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agrams are one of the most important tools to represent information on phase equilibria. A phase diagram is usually 2D and has thermodynamic state variables like temperature and composition on the axes where each point in the diagram represents the stable phases for the particular combination of state variables. With the use of today’s computer softwares such diagrams can readily be plotted with a wide choice of variables on the axes allowing the user to choose what is most convenient to address a certain problem. Hillert[1] defined a true phase diagram as a diagram where each point uniquely defines the stable phases. Points representing the same set of stable phases constitute a phase field and the phase diagram then usually shows the boundaries between the different phase fields. In contrast a phase diagram where the phase fields overlap may be thermodynamically correct in principle but is not useful due to the lack of uniqueness. Hillert showed that the choice of state variables must obey certain rules in order to have true phase diagrams. In this note we will demonstrate that although Hillert’s rules are necessary they are not sufficient to have true phase diagrams. As a starting point we show in Figure 1 the classical binary Fe-C metastable phase diagram at atmospheric pressure, i.e., graphite that usually forms very slowly has been removed and cementite Fe3C forms instead. The metastability is not important in this study; this Fe-C

JOHN A˚GREN, Professor, is with Materials Science and Engineering, KTH, 10044 Stockholm, Sweden. Contact e-mail: [email protected] RAINER SCHMID-FETZER, Professor, is with the Institute of Metallurgy, Clausthal University of Technology, 38678, Clausthal-Zellerfeld, Germany. Manuscript submitted June 25, 2014. Article published online August 1, 2014 4766—VOLUME 45A, OCTOBER 2014

system was simply chosen as a good example to demonstrate the general approach, valid for all systems. Temperature is on the vertical axis and carbon content on the horizontal axis. Inspection of the diagram reveals that this is a true phase diagram. In fact all other binary phase diagrams at a given pressure and plotted with temperature and composition are true phase diagrams. For all the following diagrams no additional phase equilibrium calculation is required because the values of all relevant thermodynamic properties along the phase boundaries are already stored in the memory during this first phase diagram calculation. The calculations can be reproduced using either Thermo-Calc,[2] as done in this study, or Pandat[3] software and the thermodynamic description of the Fe-C system.[4] In Figure 2 we have exchanged the carbon content with the carbon activity on the horizontal axis. The carbon activity aref C is related to the chemical potential of carbon lC  ref RT ln aref C ¼ lC  l C

½1

and is given relative to some arbitrarily chosen reference state having chemical potential  lref C . Here graph ref = l , i.e., the carbon activity ite is chosen,  lgra C C agra C is defined as unity in equilibrium with graphite.