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).
(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.
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
(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
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)
(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.
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.
(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
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REFERENCES AND NOTES
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