Figure 1

Dependence of the stress and total energy on the shear strain within the (0001) plane in the $\left[10\overline{1}0\right]$ direction. The strain points of O, M1, and M2 indicate the equilibrium stable hcp-derived structure and the two metastable trigonal ones formed during the shear-induced phase transformation.Reuse & Permissions

Figure 2

(Color online) VCD within the $\left(11\overline{2}0\right)$ plane at the shear strains of (a) $\gamma =0.2936$ and (b) $\gamma =0.3195$ before and after the first lattice instability, respectively, and (c) $\gamma =0.4282$ and (d) $\gamma =0.4859$ before and after the second lattice instability, respectively, shown in Fig. 1. Re denotes the rhenium and B the boron atoms. The VCD scale is from 0 (dark blue) to 0.2 (red) in units of $\text{electron}/{\text{bohr}}^3$.Reuse & Permissions

Figure 3

(Color online) (a) The equilibrium O (hcp) structure from the $\left[11\overline{2}0\right]$(upper figure) and [0001] crystallographic directions, and the sheared metastable structures of (b) M1 (trigonal) and (c) M2 (trigonal), respectively (see Fig. 1 and the text). Small and large circles represent B and Re atoms, respectively.Reuse & Permissions

Figure 4

(Color online) Valence charge density within the $\left(11\overline{2}0\right)$ plane for several significant values of shear strain $\gamma$ shown in Fig. 1. Re denotes the rhenium and B the boron atoms. The VCD scale is from 0 (dark blue) to 0.2 (red) in units of $\text{electron}/{\text{bohr}}^3$.Reuse & Permissions

Figure 5

(Color online) (a) The orbital-resolved density of state of $5d$ levels of rhenium with respect to the Fermi level at equilibrium (O) and of the sheared metastable structures M1 and M2 (see Fig. 1). The axis $x$ corresponds to the shear direction $\left[10\overline{1}0\right]$, $y$ axis is parallel to the $\left[11\overline{2}0\right]$, and $z$ to the [0001] direction. Below: the coordination of the rhenium to boron in the three structures (b) O (hcp)-, (c) M1 (trigonal)-, and (d) M2 (trigonal)-${\text{ReB}}_2$.Reuse & Permissions

Figure 6

(Color online) Top view of the changes in the coordination of Re in the three structures (a) the equilibrium O (hcp)-, and the metastable (b) M1 (trigonal)- and (c) M2 (trigonal)-${\text{ReB}}_2$ during the shear. With the Re and the 3 B (in red) as the unaffected layer below, the brownish B-“zigzag hexagon” layer moves from right to left in the figures on going from O to M1 and M2. During this process, the zigzag B-B sixfold ring flattens (M1) and the layer slips until Re comes at place directly below the sixfold B ring. In this case, the flattened B layer can be interpreted as close to a graphitic (not completely flat), i.e., B with double-bond contributions reducing the bond length (however, the bond reduction is certainly also necessary to fit the geometric extension of the unaffected layer). On further increase in strain the layer slips along the same vector until Re resides in M2 in a similar coordination as in O. However the orientation of the boron triangle above Re is turned by $60°$ relative to the bottom triangle.Reuse & Permissions

Figure 7

Line profiles of the VCD between the B-B and Re-B bonds in equilibrium and for several significant values of shear strain $\gamma$ shown in Figs. 1, 4.Reuse & Permissions