3-d Model for strain ordering in steel: I Static effects

We present a spring-defect model in 3-dimensions to describe the connection between elastic distortion and interstitial carbon ordering associated with phase transition from a body centred cubic (BCC) to body centered tetragonal (BCT) structure in BCC metals such as α-iron. The presence or the absence of the carbon is modelled in terms of a pseudo spinŝ=+1or -l.An Ising interaction between carbon atoms is recovered after eliminating the lattice degrees of freedom, which is longranged. The coupling between the spin and lattice degrees of freedom allows for a systematic study of ferroelasticity and the variation of the lattice parameter with carbon concentration. The mean field results for the paraelastic to ferroelastic transition, lattice parameter and static compliance are presented. The significant feature of this calculation is not only a derivation of the defect-defect interaction, but also an explicit calculation of the strain dipole tensor associated with each defect, from a microscopic model.