Deformation Mediated by Grain Rotation in Superhard Nanocrystalline cBN

: Superhard materials such as diamond and cubic boron nitride (cBN) are becoming ever more scientifically and technologically important, and critical and fundamental knowledge about their constitutive properties and deformational mechanisms is in increasingly high demand. Although it has long been suggested by theoretical modeling that deformation of face-centered cubic superhard materials is dominated by Shockley partial dislocations and screw dislocations, there has been a glaring lack of experimental evidence. Here, we report in situ deformation experiments of nanocrystalline cBN (nc-cBN) samples at high pressures and


Introduction
Cubic boron nitride (cBN) as conventional superhard material is technologically significant because of its excellent physical and chemical properties [1][2][3][4][5][6][7][8][9] . It is widely used for cutting, grinding, drilling and coating under some of the harshest environments. Superior chemical inertness and thermal stability (~1380 °C) 10 make cBN the only choice in place of diamond for high-speed cutting of hardened steel 3 .
Furthermore, cBN is a promising candidate for use in the extreme conditions associated with hypersonic flight, scramjet propulsion, atmospheric reentry, and rocket propulsion 11 due to its high melting temperature (>3000 °C) 12 , high thermal conductivity (740 W•K -1 ) 13 , high thermal shock resistance, low thermal expansion coefficient (1.2×10 -6 /°C) 14 , and excellent chemical inertness and mechanical strength (Vickers hardness of single crystal cBN: ~50 GPa) 1-5, 9, 15 . These potential applications demand a better knowledge of deformational and constitutive properties of cBN under extreme environment. However, as the second hardest material known to mankind, cBN is experimentally difficult to be deformed, particularly at room temperature (RT).
Current knowledge of plastic deformation in cBN or other superhard materials is mainly based on theoretical simulations and experiments under uncontrolled stress conditions [16][17][18][19][20][21] . Traditionally, the strength of superhard material can be estimated using bending, indentation and grinding at ambient pressure 20,21 or via high-pressure experiments under nonhydrostatic compression [22][23][24][25][26] , but resultant compressional or tensile strength from these studies are generally inconsistent. In addition, the strength can also be derived from analyzing diffraction peak broadening during hydrostatic compression (i.e., no external stress field) of polycrystalline samples under highpressure and high temperature [27][28][29][30] . Because previous experimental methodologies could not define the stress applied during deformation, the intrinsic strain-stress relation, which is fundamentally important to understanding the elasticity and plasticity of cBN, has yet to be established under both room and elevated temperatures.
The mechanical performance of materials is controlled by their intrinsic deformation mechanisms and dominant dislocation structures [31][32][33][34][35][36][37] . In-depth understanding of such microscopic processes or features is therefore imperative to improving effectively the mechanical properties of materials. Nanocrystalline (nc) materials have been demonstrated to be comparatively stronger than their coarsegrained counterparts via work hardening. For example, nanotwinned cBN and diamond prepared at ultrahigh pressure and temperature have been shown to be twice as hard and several times as tough as coarse-grained cBN and diamond, respectively 1,38 . A slew of mechanisms including twinning, partial and screw dislocations emitting from grain boundaries (GBs), grain boundary sliding, dislocation slip, grain rotation and even superstructures have been proposed for the deformation of superhard nc materials 33,37,39,40 . Conventional Read-Shockley model speculates that the partial dislocations at twin boundaries or a network of screw dislocations at a twist boundary govern the deformational behavior of materials with face-centered cubic (fcc) diamond structure [41][42][43][44] . However, the dominant deformation mechanism has been debated extensively in the theoretical literature due to lack of sufficient experimental evidence. Moreover, because a deformational screw dislocation is usually accompanied by large shear stress and mixed with local partial dislocations, interactions between screw dislocation and edge dislocations at grain boundaries ineluctably take place and even induce the formation of superstructure, phase transition and new transformation paths to relax shear-dominated stresses at concentrators 45,46 . Understanding the effects of these interactions and the evolution of dislocations is conducive to designing nc materials with superior mechanical and physical properties.
To address the aforementioned questions, we have systematically investigated the intrinsic strain-stress relations and evolution of deformation mechanisms of nc-cBN at high pressures via in situ deformation experiments in a deformation-DIA (D-DIA) apparatus [47][48][49][50][51][52] and microscopic studies on the recovered samples using transmission electron microscopy (TEM). The main dislocation mode at RT is manifested as GB twisting mediated by full dislocations on planes for nc-cBN without plastic yielding at uniaxial strains up to 14%. Cubic BN crystals showed remarkable ductile flow and plastic deformation at 1000 °C through GB twisting mediated by Shockley partial dislocations. Surprisingly, high shear stress even induced the formation of superstructures and local phase transition at higher pressure and temperature (4.0 GPa/1200 °C).

Results and Discussion
Experimental setups and procedures Shown in Figure 1a is a schematic diagram illustrating the setups for uniaxial deformation experiments at high pressure and temperature using a D-DIA-type cubic anvil apparatus coupled with synchrotron x-radiation. Energy-dispersive XRD data were collected with a counting-time of ~10 minutes using a ten-element Ge solid-state detector (SSD) on which all elements are arranged in a circle and each element is located at a fixed azimuth angle (22.5° apart from 0° -180°, plus one at 270°). To eliminate unwanted diffraction signals from materials surrounding the sample, a conical-slit system located between the sample and the detectors was employed to collimate and constrain the angle of the diffracted x-rays. Radiographic images were also taken, with data collection toggling continuously between diffraction and imaging modes. An amorphous boron-epoxy cube was used as pressure medium, as shown in Fig. 1b. Dense Al 2 O 3 pistons were placed at both ends of specimens, which were pre-compressed into pellets and packed into a hexagonal boron nitride (hBN) capsule; three 25-µm-thick tantalum disks were placed at the piston-specimen and specimen-specimen contacts as strain markers. The nc-cBN sample was first compressed to desired pressure at RT and then annealed at high temperature (~ 1000 o C) for 1 hour using enclosed resistive graphite heater. where L is the grain size, k the Scherrer constant correlated to crystallite shape, where is the Young's modulus of cBN (909 GPa 53 ). The differential micro-stress is defined as the difference between the micro-stresses derived from the detector elements at azimuth angles of 0° and 90°, respectively. The macroscopic differential stress ( ), or macro-stress, defined as where and are axial and radial stress, respectively, differs from the differential micro-stress and is manifested by the variations in lattice strain detected by all detectors situated along azimuth angle .
Based on the results of lattice strain theory developed by Singh et al. 26 can be further expressed as: where is the d-spacing of ( ) surveyed as a function of azimuth angel , is the d-spacing under hydrostatic pressure. By fitting the variation of versus for cBN peak ( Fig. 1d-f) according to Eq. 5, the macro-stress can be determined from the slope 56 . All fittings to data collected at different pressure and temperature are presented in Fig The micro-stresses derived from the peak-width analysis as a function of macro-strain are shown in Fig. 2b for two azimuth angles, 0° and 67.5°. It is evident that the micro-stresses at both angles experienced a step-variation, coincident with that of the macro-stress and in agreement with the notion that the brittle failures affect both external and local stresses. Similar to the macro-stress, the micro-stress at 0° increased with increasing axial strain. In contrast, the micro-stress at 67.5° remained more or less a constant, or even slightly down as the sample was deformed. This is due to the fact that, to hold the press load at a constant for the entirety of deformational process (i.e., for a constant pressure), the anvils at radial direction had to be slowly retracted (i.e., to reduce the radial stress) to accommodate the increase in axial stress.
The calculated differential micro-stresses are plotted in Fig. S6 for comparison with the macro-stresses in Fig. 2a. It is quite remarkable that the two stresses that are deduced from completely different methods agree well within experimental uncertainties, especially between ~ 6 -14% strain, i.e., after the brittle failure during the early stage of cold deformation. If the differential micro-stress is used as a proxy for the macro-stress t in the sample, then according to Equation 5, the shear modulus of the sample can be extracted from the diffraction data recorded by the multi-element detector. Therefore, this practice could be used as a new method to constrain the elastic properties of crystalline solids at high pressures, greatly mitigating the lack of routine techniques to measure the shear modulus of solids.

Stress-strain relations at elevated temperatures
For macro-stresses at high temperatures (Fig. 2a), the initial stage of stress-strain variation at both temperatures is similar to that of room-temperature in which the stress experienced a linear increase with increasing strain, i.e., as elastic deformation. However, the elastic region ended at much lower strain (~6% at 1000 °C and ~4% at 1200 °C ; for comparison, > 14% at RT). Steady-state plastic deformation (i.e., relatively constant stress with increasing strain) was observed at both high temperatures. The higher the temperature, the lower the steady-state stress (~5.8 GPa for 1000 °C vs ~3.8 GPa for 1200 °C ). Fig. 2c and indicating a dominant mechanism of brittle fracture and mechanic crushing for the deformation of nc-cBN at RT (see Fig. S5a). The fracture traces along cleavages cutting through large grains are also manifested as nanocracks emitting from the surface of grains (Fig. 3b), as in bulk diamond 48

TEM characterization and microstructures analyses at elevated temperature
The microstructure of the recovered sample deformed at 3.5 GPa/1000 °C was analyzed to explore the dominant deformation mechanism at high temperature.
Bright-field TEM images show fuzzy grain boundaries (see Fig. S5b). Majority of grains have diameters below 30 nm, with an average value of ~25 nm, indicating that dynamic recrystallization induced by plastic deformation occurred at these conditions. can be largely attributed to nc-cBN, but with an extra ring having a lattice d-spacing of ～0.358 nm, which is larger than the interplanar spacing ～0.345 nm of (002) of hBN. XRD patterns (Fig. S1) however suggest that no other secondary phases were present, indicating that this extra ring is related to super-lattice-like Moiré fringes.
Through careful examination of the trailing region of rotated grains near GB, highdensity dislocations were found, as shown in Fig. 4b. Burgers circuits are drawn to show it is a 60° full dislocation because only one set of (111) planes possess an extra half plane, which is different from the combined full dislocation with a Burgers vector along ̅ at RT since high temperature breaks the L-C locks (Fig. 4c). These 60° full dislocations as ̅ on ̅ plane can be dissociated into two 90° and 30° Shockley partial dislocations: a leading and trailing dislocation as follows: Thus, the plastic deformation of nc-cBN was mainly mediated by 90° and 30° Shockley partial dislocations near twisting GBs. Twin dislocations and other mixed dislocation interactions should also be responsible for plastic deformation of nc-cBN, as shown in Fig. 4d. The formation of twins is closely related to the stacking faults. GPa/1000 °C, the deformation mechanism at 1200 °C is dominated by plastic flow/creep which was however mediated by phase transitions (Fig. 5b-f). The traces of GB twisting were observed on planes with a d-spacing of 0.338 nm (Fig. 5b), suggesting the presence of hBN. As no hBN or wurtzite BN (wBN) impurities were detected by XRD in the starting materials (Fig. S9), it is inferred that cBN was directly converted to hBN due to shear-induced phase transition. Likewise, superlattice-like structures evolved from the original GB twisting have also been observed in SAED (inset, Fig. 5a) and FFT (Fig. 5e).

Conclusion
In summary, the inherent strain-stress relations and evolution of the deformation mechanisms of nc-cBN have been systematically investigated using a D-DIA largevolume apparatus, in situ XRD measurements at high pressure and temperature, and HRTEM. We found the differential micro-stresses derived from peak-broadening analysis can potentially be used as proxies for the macro-stresses defined by lattice  47 . One sintered polycrystalline diamond (PCD) anvil was used for the multi-element detector to receive the diffracted x-rays 48,52 . Energy-dispersive XRD data were collected with a counting-time of ~10 minutes using a ten-element Ge solid-state detector (SSD) on which each element is located at a fixed azimuth angle (22.5° apart from 0° -180°, plus one at 270°). To eliminate diffraction signals not from the sample, a conical-slit system located between the sample and the detectors was employed to collimate and constrain the angle of the diffracted x-rays. Radiographic images were taken, with data collection toggling continuously between diffraction and imaging modes. An amorphous boronepoxy cube was used as pressure medium for deformation experiments. Dense Al 2 O 3 pistons were placed at both ends of specimens, which were pre-compressed into pellets and packed into a hexagonal boron nitride (hBN) capsule; three 25-µm-thick tantalum disks were placed at the piston-specimen and specimen-specimen contacts as strain markers. The nc-cBN sample was first compressed to desired pressure at RT and then annealed at high temperature (~ 1000 o C) for 1 hour using enclosed resistive graphite heater. As the detector elements at the azimuth angle of 90° and 270° (radial direction) weren't available during all experiments, signals recorded by the element situated at 67.5° are taken as the proxies for those from the radial direction in this study. Furthermore, because diffraction peaks