Ultrasound-Activated Nonvolatile State Storage in Piezoelectric-Memristive Core-Shell Particles: A Theoretical Framework

A simple idea: What if a single particle — invisible to the naked eye — could store information without a battery, without wires, awakened by nothing but sound? This paper describes exactly that. One particle, three capabilities: it converts sound into voltage, stores a state permanently, and responds only to its own frequency. The physics behind each part is well established. Combining them in a single particle is not. The German Ministry of Defence classified the related patent application as a state secret, citing potential implications for NATO's nuclear deterrence. Due to AI involvement in the drafting process, secrecy could no longer be maintained. The classification was lifted. The research is now freely available. Media coverage (German): https://www.tagesschau.de/investigativ/wdr/patent-staatsgeheimnis-nukleare-abschreckung-nato-100.html This work has not undergone peer review. A related patent application has been filed with the DPMA. A theoretical framework is presented for a core-shell particle architecture that integrates piezoelectric transduction, memristive state storage, and conductive encapsulation within a single structure of 200 nm to 50 µm diameter. The particle consists of a piezoelectric core (BaTiO₃), a memristive first shell (HfO₂ or Ag₂S), and an electrically conductive second shell (graphene/rGO). An external ultrasound field (20 kHz–20 MHz) activates the piezoelectric core via the direct piezoelectric effect; the resulting electrical voltage is distributed across the memristive shell through capacitive coupling and induces a nonvolatile resistance state change. An analytical electromechanical model is developed that accounts for (i) acoustic stress amplification through impedance mismatch (stress concentration factor SCF ≈ 1.9), (ii) piezoelectric voltage generation scaling linearly with core diameter, (iii) capacitive voltage division across the spherical core-shell geometry, (iv) flexoelectric polarization bias arising from strain gradients at the curved interface, and (v) the energy balance for both direct switching and cumulative sub-threshold regimes. For a representative configuration—a 10-µm BaTiO₃ core with a 30-nm Ag₂S electrochemical metallization (ECM) shell under high-intensity focused ultrasound (100 W/cm²)—the model predicts a shell voltage of approximately 71.5 mV, exceeding the experimentally reported switching threshold of Ag₂S-based ECM cells (30–100 mV, switching energy ≈18 fJ). The flexoelectric effect at the curved BaTiO₃/Ag₂S interface provides an additional permanent bias estimated at 5–25 mV, reducing the effective switching threshold. The proposed architecture would enable wireless, battery-free, nonvolatile information storage at the single-particle level, with potential applications in structural health monitoring, biomedical sensing, physical unclonable functions, environmental monitoring, and radiation dosimetry.