Mechanism of the $\alpha -\epsilon$ phase transformation in iron

The $\alpha \text{-Fe}\leftrightarrow \epsilon \text{-Fe}$ pressure-induced transformation under pure hydrostatic static compression has been characterized with in situ x-ray diffraction using $\alpha \text{-Fe}$ single crystals as starting samples. The forward transition starts at 14.9 GPa, and the reverse at 12 GPa, with a width of $\alpha -\epsilon$ coexistence domain of the order of 2 GPa. The elastic stress in the sample increases in this domain, and partially relaxes after completion of the transformation. Orientation relations between parent $\alpha \text{-Fe}$ and child $\epsilon \text{-Fe}$ have been determined, which definitely validates the Burgers path for the direct transition. On the reverse transition, an unexpected variant selection is observed. X-ray diffraction data, complemented with ex situ microstructural observations, suggest that this selection is caused by defects and stresses accumulated during the direct transition.

Figure 1

(a) Sketch of the x-ray diffraction (XRD) setup. The monochromatic x-ray beam is focused on the sample (in black) which can be rotated by ${\theta }_C$ around a vertical axis. The diffracted signal is recorded on a bidimensional detector. The incoming x-ray beam position (cross) and azimuthal angle $\chi$ are indicated. (b) Composite x-ray diffraction image of the sample after pressure increase to 11.7 GPa. The $\left(hkl\right)$ Miller indices of the Bragg spots of $\alpha \text{-Fe}$ are indicated. Gray diamonds hide the XRD signal of the diamond anvils.

Figure 2

1D patterns obtained by azimuthal integration of the XRD images recorded using a liquid helium pressure transmitting medium at 380 K. The Miller indices of the XRD lines for $\alpha \text{-Fe}$ and $\epsilon \text{-Fe}$ are indicated in red and green, respectively.

Figure 3

Two-$\theta$ full width at half maximum of ${\left(110\right)}_{\mathrm{bcc}}+{\left(0002\right)}_{\mathrm{hcp}}$ XRD peaks during the first pressure cycle for the hydrostatic run (see Fig. 2). The arrows indicate in which order the data have been taken. The Greek letters indicate at which conditions $\alpha \text{-Fe}$ and $\epsilon \text{-Fe}$ are observed.

Figure 4

Fraction of $\epsilon \text{-Fe}$ on pressure increase and decrease for three runs, for (a) the first and (b) the second pressure cycle. It has been estimated using the intensity ratio between ${\left(002\right)}_{\mathrm{bcc}}$ and ${\left(10\overline{1}2\right)}_{\mathrm{hcp}}$ peaks. Different symbols and colors correspond to different runs. The symbol size corresponds to the uncertainty in pressure. The vertical dashed lines indicate the pressure for direct and reverse transitions. Literature data obtained using powder samples are also plotted as purple dotted lines (nonhydrostatic loading, Ref. [6]) and dash-dotted pink line and symbols (hydrostatic loading, Ref. [15]).

Figure 5

Volume of $\alpha \text{-Fe}$ and $\epsilon \text{-Fe}$ measured on pressure increase (inc.) and decrease (dec.), in one run (in a neon pressure medium, $T=300$ K). The vertical continuous (dashed) lines indicate the pressure of appearance (disappearance) of $\epsilon \text{-Fe}$ (in blue) and $\alpha \text{-Fe}$ (in red). Inset: evolution of the $c/a$ ratio in $\epsilon \text{-Fe}$. The corresponding data are listed in Table 1. Data from Refs. [6] and [15] are also plotted as points and dash-dotted lines.

Figure 6

(a) Burgers path for the $\alpha \text{-Fe}\to \epsilon \text{-Fe}$ transformation (see text). The gray plane on the left is the ${\left(110\right)}_{\mathrm{bcc}}$ plane, which will transform to the ${\left(0001\right)}_{\mathrm{hcp}}$ plane. The green arrows on the left indicate the direction of ${\left[001\right]}_{\mathrm{bcc}}$ compression; on the right, they represent the translation vector for the shuffle (translation of the entire plane containing dark blue atoms). (b) Expected evolution of the number of variants during one $\alpha \to \epsilon \to \alpha$ cycle. One $\alpha \text{-Fe}$ variant transforms into 6 $\epsilon \text{-Fe}$ variants and then 13 $\alpha \text{-Fe}$ variants.

Figure 7

Details of composite XRD images (see Fig. 1 for the setup) presented in the order they have been taken during two pressure cycles in one run (in a helium pressure medium, at 300 K). The gray diamonds hide the XRD signal of the diamond anvils. The observed Fe phase(s) are indicated in red. Miller indices of $\alpha \text{-Fe}\left(hkl\right)$ and $\epsilon \text{-Fe}\left[hk\right(-h-k\left)l\right]$ are specified in (a), (b), and (d). In (c), arrows of six different colors point to the main $\epsilon \text{-Fe}$ XRD spots: each color identifies two close orientations of a pseudosingle crystal (see text).

Figure 8

(a) Detail of the composite XRD image from Fig. 7. (b) Rocking curve of the ${\left(10\overline{1}1\right)}_{\mathrm{hcp}}$ peak indicated with a green arrow. The vertical bars correspond to the peak positions for two close $\epsilon \text{-Fe}$ orientations predicted by the Burgers path. (c) Profile in $\chi$ azimuthal angle of the ${\left(10\overline{1}1\right)}_{\mathrm{hcp}}$ peaks indicated with yellow and purple arrows. The vertical bars correspond to the peaks positions for four $\epsilon \text{-Fe}$ orientations predicted by the Burgers path.

Figure 9

(a) Rocking curves of the (200)${}_{\mathrm{bcc}}$ XRD peaks represented in Fig. 7, starting sample, and Fig. 7, after reversion. (b) Profile in $\chi$ azimuthal angle of the same peaks.

Figure 10

Sample recovered after two transformation cycles, in helium at 300 K. (a) TEM bright field. The sample contains a large density of dislocations which makes the observation of the microstructure very difficult. Variants of $\alpha$ with modified orientation are bordered in red. (b) Orientation map obtained in the TEM-astar. The color in the inverse pole figure map corresponds to the crystallographic orientation of the horizontal direction in the observed plane. Color variations in the background correspond to slight misorientations due to the presence of dislocations. (c) TEM dark field of the same zone. In this mode, dark lenses correspond to variants with a different orientation.