By H. Aaronson, et. al.,

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**Example text**

124, and rearranging with m ¼ xgN0 and N1 ¼ (1 À xg)N0, G gC xg ¼ RT ln 1 À (14 À 12u2 )xg ! 98 is rewritten as G gC ¼ GgC þ RT ln agC ! 126 through rewriting in terms of agC . 127 shows that w 2 zg ¼ 13 À 12u2 ¼ 13 À 12 exp À kT (1:128) Rearranging, we get 12 wg ¼ w2 ¼ kT ln 13 À zg (1:129) Thus, the carbon–carbon interaction energy in austenite wg, must vary with temperature in an appropriate manner, if zg is to be independent of temperature. 7, but on the basis of more advanced statistical thermodynamic treatments of the activity of carbon in austenite.

2! 3 2 2gV a 1 À xba b ba 4 5 xba 1þ b,r ¼ xb ab RTr xa À xba b (1:78) (1:79) This result is appropriate when a has a limited existence range and when both b and a can be considered dilute solutions. 79 is often used, b xba b,r ¼ xba b 2gV B 1þ RTr ! (1:80) b where V B is the partial molar volume of solute in the b matrix, is not correct for solid–solid transformations. , difﬁcult diffusional jumps, occurring continuously and uniformly over the area of the interphase boundary. It was felt, however, by Aaronson that this type of growth barrier is rare, at least in phase transformations investigated in detail so far, but that more proved examples of it could be discovered in the future.

As a rough estimate, the T0–x curve bisects a two-phase ﬁeld. Clearly, this estimate is more accurate, the narrower the two-phase region. But more accurate estimates of this curve are readily made. b B A (1:51) This equation can be solved for x by means of the quadratic formula. b B A stability parameters. 8. The ideal solid solution G–x curve must be concave upward because the {x ln x þ (1 À x) ln(1 À x)} term is always negative. If the Cx(1 À x) term is also negative, the concavity is merely deeper, or more pronounced.