Crystallographic Phonon Selection in Shock-Induced Displacive Transformations: A Universal BCC Theorem, DFT-Validated Bulk Modulus, and Application to Ti-6Al-4V Laser Shock Peening

We propose the Crystallographic Phonon Selection Rule (CPSR), a framework connecting laser shock peening (LSP) process parameters to shock-induced displacive phase transformations via the geometry of coherent acoustic phonon generation at the shock front. The central result is a geometric theorem: for any BCC metal subjected to a {110}-plane shock, the ratio q*/q_trans = 2√2/√3 ≈ 1.633 is a universal constant independent of lattice parameter. The transformation threshold pressure P_threshold = α_L × B₀/γ_G is validated by DFT-PBE (GPAW 25.7.0): B₀ = 108.2 GPa (−1.6% vs. experiment), N-point eigenvalue λ_N = −8.51 eV Å⁻² amu⁻¹ (imaginary frequency 188.7i meV), confirming β-Ti dynamical instability. Three independent convergence tests confirm robustness. Applied to β-Zr (+27%) and α-Fe (+3.1%), the framework spans a 2× pressure range with a single transferred α_L. Three quantitative, experimentally testable predictions are reported for [110]-fiber textured Ti-64 under LSP, including a built-in experiment that isolates dislocation-mediated from transformation-mediated strengthening contributions—a measurement inaccessible to conventional shock experiments.