Evolution of Pressure-induced Shear Amorphization in Rare-earth Hexaboride


 Research on rare-earth hexaborides mainly focuses on tuning the electronic structure from insulating-to-metallic state and vice versa (referred as exotic phenomena) by high pressure experiments via displacive phase transformations, however, the structural evolution that contributing to this underlying failure mechanism remains not well understood. Herein, we examined the pressure induced structural evolution through a model system of europium hexaboride (EuB6). Transmission electron microscopy reveal that the nanoscale amorphous shear bands mediated by dislocations play a decisive role in deformation failure of EuB6 subjected to high pressure nanoidentation at room temperature. Density functional theory simulations confirm that these amorphous bands evolve by breaking B-B bonds within B6 octahedron of EuB6 during shear deformation. Our results underscore an important damage mechanism in hard and fragile hexaborides at high shear pressures.


Introduction
Rare-earth hexaborides (RB 6 ) have attracted considerable attention due to their extraordinary combination of electrical, magnetic, thermal and mechanical properties 1 . At ambient conditions, RB 6 crystallizes in a cubic structure (i.e., CsCl-prototype, Space group: Pm m (no: 221)) 2 . The unique chemical bonding in RB 6 arises from the octahedron B 6 framework with large interstitial space to host a variety of the rare earth ions (R = Ba, Ce, Eu, La, Sm, Sr, Y etc.) at the center of cubic crystal lattice. Despite having the same crystal structure, the properties of each hexaboride are uniquely different and diversi ed from each other due to their intrinsically strong correlated electron systems 3 . For instance, CeB 6 shows dense Kondo effect and electric quadrupole ordering, SmB 6 exhibits Kondo insulating and valence uctuation, LaB 6 have low work function for thermionic emission, YB 6 possess remarkable superconductivity, CaB 6 is semiconducting, and EuB 6 displays ferromagnetic properties 1,3 .
Pressure-driven polymorphism has been predicted and observed in several hexaborides by rst principle calculations and high-pressure X-ray experiments [4][5][6][7] . For instance, Kolmogorov et al. 4 predicted that the thermodynamically unstable cubic ( ) CaB 6 structure at high pressure compression transforms to an intermediate metastable orthorhombic oS28 structure around 13 GPa before stabilizing to ground state tetragonal tI56 structure above 32 GPa. Their experimental evidence showed that the structure in threedimensional morphology remains stable up to at least 28 GPa but with certain distortion. Further, assistance of laser heating promoted the rebonding in strong covalent boron network above 31 GPa and favored the ground state structure. Similarly, Zhu et al. 5 examined a semiconducting SrB 6 ( ) and predicated new metallic polymorphs as orthorhombic (Cmmm) and tetragonal (I4/mmm) structures at high pressure of 48 and 60 GPa, respectively. These unique boron polyhedra are formed as a result of denser structural arrangement under high pressure and the formation enthalpies are decreased due to the additional B-B bonds of polyhedral networks 5 . In addition, they have also demonstrated a novel deformation mechanism with transient multicenter bonding yields in good combination of high strength and high ductility for the I4/mmm structure in SrB 6 5 . These results indicate that upon high pressure produces the complex boron networks and structural transitions in hexaborides leading to unique properties, which has created immense interest for electromechanical systems [3][4][5][6][7] .
Here, we choose EuB 6 rstly because of its semi-metallic nature and its hardness (19)(20)(21)(22)(23)(24)(25)(26) falling in range of CaB 6 (16-28 GPa) and SrB 6 (18.5-27 GPa) 8 . Secondly, EuB 6 is the only hexaboride with ferromagnetic order and low thermal expansion coe cient, which can be tuned to ground state electron system. Thirdly, single phase EuB 6 in bulk material can be easily produced using various sintering methods 2,9,10 . In addition to these applications, EuB 6 received signi cant attention in hexaboride family as a potential second phase material for structural applications owing to its high thermal stability and high neutron absorption properties 9,11 .
In this study, we used nanoindentation to impose high pressures on EuB 6 crystals, followed by microstructural characterization using Raman spectroscopy and spherical aberration (Cs) corrected TEM.
We found beneath the indentation surface, the nanoscale amorphous shear bands preceded by the emission and propagation of dislocations. The DFT simulations, which agree with experiment, reveals that the chemical bond breaking within octahedral B 6 initiates the mechanical instability leading to the localized amorphization in EuB 6 by high pressure shear deformation. Sinter, Japan) using sintering temperature of 1900 °C, held for 15 min with the applied pressure of 45

Methods
MPa. The rectangular specimens were cut from the bulk sintered B 4 C-EuB 6 composite using slow speed diamond cutter and polished with diamond lm sheets i.e., 30, 15, 9, 6 and 1 µm for microstructural characterization and nanoindentation tests. Nanoindentation (Hysitron TI950) in load control mode was utilized for determining the mechanical properties of EuB 6 . In this regard, diamond Berkovich tip was used with maximum load of 10 mN held for 2 sec. The loading and unloading rate were kept 1 mN/s. Also, a series of indentations at a maximum applied load of 500 mN were performed on EuB 6 crystals with MTS G200 system equipped with a Berkovich indenter.
Microstructural characterization. The XRD of as-synthesized samples was obtained by using Ultima IV (Rigaku, Japan) with Cu Kα (λ = 1.5418 Å), operated at 40 kV and 30 mA. The microstructural analysis of EuB 6 was carried out using SEM (Nova NanoSEM 450 (FEI)). Further, the electron backscattered diffraction (EBSD) patterns were acquired to obtain crystallographic orientation of EuB 6 and SEM-EDS was used for elemental mapping analysis. Raman micro spectroscope was carried out using Renishaw inVia Qontor with an excitation wavelength of 532 nm that has laser beam spot 1 µm. The crosssectional TEM specimens underneath the indentation were prepared by standard lift-out technique using focused ion beam (FIB) (VERSA 3D (FEI, USA)) method. The aberration-corrected TEM (JEM-ARM 200F (JEOL, Japan)) operated at 200 kV was utilized for obtaining high resolution atomic images. Further, STEM-EDS was performed for chemical analysis. The atomic TEM images were simulated using the software package of HREM Research Inc., (Japan). Local strain measurements from HRTEM images of deformation regions have been analysis using peak pair analysis software 32 .
Computational methodology. The DFT calculations were performed using Vienna ab initio simulation package (VASP) with plane wave basis set 33,34 . The generalized gradient approximation (GGA) type Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional were implemented for electronic exchange and correlation interaction 35,36 . The pseudopotentials of B and Eu were generated using the projector augmented wave (PAW) method with 2s 2 2p 1 and 5p 6 6s 2 treated as valence electrons 36 . The energy cutoff of 500 eV was set in all simulations for the good convergence of energy, force, stress and geometries. The energy convergence of 10 −6 eV for terminating electronic self-consistent eld (SCF) and the force criterion 10 -3 eV/Å were used in all simulations. A Γ-centered k-point mesh method was used for Brillouin zone integration with the mesh density a high resolution above 2π × 1/40 Å −1 .
For the pure shear and biaxial shear deformations of EuB 6 , we considered (2 2

Results
Structure characterization of as-synthesized EuB 6 . The microstructure of as-synthesized EuB 6 -boron carbide (B 4 C) composite is shown in Fig. 1. In Fig. 1(a) scanning electron microscopy (SEM) image shows the bright grains having faceted cuboidal corresponding to EuB 6 crystals which are surrounded by the grey region of B 4 C matrix. Fig. 1(b) electron back scattered diffraction (EBSD) pattern of EuB 6 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 EuB 6 are projected along the [100] and [120] zone axes in Fig. 1(c) and 1(d) as con rmed 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  Raman active (T 2g , E g and A 1g ) phonons caused by internal displacement of boron atoms in the octahedron B 6 12 . 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 reports 6, 10 . All the Raman peaks in Fig. 2 are related to the vibrations of octahedral B 6 . The E g mode is associated with compressing up and down vibrations, while T 2g mode is related to the scissoring displacement of B atoms in the octahedral B 6 13 .
Therefore, both T 2g and E g modes are modulating the B-B-B bond angles, whereas, A 1g mode is related to the stretching of B-B bond 13 . From residual indent ( Fig. 2(b)), peak broadening of T 2g and E g peaks is apparent suggesting that the structural transformations in EuB 6 may have occurred in B-B-B bonds of octahedra B 6 sites upon indentation induced high pressures.
Structural evolution observations of indentation-induced EuB 6 . In order to elucidate the underlying mechanism that drives the structural transformations in EuB 6 during high pressure deformation, crosssectional TEM specimens from multiple crystallographic orientations were prepared from the residual indents using focused ion beam (FIB) milling 14,15 (Fig. 3 and Supplementary text and Supplementary Fig.   S1). Fig. 3(a) shows low magni cation TEM image of indentation impression on the (001) surface of EuB 6 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 magni cation 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 magni ed (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, con rming 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 EuB 6 (Inset A). Further, FFTs con rm 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 48 o 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 signi cant lattice bending before the initiation of dislocations at the tip of band. Analysis of shear strain (e xy ) map from the area (Fig. 3(e)), speci cally identi es 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 EuB 6 ( 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 identi es the dislocation core ( Supplementary Fig. S2(c)). These observations indicate that these dislocations are geometrically necessary to mediate the amorphization process in EuB 6 .

DFT prediction of shear amorphization in EuB 6
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 B 6 octahedra and formation of amorphous bands in EuB 6 . Hence, we applied pure shear deformation on EuB 6 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 EuB 6 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 EuB 6 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 EuB 6 under ideal shear deformation arises from the breaking of B-B bonds that connect two nearby octahedra rst 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 EuB 6 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 EuB 6 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 EuB 6 , which further veri es the observation in the experiments.

Discussion
Amorphization has been observed in a wide variety of hard and complex crystal structures including diamond 16 , ice 17 , minerals 18 , semiconductors (Si, Ge, GaAs, InSb) [19][20][21] , ceramics (Al 2 O 3 , SiC, B 4 C, B 6 O, Si 3 N 4 ) 22-24 and intermetallics (TiNi, Ni 3 Al, SmCo 5 ) 25 and are generally related to the pressure-induce lattice destabilization [15][16][17][18][19][20][21][22][23][24][25] . Similarly, hexaborides possess strong directional bonding with relatively open structure. Thus, conventional plastic deformation associated with motion of crystal defects is very di cult at room temperature. Therefore, hexaborides crystalline structures are expected to fail easily on the relative weaker planes to became denser phase under high pressures. Additionally, structural transformations or local softening in the covalent or ionic solid materials are vastly dependent on type of applied pressure conditions. Previous studies on CaB 6 and SrB 6 hexaborides using diamond anvil cell (DAC) experiments under quasi-hydrostatic media demonstrated the polymorphic transition from a simple cubic phase into complex and more denser boron network orthorhombic and tetragonal phases 4,5 , with the assistance of temperature (laser-heating) to produce irreversible bonding for inducing structural transformations. In another study on EuB 6 under hydrostatic high pressures above 20 GPa showed magnetic transitions from ferromagnetic to paramagnetic phase with mixed valence states 26 . Further, temperature dependent Raman scattering and rst-principle calculations showed evidence that the cubic symmetry breaking induces a non-cubic environment in the B 6 octahedron in EuB 6 6 . All these studies performed by hydrostatic or quasi-hydrostatic DAC experiments have not predicted or reported amorphization in hexaborides [4][5][6]26 . However, a study by Yan et al. 27 reported amorphization in superhard B 4 C during depressurization in a non-hydrostatic stress using DAC, while in hydrostatic or quasihydrostatic stresses the amorphization was not detected suggesting the nature of the applied stresses play an important role in mechanical instabilities of crystalline structure.
Here we used nanoindentation to induce structural transformations in EuB 6 , which comprises both hydrostatic and non-hydrostatic (shear) stresses. Our TEM observations beneath the indent surface showed that the nano-sized amorphous bands are initiated by dislocations. Such nucleation of dislocations is believed to evolve within the indentation region of a material as the applied load approaches above the critical resolve shear stress (CRSS) 28-30 . The measured angle between indentation surface plane and amorphous slip plane of EuB 6 is approximately 40-50 o suggesting shear stresses play vital role to this process (Fig. 3). The DFT simulations further provided evidence of crystal-to-amorphous transition along two major slip systems of EuB 6 . Under pure-shear deformation (( Fig. 4 and Fig. S4)), the B-B bonds in the octahedron is gradually stretched and nally the structure failed initiating the deconstruction of octahedra. While in the biaxial shear deformation 31 (Fig. 5), the failure is caused directly by breaking of B-B bond within the octahedron of EuB 6 (Fig. 4). This result of biaxial shear is consistent with the bond distortions beneath the residual indent observed by micro-Raman spectroscopy (Fig. 2). Therefore, our study con rms that the nanoscale amorphous bands in EuB 6 is mediated by the dislocations on relatively easier slip planes by breaking the B-B bond of octahedral B 6 during the shear deformation.
In summary, we employed the nanoindentation to investigate the structural transitions on a EuB 6 , combining with Raman spectroscopy, Cs-corrected TEM and DFT simulations. We found localized amorphization in EuB 6 is mediated by dislocations on very speci c crystallographic orientations. The simulations indicate that this amorphization process is triggered by breaking B-B chemical bonds in octahedral B 6 upon shear deformation, in line with experimental observations. We believe that our observation underlying mechanism of shear induced amorphization mediated by dislocations in a model hexaboride system offers opportunities for controlling the exotic states deformation structures and to tune their properties at high pressures.
Declarations Figure 1 Electron are represented by open circles with green and magenta colors, respectively. The indexed DP's along same zone axes are also shown at the rightmost upper corner of the images.  shear strain (εxy) map obtained from same region of (e).