Pergamon Chemical Engineerin 9 Science, Vol 50, No. 3, pp. 417 431. 1995 Copyright ~i'~ 1995 Elsevier Science Lid Printed in Great Britain. All rights reserved 0099 2509!95 t/.5(I + 0.00 0009-2509(94)00244-4 THE RELATIONSHIP BETWEEN THE PEAK SHAPE OF A DTA CURVE AND THE SHAPE OF A PHASE DIAGRAM S1NN-WEN CHEN,* CHENG-CHIA HUANG Department of Chemical Engineering, National Tsing-Hua University, Hsin-Chu, Taiwan 30043, R.O.C. and JEN-CHWEN LIN Surface Technology Division, Alcoa Laboratories, Alcoa Center, PA 15069, U.S.A. (Received 24 February 1994; accepted in revised form 8 October 1994) Abstraet--DTA curves are simulated based on the heat transfer modeling of the DTA cells. The calculated results are compared with the experimental determinations, The rates of heat evolution or absorption of the specimens under the DTA scan are correlated with the shapes of phase diagrams. The relationships between the shapes of DTA curves and the shapes of phase diagrams are discussed. I. INTRODUCTION Phase diagrams, known as the "road maps of mat- erials", contain condensed information of the physical states of materials. Phase diagrams are essential for new materials development, failure analysis of mat- erials, and materials processing. Differential thermal analysis (DTA) is a technique which measures the temperature difference developed between a sample cell and a reference cell under the same heating (or cooling) environment (Cunningham and Wilburn, 1970; Blazek, 1972; Pope and Judd, 1977; Wenlandt, 1986). Among other applications, DTA is often used for phase diagram determination (Cunningham and Wilburn, 1970; Blazek, 1972; Pope and Judd, 1977; Wenlandt, 1986; Fink, 1949; Noyak and Oelsen, 1969; Nedumov, 1970; Capelli et al., 1976; Bruzzone, 1985; Zhu and Devletian, 1991). As shown in Fig. I, the temperatures of the solidus and liquidus are deter- mined from a DTA heating scan. Besides these reac- tion temperatures, the DTA curves also contain the information of the shapes of the phase diagrams, illus- trated as follows. The shape of the DTA curve de- pends on the scanning rate and the temperature differ- ence between the sample and reference cells. The tem- perature difference mainly originates from the heat evolution or the absorption of the phase transforma- tions of the specimens which occurs during heating and cooling. When different materials are subjected to the DTA under the same scanning rate, they generate different shapes of DTA curves resulting from the difference of the phase transformation rates. With the assumption of the validity of the lever rule (Rhines, 1956), the phase transformation rates can be deter- mined from the phase diagram and the predetermined *Author to whom correspondence should be addressed. scanning rate. Phase diagrams of the two different hypothetical systems A-B and C-D are shown in Figs 2(a) and 3(a). Under a constant heating rate of lff'C/min, the phase transformation rates of the samples of the nominal compositions A-25 at% B and C-25at% D are shown in Figs 2(b) and 3(b), respec- tively. Since the transformation rates for the two samples of the different phase diagrams are varied, the different shapes of DTA curves can thus be expected. In this study, the relationships between the shapes of the phase diagrams and the shapes of the DTA curves are investigated. 2. THE PHYSICALAND MATHEMATICAL DESCRIPTION OF THE DTA A schematic plot of the DTA is shown in Fig. 4(a). In the DTA, usually the temperature of the furnace is increased at a controlled constant rate. The DTA records the difference between the sample and the reference cells. A mathematical model is proposed by Gray (1968) to describe the heat flow of the DTA cells as shown in Fig. 4(b). They consist of the sample (or reference) and its container at a temperature, T, (or T,); a source of thermal energy at Tp, and a path having a certain thermal resistance, R, through which the thermal energy flows to or from the sample (or the reference). By having assumed that the specimen tern- perature, Ts (or T,), is uniform and equals to that of the container, Gray gave the thermal balance equa- tion for the DTA sample cell: dh dTs (Tp- Ts) ~- (t) Cs dt= R dt where t is the time, Cs the heat capacity of the sample cell (including the sample) and dh/dt, the rate of heat generation of the sample. 417