Nonlinear Multiphysics Modeling of Diamond Formation: Integrating Geometry, Bonding, Thermodynamics, and Economic Feasibility

This study develops a unified, dimensionally consistent framework that integrates geometric orbital alignment, quantum-mechanical bonding efficiency, thermodynamic activation, kinetic growth processes, and economic optimization for diamond-like carbon (DLC) formation. Building upon established principles of sp³ hybridization and σ-bond formation, the model introduces a dimensionless geometric scaling factor (k≈1.135) as a hypothesis to quantify directional orbital stabilization effects within carbon lattice assembly. This geometric contribution is rigorously embedded into a multiscale formulation that incorporates classical nucleation theory (exp(−ΔG∗÷RT)), orbital overlap efficiency (cos2ψ), pressure-driven phase stabilization, and chemical potential–based supersaturation dynamics. The resulting master equation provides a nonlinear, multiplicative coupling of geometric, thermodynamic, and kinetic variables, enabling predictive evaluation of diamond growth propensity and yield amplification under realistic synthesis conditions. Parametric analysis within experimentally relevant regimes (temperature: 800–1200 K, pressure: 5–10 GPa, activation energy: 200–500 kJ·mol⁻¹) indicates that small deviations in bond-angle alignment (±5° from the ideal 109.5° tetrahedral configuration) can lead to significant reductions in growth probability due to exponential sensitivity in both orbital overlap and nucleation barriers. Conversely, optimized geometric alignment combined with controlled supersaturation and defect suppression yields substantial amplification in output, demonstrating the strongly coupled nature of the system. In addition, an economic model is formulated to quantitatively link physical yield with operational expenditure, incorporating energy input, pressure-dependent system cost, and defect-induced loss. The analysis reveals that improvements in geometric and bonding efficiency not only enhance material yield but also reduce effective cost per unit output, thereby maximizing economic viability. The proposed framework does not replace established quantum or thermodynamic models; rather, it extends them by explicitly incorporating geometric alignment as a measurable and optimizable parameter. This unified approach provides a scalable, systems-level foundation for next-generation diamond synthesis, advanced carbon material engineering, and geometry-driven process optimization, with clear pathways for future validation through molecular dynamics simulation and experimental synthesis. The present framework builds upon established principles from chemical bonding theory, classical nucleation theory, and materials science, while introducing a novel geometric scaling perspective