Electronic Origins of Anomalous Twin Boundary Energies in Hexagonal Close Packed Transition Metals

Density-functional-theory calculations of twin-boundary energies in hexagonal close packed metals reveal anomalously low values for elemental Tc and Re, which can be lowered further by alloying with solutes that reduce the electron per atom ratio. The anomalous behavior is linked to atomic geometries in the interface similar to those observed in bulk tetrahedrally close packed phases. The results establish a link between twin-boundary energetics and the theory of bulk structural stability in transition metals that may prove useful in controlling mechanical behavior in alloy design.

Figure 1

Calculated $\{10\overline{1}1\}$ and $\{11\overline{2}1\}$ twin-boundary energies versus calculated values of $G{\mathrm{\Omega }}^{1/3}$, where $G$ and $\mathrm{\Omega }$ are shear modulus and atomic volume, respectively. Dashed lines are least-squares fits excluding the data for Re and Tc.

Figure 2

Electron backscattered diffraction scans of (a) pure Re deformed 6.8% and (b) a Re-10 at. % W alloy deformed 7.8%. The colors represent crystallographic orientation as described by the legend at top right. Black areas represent regions that were unable to be indexed due to surface pitting.

Figure 3

For Re-9.8 at. % $X$ alloys, variations as a function of solute $X$, for (a) the $\{11\overline{2}1\}$ TB energy as calculated from SQS, VCA, and KKR-CPA, (b) $\{0001\}$ surface energy calculated from SQS, and (c) a ductility parameter, $D={\gamma }_s/{\gamma }_t$.

Figure 4

(a) The $\{11\overline{2}1\}$ TB, viewed in projection along an $[1\overline{1}00]$ direction, highlighting a distorted icosahedron on the TB plane, (b) detailed view of the distorted icosahedron as found in the $\{11\overline{2}1\}$ TB, (c) an undistorted Z12 icosahedron, and (d) the calculated bimodality parameter $s$ as a function of distance relative to the TB plane.