraction measurements similar to those made via the presented technique; however, its requirement for subgram-sized samples limits DSC’s applicability to full-scale systems. Furthermore, DSC’s accuracy is limited by the fact that it measures the power response of a furnace to the temperature of a crucible that contains the sample, rather than a direct measurement of any sample property. Single-pan calorimetry is a technique that produces similar results to DSC but with a simpler experimental apparatus and larger possible sample sizes.[2] The singlepan calorimetry technique has been used to make phase fraction measurements of solidification reactions[3]; although currently no published effort is being made to do so for solid-state reactions. Quantitative cooling curve analysis efforts have also been directed primarily at solidification reactions.[4–7] Until recently, these analysis techniques have been based on gra
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