Instability of the body-centered tetragonal phase of iron under extreme conditions

The influence of the tetragonal and orthorhombic axial distortions on the body-centered cubic (bcc) phase of Fe at extreme conditions has been studied by means of first-principles calculations. We unambigiously demonstrate that the energy minimum corresponding to the body-centered tetragonal (bct) $\left(c/a\approx 0.9\right)$ structure, previously found in Fe upon the axial tetragonal distortion of the bcc phase along the Bain’s path under compression at zero temperature, is an artifact of the structural constraint. When the bcc structure is examined using the orthorhombic distortion involving the tetragonal distortion as a particular case, the bct $\left(c/a\approx 0.9\right)$ structural framework represents a saddle point between two mirrored face-centered cubic minima rather than a local minimum. Therefore we conclude that there is no ground to emphasize on possible thermal stabilization of the bct structure with a particular $c/a$ ratio apart from the whole family of structures obtained by tetragonal, orthorhombic, or another type of axial distortions.

Figure 1

Structural relation between the face-centered and body-centered crystal structures.

Figure 2

Enthalpy difference $H-H_{\text{bcc}}$ of the bct structural arrangements of Fe as a function of $c/a$ ratio along the Bain’s path at 330 GPa and 0 K. $c/a=\sqrt{2}$ corresponds to the fcc and $c/a=1.0$ to the bcc structure.

Figure 3

(Color online) Enthalpy difference $H-H_{\text{bcc}}$ of the body-centered orthorhombic (bco) structural arrangements of Fe as a function of $c/a$ and $b/a$ at 330 GPa and zero temperature. Notice that the point $\left(b/a=c/a=1\right)$ corresponds to the bcc structure; the lines $\left(b/a=1,c/a\ne 1\right)$, $\left(b/a\ne 1,c/a=1\right)$, and $\left(b/a=c/a\ne 1\right)$ correspond to the bct structures; the points $\left(b/a=1,c/a=\sqrt{2}\right)$, $\left(b/a=\sqrt{2},c/a=1\right)$, and $\left(b/a=c/a=1/\sqrt{2}\approx 0.7071\right)$ correspond to the fcc phase; the points $\left(b/a=1,c/a\approx 0.9\right)$, $\left(b/a\approx 0.9,c/a=1\right)$, and $\left(b/a=c/a\approx 1.11\right)$ correspond to bct $\left(c/a\approx 0.9\right)$ phase.