Structure characterization of as-synthesized EuB6. The microstructure of as-synthesized EuB6-boron carbide (B4C) composite is shown in Fig. 1. In Fig. 1(a) scanning electron microscopy (SEM) image shows the bright grains having faceted cuboidal corresponding to EuB6 crystals which are surrounded by the grey region of B4C matrix. Fig. 1(b) electron back scattered diffraction (EBSD) pattern of EuB6 acquired from the same region of Fig. 1(a), displays the crystallographic orientation for the grain facets of square as (100) plane, rectangle as (110) plane and triangle as (111) plane, respectively. High resolution TEM (HRTEM) images of EuB6 are projected along the [100] and [120] zone axes in Fig. 1(c) and 1(d) as confirmed by selected area electron diffraction (SAED) patterns shown in the inset at the upper right corner of Fig. 1(c) and (d). Further, simulated atomic images projected along the same zone axes are superimposed at the lower right corner of the HRTEM images (Fig. 1(c) and 1(d)). The comparison of experimental and simulated TEM images (Fig. 1(c) and 1(d)) reveals that the bright spots belong to europium (Eu) individual atomic sites and grey spots are corresponding to the boron (B6) clusters, where Eu and B atoms are represented by open circles with magenta and green colors, respectively.
Raman Spectroscopy of pristine and deformed EuB6. In order to determine the mechanical properties and introduce structural transformations in EuB6 crystals, we performed nanoindentation on different facets of EuB6. The measured hardness and elastic modulus for (100), (110) and (111) facets are 28.52 ± 0.42 GPa, 28.88 ± 0.72 GPa, 27.72 ± 1.05 GPa and 231 ± 2.5 GPa, 240 ± 5 GPa, 225 ± 8.7 GPa, respectively. Fig. 2(a) shows the representative SEM image of residual indentation taken on the grain of square ((001) plane) facet. The Raman spectra acquired from the residual indent (black solid line) and pristine (red dotted line) of EuB6 are presented in Fig. 2(b). Since EuB6 belongs to the cubic Oh group, there are three Raman active (T2g, Eg and A1g) phonons caused by internal displacement of boron atoms in the octahedron B612. In this study, these characteristic peaks are found at 768 cm-1, 1112 cm-1 and 1256 cm-1, respectively, which are in good agreement with the previous reports6,10. All the Raman peaks in Fig. 2(b) are related to the vibrations of octahedral B6. The Eg mode is associated with compressing up and down vibrations, while T2g mode is related to the scissoring displacement of B atoms in the octahedral B613. Therefore, both T2g and Eg modes are modulating the B-B-B bond angles, whereas, A1g mode is related to the stretching of B-B bond13. From residual indent (Fig. 2(b)), peak broadening of T2g and Eg peaks is apparent suggesting that the structural transformations in EuB6 may have occurred in B-B-B bonds of octahedra B6 sites upon indentation induced high pressures.
Structural evolution observations of indentation-induced EuB6. In order to elucidate the underlying mechanism that drives the structural transformations in EuB6 during high pressure deformation, cross-sectional TEM specimens from multiple crystallographic orientations were prepared from the residual indents using focused ion beam (FIB) milling14,15 (Fig. 3 and Supplementary text and Supplementary Fig. S1). Fig. 3(a) shows low magnification TEM image of indentation impression on the (001) surface of EuB6 cuboidal square. The microcracks and nanoscale bands (marked with dark and white arrow heads, respectively in Fig. 3(a)) can be seen from low TEM magnification image, indicating severe damage and plastic deformation within the indentation region. These observed bands have width of ~ 3 to 8 nm and length ranging from 100 to 500 nm. The magnified (Fig. 3(b)) TEM image shows a single band length of about 120 nm, which is surrounded by high density of planar defects (indicated by red arrows). HRTEM image acquired from the nanosized band reveal the loss of crystallinity (Fig. 3(c)). Fast Fourier transforms (FFT) taken from the region B, shows a diffuse halo without any diffraction spots, confirming the occurrence of amorphous structure within the band. On the other hand, FFT pattern taken from the crystalline structure on either side of band along the [120] crystallographic direction displays Pm m symmetry of EuB6 (Inset A). Further, FFTs confirm the formation of amorphous band roughly aligned on a (2 2) plane. The measured angle between the (001) surface plane and slip plane is about 48o suggesting that the amorphous bands are induced by high shear stresses. Fig. 3(d) is the HRTEM image taken from tip of the amorphous band, as shown in white box of Fig. 3(a). The Burgers loop from the tip of amorphous band drawn by white dotted lines in Fig. 3(d) reveals obvious shear displacement of about ~2 Å. Moreover, Eu and B atomic overlay in Fig. 3(d) at near amorphous band providing evidence of crystal lattice deregister from the boron clusters, rather than Eu atoms. Fig. 3(e) is the grid generated through the Peak Pair Analysis algorithm in the same area. The grid lines in image (Fig. 3(e)) clearly shows significant lattice bending before the initiation of dislocations at the tip of band. Analysis of shear strain (exy) map from the area (Fig. 3(e)), specifically identifies a maximum absolute shear strain of about 25% (Fig. 3(f)) as estimated from the proximity of dislocation core in a nano-strained band region compared to the parent crystalline structure. We also characterized the indentation impression profuse on the (011) rectangle surface of EuB6 (Supplementary Fig. S2). TEM characterization along the zone axis (Supplementary Fig. S2 (a,b)) shows the nanosized amorphous bands roughly aligned parallel to the plane. A HRTEM image obtained from the tip of amorphous band identifies the dislocation core (Supplementary Fig. S2(c)). These observations indicate that these dislocations are geometrically necessary to mediate the amorphization process in EuB6.
DFT prediction of shear amorphization in EuB6
Based on the TEM observations (Fig.3 and Fig. S2), we assumed that the (2 2)[120] and (110)[1 0] are two possible slip systems to initiate the deconstruction of B6 octahedra and formation of amorphous bands in EuB6. Hence, we applied pure shear deformation on EuB6 along these two slip systems. The obtained shear-stress-shear-strain relationship is shown in Fig. 4(a). The ideal shear strength along (2 2)[120] is 29.09 GPa, which is much lower than that (41.67 GPa) along (110)[1 0]. This suggests that (2 2)[120] is more plausible slip system, which agrees very well with the experimental observation. Then, we examined the deformation and failure mechanism of EuB6 along (2 2)[120] slip system, as shown in Fig. 4(b-f). The intact structure before shear is shown in Fig. 4(b). It is worth noting that the structure is shown along “B” axis ([ 01] direction) rather than “A” axis (shear direction of [120]) to better describe the failure mechanism. The atomic structure viewed along [120] direction is shown in Supplementary Fig. S3. As shear strain increases to 0.465, the B22-B32 bond between two octahedra is gradually stretched from original 1.68 Å to 2.15 Å without breaking, as shown in Fig. 4(c). When the shear strain continuously increases to 0.489, the B22-B32 bond is stretched to 2.26 Å and breaks, as shown in Fig. 4(d). This bond breaking also slightly releases the shear stress from the maximum of 29.09 GPa to 28.29 GPa. Then, with the increase of shear strain, B22 and B32 atoms move far from each other, leading to further decrease of shear stress. In particular, at 0.514 shear strain, the distance between B22 and B32 atoms is 2.42 Å, as shown in Fig. 4(e). Finally, at 0.539 shear strain, the B16-B28 bond in the octahedron is stretched from original 1.75 Å to 1.90 Å and breaks (Fig. 4(f)), initiating the deconstruction of octahedra, which agrees with the results in experiments. This structural failure further releases the shear stress to 5.33 GPa.
In addition to (2 2)[120], we also examined the failure mechanism of EuB6 along (110)[1 0], as shown in Supplementary Fig. S4. Supplementary Fig. S4(a) shows the intact structure. At 0.245 shear strain corresponding to the ideal shear strength, the B25-B32 connecting two nearby octahedra is gradually stretched from original 1.68 Å to 2.13 Å, as shown in Supplementary Fig. S3(b). However, this bond is not broken. Then, at 0.263 shear strain, the B25-B32 bond is drastically stretched to 2.36 Å and breaks, as shown in Fig. S4(c). This bond breaking releases shear stress to 39.65 GPa. After that, with increase of shear strain, the B25 and B32 atoms is stretched far from each other, leading to the further release of shear stress. Particularly, at 0.297 shear strain, the distance of B25 and B32 atoms is 2.88 Å, as shown in Fig. S4(d). The corresponded shear stress also decreases to 27.01 GPa. The above results indicate that the failure mechanism of EuB6 under ideal shear deformation arises from the breaking of B-B bonds that connect two nearby octahedra first and then the deconstruction of octahedra.
To mimic the complex stress condition in the indentation experiments, we also applied biaxial shear deformation along the plausible slip system of (2 2)[120]. The shear-stress-shear-strain relationship of EuB6 along (2 2)[120] is shown for biaxial shear deformation in Fig. 5. The ideal shear strength is 23.31GPa (Fig. 5(a)), which is lower than 29.09 GPa for ideal shear deformation (Fig. 4(a)). The obtained failure mechanism is shown in Fig. 5(b-f). The initial structure is shown in Fig. 5(b). At 0.209 shear strain, the shear stress reaches to its maximum value of 23.31GPa. The B35-B16 and B53-B23 bonds in octahedron are slightly stretched from original 1.75Å to 1.78Å and 1.82 Å, respectively, as shown in Fig. 5(c). Then, when the shear strain continuously increases to 0.232, these bonds are further stretched to 1.88Å for B35-B16 and 1.91Å for B53-B23 and break, as shown in Fig. 5(d). This bond breaking also releases the stress from 23.31GPa to 15.71GPa. As shear strain further increases to 0.276, the B53-B6 bond is gradually stretched to 1.92Å, as shown in Fig. 5(e). However, it does not break at this shear strain. Next, at 0.299 shear strain, the B53 atom is stretched out of octahedron and B6-B53 bond breaks, as shown in Fig. 5(f). The deconstruction of octahedron releases the shear stress to 4.96 GPa. Therefore, the failure mechanism of EuB6 under biaxial shear deformation arises from the B-B bond breaking within the octahedra. This deconstruction of octahedra will initiate the formation of amorphous shear in EuB6, which further verifies the observation in the experiments.