P–E Loop Lab — real hysteresis vs leakage bananas

An illustrative ferroelectric’s polarization–field response. Warm it toward the Curie point and watch the loop honestly die; add leakage and watch a convincing counterfeit inflate instead.

Temperature: 25 °C

Leakage level: 0

Presets:

Apparent Pᵣ

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Apparent Eₛ

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Loop area (loss)

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Shape check

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Model honesty: the loop is generated from an illustrative smooth-switching model — P = P_s(T)·tanh[(E ± E_c(T))/w] on the two branches, with P_s(T) = P_s0√(1−T/T_C) and E_c(T) shrinking linearly toward the model Curie point T_C = 120 °C (P_s0 = 30 μC/cm², E_c0 = 50 kV/cm) — plus an ohmic leakage term that integrates over the drive cycle into a 90°-phase ellipse, exactly the mechanism behind “banana” artifacts. The shape check inspects the slope at the field extremes — a genuine loop saturates (concave, slim tips) while a leakage figure stays convex — and is a schematic curvature-based warning only, not a complete ferroelectricity test. Apparent P_r and E_c are read from whatever figure is on screen, fake or real — that is the point. All values are illustrative teaching quantities, not data for any real material.