User Defined Contour Diagram

Contour diagram can be any type of customized properties defined by the user using a mathematical expression. Contour diagram can therefore be used to plot some special property lines. For example, we want to calculate Curie temperature Tc curves in the Fe-Cr system. A Tc curve can be considered as a special contour line when T equals to Tc, which means the constraint: T-Tc=0 is set on the Tc curve. Figure 1 is the input window for calculating the Tc contour curves. Since the constraint is T-Tc(@*)=0, the “Start” and “Stop” values are both set to be zero, and “Step” value is ignored. @* means in every phase. Figure 2 is the calculated Fe-Cr phase diagram with the Tc curves of the Bcc phase.

Figure 1:   Input windows for Tc curves in Fe-Cr system

Figure 2:   Phase diagram of Fe-Cr with Curie temperature curves (in red color) of Bcc phase

A second order transition curve could also be calculated as a contour curve. Fe-Al binary system [2009Sun] is given as an example here. Figure 3 is the calculated Fe-Al binary phase diagram with Tc curves and the second order transition curves. The Tc curves can be calculated the same way as that shown in this section for the Fe-Cr system.

Figure 3:  Phase Diagram of Fe-Al with the Tc curves and the 2nd order transition curves between Bcc and B2 and between B2 and D03

The calculation of the second order transition needs special contour property definition. For the Bcc/B2, the contour property is defined as

abs(y(Fe#2@BCC_4SL)-y(Fe#3@BCC_4SL))

which represents the absolute value of the difference between the site fractions of Fe on the 2nd and 3rd sublattices. The “start” and “stop” values are set to be “0.05”, which avoids the numerical difficulty in calculation and gives a very good approximation of the order/disorder transition curves.

The contour property for the second order transition between B2 and D03 is defined as

abs(y(Fe#3@BCC_4SL)-y(Fe#4@BCC_4SL))

with the “start” and “stop” values of “0.05”. A constraint is also added in this contour calculation to make sure that the first and second sublattices have the same site fractions,

abs(y(Fe#1@BCC_4SL)-y(Fe#2@BCC_4SL))<0.001

Pandat™ batch file is written in the language of XML(Extensible Markup Language). The less-than “<” and great-than “>” characters are reserved as the XML special characters. In an XML file, the less-than “<” and great-than “>” symbols are written as “&lt;” and “&gt;”. Above constraint is written in a Pandat batch file as

abs(y(Fe#1@BCC_4SL)-y(Fe#2@BCC_4SL))&lt;0.001

[2009Sun] B. Sundman, et al., “An assessment of the entire Al-Fe system including D03 ordering”, Acta Mater., 57 (2009): 2896-2908.