Research ArticleMATERIALS SCIENCE

Dislocation-mediated shear amorphization in boron carbide

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Science Advances  17 Feb 2021:
Vol. 7, no. 8, eabc6714
DOI: 10.1126/sciadv.abc6714

Abstract

The failure of superhard materials is often associated with stress-induced amorphization. However, the underlying mechanisms of the structural evolution remain largely unknown. Here, we report the experimental measurements of the onset of shear amorphization in single-crystal boron carbide by nanoindentation and transmission electron microscopy. We verified that rate-dependent loading discontinuity, i.e., pop-in, in nanoindentation load-displacement curves results from the formation of nanosized amorphous bands via shear amorphization. Stochastic analysis of the pop-in events reveals an exceptionally small activation volume, slow nucleation rate, and lower activation energy of the shear amorphization, suggesting that the high-pressure structural transition is activated and initiated by dislocation nucleation. This dislocation-mediated amorphization has important implications in understanding the failure mechanisms of superhard materials at stresses far below their theoretical strengths.

INTRODUCTION

Dislocations not only play an important role in strength and ductility of engineering materials but also are responsible for incipient plasticity of crystalline solids (1). However, for superhard materials with strong covalent bonds, such as a diamond and boron carbide (nominally B4C), dislocation activities and thus dislocation plasticity are not expected under conventional loading conditions at room temperature due to high lattice resistance and barrier energy (2, 3). B4C is an important armor material owing to its exceptional lightweight (~2.5 g/cm3), together with the ultrahigh hardness and high Hugoniot elastic limit (3, 4). The extraordinary physical and mechanical properties of B4C have been attributed to the unique crystal structure, which is composed of 12-atom icosahedra connected by a 3-atom chain in a rhombohedral unit cell (5, 6). However, B4C undergoes an anomalous reduction in shear strength at a critical shock pressure of ~20 to 26 GPa (7–10). Transmission electron microscopy (TEM) has revealed that the shear softening of B4C is associated with localized amorphization (11), which has been confirmed by high-pressure diamond anvil cell and indentation experiments as well as dynamic scratching and laser shocking (12, 13). Quantum mechanics simulations also verify the pressure-induced amorphization in B4C (13–15). However, different amorphization mechanisms have been proposed from carbon cluster formation to three-atom-chain bending and icosahedral cluster breaking. It remains unclear how the localized amorphization and thereby material failure take place in the superhard materials at applied stresses far below the theoretical strength (higher than 39 GPa) predicated by density functional theory (16, 17). In particular, experimental insights into the amorphization mechanisms are still missing.

Nanoindentation has been proven to be a powerful technique to characterize mechanical response of materials because of the ultrahigh resolutions in both forces and displacements (18). The discontinuity in the nanoindentation load-displacement curves, referred to as a pop-in, has been widely used to study stress-induced phase transformation, dislocation activation, and shear instability, which occur within a small volume of materials beneath a diamond indenter (18, 19). The transition portions of load-displacement curves from elastic to inelastic have been ubiquitously used to assess the activation volume and barrier energy of dislocation nucleation in crystalline materials and shear band initiation in disordered glasses (18–20). Since the amorphization of B4C only causes a very small volume change of ~4% reduction, the onset of the first-order phase transformation has not been detected by pressure-volume experiments, such as diamond anvil cells (12). However, the localized amorphization of B4C results in the formation of nanosized shear bands (11–17, 21, 22), similar to glassy materials (23). Therefore, the detection and quantitative measurements of the shear band initiation in B4C will provide a unique way to explore the kinetics of amorphization and thus underlying mechanisms.

Here, we use depth-sensitive nanoindentation to probe the structural evolution of single-crystal B4C. The pop-in displacements in load-depth curves are demonstrated to originate from the onset of amorphous shear bands, and the corresponding activation volume and energy are close to those of dislocation nucleation and propagation. TEM characterization provides compelling evidence that the amorphization of B4C is mediated by dislocations, rather than a direct crystal-to-amorphous transition by chemical bond breaking.

RESULTS

Pop-ins in B4C single crystals

The nanoindentation experiments of a single-crystal B4C are schematically illustrated in Fig. 1A, together with possibly activated slip systems in the B4C single crystals (Table 1). Raman spectra taken from the (214), (223), and (104) single crystals are displayed in fig. S1, showing the clear difference in relative intensity of sharp peaks at 482- and 534-cm−1 modes, which are associated with stretching of three-chain atom chains and rigid rotation of icosahedra in B4C (Supplementary Text). The load-displacement curves of the (214) crystal at a loading rate of 0.125 mN/s are shown in Fig. 1B. When the applied load (p) is smaller than ~7 mN, the loading-unloading curves are fully overlapped (fig. S2), suggesting that only elastic deformation takes place. When the applied load is increased to 25 mN, a sudden displacement (i.e., pop-in) occurs during loading as marked by a box and highlighted by the inset in Fig. 1B. The transition from elastic to permanent deformation by a pop-in event has a displacement of ~3.5 nm. The pop-in phenomenon is often related to the incipient plasticity by the nucleation and propagation of a dislocation or twin along a specific slip system of crystals (1, 16), or a shear band formation in amorphous materials (17–19). Although the mechanical properties and stress-induced amorphization of B4C have been extensively studied using instrumented indentation in the past two decades, the pop-in events in load-displacement curves have not been observed before (3, 4, 13, 20, 22). We noticed that the pop-ins are only visible at lower loading rates (Fig. 1C) and disappear when the loading rate is higher than ~0.125 mN/s. Although the loading rate does not have an obvious effect on the hardness of the single-crystal B4C (Fig. 1D), the rate dependence of the pop-in events indicates that the initiation of the stress-induced structural instability may be time dependent and governed by a thermal activation process. Although the displacement resolution of the nanoindentation may also affect the visibility of pop-ins in loading curves, the several-nanometer displacements of pop-ins are one order of magnitude larger than the resolution of our instrument at the loading rate of 1.0 mN/s. Besides the loading rate dependence, the pop-in events also depend on crystallographic orientations of B4C single crystals. Similar to the (214) crystal (Fig. 1B), the pop-ins can be well identified in the loading curves of (223) crystals at a slow loading rate of 0.125 mN/s (fig. S3). However, for (104) crystal, the loading and unloading curves smoothly change with displacement, and a pop-in event cannot be seen at the slow loading rate of 0.125 mN/s (fig. S4).

Fig. 1 Nanoindentation experiments on the characterization of the onset of shear amorphization in single-crystal B4C.

(A) A schematic illustration of nanoindentation experiments performed on single-crystal B4C, together with possibly activated slip systems in B4C single crystals. (B) A representative load-displacement curve from the nanoindentation at a maximum load of 25 mN and a loading rate of 0.125 mN/s of single-crystal (214) B4C. A pop-in, as shown in a box, can be detected, which corresponds to the initiation of amorphous shear band by shear amorphization. The red line fitting is the prediction from Hertzian elastic contact theory. The inset shows the zoomed-in plot of the discontinuous displacement of about ~3.5 nm at pop-in. (C) Load-displacement curves measured at different loading rates from 0.125 to 1.0 mN/s. The disappearance of pop-in events with increase in loading rate is indicated with arrows and shown in the box. (D) Dependence of measured hardness on loading rates at the maximum force of 25 mN.

Table 1 Summary of possible slip systems with their Burgers vectors and lattice plane shift in B4C.

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Microstructural characterization of pop-ins

To understand the underlying mechanisms of the pop-in displacements, we investigated the microstructure of the deformed regions underneath indenter, which undergo the discrete deformation. Figure 2A is a representative scanning electron microscopy (SEM) image of an indentation impression produced on the (214) crystal at the maximum load of 25 mN and the loading rate of 0.125 mN/s. The characteristics of slip bands are visible on the three faces of the Berkovich impression. No cracks can be observed within and at the corners of the indent region. Raman spectra taken from the indented region show three additional broad peaks at 1340, 1550, and 1810 cm−1 as compared with the pristine single-crystal B4C (Fig. 2B). These Raman bands have been identified as the characteristic Raman modes of amorphous B4C (a-B4C) (3–4, 12–13, 21–22). TEM image taken from the cross-sectioned indented region of fig. S5 displays with a shear band of ~300 nm in length and ~1 to 4 nm in width (Fig. 2C). High-resolution TEM (HRTEM) image (Fig. 2D) shows the loss of crystal lattices in the shear band. The diffuse halo ring of the fast Fourier transform pattern (FFT) (the inset b of Fig. 2D) further confirms the amorphous nature of the shear band as compared to the crystalline matrix on either side of [201¯]zone axis (the inset a of Fig. 2D). An HRTEM image reveals that the formation of an amorphous shear band is on a (122) plane. A series of HRTEM images obtained along the amorphous band confirmed that the deviation is <2° on either side of crystal plane. The observations of amorphous band width in the range of ~1 to 4 nm are consistent with previous experimental and simulations studies (3, 11–17, 22). The zoom-in lattice images (Fig. 2, E and F) show that the displacement generated by the amorphous band can be described by a pair of dislocation dipoles with the Burgers vector of 〈11¯2〉and the relative lattice plane shift of ∼1.7Å as marked by the loop in Fig. 2 (E and F). Simulated TEM images overlaid on experimental images of Fig. 2 (E and F) suggest that the amorphization is along the (122) plane of the rhombohedral B4C unit cell. We also characterized the structural evolution of the (223) crystal, which also experiences the pop-in displacements. Similar to the (214) crystal, nanosized amorphous bands with shear displacements can also be observed and the relative lattice plane shift is of ~1.3Å as shown in figs. S6 and S7 and Table 1. These observations demonstrate that the amorphous band formation is responsible for the discrete pop-in events. The localized amorphization results in shear deformation and appears to be associated with the dislocation formation. In contrast, multiple amorphous bands can be faintly identified from the deformed (104) crystal (fig. S8), indicating that this orientation is not favorable to access shear deformation along the indentation projection by a single shear band as shown schematically in Fig. 1A and Supplementary Text. Upon examination under the same orientation of 〈11¯0〉 for the (104) crystal (fig. S9), we have noticed that the amorphous bands are apparent and dislocation nucleation can be seen along the (113) plane, suggesting that the indentation geometry is important to activate preferentially slip systems (Table 1). The smooth load-displacement curves of the (104) crystal may be caused by the activation of multiple shear bands, and the elastic-to-plastic transition takes place by continuous deformation, instead of a single pop-in event. In a similar way, a higher loading rate may also promote multiple shear band formation, while a lower loading rate provides sufficient time for a single shear band initiation with a visible pop-in in the load-displacement curves.

Fig. 2 Microstructural characterization of (214) single crystal after nanoindentation testing.

(A) Scanning electron microscopy (SEM) image of nanoindentation impression of B4C at the applied load of 25 mN. No cracks can be found at the corners of indent region. (B) Raman spectra taken from pristine B4C (black curve) and residual indentation (red curve) of single-crystal B4C. a.u., arbitrary units. (C) The cross-sectioned TEM image displaying a shear band with the length of ~300 nm and width of ~1 to 4 nm. (D) A magnified TEM image of shear band confirming amorphous structure along the (122) plane. Fast Fourier transform (FFT) pattern taken from the band shows the amorphous diffuse halo ring pattern (inset b). The inserted FFT pattern acquired from the lattice image corresponds to the [201¯]direction of rhombohedral B4C (inset a). (E) High-resolution TEM (HRTEM) image displaying the shear displacement, equivalent to dislocation dipoles, at the origin of tip of the amorphous shear band. (F) HRTEM image acquired from the other end of the amorphous shear band revealing the shear displacement at the termination. The simulated images and atomic models are overlaid on the HRTEM images in (E) and (F), showing the consistence with the experimental lattice spacing of the [201¯]projection.

Stochastic analysis of the first pop-ins measured from B4C single crystals

The onset forces of pop-ins measured from a large number of independent tests distribute in a wide range from ~7 to 20 mN at a loading rate of 0.125 mN/s, suggesting that the discontinuous transition is stochastic (fig. S10). By normalizing the applied forces using the nominal contact area from the geometrically self-similar Berkovich indenter, the force-depth curves can be converted to the contact press Pm versus displacement curves (fig. S11). The plot of first pop-in width against the contact pressure drop (fig. S11) also demonstrates that the pop-in events are stochastic. The cumulative displacements at first pop-ins fall in the range of 1 to 4 nm (fig. S10), which coincides with the amorphous shear band widths observed by TEM (11–14, 22). On the basis of the load-displacement plots, the critical shear stresses (τcritical) under the Berkovich indenter are evaluated from the applied force (P) at the initialization of first pop-ins using the following equation (24)τcritical=0.31 (6PE*2π3R2)(1)where R is the tip radius of the indenter, and E* is defined as effective elastic modulus (~350 to 410 GPa). Correspondingly, the distributions of the critical shear stresses for both (214) and (223) crystals are stochastic and fall in a wide range from 23 to 38 GPa for the (214) crystal and 25 to 40 GPa for the (223) crystal (Fig. 3, A and D). To determine the nucleation rate, activation volume, and activation energy of the first pop-in events from the loading curves, the statistical analysis of instantaneous shear stresses (τ) beneath the indenter is given by Eq. 2 (25)f=1−exp(−ηkTτ·υ*.exp(τυ*kT))(2)where η is the nucleation rate, υ* is the activation volume for the nucleation of pop-ins, T is the testing temperature (herein, room temperature), k is the Boltzmann constant, τ·is the loading rate, and τ is the critical shear stress for the first pop-ins. Before the first pop-ins, the load-displacement curves are fitted to the Hertzian contact solution for determining the radius R=(P.34.E*.h32)2, where is h maximum depth, and E* can be obtained from 1E*=1−νm2Em+1−νi2Ei for elastically anisotropic specimen. Here, Em and νm are the Young’s modulus and Poisson’s ratio of specimens, and Ei and νi are the Young’s modulus and Poisson’s ratio of the diamond indenter (26). The cumulative distribution of the critical shear stress at the constant loading rate of 0.125 mN/s for the (214) crystal is shown in Fig. 3B. The activation volume υ* and nucleation rate η can be determined by the linear least-squares method by plotting ln [ln(1 − f)−1] versus τ as shown in Fig. 3C. The activation volume υ* is directly obtained from the slope of the plot, while η is subsequently derived from the intercept. Also, we have estimated υ* and η of the (223) crystal by linear least-squares fitting of critical shear stress (τ) (Fig. 3, E and F). The measured υ* and η for both (214) and (223) crystals are given in Table 2. The deviations of the linear fitting for Fig. 3 (C and F) could be related to the surface roughness variation and chemical and structural fluctuation of samples, which are commonly observed in stochastic indentation tests (24, 26). On the basis of the stochastic data analysis, the activation volumes of the first pop-ins are estimated to be ∼2.5Å3 for the (214) crystal and ∼1.8Å3 for the (223) crystal. Note that the volumes are just about one eighth the size of the B12 icosahedron in the B4C unit cell, suggesting that the initiation of the pop-ins and amorphization only requires a part of atoms within a unit cell of B4C for the structural and dynamic transitions. We compared the estimated activation volumes and nucleation rates of the pop-in events of B4C with those of metallic and ceramic crystals and amorphous alloys subjected to the similar loading conditions as shown in Table 2 (18–20, 25, 27). The small activation volumes are similar to those of dislocation nucleation in crystalline materials, but orders of magnitude smaller than that of shear band formation in amorphous alloys. The activation volumes of B4C are too small to explain the first-order phase transition of amorphization but are close to that of dislocation nucleation and propagation in many crystals (28). Moreover, the nucleation rates of pop-ins are sluggish and akin to that of dislocation nucleation in covalent-bond ceramics, such as silicon carbide. Therefore, it is most likely that the pop-ins and the resulting localized amorphization are kinetically mediated by dislocation nucleation, rather than the direct phase transition from crystalline to amorphous B4C. We also estimated the activation energy Ea of the first pop-ins using the nucleation rate equation (29), n·=ηexp(−EakT), where k is the Boltzmann’s constant, T is the temperature (herein, room temperature), Ea is the activation energy for dislocation nucleation, Ea = ΔH − τυ*, in which ΔH is the activation enthalpy, τ is the shear stress, and υ* is the activation volume. The experimentally measured ΔH is 1.674 ( ± 0.004) eV (Supplementary Text and fig. S12) obtained from best fitting of cumulative load statistics function f(P) using the equation given in the supplementary information of (25). From this analysis, we evaluated the activation energy of Ea~1.6 ± 0.1 eV for both B4C single crystals, which is consistent with the value estimated by electric field pulse experiments on the initialization of B4C amorphization (30, 31) and falls in the range of dislocation nucleation and motion in covalently bonded inorganic materials (32, 33).

Fig. 3 Stochastic analysis of the first pop-ins measured from (214) and (223) B4C single crystals.

(A) Distribution of the critical shear stress of first pop-ins in the (214) crystal. (B) Plot of the critical shear stress versus cumulative frequency distribution and (C) illustration of the plots of ln(ln(1 − f)−1) versus the critical shear stress at first pop-in of the (214) crystal. (D) Distribution of the critical shear stress of first pop-ins in (223) crystals. (E) Plot of the critical shear stress versus cumulative frequency distribution and (F) illustration of the plots of ln(ln(1 − f)−1) versus the critical shear stress at first pop-in of the (223) crystal. The values of activation volumes (ν*) and nucleation rates (η) are obtained from the slopes and intercepts of the linear least-squares fitting.

Table 2 Nucleation rates and activation volumes of different materials compared with single-crystal boron carbide.

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DISCUSSION

Shear amorphization has been widely observed in complex crystals, such as ice, minerals (e.g., α-quartz and coesite), semiconductors (e.g., silicon and germanium), intermetallic (e.g., Ni3Al and Ti3Al), and covalently bonded boron-rich ceramics (B4C, B12O2, and B12P2), and is generally related to shear-induced lattice destabilization (34–39). However, the underlying mechanisms of the localized crystal to amorphous transition have not been well understood because of the challenges of conventional microscopic diffraction and scattering techniques in detecting heterogeneous nanoscale transition under extreme loading conditions of high nonhydrostatic pressures and/or fast loading rates. Previous microscopic observations have found that the shear local amorphization often coincides with inherent planes of stacking faults and twins (14, 38), indicating certain correlation between amorphization and crystal defects. In this study, the small activation volume, slow nucleation rate, and lower activation energy derived from the stochastic analysis of the onset of amorphization, divulged by the pop-ins in load-displacement curves, provide kinetic evidence that the shear amorphization of B4C is mediated by dislocation formation, rather than direct phase transition from crystalline to amorphous structures, as shown in the schematic diagram (Fig. 4). Separate HRTEM observations endow additional evidence to support the novel amorphization mechanisms in ultrahard covalent materials. Although the underlying mechanisms of the dislocation-mediated amorphization require further theoretical and experimental investigations, it is apparent that the relatively low energy barrier of dislocation nucleation, in comparison with that of the first-order phase transition, favors the activation of dislocations by nucleating new dislocations or motivating existing dislocations under high nonhydrostatic pressures (40). The high lattice resistance, arising from the strong covalent bonds, may prevent dislocation motion by conventional lattice sliding at room temperature, and instead, the large lattice distortion and symmetry breaking at dislocation cores can initiate amorphization and amorphous band formation under high shear stresses.

Fig. 4 Schematic illustration shows the dislocation-mediated amorphization in B4C.

(A) Perfect crystal before deformation. (B) Shear deformation distorting the lattice. (C) Dislocation kink formation under shear deformation. (D) Amorphization under shear deformation, initiating from dislocation.

In summary, we used the depth-sensitive indentation technique to characterize the onset of shear amorphization in B4C. Stochastic analysis of the first pop-in events, which correspond to the formation of amorphous shear bands, reveals the kinetic variables of shear amorphization. The measured activation volumes, activation energies, and nucleation rates from two single-crystal B4C are consistent with those of dislocation nucleation in covalent ceramics and much lower than those of the direct crystal-amorphous transition. This finding provides new insights into the mechanisms of shear amorphization of B4C. The novel amorphization mechanisms unveiled by this study may be applicable to the failure and damage of other ultrahard and covalent materials under extreme loading conditions.

MATERIALS AND METHODS

High-quality B4C single crystals were prepared using a float zone method. The single crystals of (214), (223), and (104) orientations were prepared from different runs and polished to have mirror finish surfaces for the nanoindentation experiments. These orientations have been confirmed to experience the amorphization transition under indentation and high-pressure diamond anvil cell experiments by in situ Raman spectroscopy and postmortem TEM characterization in our previous studies (9, 10, 19, 20). The crystallographic orientations of the single-crystal B4C samples used this study are calibrated to be within 2° of their designed directions by x-ray diffraction. The Raman spectra taken from the polished (214), (223), and (104) surfaces illustrated in fig. S1 show the crystal orientation dependence of Raman modes. A nanoindenter (MTS G200, Oak Ridge, TN) with a Berkovich diamond indenter tip was used in this study. Before the measurements, the system was calibrated with a standard fused-silica specimen. A series of indentation tests with a spacing of 10 μm between the indents were conducted at loading rates ranging from 0.125 to 1.0 mN/s and a maximum load of 25 mN. The dwell time of 30 s was used before unloading. A Renishaw micro–Raman spectrometer with the excitation laser line at 514 nm was used to characterize the structural evolution beneath indentation. A scanning electron microscope (Helios NanoLab ×50 Dual Beam TM series) and a transmission electron microscope operated at an acceleration voltage of 200 kV (JEOL-ARM 200F) were used to characterize the deformation microstructure of all the single crystals. The cross-sectional TEM specimens of the indents were prepared using a focusing ion beam milling system. HRTEM image simulations were performed by using the Win HREM (HREM Research Inc.). R-Lattice 1.3 was used to calculate the angle between the loading plane and amorphous band plane. For all TEM images, boron carbide was assigned with the rhombohedral crystallographic planes as (hkl) and crystallographic direction [uvw] notations (41).

SUPPLEMENTARY MATERIALS

Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/7/8/eabc6714/DC1

https://creativecommons.org/licenses/by-nc/4.0/

This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial license, which permits use, distribution, and reproduction in any medium, so long as the resultant use is not for commercial advantage and provided the original work is properly cited.

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Acknowledgments: Funding: This work was sponsored by the MOST 973 of China (grant no. 2015CB856800), the National Natural Science Foundation of China (grant nos. 11327902, 51271113, 11704245, 51821001, and 51850410501), and the fusion research program of “World Premier International Research Center (WPI) Initiative” by MEXT, Japan. M.C. was sponsored by the Whiting School of Engineering, the Johns Hopkins University, and the NSF (NSF NSF-DMR-1804320). Author contributions: M.C. conceived and supervised this study. K.M.R. conducted nanoindentation measurements, TEM characterization, and stochastic analysis. S.S. contributed to the nanoindentation measurements. C.C., J.H., and X.W. contributed to the TEM sample preparation and characterization. D.G. and Q.A. contributed to the data analysis. K.M.R. and M.C. wrote the manuscript. All the authors discussed the results and commented on the manuscript. Competing interests: The authors declare that they have no competing interests. Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. Additional data related to this paper may be requested from the authors.
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