Nucleation of Solids in Solids: Ferrites and Martensites

When a solid such as iron is cooled across a structural transition, its final microstructure depends sensitively on the cooling rate and the depth of quench. For instance, an infinitesimally slow cooling or a shallow quench results in an equilibrium “ferrite,” while a rapid cooling or a deep quench gives rise to a metastable twinned “martensite.” In this paper, we arrive at a single formalism which qualitatively describes the transformation to both a ferrite and a martensite. Fundamental to this understanding is our identification of the crucial dynamical role played by nonelastic degrees of freedom in determining the final microstructure of the product solid.

Figure 1

Equilibrium phase diagram for $N=2499$ at $⟨\rho ⟩=1.05$, showing the square (□) and triangle (△) phases separated by a phase boundary (dark line). Arrows $T_1$ and $T_2$ are the constant temperature transformation protocols into the region where square is metastable (bounded by dotted line [6]). Inset: $⟨\Omega ⟩$ versus $t$ for the two transformation protocols.

Figure 2

MD snapshot of a ${110}^2$ system (a) isotropic ferrite nucleus at $t={10}^4$ (inset: trajectories of five chosen particles). (b) Anisotropic twinned nucleus at $t=6\times {10}^3$ (inset: trajectories of five chosen particles which move from bottom to top). Colors (gray scale) code the local order parameter $⟨{\Omega }_i⟩$ going from red (dark)—□ to blue (light)—△.

Figure 3

Profile of $\varphi$ at $t=t_1(2000)$ and $t_2(5000)$. Arrow shows the direction of particle displacements resulting in increased density at one end of the nucleus and reduced density at the other. Inset: profile of ${ϵ}_{xy}$ at the two times.

Figure 4

First-passage time ${\tau }_n$ versus parameter $a$ and diffusion coefficient $D_v$. Hatched area is the region in which solid transformation does not occur. The inset shows the cut across the 3D plot when $D_v=D_{\infty }\exp (-A/k_{B}T)$ ($D_{\infty }={10}^{14}$, $A=7$, $\gamma =0.2$ and $C=0$). Upper dotted line is the equilibrium transition. At lower $a$, the single twin nucleates faster (bold line) than the ferrite (lower dotted line). Arrow ($M_s$) shows the value of $a$ below which the twinned nucleus forms.