The direct (catalyst-free) graphite-to-diamond transformation under high pressure and high temperature proceeds, under mild quasi-hydrostatic conditions, by a diffusionless nucleation-growth mechanism mediated by intermediate puckered graphite phases, but macroscopic single-crystalline hexagonal diamond (HD, lonsdaleite) has not been synthesized. The source work (Luo et al., Carbon 2024) established the orthorhombic-graphite-mediated nucleation pathway from atomic-resolution experiments and simulation. The open problem is the synthesis of macroscopic, strictly single-crystalline HD via the direct transformation, using the established nucleation mechanism and transformation pathway to guide possible routes.

Background

Carbon's two classic crystalline polymorphs are graphite (sp2-bonded, layered) and diamond (sp3-bonded, tetrahedral). Under static compression above roughly 10-20 GPa, hexagonal graphite (HG, the common AB-stacked form) converts to a transparent high-pressure 'post-graphite' phase that reverts on decompression; heating under pressure above roughly 1000-2000 K yields diamond without any catalyst - the 'direct' graphite-to-diamond (G-D) transformation, achievable by static compression in presses or diamond anvil cells (DACs) or by explosive/shock compression. Diamond itself has two stacking polytypes: cubic diamond (CD, the gem variety, ABC stacking) and hexagonal diamond (HD, also called lonsdaleite, the wurtzite-type AB-stacked polytype), first made statically and identified in shocked meteorites (Bundy and Kasper, 1967). Whether HD exists as a genuinely discrete, quenchable phase - rather than as nanoscale stacking faults and twins in CD ('diaphite' intergrowths) - was contested for a decade (Németh et al., 2014, DOI: 10.1038/ncomms6447, argued lonsdaleite is faulted and twinned cubic diamond). First-principles calculations predicted that HD's ideal indentation strength exceeds CD (Pan et al., 2009), motivating synthesis attempts, while applications such as nitrogen-vacancy (NV) centers - the substitutional nitrogen-plus-vacancy defect used as a quantum sensor qubit in CD - are predicted to have different, potentially useful optical properties in HD. Mechanistically, the transformation has been described both as a concerted, martensitic restructuring of whole graphite layers - as in the neural-network-potential molecular dynamics (MD) study of Khaliullin et al. (2011) - and as a nucleation-and-growth process; shock experiments (Turneaure et al., 2017) showed graphite converts to HD on nanosecond timescales. The source work (Luo et al., Carbon 2024) recovered DAC samples at early conversion stages and combined atomic-resolution electron microscopy with large-scale MD (using bond-order potentials, i.e. empirical interatomic potentials whose bond stiffnesses adapt to the local coordination so that bonds can form and break during the transformation) and density-functional theory (DFT, the standard quantum-mechanical method for total-energy calculations) calculations. It concluded that under mild high-pressure/high-temperature (HPHT) conditions (below about 20 GPa) a diffusionless nucleation-growth mechanism operates, mediated by an intermediate orthorhombic graphite (OG) phase: graphite transforms to OG, and OG converts to HD by 'boat'-buckling or to CD by 'chair'-buckling of the puckered layers; rhombohedral graphite (RG, ABC-stacked) provides a further route to CD. The paper reported that OG always forms together with RG or HG and that no isolated orthorhombic crystallites were detected, indicating that OG is hard to quench unless stabilized by adjacent phases; it acknowledged that the experimental and simulation conditions differ greatly (strain rates, model sizes, timescales), so that the MD results are qualitatively - not quantitatively - consistent with the experimental observations; and no single-crystal HD had been successfully synthesized, so the predicted superior hardness could not be reliably verified and HD's suitability for NV-based quantum applications was untested - understanding the direct G-D nucleation mechanism and the corresponding transformation pathway guides possible routes to synthesize single-crystal HD. Between February 2025 and March 2026 this landscape changed substantially: bulk, millimetre-sized, (nearly) phase-pure HD was reported by three groups (Chen et al., Nature Materials 2025, via heating compressed graphite through post-graphite phases with temperature gradients; Yang et al., Nature 2025, from single-crystal graphite under quasi-hydrostatic HPHT (pressure applied nearly uniformly, with minimal deviatoric stress); Lai et al., Nature 2026, from c-axis-compressed highly oriented pyrolytic graphite), with measured hardness only slightly above CD and claims that the discrete-phase controversy is resolved. Each of these bulk HD materials is texturally nanocrystalline - a threefold intergrowth of roughly 100-nm crystals (Yang et al.) or a block of stacked single-crystal-like nanolayers (Chen et al.) - not a macroscopic single crystal.

Problem Statement

Synthesize macroscopic, strictly single-crystalline hexagonal diamond via the catalyst-free direct graphite-to-diamond transformation, informed by the established orthorhombic-graphite-mediated diffusionless nucleation-growth mechanism under mild quasi-hydrostatic HPHT conditions (HG→OG→HD by 'boat'-buckling of the puckered layers; HG→OG→CD by 'chair'-buckling; HG→RG→CD) for possible growth routes. 'Strictly single-crystalline' is meant in the standard crystallographic sense: a continuous, unbroken crystal lattice extending across the macroscopic specimen - a single coherent diffraction domain - rather than the textures of all bulk HD reported through early 2026 (a threefold intergrowth of roughly 100-nm crystals, a block of stacked single-crystal-like nanolayers, or phase-pure polycrystalline bulk). Identification of the product as single-crystalline HD requires convergent structural evidence of the kind practiced in the source work and the 2025-2026 bulk-HD studies: simulation-matched electron diffraction, atomic-resolution imaging, and complementary characterization such as electron energy-loss spectroscopy and X-ray diffraction. As motivation stated by the source rather than as deliverables of this problem, such a crystal would enable the first reliable verification of intrinsic properties - the predicted hardness advantage over cubic diamond - and may provide a platform for hosting nitrogen-vacancy or other defect qubits; accordingly, measuring mechanical hardness or demonstrating defect qubits in HD is not a completion requirement. The sole deliverable is a mechanism-guided synthesis route - precursor, P-T path, recovery, and an identification protocol - predicted to yield macroscopic, strictly single-crystalline HD. A route that specifies these elements and is informed by the established nucleation mechanism and transformation pathway resolves the task.

References

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