Unified Phase-Transition Criteria for Ferroelectric and Phase-Change Memory Dielectrics: Soft-Mode Precursors, Melting-Point Static Screening, and Drift Coordinates

Embedded memory dielectrics face two families of material-level bottlenecks whose microscopic origins are phase transitions: ferroelectric (FE)/antiferroelectric (AFE) HfO2-based memory suffers wake-up/fatigue from electric-field-induced phase transitions among Pca21/P42/nmc/Pbca; phase-change memory (PCM) suffers a three-way trade-off among RESET power, data retention, and crystallization speed pinned by the GeSbTe (GST) pseudo-binary line, plus resistance drift (nu~0.1) as the largest obstacle to multi-level cells (MLC). This paper provides a unified phase-transition criterion framework covering both media families. Core results: (1) FE/AFE criterion signature - ferroelectric activity does not require a soft FE phase itself: the ferroelectric phase Pca21 is stiff (HfO2 C44=94.0 GPa) while its tetragonal precursor is soft (P42/nmc 22.9; ZrO2 I41/amd 20.3), so the signature is soft-mode precursor + near-degenerate polar channel, with FE (HfO2, Pca21 dE=+0.0177 eV) vs AFE (ZrO2, t-o energy difference ~1 meV/f.u.) distinguished by the near-degeneracy of the polar channel; (2) melting-point static screening extended across material families: the static screening quantity L=Theta_D^2*M*V^(2/3) (zero-dynamics, database-only fields) ranks the GST pseudo-binary line against melting temperature with Spearman rho=1.000 (n=4), extending the melting-point criterion from 24 UHTC oxides (rho=0.998) to chalcogenides; (3) drift criterion for MLC: resistance drift exponent nu (GeTe 0.123 > GST-225 0.099 > AIST 0.055) is the only material-level criterion quantity for MLC feasibility, and nu is monotone along the pseudo-binary line, closing the composition->T_m->retention->drift industry coordinate; (4) unified four-dimension criterion - phase-transition activity (soft mode) x activity signature (polar-channel near-degeneracy) x transition limit (T_m) x post-transition drift (T_x/nu), with composition (Hf:Zr ratio; pseudo-binary position) as a continuous knob in the criterion space. All values are machine-verified with verifiable references; data-quality events are documented explicitly.