The following is an empirical equation from experimental dil

The following is an empirical equation (from experimental dilatometry data) for the percentage volume change when going from austenite (the gamma phase, i.e., f.c.c. iron with carbon in solid solution) to martensite (M) (obviously by a displacive transformation): % volume change on transformation = 4.64-0.53 x wt% carbon Why should this equation give the correct volume change for the diffusive transformation of pure f.c.c. iron to b.c.c. iron? How does the value obtained from this equation at zero wt% carbon compare with the answer 4.58%.

Solution

(1) One is that the volume change is delta V/Vsub0 = 4.64-0.53% times the carbon content (meaning that the displacive transformation is greatest at zero carbon)
(2) The other is a linear relationship strain = 0.01 x Carbon content approx (meaning that at zero carbon, the martensite formed is zero) Assuming that steel is isotropic (not strictly true due to rolling texture,) that makes delta V/Vsub0 = (1+%C/100)^3

I\'d instinctively choose the second based upon my understanding of theory, however, I also know and understand that heat treatment gives the first credence, to a point where it\'s referenced multiple times in ASM handbooks. BEng Hons (Materials)

One of the differences between the two phases is that martensite has a body-centered tetragonal (BCT) crystal structure, whereas austenite has a face-centered cubic (FCC) structure

Volume changes associated with phase transformation are predictable based on equations in ASM Handbook, Volume 4, Heat Treating. Linear changes are approximately 1/3rd of the volume change predicted by

Delta Volume of Austenite-Martensite = 4.64-0.53 × (%C)

Looking at atomic volume changes from ASM Hanbook, Volume 4A

Austenite 11.401 + 0.329 C(%) apparent atomic volume in Angstroms
Martensite 11.789 + 0.370 C(%)