Muggianu and toop-muggianu interpolations comment on a comment by L. Kaufman (CALPHAD [formula omitted], 225 (1981)) On brynestad's paper (CALPHAD, [formula omitted], 103 (1981))

It is shown that the Muggianu interpolation procedure for ternary calculations approximated from binary data has the advantages of the Kohler method without the mathematical difficulty pointed out by Brynestad. It is suggested that the Muggianu interpolation should be used in the kinds of situations where Kohler interpolations have been used, and that Toop interpolations should be replaced by Hillert's second new method for which the name of Toop-Muggianu interpolation can be used. A fourth power polynomial approximation to the Kohler interpolation is also described. The Muggiann, Kohler, and fourth power methods are compared for the Fe-Cr-Ni ternary system, illustrating the problems with the Kohler method.