Nature Synthesis nature synthesis https://doi.org/10.1038/s44160-024-00707-1 Article Enhancing the hardness of diamond through twin refinement and interlocked twins Pan Ying 1,2,5 , Baozhong Li 1,5 , Mengdong Ma 1,3,5 , Yufei Gao 1 , Rongxin Sun 1 , Zihe Li 1 , Shuai Chen 1 , Bin Zhang 1 , Hefei Li 1 , Bing Liu 1 , Lei Sun 1 , Song Zhao 1 , Ke Tong 1 , Wentao Hu 1 , Yilong Pan 1,4 , Guodong Tang 2 , Dongli Yu 1 , Zhisheng Zhao 1 , Bo Xu 1 & Yongjun Tian 1 Nanostructuring strategies are widely recognized for their ability to substantially enhance the mechanical properties of materials. Among them, nanotwinning stands out for its effectiveness in enhancing the mechanical attributes of diamond by impeding dislocation movement at twin boundaries. However, the precise mechanisms that control nanotwinning and the distinct strengthening effects of various twin configurations remain inadequately understood. Here bulk diamonds were synthesized from onion-like carbon nanoparticles of different sizes, graphite nanopowder and diamond nanopowder under high-pressure and high-temperature conditions. Smaller onion-like carbon particles facilitated the formation of finer diamond grains with thinner twins, leading to a substantial increase in hardness. This approach yielded a hardness of 276 GPa for diamond with an average twin thickness of 2.3 nm. By contrast, diamonds sintered from diamond nanopowder or synthesized from graphite nanopowder exhibited minimal nanotwinning and consequently lower hardness values. Microstructure analyses revealed two predominant twin configurations: interlocked and penetrating twins. The updated diamond model that incorporates both twin configurations revealed a strong correlation between the predicted and experimental hardness values, especially when the model microstructure closely matched that of synthesized diamonds. This research explains the mechanisms of twin-induced hardness enhancement in diamond and suggests strategies for tailoring the microstructure of diamond to achieve precisely controlled properties. Diamond is indispensable in numerous industrial machining pro- cesses such as turning, cutting, boring, drilling and grinding due to its unmatched hardness, which correlates directly with machining effi- ciency and durability. Consequently, enhancing the hardness of diamond remains a primary focus in the field of superhard materials. The pre- dominant method for this enhancement is grain refinement, using the Hall–Petch effect 1 . A notable example is nanopolycrystalline diamond (NPD), which is directly transformed from graphite under conditions of 12–25 GPa and 2,300–2,500 °C, and features grain sizes of 10–30 nm and a Knoop hardness of 110–140 GPa (ref. 2). However, refining the grain size of NPD further while maintaining a high sinterability is challenging due to notable grain growth under high-pressure and high-temperature (HPHT) conditions 3 . This undesired growth, driven by the high energy of nanoscale grain boundaries, impedes further grain refinement. Nanotwinning offers an alternative strengthening strategy that enhances mechanical performance without the limitations associated Received: 27 July 2024 Accepted: 19 November 2024 Published online: xx xx xxxx Check for updates A full list of affiliations appears at the end of the paper. e-mail: tongke@ysu.edu.cn; panyilong@nbu.edu.cn; tangguodong@njust.edu.cn; zzhao@ysu.edu.cn; bxu@ysu.edu.cn Nature Synthesis Article https://doi.org/10.1038/s44160-024-00707-1 phase transformation 6 or deformation 11 under HPHT conditions, lead- ing to twins with various configurations. For instance, deformation twins may be induced by shearing during HPHT sintering, and usually present as penetrating twins that intensify at elevated temperature 12 Currently, onion-like carbon (OC) nanoparticles appear to be the most effective precursor for synthesizing diamond with a high-density, varying-configuration nanotwinned substructure 6,13–15 . Nonetheless, fine-tuning the twin thickness in diamond and understanding the strengthening mechanisms of different twin configurations require further investigation. Here we used three distinct precursors, an OC precursor with vari- ous particle sizes, graphite nanopowder and diamond nanopowder, to fabricate diamonds bulks under HPHT conditions. Microstructural characterization revealed that smaller OC particles led to diamond bulks with smaller grains that contain finer twins, whereas diamond sintered from diamond nanopowder or synthesized from graphite nanopowder exhibited minimal twinning. This microstructural dif- ference was also reflected in their hardness values. Diamonds with the refined twin thickness display a much higher hardness compared with those with minimal twinning. Our diamond model, which incorporates with grain refinement. It has been experimentally confirmed that the strengthening capability of nanotwinning is comparable to that of grain refinement 4–8 . Compared with typical grain boundaries, the much lower excess energy of twin boundaries facilitates the development of a finer nanostructure through nanotwinning, thereby avoiding issues related to nanograin growth 9 . This approach has been implemented effectively in covalent materials such as cubic boron nitride (cBN) and diamond, achieving exceptional hardness values of 108 GPa (ref. 5) and 200 GPa (ref. 6) for nanotwinned cBN and diamond with ultrafine twin thick- nesses of 3.8 nm and 5 nm, respectively. Impressively, these materials exhibit a continuous hardening effect down to the deep nanoscale, devoid of the inverse Hall–Petch effect that is typical for metals. Recent atomic-scale observations have unambiguously confirmed that most incoherent twin boundaries in nanotwinned diamond are asymmetric and less mobile, which is essential for the continuous hardening effect, even when the twin thickness is as thin as 1–2 nm (ref. 10). Therefore, it is plausible that even harder cBN and diamond could be synthesized with further refinement of the twin thickness. However, modulating the nanotwinned substructure within diamond grains is complex. Unlike metallic materials, twinning in diamond typically arises from 50 nm 100 nm e 100 nm c d f g h 5 nm 3 nm a b 0 10 20 30 20 40 60 80 100 Particle size (nm) Percentage (%) Percentage (%) 0 5 10 15 20 30 40 50 60 Particle size (nm) 70 20 Percentage (%) 0 5 10 15 12 16 20 24 28 Particle size (nm) 32 20 Fig. 1 | Characterization of the OC precursors. a , b , High-resolution transmission electron microscopy (HRTEM) images of the OC particles with a size of 45 nm ( a ) and 30 nm ( b ). c – h , TEM images ( c – e ) and statistical particle size distributions ( f – h ) of raw OC particles ( c , f ) and OC particles centrifugally separated at 20,000 × g ( d , g ) and 100,000 × g ( e , h ). Nature Synthesis Article https://doi.org/10.1038/s44160-024-00707-1 both interlocked and penetrating twins, emphasizes that interlocked twinning provides a superior strengthening effect on diamonds, thus accounting for the experimental results. Results and discussion The synthesis of nanotwinned diamonds via the HPHT method is notably influenced by the choice of precursor material, which plays a crucial role in determining both the grain size and the nanotwinned substructure within the grains. OC nanoparticles, which are char- acterized by their spherical carbon layers and interlayer defects, have emerged as a particularly effective precursor for promoting nanotwinned diamonds. The abundance of puckered atomic layers and stacking faults in OC nanoparticles provides critical sites for dia- mond nucleation and twin formation during the phase transition. Microstructural analysis of the OC nanoparticles revealed an inverse relationship between particle size and defect concentration, which is attributed to the increased curvature of smaller particles (Fig. 1a,b). This observation led to the expectation that smaller OC particles, with a higher curvature and defect density, would further refine the grain size and twin thickness in synthesized diamonds. To confirm this expectation, we used a high-speed centrifugal sorting method to separate OC particles into three distinct groups with average particle sizes of 46, 38 and 22 nm (Fig. 1c–h). These size-sorted OC nanopar- ticles were subsequently used to synthesize nanotwinned diamonds under conditions of 25 GPa and 2,100 °C. These HPHT conditions can ensure complete transformation of the OC precursor to nanotwinned diamond, eliminating potential by-products such as graphitic-like structures or diamond polytypes 6,13 . For comparison, diamond bulks were also synthesized using graphite nanopowder or diamond nano- powder as the precursor under identical conditions. The microstruc- ture and property differences between these three sets of diamond bulk were systematically investigated. 100 nm 100 nm 100 nm 10 nm 10 nm 10 nm a b c d 0 1 2 3 2 6 10 Twin thickness (nm) 4 14 18 Percentage (%) 0 1 2 3 2 6 10 Twin thickness (nm) 14 18 Percentage (%) 0 1 2 3 2 6 10 Twin thickness (nm) 4 14 18 5 0 20 40 Grain size (nm) 60 0 20 40 Grain size (nm) 60 0 5 0 20 40 Grain size (nm) 60 10 80 Percentage (%) Percentage (%) Percentage (%) 0 5 10 Percentage (%) 0 5 10 15 TBs TBs TBs Fig. 2 | Microstructural analysis of diamonds synthesized from the OC precursors. a – d , Bright-field STEM images ( a ), statistical distribution of grain size ( b ), HRTEM images of diamond nanograins viewed along the [101] zone axis, showing ultrafine twinning substructures ( c ) and statistical distribution of the twin thickness ( d ) of diamond bulks synthesized from OC precursors with an average size of 46 nm (left), 38 nm (middle) and 22 nm (right). TB, twin boundary. Nature Synthesis Article https://doi.org/10.1038/s44160-024-00707-1 X-ray diffraction analysis confirmed the formation of a pure cubic diamond phase in all bulk diamond synthesized from the OC precur- sors (Extended Data Fig. 1). The samples exhibited either translucent or transparent qualities, indicating excellent sinterability and high purity (Extended Data Fig. 2). Notably, a substantial broadening of the full-width at half-maximum was observed with decreasing OC particle size, suggesting a concomitant reduction in the grain sizes of the resultant diamond bulks. This observation was corroborated by detailed transmission electron microscopy (TEM) analysis, as shown in Fig. 2a,b. Statistical analysis of over 1,000 grains, on the basis of scanning transmission electron microscopy (STEM) measurements, revealed that diamonds synthesized from OC with particle sizes of 46, 38 and 22 nm exhibited average grain sizes of 26, 25 and 18 nm, respectively. The reduction in grain size can be attributed to the phase-transition-induced density changes. By contrast, the average grain size of the diamond bulks synthesized from diamond nanopowder and graphite nanopowder was 24 and 50 nm, respectively (Extended Data Fig. 3). Notable differences were also observed in the twinning structures between the three sets of diamonds. For diamond synthe- sized from the OC precursors, penetrating twins and interlocked twins coexisted, and a marked refinement in the twin thickness was observed as the size of the OC particles decreased, with average twin thicknesses of 5.2, 4.3 and 2.3 nm, respectively (Fig. 2c,d). Conversely, diamonds sintered from diamond nanopowder or synthesized from graphite nanopowder showed only sporadic penetrating twins (Extended Data Fig. 3). The twin configurations in NPDs are intrinsically linked to the precursor materials and their formation processes. Diamond nanopow- der contains very few pre-existing twins, mainly penetrating twins that are inherited during sintering, resulting in a lack of interlocked twins in the final product. By contrast, OC and graphite precursors favour the development of twins through phase transformation. For the OC precursor, numerous layered defects such as stacking faults and puck - ered atomic layers provide abundant diamond nucleation sites, and the spherical shape of the OC particle ensures sufficient misorientation between neighbouring diamond nuclei, facilitating twin formation. Smaller OC particles, with a greater curvature, further promote the formation of interlocked twins by increasing the likelihood of twinning with larger orientation differences (Extended Data Fig. 4). Conversely, the graphite precursor, with a planar morphology, tends to transform into diamond with occasionally penetrating twins. The microstructural variations notably influence hardness of the produced diamonds. Specifically, diamond bulks synthesized from OC particles, with average twin thicknesses of 5.2, 4.3 and 2.3 nm, exhibited Vickers hardness ( H V ) values of 186 ± 5, 215 ± 9 and 276 ± 7 GPa, respectively (Extended Data Fig. 5). By contrast, the diamond bulks synthesized from graphite nanopowder or sintered from diamond nanopowder, with a respective average grain size of 50 and 24 nm, with occasional twins, displayed notably lower hardness values of 119 ± 7 and 125 ± 6 GPa, consistent with previous reports on NPDs 2,3,16,17 . Accord- ing to the established hardness model for polycrystalline covalent materials 18,19 , the observed increase in hardness due to nanostructuring can be attributed to two primary mechanisms: the Hall–Petch effect and the quantum confinement effect. The Hall–Petch effect arises from grain and twin boundaries induced by nanostructuring, which impede dislocation motion, contributing to hardening as described by H HP = K HP D −1/2 , where H HP is the hardening due to the Hall–Petch effect, K HP is the Hall–Petch hardening coefficient and D is the characteristic size (grain size or twin thickness, in nanometres) of the microsctruc- ture. The quantum confinement effect, on the other hand, is related to the bandgap opening at the nanoscale, which introduces additional hardening in covalent nanocrystals as H QC = K QC D −1 (ref. 19), where H QC is the hardening due to the quantum confinement effect and K QC is the quantum confinement hardening coefficient. Incorporating both hardening effects, the hardness of a polycrystalline covalent material can be expressed as H V = H 0 + K HP D −1/2 + K QC D −1 , where H 0 is the intrinsic hardness of a covalent single crystal 9,19 . For diamond, the values of H 0 , K HP and K QC are 90 GPa, 164 GPa nm 1/2 and 189.7 GPa nm, respectively 9 . Using this equation and substituting the measured twin thickness or grain size data, the hardness values of the diamond bulks synthesized from the OC precursors with decreasing particle sized were estimated as 198, 213 and 279 GPa, whereas the hardness of diamond synthesized from graphite nanopowder or sintered from diamond nanopowder was estimated as 117 and 131 GPa, respectively. These theoretical estimations closely match the experimentally measured results (Fig. 3a), validating the proposed hardening mechanisms in nanotwinned diamonds. To elucidate the contribution of twinning to diamond hardening, several models have been proposed to explore the intricate interplay between dislocations and twins 20–24 . Diamond, which is conceptualized as two interpenetrating face-centred cubic lattices, exhibits {111} planes a 1 2 3 4 5 6 7 8 Twin thickness (nm) 200 300 400 500 600 10 20 30 40 50 60 Grain size (nm) 100 150 200 250 Vickers hardness (GPa) b High-order twins Interlocked twins Interlocked twins (60%) + penetrating twins (40%) Penetrating twins Nanotwinned diamond synthesized in this work Nanotwinned diamond synthesized in previous work 0 2 4 6 8 10 Twin thickness (nm) 100 200 300 400 500 Vickers hardness (GPa) Vickers hardness (GPa) Fig. 3 | Hardness as a function of the twin thickness for diamond. a , Comparison of the experimentally measured hardness values for diamonds synthesized from OC precursors (circle symbols) and that indicated by the hardness equation for polycrystalline covalent materials (dashed line, inset also). The filled and open symbols are the experimental data from nanotwinned diamonds synthesized, respectively, in this work and in previous work 6 . The inset shows a comparison of the measured hardness values for polycrystalline diamond synthesized from graphite nanopowder (right symbol) and sintered from diamond nanopowder (left symbol). b , Hardness calculated from different twinning substructure models (penetrating twins, interlocked twins, high-order twins) that are based on dislocation theory, in comparison with experimentally measured hardness values for the nanotwinned diamonds described in a . Our model, which precisely reflects the observed twinning configurations and their respective proportions, shows the best alignment with the experimentally measured values. Nature Synthesis Article https://doi.org/10.1038/s44160-024-00707-1 as the primary twinning planes. Consequently, each grain possesses four potential twinning planes, and under favourable conditions, twins with boundaries on differently oriented planes can form. During growth, twins with different orientations intersect to create interlocked twins or high-order twins, whereas those with the same orientation grow in parallel, eventually penetrating the entire grain. Building on this foundation, models focusing primarily on either penetrating twins or high-order twins have been developed 20,23 . These models represent initial attempts to elucidate the exceptional hardness of diamond from the perspective of dislocation theory. However, our observations dis- closed the concurrent presence of interlocked and penetrating twins in diamonds synthesized from OC precursors (Fig. 4a,b). A comprehen- sive statistical analysis based on high-magnification annular dark-field STEM images (Extended Data Fig. 6) demonstrated that approximately 60% of the grains contained interlocked twins, while the remaining 40% predominantly exhibited penetrating twins. This finding suggests that relying solely on models of either penetrating twins or high-order twins may not fully account for the hardness of our synthesized diamond. Notably, high-order twins, commonly observed in metals 25–28 , were absent in these samples. To provide a more comprehensive framework for understanding complex twinning structures in synthetic diamonds and their impact on mechanical properties, we developed an NPD model that incorpo- rates both penetrating and interlocked twins. This model accurately represents the observed twinning configurations and their respective proportions in our synthesized diamonds. Figure 4c shows a schematic of the microstructure considered in our updated model, which focuses on equiaxed diamond crystallites with an average grain size of 20 nm, following a Gaussian distribution (Extended Data Fig. 7a). Twin thicknesses are also assumed to follow a similar Gaussian distri- bution (Extended Data Fig. 7b). Among the various types of dislocation in diamond, the shuffle-set 0° perfect dislocation along the <110> direction is of particular signi- ficance due to its lowest Peierls-Nabarro stress and minimal resistance when interacting with twin boundaries 20,29 . This characteristic sug- gests its dominant influence on diamond hardness. Consequently, our assessment of diamond hardness focuses primarily on these specific dislocations. For grains with penetrating twins, we adopt the yield-strength-evaluation approach that was used effectively in previous studies 20 . In the case of grains with interlocked twins, the substructure within the grain can be conceptualized as twin bound- ary TB 2 terminating at twin boundary TB 1 , as illustrated in Fig. 4d. This twin configuration can be represented by a combination of three Thompson tetrahedra: ABCD, A 1 BCD and ABCD 1 . The edges of the tetrahedron the correspond to <110> directions, which are parallel to the dislocation-line directions. Each face of the tetrahedron repre- sents a potential slip plane for dislocations, with the ABC and BCD faces corresponding to twin boundaries TB 1 and TB 2 , respectively. On the basis of the dislocation-line direction, slip-plane orientation and dislocation-motion direction, we have identified and illustrated five distinct dislocation slip modes in Fig. 4d: parallel to twin boundary slip (PTS) mode, slip transfer (ST) mode, confined layer slip (CLS) mode, CST-I 10 nm 10 nm a b d c TB 1 TB 2 A B D C A 1 D 1 CLS PTS ST CST-II Fig. 4 | Typical twinning structures and schematic illustration of the polycrystalline diamond model that contains these twin configurations. a , b , Diamond grains comprising interlocked ( a ) and penetrating ( b ) twins, where the white lines denote the twin boundaries. Stacking faults are marked with orange arrowheads. c , Schematic illustration of our diamond model containing various twin configurations within individual grains, where the black lines represent grain boundaries and the blue lines represent twins. d , Schematic illustration of five dislocation slip modes: parallel to twin boundary slip (PTS) mode, slip transfer (ST) mode, confined layer slip (CLS) mode, confined slip transfer I (CST-I) mode and confined slip transfer II (CST-II) mode. The cyan and orange planes represent the intersected twin boundaries TB 1 and TB 2 , respectively. Slip systems in the interlocked twins of diamond are represented using Thompson tetrahedra, denoted by dashed lines between vertices ABCD, A 1 BCD and ABCD 1 Nature Synthesis Article https://doi.org/10.1038/s44160-024-00707-1 confined slip transfer I (CST-I) mode and confined slip transfer II (CST-II) mode. In the PTS mode, dislocations parallel to BC (the intersection of two twin boundaries) slip away from BC on the corresponding face of a Thompson tetrahedron. Consequently, dislocation movement in the PTS mode is primarily impeded by the grain boundary. In the ST mode, dislocations parallel to BC slip on the ABC or BCD face towards the intersection of the twin boundaries. The CLS mode is characterized by a slip plane parallel to the ABC or BCD face, but with a dislocation line non-parallel to BC (along the AB, AC, BD or CD direction). If the slip plane is parallel to neither ABC nor to BCD, the dislocation slip mode is classified as CST, which can be further subdivided into CST-I mode and CST-II mode, depending on whether the dislocation line is parallel to a twin boundary. For the CLS, CST-I and CST-II modes, dislocations invariably cross the twin boundary regardless of its motion direction, resulting in the critical resolved shear stress being independent of the motion direction. To determine the critical resolved shear stress ( τ CRSS ), which represents the stress required to initiate dislocation motion, we use the following equations that are based on previous research 20,30–32 : τ PTS CRSS = τ 0 + Kd − 1 / 2 , (1) τ ST CRSS = τ 0 + ( τ ST TB Gb π λ ) 1 / 2 , (2) τ CLS CRSS = τ 0 + Gb [ 1 − ν cos 2 ( φ )] sin θ 2π ( 1 − ν ) λ ln ( λα b ) , (3) τ CTS - I CRSS = τ 0 + ( τ CTS - I TB Gb π λ ) 1 / 2 + Gb [ 1 − ν cos 2 ( φ )] sin θ 2π ( 1 − ν ) λ ln ( λα b ) , (4) τ CTS - II CRSS = τ 0 + ( τ CTS - II TB Gb π λ ) 1 / 2 + Gb [ 1 − ν cos 2 ( φ )] sin θ 2π ( 1 − ν ) λ ln ( λα b ) , (5) where τ 0 is the lattice frictional stress, G is the shear modulus, b is the magnitude of the Burger vector, λ is the twin thickness within the inves- tigated grain, τ TB is the barrier strength when the shuffle-set 0° perfect dislocation reacts with the twin boundary, ν is the Poisson ratio, φ is the misorientation between the dislocation line and the Burger vector, θ is the angle between the slip plane and the twin plane, α is the disloca- tion core parameter, K is the Hall–Petch strengthening coefficient in dislocation theory and d is the grain size. The specific values for these parameters used in our calculations are listed in Table 1. Figure 3b compares the hardness values predicted by our diamond model with those obtained from experimental measurements. Our model, which incorporates both interlocked and penetrating twins, reveals a strong correlation between the diamond hardness and twin thickness. When adjusted to include only penetrating twins, the model aligns with the previous hardness model 20 . However, this simplified version consistently underestimates the hardness values, indicating that penetrating twins alone cannot account for the exceptionally high hardness observed in our experiments. Conversely, when the model primarily comprises interlocked twins or high-order twins, the calculated hardness values exceed those of our experimental meas- urements. Notably, when the twin structures in the model closely match the experimentally observed microstructure, the predicted and measured hardness values demonstrate remarkable congruence. These findings underscore the notable influence of twin configurations and dimensions on diamond hardness, suggesting that manipulating these features could be a viable approach for fine-tuning the hardness of diamond. The inverse Hall–Petch effect, common in metals 4,7 , is absent in our work on diamond. This difference stems from the contrasting bonding nature and microstructure of metals and diamond. Metallic bonds, being delocalized, allow substantial dislocation motion in plastic defor- mation. Below a critical twin thickness, the inverse Hall–Petch effect occurs in metals due to detwinning from easier dislocation nucleation at the twin boundary and its subsequent migration 4,7 . By contrast, the directional covalent bonds of diamond notably restrict atomic move- ment. In addition, most incoherent twin boundaries in diamond are asymmetric and less mobile, and crucial for the continuous hardening effect and thus avoiding the inverse Hall–Petch effect 10 Conclusion We successfully synthesized diamonds with various twin thicknesses and configurations under HPHT conditions using OC precursors of dif- ferent particle sizes, graphite nanopowder and diamond nanopowder precursors. Remarkably, diamond produced from smaller OC particles exhibited notably refined nanotwins, achieving a hardness of 276 GPa with an average twin thickness of 2.3 nm. Our experimental observa- tions identified two primary twin configurations within the grains of nanotwinned diamond: interlocked twins and penetrating twins. On the basis of these findings, we developed a diamond model that accurately represents these microstructural features. Subsequent hardness evaluations indicated that interlocked twins provide greater hardening compared with penetrating twins, underscoring a strong correlation between the twinning structure and the material hardness. This research provides new opportunities for developing superhard materials with properties that can be precisely tailored on the basis of their microstructure. Methods Precursor preparation and segregation The OC nanopowder samples were fabricated using carbon black nanopowder as the starting material. Initially, carbon black powder (1 g) was dispersed in ethanol (100 ml) and subsequently processed using an impinging-streams treatment. The treated suspension underwent drying and mechanical milling, yielding the OC nanopowder with particle diameter values ranging from 10 to 100 nm. Subsequently, this raw powder was dispersed in alcohol and subjected to centrifu- gation to segregate the nanoparticles on the basis of their average particle size. The concentration of the suspension solution was main- tained at 2 g per litre. Centrifugation was performed using two distinct devices: a high-speed centrifuge (Thermo Heraeus Multifuge X3R) and an ultrahigh-speed centrifuge (Hitachi Himac CP80NX), which generated centrifugal forces of 20,000 × g and 100,000 × g , respec- tively. The temperature within the centrifugal environment was strictly controlled at 4 °C. Sample synthesis Diamond bulks were synthesized from the carefully segregated OC nanoparticles (selected on the basis of distinct average sizes), high- purity graphite nanopowder (99.9% purity, Alfa Aesar) and high-purity diamond nanopowder (99.9% purity, 10 nm average size, Alfa Aesar) at 25 GPa and 2,100 °C using a 10 MN double-stage large-volume multi-anvil system. The experimental set-up included a standard COMPRES 8/3 sample assembly, which includes an 8 mm spinel + MgO octahedron equipped with a rhenium heater and a LaCrO 3 thermal Table 1 | Parameters used to evaluate the critical resolved shear stress of each slip mode τ 0 (GPa) G (GPa) b (nm) τ τ τ ST TB (GPa) τ τ τ CST − I TB (GPa) τ τ τ CST − II TB (GPa) ν α 10.3 540 0.25 19.2 47.7 19.2 0.078 3.33 Nature Synthesis Article https://doi.org/10.1038/s44160-024-00707-1 insulator. The temperature was measured using a type-C thermo- couple, while the pressure was estimated on the basis of previously established calibration curves. The octahedron assembly was aligned precisely against eight tungsten carbide anvils with a truncation edge length of 3 mm. The dimensions of the recovered samples were approxi- mately 1.0 mm in diameter and 0.5–1.2 mm in height. Structure characterization The phase structures of the HPHT products were characterized using an X-ray diffractometer (Bruker D8 ADVANCE, Cu Kα). For the prepara- tion of TEM specimens, a focused ion beam instrument (FEI Scios) was used. Initially, an accelerating voltage of 30 kV and a current of 27 nA were used to cut a wall approximately 1 μm in thickness. Subsequently, the wall was removed and polished meticulously into a slice with a thickness of less than 100 nm. This polishing procedure involved a gradual reduction in the current from 15 to 7, 5, 1 and 0.5 nA to achieve the desired thinness. After that, the slice surface was cleaned using low-energy ion beam operated at a voltage of 5 kV and a current of 16 pA to minimize potential irradiation damage, followed by low-energy argon milling (Fischione Model 1040 NanoMill) to further reduce the knock-out damage on the slice. TEM observation was carried out using an FEI Talos F200X TEM/STEM instrument operating at an accelerating voltage of 200 kV. Hardness measurement The Vickers hardness ( H V ) of the HPHT products was measured on care- fully polished surfaces using a microhardness tester (KB 5 BVZ). The H V values were calculated as H V = 1,854.4 F / L 2 , where F (in newtons) is the applied force and L (in micrometres) is the arithmetic mean of the two diagonal lengths of the Vickers indentation. The reported hardness values are the average of five distinct measurements, each conducted with an applied load of 4.9 N, ensuring consistency and accuracy in the determination of the material’s hardness. Diamond model and hardness evaluation A polycrystalline model, comprising 6,000 randomly oriented dia- mond grains, was constructed. The average grain size was 20 nm, with a standard deviation of 2.5. Concurrently, the standard deviation for the twin thickness was designated as 0.5. H V values were determined according to Tabor’s formula, which is expressed as H V = α 0 σ y , where α 0 is the Tabor factor and σ y is the yield strength 33 . The yield strength was evaluated on the basis of the Sachs model for a polycrystalline material, which is considered to have yielded when 90% of its grains have yielded 34 . The stress corresponding to this state is defined as the yield strength. It is important to note that during the estimation of hardness, potential phenomena such as grain rotations and grain boundary migration are not accounted for. Data availability The data that support this study’s findings are available within the Article. In addition to Figs. 1 and 2, further TEM images for the statisti- cal analysis of particle size, grain size and twin thickness are available from the corresponding author upon reasonable request. Source data are provided with this paper. References 1. Petch, N. J. The cleavage strength of polycrystals. J. 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Acknowledgements This work is supported by the National Key R&D Program of China (numbers 2018YFA0703400 (Y.T.) and 2023YFA1406200 (B.X.)), the National Natural Science Foundation of China (numbers 52288102 (Y.T.), 52325203 (Z.Z.), 52090020 (Y.T.), 52202049 (P.Y.), 52103322 (Y.G.), 52302117 (K.T.), 52302063 (M.M.), 52302072 (B. Li) and 12302136 (Z.L.)), the Natural Science Foundation of Hebei Province of China (numbers E2022203109 (B.X.), E2023203256 (Z.Z.) and E2023203126 (B. Li)), the Innovation Capacity Enhancement Program of Hebei Province (no. 24461901D (M.M.)), the Talent research project in Hebei Province (no. B2024005011 (L.S.)), the China Postdoctoral Science Foundation (numbers 2023M732977 (B. Li) and GZC20231162 (B. Liu)), the China Postdoctoral Science Foundation-Tianjin Joint Support Program (no. 2023T019TJ (B. Liu)), the Fundamental Research Funds for the Central Universities (no. 30924010206 (P.Y.)) and the Opening Project of State Key Laboratory of Metastable Materials Science and Technology of Yanshan University (no. 202408 (P.Y.)). Author contributions Y.T., B.X., Z.Z., G.T., K.T. and Y.P. conceived this project; P.Y., B. Li, M.M. and Y.P. prepared the samples; P.Y., B. Li, M.M. and Y.G. performed the X-ray diffraction measurements; P.Y., B. Li, Z.L. and W.H. conducted the TEM characterization; P.Y., Y.G., M.M. and B. Liu performed the hardness measurements; K.T. developed the model and conducted the hardness simulations; P.Y., B. Li, M.M., Y.G., R.S., Z.L., S.C., B.Z., H.L., B. Liu, L.S., S.Z., K.T., W.H., Y.P., G.T., D.Y., Z.Z., B.X. and Y.T. analysed the data; and P.Y., B. Li, M.M., K.T., Y.P., G.T., Z.Z. and B.X. drafted the manuscript with contributions from all authors. Competing interests The authors declare no competing interests. Additional information Extended data is available for this paper at https://doi.org/10.1038/s44160-024-00707-1. Supplementary information The online version contains supplementary material available at https://doi.org/10.1038/s44160-024-00707-1. Correspondence and requests for materials should be addressed to Ke Tong, Yilong Pan, Guodong Tang, Zhisheng Zhao or Bo Xu. Peer review information Nature Synthesis thanks Pinwen Zhu and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Primary Handling Editor: Peter Seavill, in collaboration with the Nature Synthesis team. Reprints and permissions information is available at www.nature.com/reprints. Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. © The Author(s), under exclusive licence to Springer Nature Limited 2025 1 Center for High Pressure Science, State Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao, China. 2 National Key Laboratory of Advanced Casting Technologies, MIIT Key Laboratory of Advanced Metallic and Intermetallic Materials Technology, Engineering Research Center of Materials Behavior and Design, Ministry of Education, Nanjing University of Science and Technology