I now know why Boron Carbide shatters

Hard high-temperature ceramics is an area I've been involved with throughout my career. One of these materials is Boron Carbide. The B₄C polymorph is one of the hardest known materials and is incredibly lightweight due to its constituents and density. These attributes make B₄C a leading candidate for personal body armor, vehicle shielding, and other high-impact applications. Its remarkable properties originate from its rhombohedral crystal structure that consists of a 12-atom icosahedra that are connected by stiff three-atom chains.

Figure 1. Unit cell of B₄C with 12-atom icosahedra & C-B-C fragment (Materialscientist, CC BY-SA)

Despite its exceptional hardness boron carbide exhibits a critical weakness under high-speed impact: it can fail catastrophically through amorphization, where the ordered crystal collapses into a glassy/disordered state. This phase change results in loss of outstanding hardness and strength. For a long time the atomic-scale mechanisms behind this phenomenon weren't really well characterized or understood. I remember shock physics molecular dynamics studies trying to look at this and it was never quite clear what the incipient (i.e. onset/preceding) steps were to amorphiziation. From a modeling perspective, a lot of it is related to the ability of interatomic potentials to capture the atomic-scale process. That seems to have changed. A recent study by Ghaffari et al. [1] used machine-learned interatomic potentials (MLIPs) and MD simulations to reveal how the crystal orientation, polymorphism, and velocity impact the amorphization failure process.

One of the nails in the coffin, so to speak, is shown in Figure 2, which reveals thin amorphous bands forming at ~45° relative to the impact direction, demonstrating the shear-driven nature of failure. Previous MD simulations could not reproduce this experimentally observed phenomenon.

Figure 2. Amorphous bands at ~45° relative to impact (Fig. 4 from Ghaffari et al. 2025)

The Paradox of Boron Carbide

The exceptional hardness of most carbides, like B₄C (Vickers ≥ 30 GPa)¹, originate from the covalent bonds, and in the case of B₄C its icosahedra and three-atom chains. However, under dynamic loading beyond its Hugoniot Elastic Limit (HEL), which is the transition condition where a material goes from elastic to plastic deformation under shock loading and for B₄C it is experimentally around 20 to 25 GPa. So under shock loading B₄C softens instead of hardening, exhibiting glass-like mechanical behavior [1]. Amorphization degrades the structure of the material by breaking up icosahedral cages, resulting in loss of long-range order, and therefore sharp reduction in shear strength and hardness. In experiments they have observed narrow amorphous bands forming along shear planes [2-4], but these of course lacked temporal and spatial resolution to identify the atomic processes responsible for the amorphization.

New kid on the block: MLIPs

I've posted a bit on this blog about machine-learned interatomic potentials (MLIPs) because they have shifted the type of classical atomistic simulations that can be now, mostly in terms of chemistries simulated, but with the work by Ghaffari et al. [1] its pushed this to new physics regimes and mechanisms. From what I recall, simulating shock physics amorphization in carbides has been a challenge with classical interatomic potentials. I'm sure some have tried AIMD but the spatial scale would always be the limiting factor, i.e., nearly impossible to capture the amorphous band formation. Force fields such as ReaxFF have been tried [5] but fail to reproduce the observed experimental features. Ghaffari et al. [1] address this by developing a machine-learned interatomic potential trained on DFT-calculated structures for four dominant polymorphs, amorphous phases, and high-pressure states. Using DeePMD-kit, the resulting model achieved high accuracy and enables MD simulations of systems scaled up to ~450K atoms.

tl;dr

Simulations using their trained boron carbide MLIP model successfully capture shear-induced amorphous band formation for the first time, directly matching experimental observations and providing atomistic process responsible for the amorphization.

So what did they find?

I mentioned earlier in Figure 2 that the amorphous bands formation being directly observed in the MD simulations. This was one of the key results that they were able to achieve, but some other important details were also revealed.

1. Crystal Orientation Strongly Influences HEL

The HEL depends strongly on the orientation of the three-atom chain relative to the impact direction. The lowest HEL values, between 18 and 22 GPa, occurred when the chains were either aligned parallel or perpendicular to the impact. In contrast, orientations such as 45° and 60° showed the highest HEL values, between 32 and 38 GPa [1]. This seems to overturn the earlier assumptions from ReaxFF-based simulations [5] that aligning the orientation with the least compliance with the impact direction would maximize strength. But what the results in the paper indicate is the failure is driven primarily by shear stress rather than compression. Amorphous bands consistently form at planes oriented approximately 45° from the impact direction, corresponding to the planes of maximum shear stress.

2. Polymorphism Governs Toughness

Boron carbide polymorphs differ subtly in atomic arrangement but behave very differently under shock loading, as highlighted in Figure 3. The paper directly compares B₁₂(CBC), which contains a C–B–C chain, and B₁₂(CCC), which has a C–C–C chain, revealing how polymorphism controls toughness. B₁₂(CBC) exhibits the highest Hugoniot Elastic Limit (HEL) and the greatest resistance to amorphization, surviving shock by forming amorphous bands that expand in volume. In contrast, B₁₂(CCC) has a much lower HEL and fails via irreversible structural collapse and significant volume shrinkage. This difference is directly linked to the atomic arrangement: in B₁₂(CBC), the middle boron atom temporarily migrates into a cage space during compression and returns upon unloading, resulting in reversible chain bending and recovery of the lattice structure. For B₁₂(CCC), the central carbon atom instead forms permanent bonds with nearby icosahedra due to the higher bond dissociation energy of C–B bonding (448 KJ/mol) relative to B–B bonding (297 KJ/mol), leading to irreversible bonding, collapse, and densification. Figure 4 provides side-by-side atomistic snapshots of these chain mechanics, illustrating the reversible bending and recovery in CBC versus the irreversible bonding and collapse in CCC. Figure 5 further strengthens this mechanistic explanation by showing the cage-space migration pathway that enables reversibility in CBC.

Figure 3. Reversible vs Irreversible Chain Bending (Fig. 8 from Ghaffari et al. 2025)

Figure 4. Reversible vs Irreversible Chain Bending (Fig. 10 from Ghaffari et al. 2025)

Figure 5. Cage-Space Migration (Fig. 11 from Ghaffari et al. 2025)

3. Two Distinct Regimes of Amorphization

The study also identifies two fundamentally different deformation regimes controlled by impact velocity [1]. In Figure 6 the response to 2.5, 3.0, and 4.0 km/s shocks is shown and it establishes distinct band-dominated versus collapse-dominated regimes. At 2.5 km/s, localized amorphous bands dominate, and the volume inside these bands expands by ~6% relative to the surrounding crystal lattice, which then suppresses crack initiation (i.e. extrinsic toughening). At 3.0 km/s, amorphous banding and partial structural collapse both coexist. But at 4.0 km/s and above, widespread collapse of icosahedral units occurs, producing significant volume shrinkage and creating voids that promote crack growth. The preservation or destruction of icosahedral motifs determines whether a region undergoes expansion, local compressive shielding, or irreversible densification.

Figure 6. Atomic Volume Variation

Implications for Materials Design

The results from Ghaffari et al. [1] provide an atomic-level framework for designing boron carbide that is more resistant to amorphization. Orienting grains to align their stiffest chains with the planes of maximum shear resistance, approximately 45°, increases HEL and delays failure. Favoring polymorphs containing C–B–C chains during synthesis improves toughness by enabling reversible chain bending and reducing susceptibility to catastrophic collapse. Furthermore, the demonstrated accuracy of machine-learned interatomic potentials shows that AI-driven simulations are now a critical tool for predicting material behavior under extreme conditions and guiding the design of next-generation superhard ceramics.

Footnotes

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1. In contrast to Boron Carbide, Tungsten carbide is another hard and refractory material, but Tungsten carbide density is ~7x (15.7 g/cm³) that of Boron Carbide. I believe the hardness of Boron Carbide is also slightly higher than that of Tungsten carbide. ↩

References

[1] K. Ghaffari, S. Bavdekar, D.E. Spearot, G. Subhash, Influence of Crystal Orientation and Polymorphism on the Shock Response of Boron Carbide, SSRN Preprint, (2025). https://ssrn.com/abstract=5186595.

[2] G. Parsard, G. Subhash, P. Jannotti, Amorphization-Induced Volume Change and Residual Stresses in Boron Carbide, Journal of the American Ceramic Society. 101 (2018) 2606–2615. https://doi.org/10.1111/jace.15442.

[3] M. Chen, J.W. McCauley, K.J. Hemker, Shock-Induced Localized Amorphization in Boron Carbide, Science. 299 (2003) 1563–1566. https://doi.org/10.1126/science.1080067.

[4] K.M. Reddy, P. Liu, A. Hirata, T. Fujita, M.W. Chen, Atomic Structure of Amorphous Shear Bands in Boron Carbide, Nature Communications. 4 (2013) 2483. https://doi.org/10.1038/ncomms3483.

[5] A.A. Cheenady, A. Awasthi, M. DeVries, C. Haines, G. Subhash, Shock Response of Single-Crystal Boron Carbide Along Orientations with the Highest and Lowest Elastic Moduli, Physical Review B 104 (2021) 184110. https://doi.org/10.1103/PhysRevB.104.184110

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