$\alpha -\epsilon$ transition pathway of iron under quasihydrostatic pressure conditions

We have carefully investigated the $\alpha -\epsilon$ transition pathway of iron under quasihydrostatic pressures. For this purpose, combined measurements of extended x-ray absorption fine structure (EXAFS) and x-ray magnetic circular dichroism at the Fe $K$ edge were performed using a helium pressure-transmitting medium. Collapse of the ferromagnetism simultaneously occurs with the $\alpha -\epsilon$ structural transition, which is in contrast to the scenario that the transition is driven by the pressure-induced instability of the ferromagnetism in $\alpha$ phase of iron. We conclude that shear stress is important to initiate the $\alpha -\epsilon$ transition. Our model to fit the EXAFS profile demonstrates that the local atomic arrangement in $\epsilon$ phase is slightly distorted due to unfinished shuffle motion, whereas shear motion finishes at the beginning of the transition.

Figure 1

XMCD (top) and x-ray absorption (XANES: bottom) spectra of iron at the Fe $K$ edge under selected pressures. Each spectrum is shifted upward for clarity.

Figure 2

Pressure dependence of normalized ferromagnetic phase fraction and relative $\alpha$ phase abundance $\left(w_{\alpha }\right)$ evaluated from the XMCD and EXAFS spectra, respectively. For comparison, the ferromagnetic phase fraction is normalized by the average value of $I_{\text{XMCD}}$ in the range between 13 GPa and $P_{\text{t}}$. The (blue) horizontal line indicates the normalized magnitude of $I_{\text{XMCD}}$ at AP.

Figure 3

(a) The $\chi \left(k\right)k^2$ profile obtained from the first run. (b) Magnitude of the Fourier transforms of the $\chi \left(k\right)k^2$ (thick solid lines), the fitted curves of the $\alpha +\epsilon$ model (thin solid lines), and the curves of the $\alpha +\mathrm{IM}$ model (thin broken lines) at selected pressures.

Figure 4

Fitted results of lattice constants and $c/a$ ratio obtained using the $\alpha +\epsilon$ model. Open and closed symbols correspond to the results from the first and second runs, respectively. The thin solid lines indicate the data taken from Ref. [13] for comparison.

Figure 5

Fitting results of the $\alpha +\mathrm{IM}$ model. Open and closed symbols correspond to the data of first and second runs, respectively. Solid lines are guides to the eye.

Figure 6

Schematic of the martensitic transition of iron based on the Burgers model. The atomic arrangements are viewed from the ${\left[001\right]}_{\text{IM}}$ direction [24]. The broken-line rectangles depict unit cells of the orthorhombic lattice (space group $Cmcm)$ for each phase. The small arrows in the martensitic phase indicate displacements related to the $y$ parameter due to shuffle motion. These figures are depicted on the basis of the configuration that $l_{\text{b}}$ is unchanged by the shear motion.

Figure 7

Comparison of (a) reduced $\chi$-square $\left({\chi }_{\nu }^2\right)$ and (b) $R$ factor between $\alpha +\epsilon$ model (closed squares) and $\alpha +\mathrm{IM}$ model (open circles). All data are taken from the first run.