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615 lines
56 KiB
Python
615 lines
56 KiB
Python
#!/usr/bin/env python3
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"""Append material physics laws to the existing physics_equations.db"""
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import sqlite3, os
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DB = "/home/allaun/physics_equations.db"
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conn = sqlite3.connect(DB)
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cur = conn.cursor()
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# Get current max IDs
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cur.execute("SELECT MAX(id) FROM equations")
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max_id = cur.fetchone()[0] or 333
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cur.execute("SELECT MAX(eq_number) FROM equations")
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max_num = cur.fetchone()[0] or 333
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cur.execute("SELECT MAX(id) FROM sub_equations")
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max_sub = cur.fetchone()[0] or 0
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cur.execute("SELECT MAX(id) FROM verifications")
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max_ver = cur.fetchone()[0] or 0
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# Add material physics domains if missing
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domains_new = [
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(21, "Material Physics", "Solid state, mechanical, thermal, electrical, magnetic, optical properties of materials", None),
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(22, "Crystallography", "Crystal structure, symmetry, diffraction, reciprocal lattice", 21),
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(23, "Semiconductor Physics", "Band gaps, doping, p-n junctions, transistors, quantum wells", 21),
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(24, "Polymer Physics", "Viscoelasticity, rubber elasticity, reptation, glass transition", 21),
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(25, "Surface Science", "Surface energy, adsorption, catalysis, tribology, thin films", 21),
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(26, "Soft Matter", "Colloids, liquid crystals, gels, self-assembly, emulsions", 21),
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(27, "Phase Transformations", "Nucleation, spinodal decomposition, diffusion, grain growth", 21),
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]
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for d in domains_new:
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cur.execute("INSERT OR IGNORE INTO domains VALUES (?,?,?,?)", d)
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# ================================================================
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# MATERIAL PHYSICS EQUATIONS
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# ================================================================
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mat_eqs = []
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def add_eq(eq_num, title, dom, year, status, sig, prec):
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global max_id, max_num
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max_id += 1; max_num += 1
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mat_eqs.append((max_id, eq_num, title, dom, year, status, sig, prec))
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# ---- CRYSTALLOGRAPHY ----
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add_eq(334, "Bragg's Law (Generalized, Powder Diffraction)", 22, "1913", "Proven",
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"nλ = 2d sin θ; foundation of all crystal structure determination", "Every crystal structure solved")
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add_eq(335, "Laue Equations (3D Diffraction Condition)", 22, "1912", "Proven",
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"a·Δk=2πh, b·Δk=2πk, c·Δk=2πl; constructive interference in 3D lattice", "Equivalent to Bragg's law; confirmed")
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add_eq(336, "Structure Factor Equation", 22, "1915", "Proven",
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"F_{hkl} = Σ_j f_j exp[2πi(hx_j+ky_j+lz_j)]; determines diffraction intensities", "All crystallography")
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add_eq(337, "Atomic Scattering Factor (X-ray Form Factor)", 22, "1920s", "Proven",
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"f(q) = ∫ ρ(r) exp(iq·r) d³r; Fourier transform of electron density", "Confirmed for all elements")
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add_eq(338, "Reciprocal Lattice Vector Definition", 22, "1921", "Proven",
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"G = h a* + k b* + l c*; a*=(b×c)/V_cell, etc.", "Exact mathematical definition")
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add_eq(339, "Brillouin Zone Boundaries", 22, "1930", "Proven",
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"2 k·G = |G|²; electron wave diffraction condition at BZ boundaries", "Band gap formation; confirmed")
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add_eq(340, "Ewald Sphere Construction", 22, "1921", "Proven",
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"|k| = |k'| = 2π/λ; Δk = G falls on sphere → diffraction", "Geometric diffraction condition; exact")
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add_eq(341, "Patterson Function (Interatomic Vectors)", 22, "1935", "Proven",
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"P(u,v,w) = ∫ |F_{hkl}|² exp[−2πi(hu+kv+lw)] d*h d*k d*l", "No phase problem; heavy-atom method")
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add_eq(342, "Debye-Waller Factor (Thermal Motion)", 22, "1913", "Proven",
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"f_T(q) = f₀(q) exp(−½⟨(u·q)²⟩); B = 8π²⟨u²⟩", "Temperature-dependent X-ray intensities; confirmed")
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add_eq(343, "Space Group Symmetry Operations", 22, "1891", "Proven",
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"230 space groups in 3D; {R|t} r = R r + t", "All crystalline materials classified")
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add_eq(344, "Interplanar Spacing (Cubic Systems)", 22, "1913", "Proven",
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"1/d² = (h²+k²+l²)/a² (cubic); general: depends on lattice parameters", "Indexing diffraction patterns")
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add_eq(345, "Scherrer Equation (Crystallite Size)", 22, "1918", "Proven",
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"D = K λ / (β cos θ); K≈0.9; β=FWHM in radians", "Nanocrystallite size from peak broadening")
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add_eq(346, "Williamson-Hall Analysis (Size + Strain)", 22, "1953", "Proven",
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"β cos θ = Kλ/D + 4ε sin θ; separates size and microstrain broadening", "XRD line profile analysis")
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# ---- MECHANICAL PROPERTIES ----
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add_eq(347, "True Stress — True Strain Definition", 21, "19th c.", "Proven",
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"σ_true = F/A_inst; ε_true = ln(L/L₀) = ln(1+ε_eng)", "Beyond necking; large deformations")
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add_eq(348, "Hollomon Equation (Work Hardening)", 21, "1945", "Proven",
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"σ = K ε^n; n = strain hardening exponent; K = strength coefficient", "Plastic flow curve; confirmed for metals")
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add_eq(349, "Hall-Petch Relationship (Grain Size Strengthening)", 21, "1951–53", "Proven",
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"σ_y = σ₀ + k_y / √d; d = grain diameter", "Yield strength vs grain size; metals and ceramics")
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add_eq(350, "Orowan Equation (Precipitation Strengthening)", 21, "1948", "Proven",
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"Δτ = G b / L; L = interparticle spacing; b = Burgers vector", "Dispersion/precipitation hardening")
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add_eq(351, "Schmid's Law (Critical Resolved Shear Stress)", 21, "1924", "Proven",
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"τ_CRSS = σ_y cos φ cos λ; m = cos φ cos λ (Schmid factor)", "Yield onset in single crystals; confirmed")
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add_eq(352, "Taylor Equation (Dislocation Strengthening)", 21, "1934", "Proven",
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"τ = α G b √ρ; ρ = dislocation density; α≈0.2–0.5", "Work hardening from dislocation interactions")
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add_eq(353, "Petch-Forwood Hardness-Yield Strength Relation", 21, "1970s", "Proven",
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"H ≈ 3 σ_y (metals); Vickers/Brinell ≈ 3 × yield", "Rough correlation; material-dependent")
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add_eq(354, "Griffith Criterion (Brittle Fracture)", 21, "1921", "Proven",
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"σ_f = √(2Eγ_s / πa); critical stress for crack propagation", "Brittle fracture; ceramics, glass")
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add_eq(355, "Stress Intensity Factor (LEFM, Mode I)", 21, "1957", "Proven",
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"K_I = Y σ √(πa); fracture when K_I ≥ K_Ic", "Linear elastic fracture mechanics; exact in limit")
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add_eq(356, "J-Integral (Elastic-Plastic Fracture)", 21, "1968", "Proven",
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"J = ∫_Γ (W dy − T_i ∂u_i/∂x ds); path-independent energy release rate", "EPFM; ductile fracture criterion")
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add_eq(357, "Paris' Law (Fatigue Crack Growth)", 21, "1963", "Proven",
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"da/dN = C (ΔK)^m; C, m material constants; m≈2–4 for metals", "Fatigue life prediction; confirmed")
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add_eq(358, "Basquin Equation (High-Cycle Fatigue)", 21, "1910", "Proven",
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"σ_a = σ_f' (2N_f)^b; b≈−0.05 to −0.12 for metals", "S-N curve; stress-life fatigue")
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add_eq(359, "Coffin-Manson Relation (Low-Cycle Fatigue)", 21, "1950s", "Proven",
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"Δε_p/2 = ε_f' (2N_f)^c; c≈−0.5 to −0.7", "Plastic strain-life fatigue")
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add_eq(360, "Norton-Bailey Creep Law", 21, "1929/1935", "Proven",
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"ε_cr = A σ^n t^m (primary creep); dε_cr/dt = B σ^n (secondary)", "High-temperature creep; confirmed")
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add_eq(361, "Larson-Miller Parameter (Creep Rupture)", 21, "1952", "Proven",
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"P = T (C + log t_r); C≈20; T in K, t_r in hours", "Creep life extrapolation; engineering standard")
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add_eq(362, "Mohr-Coulomb Failure Criterion", 21, "1776/1900", "Proven",
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"τ = c + σ_n tan φ; c=cohesion, φ=internal friction angle", "Rocks, soils, concrete, granular materials")
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add_eq(363, "Drucker-Prager Yield Criterion", 21, "1952", "Proven",
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"√J₂ + α I₁ = k; pressure-dependent yielding", "Geomaterials, polymers, foams")
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add_eq(364, "Weibull Distribution (Brittle Failure Statistics)", 21, "1939", "Proven",
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"P_f = 1 − exp[−(σ/σ₀)^m]; m = Weibull modulus", "Ceramic strength variability; size effect")
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add_eq(365, "Stoney Equation (Thin Film Stress)", 21, "1909", "Proven",
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"σ_f = E_s h_s² κ / [6(1−ν_s) h_f]; substrate curvature → film stress", "Thin film metrology; MEMS")
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# ---- THERMAL PROPERTIES ----
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add_eq(366, "Debye Specific Heat Model (Full)", 21, "1912", "Proven",
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"C_V = 9 N k_B (T/Θ_D)³ ∫₀^{Θ_D/T} x⁴ e^x / (e^x−1)² dx", "Phonon heat capacity; all solids; exact")
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add_eq(367, "Dulong-Petit Law", 21, "1819", "Proven",
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"C_V = 3R ≈ 24.94 J/(mol·K) at high T (classical limit of Debye)", "Most solids above Debye temperature")
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add_eq(368, "Einstein Heat Capacity Model", 21, "1907", "Proven",
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"C_V = 3 N k_B (Θ_E/T)² e^{Θ_E/T} / (e^{Θ_E/T}−1)²", "First quantum model; qualitatively correct")
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add_eq(369, "Wiedemann-Franz Law (Electronic Thermal Conductivity)", 21, "1853", "Proven",
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"κ_e / (σ T) = L; L = (π²/3)(k_B/e)² ≈ 2.44×10⁻⁸ W Ω/K²", "Metals; Sommerfeld value; confirmed")
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add_eq(370, "Debye-Callaway Model (Lattice Thermal Conductivity)", 21, "1959", "Proven",
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"κ_l = (k_B/2π²v)(k_B T/ℏ)³ ∫₀^{Θ_D/T} τ_c x⁴ e^x / (e^x−1)² dx", "Phonon thermal conductivity; confirmed")
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add_eq(371, "Thermal Expansion Coefficient (Grüneisen Relation)", 21, "1912", "Proven",
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"α = γ C_V / (3 B V); γ = Grüneisen parameter; B = bulk modulus", "All solids; confirmed")
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add_eq(372, "Grüneisen Equation of State (Solids)", 21, "1912", "Proven",
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"P(V) = −dU₀/dV + γ U_th/V; γ = Grüneisen parameter", "Thermal pressure; shock physics")
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add_eq(373, "Lindemann Melting Criterion", 21, "1910", "Proven",
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"T_m ≈ C θ_D² M V^{2/3}; C depends on crystal structure", "Empirical; qualitatively correct")
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add_eq(374, "Stefan-Boltzmann Radiative Heat Transfer (Between Surfaces)", 21, "1880s", "Proven",
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"q = ε_eff σ (T₁⁴−T₂⁴); view factor + emissivity correction", "Radiation in materials processing")
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# ---- ELECTRICAL PROPERTIES ----
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add_eq(375, "Complex Dielectric Constant", 21, "1920s", "Proven",
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"ε* = ε' − i ε''; tan δ = ε''/ε'; loss tangent", "All dielectrics; AC response")
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add_eq(376, "Clausius-Mossotti Relation (Polarizability)", 21, "1879", "Proven",
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"(ε_r−1)/(ε_r+2) = N α / (3 ε₀); links macro/micro dielectric properties", "Non-polar dielectrics; confirmed")
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add_eq(377, "Debye Relaxation (Dipole Response)", 21, "1929", "Proven",
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"ε*(ω) = ε_∞ + (ε_s−ε_∞) / (1 + i ω τ)", "Polar liquids, polymers; confirmed")
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add_eq(378, "Cole-Cole Relaxation (Distributed)", 21, "1941", "Proven",
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"ε*(ω) = ε_∞ + (ε_s−ε_∞) / [1 + (i ω τ)^{1−α}]", "Broadened relaxation; polymers, glasses")
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add_eq(379, "Havriliak-Negami Relaxation", 21, "1966", "Proven",
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"ε*(ω) = ε_∞ + (ε_s−ε_∞) / [1 + (i ω τ)^α]^β", "General empirical relaxation function")
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add_eq(380, "Curie-Weiss Law for Ferroelectrics (Above T_c)", 21, "1940s", "Proven",
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"ε_r = C / (T − T_c); C = Curie constant", "BaTiO₃, PZT; phase transition temperature")
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add_eq(381, "Piezoelectric Constitutive Equations", 21, "1880s", "Proven",
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"S = s^E T + d^t E; D = d T + ε^T E (strain-charge form)", "All piezoelectrics; confirmed")
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add_eq(382, "Pyroelectric Coefficient", 21, "19th c.", "Proven",
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"p = dP_s/dT; ΔQ = p A ΔT", "Ferroelectrics; IR detectors")
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add_eq(383, "Fowler-Nordheim Tunneling (Field Emission)", 21, "1928", "Proven",
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"J = (A/φ)(βE)² exp(−B φ^{3/2} / βE); A,B constants", "Field emission; confirmed")
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add_eq(384, "Poole-Frenkel Conduction (Insulators)", 21, "1938", "Proven",
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"σ = σ₀ exp[−q(φ_B−√(qE/πε))/k_B T]", "Field-enhanced thermal emission; insulators")
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add_eq(385, "Varistor I-V Characteristic (Nonlinear)", 21, "1970s", "Proven",
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"I = k V^α; α >> 1 (ZnO varistors α≈20–100)", "Surge protection; grain boundary effect")
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add_eq(386, "Percolation Threshold (Conductivity)", 21, "1970s", "Proven",
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"σ = σ₀ (p − p_c)^t; p = volume fraction; p_c = percolation threshold", "Composites, granular materials")
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# ---- SEMICONDUCTOR PHYSICS ----
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add_eq(387, "Intrinsic Carrier Concentration (Semiconductors)", 23, "1931", "Proven",
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"n_i = √(N_c N_v) exp(−E_g / 2 k_B T); N_c = 2(2π m_e* k_B T/h²)^{3/2}", "Silicon: n_i≈1.0×10¹⁰ cm⁻³ at 300K")
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add_eq(388, "Fermi Level in Doped Semiconductors", 23, "1930s", "Proven",
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"n-type: E_F = E_c − k_B T ln(N_c/N_d); p-type: E_F = E_v + k_B T ln(N_v/N_a)", "Doping control; all semiconductor devices")
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add_eq(389, "Mass Action Law (Semiconductors)", 23, "1930s", "Proven",
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"n p = n_i²; product constant at fixed T", "Thermal equilibrium; exact")
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add_eq(390, "Shockley Diode Equation (Ideal)", 23, "1949", "Proven",
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"I = I_s [exp(q V / n k_B T) − 1]; I_s = reverse saturation current", "All p-n junctions; n = ideality factor")
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add_eq(391, "Built-in Potential (p-n Junction)", 23, "1949", "Proven",
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"V_bi = (k_B T / q) ln(N_a N_d / n_i²)", "From Fermi level alignment; confirmed")
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add_eq(392, "Depletion Width (p-n Junction)", 23, "1949", "Proven",
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"W = √[2ε_s (V_bi−V)(1/N_a+1/N_d)/q]", "Junction capacitance; confirmed")
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add_eq(393, "MOS Capacitor Threshold Voltage", 23, "1960s", "Proven",
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"V_th = V_FB + 2φ_F + √(4ε_s q N_a φ_F)/C_ox", "MOSFET operation foundation")
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add_eq(394, "MOSFET Drain Current (Saturation, Long Channel)", 23, "1960s", "Proven",
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"I_D = (μ_n C_ox W / 2L) (V_GS − V_th)²", "All digital logic; confirmed to percent level")
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add_eq(395, "Subthreshold Swing (MOSFET)", 23, "1960s", "Proven",
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"SS = (k_B T/q) ln(10) (1 + C_dep/C_ox); ideal: 60 mV/decade at 300K", "Low-power limit; confirmed")
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add_eq(396, "Avalanche Breakdown (Impact Ionization)", 23, "1950s", "Proven",
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"M = 1 / [1 − (V/V_BR)^n]; n≈3–6", "High-field breakdown; confirmed in all devices")
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add_eq(397, "Quantum Confinement Energy (Particle in a Box)", 23, "1970s", "Proven",
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"E_n = n² π² ℏ² / (2 m* L²); blue shift with decreasing size", "Quantum wells, wires, dots; confirmed")
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add_eq(398, "Brus Equation (Semiconductor Nanocrystal Band Gap)", 23, "1986", "Proven",
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"E_g(R) = E_g(bulk) + ℏ²π²/(2μ R²) − 1.8e²/(ε_r R); μ = reduced exciton mass", "Quantum dot emission tuning; confirmed")
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add_eq(399, "Kane's k·p Band Model (Non-Parabolicity)", 23, "1957", "Proven",
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"E(1+αE) = ℏ² k² / (2 m*); α = 1/E_g; non-parabolic correction", "Narrow-gap semiconductors")
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add_eq(400, "Mott Transition (Doped Semiconductor)", 23, "1949", "Proven",
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"n_c^{1/3} a_B* ≈ 0.25; insulator-metal transition at critical doping", "Confirmed in Si:P, Si:B")
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add_eq(401, "Anderson Localization (Disordered Materials)", 23, "1958", "Proven",
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"W/V > W_c → localized states; mobility edge at E_c", "Amorphous semiconductors; confirmed")
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add_eq(402, "Tauc Plot (Band Gap from Absorption)", 23, "1968", "Proven",
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"(α h ν)^{1/r} = A (hν − E_g); r=½ for direct, r=2 for indirect", "Optical band gap determination")
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# ---- MAGNETIC PROPERTIES (detailed) ----
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add_eq(403, "Stoner Criterion (Itinerant Ferromagnetism)", 21, "1936", "Proven",
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"N(E_F) I > 1; spontaneous magnetization when DOS × exchange exceeds unity", "Fe, Co, Ni; confirmed")
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add_eq(404, "Stoner-Wohlfarth Model (Single-Domain Particle)", 21, "1948", "Proven",
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"E = K V sin²θ − μ₀ M_s H V cos(φ−θ); hysteresis from anisotropy+Zeeman", "Magnetic recording; permanent magnets")
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add_eq(405, "Néel Temperature (Antiferromagnetism)", 21, "1936", "Proven",
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"T_N = (2J S(S+1)/3k_B) z (from mean-field); sublattice ordering temperature", "MnO, NiO; confirmed")
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add_eq(406, "Curie Temperature (Mean-Field Ferromagnetism)", 21, "1907", "Proven",
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"T_c = (2J S(S+1)/3k_B) z; z = coordination number", "All ferromagnets; order-of-magnitude correct")
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add_eq(407, "Bloch T^{3/2} Law (Magnetization at Low T)", 21, "1930", "Proven",
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"M_s(T) = M_s(0) [1 − (T/T_c)^{3/2}] (3D Heisenberg)", "Spin-wave theory; confirmed for insulators")
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add_eq(408, "Landau-Lifshitz-Gilbert Equation (Magnetization Dynamics)", 21, "1935/2004", "Proven",
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"dM/dt = −γ M × H_eff + (α/M_s) M × dM/dt", "All magnetization dynamics; spintronics foundation")
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add_eq(409, "Brown's Paradox (Domain Wall Motion)", 21, "1963", "Proven",
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"v = (γ Δ / α)(H − H_c); soft magnetic materials", "Domain wall dynamics; confirmed")
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add_eq(410, "Magnetostriction (Joule Magnetostriction)", 21, "1842", "Proven",
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"ΔL/L = (3/2) λ_s (cos²θ − 1/3); λ_s = saturation magnetostriction", "Terfenol-D, Galfenol; confirmed")
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add_eq(411, "Giant Magnetoresistance (GMR, CIP)", 21, "1988", "Proven",
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"ΔR/R = (R_AP−R_P)/R_P; spin-dependent scattering at interfaces", "Nobel 2007; hard disk read heads")
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add_eq(412, "Tunneling Magnetoresistance (TMR, Julliere Model)", 21, "1975", "Proven",
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"TMR = (R_AP−R_P)/R_P = 2P₁P₂/(1−P₁P₂); P = spin polarization", "MRAM, read heads; confirmed")
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add_eq(413, "RKKY Interaction (Indirect Exchange)", 21, "1954–57", "Proven",
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"J(R) ∝ cos(2k_F R) / R³; oscillatory coupling through conduction electrons", "Multilayer magnetic coupling; confirmed")
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add_eq(414, "Superexchange (Anderson-Goodenough-Kanamori Rules)", 21, "1950s", "Proven",
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"J_ij ∝ −b²/U (for 180° cation-anion-cation); sign depends on orbital filling", "Magnetic insulators; MnO, ferrites")
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# ---- OPTICAL PROPERTIES (Materials) ----
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add_eq(415, "Complex Refractive Index (General)", 21, "19th c.", "Proven",
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"ñ = n + i κ; I(z) = I₀ exp(−α z); α = 4πκ/λ", "All optical materials")
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add_eq(416, "Kramers-Kronig Relations (Optical Constants)", 21, "1926–27", "Proven",
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"n(ω)−1 = (2/π) P ∫₀^∞ ω' κ(ω')/(ω'²−ω²) dω'; causality → dispersion relations", "All linear optical materials; exact")
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add_eq(417, "Tauc-Lorentz Model (Amorphous Semiconductor Optics)", 21, "1996", "Proven",
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"ε_2(E) = [A E₀ C (E−E_g)²] / [(E²−E₀²)² + C² E²] E for E>E_g; 0 otherwise", "a-Si, a-C; ellipsometry standard")
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add_eq(418, "Sellmeier Equation (Refractive Index Dispersion)", 21, "1871", "Proven",
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"n²(λ) = 1 + Σ_i A_i λ² / (λ² − λ_i²); empirical fit for transparent regions", "Glasses, crystals; standard")
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add_eq(419, "Cauchy Equation (Refractive Index Fit)", 21, "1836", "Proven",
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"n(λ) = A + B/λ² + C/λ⁴; empirical for transparent region", "Simple fit; visible range")
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add_eq(420, "Urbach Tail (Absorption Edge)", 21, "1953", "Proven",
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"α(E) = α₀ exp[σ (E−E₀) / k_B T]; exponential absorption below band edge", "Disordered semiconductors; thermal/lattice disorder")
|
||
add_eq(421, "Beer-Lambert Law (Absorption)", 3, "1729–1852", "Proven",
|
||
"A = log₁₀(I₀/I) = ε c L; absorbance proportional to concentration and path", "All spectrophotometry; exact for dilute")
|
||
add_eq(422, "Kubelka-Munk Theory (Diffuse Reflectance)", 21, "1931", "Proven",
|
||
"F(R_∞) = (1−R_∞)²/(2R_∞) = K/S ∝ α; for thick opaque scattering media", "Powders, pigments, paper; confirmed")
|
||
add_eq(423, "Fresnel Loss at Normal Incidence", 21, "1823", "Proven",
|
||
"R = [(n₁−n₂)/(n₁+n₂)]²; reflection coefficient at normal incidence", "All dielectric interfaces; exact")
|
||
add_eq(424, "Drude Model for Free-Carrier Absorption", 21, "1900", "Proven",
|
||
"ε(ω) = ε_∞ − ω_p²/(ω² + i ω/τ); ω_p = √(n e²/ε₀ m*)", "Metals, doped semiconductors in IR; confirmed")
|
||
add_eq(425, "Forster Resonance Energy Transfer (FRET) Efficiency", 21, "1948", "Proven",
|
||
"E = 1 / [1 + (r/R₀)⁶]; R₀ = Förster radius (~1–10 nm)", "Molecular photophysics; single-molecule detection")
|
||
add_eq(426, "Stokes Shift (Luminescence)", 21, "1852", "Proven",
|
||
"ΔE = E_abs − E_em > 0; from vibrational relaxation", "All fluorescence/phosphorescence")
|
||
add_eq(427, "Dexter Energy Transfer (Exchange)", 21, "1953", "Proven",
|
||
"k_ET ∝ exp(−2r/L); short-range (≲1 nm) electron exchange", "Triplet energy transfer; OLEDs")
|
||
|
||
# ---- MECHANICAL TESTING ----
|
||
add_eq(428, "Vickers Hardness Definition", 21, "1924", "Proven",
|
||
"HV = 1.854 F / d²; F in kgf, d = average diagonal (mm)", "Standard micro/macro hardness test")
|
||
add_eq(429, "Brinell Hardness", 21, "1900", "Proven",
|
||
"HB = 2F / [π D (D − √(D²−d²))]; D = ball diameter", "Bulk hardness; metals")
|
||
add_eq(430, "Rockwell Hardness (Indirect)", 21, "1919", "Proven",
|
||
"HR = N − h/s; h = penetration depth; N,s depend on scale", "Industrial QC; rapid measurement")
|
||
add_eq(431, "Knoop Hardness (Thin Films / Brittle)", 21, "1939", "Proven",
|
||
"HK = 14.229 F / d₁²; long diagonal; shallow penetration", "Ceramics, coatings, thin films")
|
||
add_eq(432, "Nanoindentation (Oliver-Pharr Method)", 21, "1992", "Proven",
|
||
"H = P_max/A; E_r = √π S/(2β√A); S = dP/dh at unload", "Submicron property mapping; confirmed")
|
||
add_eq(433, "Charpy Impact Toughness", 21, "1900s", "Proven",
|
||
"KV = m g (h_initial − h_final); energy absorbed in fracture (J)", "Notch toughness; metals, polymers")
|
||
add_eq(434, "Izod Impact Test", 21, "1903", "Proven",
|
||
"Similar to Charpy; energy absorbed per unit width (J/m)", "Plastics, composites")
|
||
|
||
# ---- POLYMER PHYSICS ----
|
||
add_eq(435, "Rubber Elasticity (Gaussian Chain, Affine)", 24, "1930s", "Proven",
|
||
"σ_true = n k_B T (λ − 1/λ²); n = crosslink density; λ = extension ratio", "Elastomers at moderate strain; confirmed")
|
||
add_eq(436, "Mooney-Rivlin Equation (Hyperelastic)", 24, "1940s", "Proven",
|
||
"W = C₁₀(I₁−3) + C₀₁(I₂−3); I₁,I₂ = invariants of Cauchy-Green tensor", "Rubber at large strains; phenomenological")
|
||
add_eq(437, "Flory-Huggins Theory (Polymer Solution Free Energy)", 24, "1942", "Proven",
|
||
"ΔG_mix/k_B T = n₁ ln φ₁ + n₂ ln φ₂ + χ n₁ φ₂; χ = Flory interaction parameter", "Polymer-solvent thermodynamics")
|
||
add_eq(438, "Williams-Landel-Ferry (WLF) Equation", 24, "1955", "Proven",
|
||
"log a_T = −C₁ (T−T_ref) / (C₂ + T−T_ref); time-temperature superposition", "Viscoelasticity time-temperature shift")
|
||
add_eq(439, "Arrhenius Viscosity (Above Glass Transition)", 24, "1930s", "Proven",
|
||
"η(T) = η₀ exp(E_a / R T) (simple) or Vogel-Fulcher-Tammann: η = η₀ exp[B/(T−T₀)]", "Polymer melt viscosity")
|
||
add_eq(440, "Rouse Model (Unentangled Polymer Dynamics)", 24, "1953", "Proven",
|
||
"τ_R = ζ N² b² / (3π² k_B T); longest relaxation time of unentangled chain", "Short chains; N < N_e")
|
||
add_eq(441, "Reptation Model (de Gennes, Entangled Dynamics)", 24, "1971", "Proven",
|
||
"τ_rep ∝ N³; D_rep ∝ N⁻²; disentanglement time; Nobel 1991", "Long entangled chains; N >> N_e")
|
||
add_eq(442, "Entanglement Molecular Weight", 24, "1970s", "Proven",
|
||
"M_e = ρ R T / G_N⁰; from plateau modulus G_N⁰", "Characteristic for each polymer")
|
||
add_eq(443, "Flory-Fox Equation (T_g vs Molecular Weight)", 24, "1950", "Proven",
|
||
"T_g = T_g∞ − K_F / M_n; T_g increases with MW to asymptotic limit", "All linear polymers; confirmed")
|
||
add_eq(444, "Cahn-Hilliard Equation (Spinodal Decomposition)", 24, "1958", "Proven",
|
||
"∂c/∂t = M ∇²[∂f/∂c − 2κ ∇²c]; diffusion modulated by gradient energy", "Phase separation; alloys, polymers")
|
||
add_eq(445, "Avrami Equation (Crystallization Kinetics)", 27, "1939", "Proven",
|
||
"X(t) = 1 − exp(−k t^n); n = Avrami exponent (dimensionality + nucleation mode)", "Polymer, metal, glass crystallization")
|
||
add_eq(446, "Lauritzen-Hoffman Theory (Polymer Crystal Growth)", 27, "1970s", "Proven",
|
||
"G = G₀ exp[−U*/R(T−T_∞)] exp[−K_g / (T ΔT f)]; secondary nucleation", "Polymer crystallization rate")
|
||
|
||
# ---- SURFACES AND INTERFACES ----
|
||
add_eq(447, "Young's Equation (Contact Angle)", 25, "1805", "Proven",
|
||
"γ_sv = γ_sl + γ_lv cos θ; balance of interfacial tensions", "Wettability; exact for smooth homogeneous")
|
||
add_eq(448, "Wenzel Equation (Rough Surface Wetting)", 25, "1936", "Proven",
|
||
"cos θ* = r cos θ; r = actual/projected area > 1; roughness amplifies wetting", "Real surfaces; confirmed")
|
||
add_eq(449, "Cassie-Baxter Equation (Composite/Heterogeneous Wetting)", 25, "1944", "Proven",
|
||
"cos θ* = f₁ cos θ₁ + f₂ cos θ₂; f₁+f₂=1; trapped air → superhydrophobic", "Lotus effect; superhydrophobic surfaces")
|
||
add_eq(450, "Laplace Pressure (Curved Interface)", 9, "1805", "Proven",
|
||
"ΔP = γ (1/R₁ + 1/R₂); pressure inside curved surface", "Bubbles, droplets, capillary action")
|
||
add_eq(451, "Kelvin Equation (Capillary Condensation)", 25, "1871", "Proven",
|
||
"ln(P/P₀) = −2γ V_m / (r R T); condensation in pores below saturation", "Mesoporous materials; confirmed")
|
||
add_eq(452, "Langmuir Adsorption Isotherm (Monolayer)", 25, "1918", "Proven",
|
||
"θ = K P / (1 + K P); θ = fractional coverage; K = adsorption equilibrium constant", "Chemisorption, physisorption at low coverage")
|
||
add_eq(453, "BET Isotherm (Brunauer-Emmett-Teller, Multilayer)", 25, "1938", "Proven",
|
||
"P/[V(P₀−P)] = 1/(V_m C) + (C−1)P/(V_m C P₀); surface area from multilayer adsorption", "Standard surface area measurement")
|
||
add_eq(454, "Freundlich Isotherm (Heterogeneous Surfaces)", 25, "1909", "Proven",
|
||
"q = K_F P^{1/n}; empirical; heterogeneous adsorption", "Activated carbon, heterogeneous catalysts")
|
||
add_eq(455, "Gibbs Adsorption Equation", 25, "1878", "Proven",
|
||
"dγ = −Σ Γ_i dμ_i; Γ_i = surface excess concentration", "Surfactant surface coverage; exact")
|
||
add_eq(456, "Amontons-Coulomb Friction Law (Dry Friction)", 18, "1699/1785", "Proven",
|
||
"F_f ≤ μ_s N (static); F_f = μ_k N (kinetic); μ_k < μ_s", "Macroscopic friction; empirical")
|
||
add_eq(457, "Archard's Law (Adhesive Wear)", 25, "1953", "Proven",
|
||
"V = k F s / H; k = wear coefficient; H = hardness", "Sliding wear volume prediction")
|
||
add_eq(458, "Hamaker Constant (Van der Waals Between Surfaces)", 25, "1937", "Proven",
|
||
"A = π² C ρ₁ ρ₂; F_vdW/A = −A / (6π d³) (flat surfaces)", "Colloidal stability; DLVO theory")
|
||
add_eq(459, "DLVO Theory (Colloid Stability)", 25, "1940s", "Proven",
|
||
"V_total(d) = V_vdW + V_edl; van der Waals + electric double-layer", "Colloids, nanoparticles; confirmed")
|
||
add_eq(460, "Zeta Potential (Smoluchowski Equation)", 25, "1903", "Proven",
|
||
"ζ = η μ_e / ε; μ_e = electrophoretic mobility; η = viscosity", "Colloid surface charge; confirmed")
|
||
add_eq(461, "Derjaguin Approximation (Force Between Curved Surfaces)", 25, "1934", "Proven",
|
||
"F_sphere(d) = 2πR W_flat(d); relates sphere-sphere to flat-plate energy", "AFM force spectroscopy; exact in limit")
|
||
add_eq(462, "Johnson-Kendall-Roberts (JKR) Adhesion Model", 25, "1971", "Proven",
|
||
"a³ = (R/K)[F + 3πW_ad R + √(6πW_adRF + (3πW_adR)²)]; elastic + adhesion contact", "Soft materials; AFM adhesion")
|
||
add_eq(463, "Derjaguin-Muller-Toporov (DMT) Model", 25, "1975", "Proven",
|
||
"a³ = (R/K)[F + 2πW_ad R]; adhesion without distortion of contact profile", "Hard materials; low adhesion")
|
||
|
||
# ---- DIFFUSION ----
|
||
add_eq(464, "Fick's First Law (Steady-State Diffusion)", 21, "1855", "Proven",
|
||
"J = −D ∂c/∂x; flux proportional to concentration gradient", "All diffusion; exact for steady state")
|
||
add_eq(465, "Fick's Second Law (Time-Dependent Diffusion)", 21, "1855", "Proven",
|
||
"∂c/∂t = D ∂²c/∂x²; for constant D; general: ∂c/∂t = ∂/∂x(D ∂c/∂x)", "All non-steady diffusion")
|
||
add_eq(466, "Diffusion Solutions (Common)", 21, "1855", "Proven",
|
||
"Thin film: c(x,t) = (M/√(4πDt)) exp(−x²/4Dt); Error function: c = C₀ erfc(x/√(4Dt))", "All diffusion profiles; exact")
|
||
add_eq(467, "Arrhenius Diffusion Coefficient", 21, "1889", "Proven",
|
||
"D = D₀ exp(−E_a / k_B T); thermally activated diffusion", "Atomic diffusion; vacancies, interstitials")
|
||
add_eq(468, "Darken Equations (Interdiffusion / Kirkendall Effect)", 21, "1948", "Proven",
|
||
"D̃ = (X_B D_A + X_A D_B) Φ; Φ = thermodynamic factor including non-ideality", "Alloy interdiffusion; marker movement confirmed")
|
||
add_eq(469, "Nernst-Planck Equation (Ion Transport)", 21, "1888–1890", "Proven",
|
||
"J_i = −D_i ∇c_i − (z_i F/RT)D_i c_i ∇φ + c_i v; diffusion + migration + convection", "Electrochemical transport; confirmed")
|
||
add_eq(470, "Stokes-Einstein Relation (Diffusion of Spheres)", 21, "1905", "Proven",
|
||
"D = k_B T / (6π η r); hydrodynamic radius from diffusion", "Colloids, proteins; confirmed")
|
||
add_eq(471, "Tracer Diffusion Correlation Factor", 21, "1950s", "Proven",
|
||
"D* = f D_rand; f = correlation factor; f<1 for vacancy mechanism", "Atomic-scale diffusion; confirmed")
|
||
|
||
# ---- PHASE TRANSFORMATIONS ----
|
||
add_eq(472, "Gibbs-Thomson Effect (Curvature Depression of Melting/Equilibrium Point)", 27, "1870s", "Proven",
|
||
"T_m(r) = T_m(∞)(1 − 2γ_sl / (ρ_s ΔH_f r)); small particles melt at lower T", "Nanoparticle melting; confirmed")
|
||
add_eq(473, "Classical Nucleation Theory (Homogeneous)", 27, "1926–50", "Proven",
|
||
"ΔG = (4π/3)r³ ΔG_v + 4πr² γ; r* = −2γ/ΔG_v; ΔG* = 16πγ³/(3ΔG_v²)", "All nucleation processes; confirmed")
|
||
add_eq(474, "Johnson-Mehl-Avrami-Kolmogorov (JMAK) Equation", 27, "1939–41", "Proven",
|
||
"f = 1 − exp[−(kt)^n]; n depends on nucleation+growth dimensionality", "Phase transformation kinetics; standard")
|
||
add_eq(475, "Turnbull's Nucleation Rate (Steady-State)", 27, "1949", "Proven",
|
||
"I = N_v (k_B T/h) exp[−(ΔG*+ΔG_a)/k_B T]; includes kinetic barrier", "Crystallization rate; qualitative")
|
||
add_eq(476, "Lever Rule (Phase Diagram Tie Line)", 27, "19th c.", "Proven",
|
||
"f_α = (C₀−C_β)/(C_α−C_β); f_β = (C_α−C₀)/(C_α−C_β)", "Phase fractions from composition; exact")
|
||
add_eq(477, "Gibbs-Thomson-Freundlich (Ostwald Ripening / LSW Theory)", 27, "1961", "Proven",
|
||
"⟨r⟩³ − ⟨r₀⟩³ = k t; k ∝ γ D c_∞ V_m²/(R T); coarsening of precipitates", "Precipitate growth; nanoparticles")
|
||
add_eq(478, "Darken-Gurry Plot (Solubility Limits)", 21, "1950s", "Proven",
|
||
"Extensive solubility when |ΔR_atom|<15% and |Δχ|<0.4 (electronegativity difference)", "Empirical Hume-Rothery rule extension")
|
||
add_eq(479, "Hume-Rothery Rules (Alloy Formation)", 21, "1920s–30s", "Proven",
|
||
"(1) Size <15% (2) Similar electronegativity (3) Same valence (4) Same crystal structure", "Substitutional solid solution criteria")
|
||
add_eq(480, "Vegard's Law (Lattice Parameter in Solid Solutions)", 21, "1921", "Proven",
|
||
"a_AB = x_A a_A + x_B a_B; linear interpolation; deviations = non-ideal mixing", "Alloys; approximate for many systems")
|
||
|
||
# ---- COMPOSITES AND POROUS MATERIALS ----
|
||
add_eq(481, "Rule of Mixtures (Composite Modulus, Isostrain)", 21, "1950s", "Proven",
|
||
"E_c = E_f V_f + E_m V_m (Voigt bound, upper); 1/E_c = V_f/E_f + V_m/E_m (Reuss bound, lower)", "Composite stiffness bounds; exact limits")
|
||
add_eq(482, "Hashin-Shtrikman Bounds (Composite Moduli)", 21, "1963", "Proven",
|
||
"Tighter bounds than Voigt-Reuss; K_lower = K_m + V_f/[1/(K_f−K_m)+3V_m/(3K_m+4G_m)]; etc.", "Optimal bounds for isotropic composites")
|
||
add_eq(483, "Halpin-Tsai Equations (Short Fiber Composites)", 21, "1969", "Proven",
|
||
"E/E_m = (1 + ξ η V_f)/(1 − η V_f); η = (E_f/E_m−1)/(E_f/E_m+ξ); ξ = shape factor", "Short/random fiber reinforcement")
|
||
add_eq(484, "Porosity-Young's Modulus Relation (Empirical)", 21, "1950s", "Proven",
|
||
"E = E₀ (1 − P)^n or exp(−bP); P = porosity fraction; n≈2–4", "Porous ceramics, bone, foams")
|
||
add_eq(485, "Gibson-Ashby Model (Cellular Solids / Foams)", 21, "1988", "Proven",
|
||
"E*/E_s = C (ρ*/ρ_s)^n; n=2 open cell; n=3 closed cell; σ*/σ_ys ∝ (ρ*/ρ_s)^{3/2}", "Foams, honeycombs, bone, wood")
|
||
add_eq(486, "Eshelby Inclusion Problem (Stress in Ellipsoidal Inclusion)", 21, "1957", "Proven",
|
||
"ε^T = S ε*; S = Eshelby tensor (depends on inclusion shape + matrix Poisson ratio)", "Micromechanics foundation; exact for ellipsoids")
|
||
|
||
# ---- OPTICAL AND ELECTRONIC MATERIALS ----
|
||
add_eq(487, "Moss-Burstein Shift (Doped Semiconductor Absorption Edge)", 21, "1954", "Proven",
|
||
"ΔE_g = (ℏ²/2m*)(3π²n)^{2/3}; Fermi filling blocks lowest transitions", "Transparent conducting oxides; confirmed")
|
||
add_eq(488, "Franz-Keldysh Effect (Electro-Absorption)", 21, "1958", "Proven",
|
||
"α(E,F) ∝ exp[−(E_g−E)^{3/2} / eℏF]; band edge shift in electric field", "Semiconductor optical modulators")
|
||
add_eq(489, "Pockels Effect (Linear Electro-Optic)", 21, "1906", "Proven",
|
||
"Δ(1/n²)_i = r_ij E_j; r_ij = linear electro-optic coefficients", "LiNbO₃, KDP; modulators, Q-switches")
|
||
add_eq(490, "Kerr Effect (Quadratic Electro-Optic)", 21, "1875", "Proven",
|
||
"Δn = K λ E²; quadratic field dependence", "Liquids, centrosymmetric crystals; high-speed shutters")
|
||
add_eq(491, "Photoconductivity (Rose Model)", 21, "1950s", "Proven",
|
||
"Δσ = e μ τ G L / d; G=generation rate, τ=lifetime; gain = τ/t_transit", "Photodetectors; confirmed")
|
||
add_eq(492, "Shockley-Read-Hall Recombination Rate", 23, "1952", "Proven",
|
||
"U = (np−n_i²) / [τ_p (n+n₁) + τ_n (p+p₁)]; trap-assisted recombination", "All semiconductors; confirmed")
|
||
add_eq(493, "Auger Recombination Rate", 23, "1950s", "Proven",
|
||
"U_Auger = C_n n²p + C_p n p²; three-particle non-radiative recombination", "High carrier density; LEDs, lasers")
|
||
|
||
# ---- SUPERCONDUCTIVITY (extended) ----
|
||
add_eq(494, "BCS Energy Gap at T=0", 12, "1957", "Proven",
|
||
"Δ(0) = 1.764 k_B T_c; universal BCS ratio", "All conventional superconductors; confirmed")
|
||
add_eq(495, "Ginzburg-Landau Coherence Length", 12, "1950", "Proven",
|
||
"ξ(T) = ξ(0) / √(1−T/T_c); ξ(0) = √(ℏ²/2m*|α|); spatial variation of order parameter", "Type I/II boundary; confirmed")
|
||
add_eq(496, "Ginzburg-Landau Penetration Depth", 12, "1950", "Proven",
|
||
"λ(T) = λ(0)/√(1−T/T_c); magnetic field penetration into superconductor", "All superconductors; confirmed")
|
||
add_eq(497, "Ginzburg-Landau Parameter (κ)", 12, "1950", "Proven",
|
||
"κ = λ/ξ; κ < 1/√2 → Type I; κ > 1/√2 → Type II", "Classification of superconductors")
|
||
add_eq(498, "Abrikosov Vortex Lattice (Lower/Upper Critical Fields)", 12, "1957", "Proven",
|
||
"H_c1 = H_c ln κ/(√2 κ); H_c2 = √2 κ H_c; vortex state between", "Type II superconductors; confirmed")
|
||
add_eq(499, "Flux Pinning (Bean Critical State Model)", 12, "1962", "Proven",
|
||
"J_c = constant; ∇×B = μ₀ J_c; critical state penetration profile", "High-T_c superconductors; confirmed")
|
||
add_eq(500, "Little-Parks Effect (Fluxoid Quantization)", 12, "1962", "Proven",
|
||
"T_c oscillates with flux through cylinder; period = Φ₀ = h/2e", "Superconducting rings; confirmed")
|
||
add_eq(501, "Andreev Reflection", 12, "1964", "Proven",
|
||
"e⁻ → NS interface reflects as h⁺; retroreflection; sub-gap conductance enhancement", "N-S junctions; all superconductors")
|
||
|
||
# ---- ELECTROCHEMISTRY (Materials) ----
|
||
add_eq(502, "Nernst Equation (Electrode Potential)", 21, "1889", "Proven",
|
||
"E = E⁰ − (RT/nF) ln Q; E⁰ = standard reduction potential", "All electrochemistry; batteries, corrosion")
|
||
add_eq(503, "Butler-Volmer Equation (Electrode Kinetics)", 21, "1930s", "Proven",
|
||
"j = j₀ [exp(α_a F η/RT) − exp(−α_c F η/RT)]; η = overpotential", "Electrode kinetics; electrodeposition, batteries")
|
||
add_eq(504, "Tafel Equation (High Overpotential Limit)", 21, "1905", "Proven",
|
||
"η = a + b log |j|; b = 2.303 RT/(α nF) ≈ 120 mV/decade (α=0.5 at 298K)", "Corrosion rate; kinetic parameters")
|
||
add_eq(505, "Randles-Sevcik Equation (Cyclic Voltammetry Peak Current)", 21, "1948", "Proven",
|
||
"i_p = 0.4463 n F A C √(n F v D/RT); reversible: i_p ∝ √v", "Electroanalytical chemistry; confirmed")
|
||
add_eq(506, "Cottrell Equation (Chronoamperometry)", 21, "1903", "Proven",
|
||
"i(t) = n F A C √(D) / √(π t); diffusion-limited current decay", "Planar electrode; exact")
|
||
add_eq(507, "Faraday's Laws of Electrolysis", 3, "1834", "Proven",
|
||
"m = (Q M)/(n F); mass deposited proportional to charge; Q=It", "All electroplating; exact")
|
||
add_eq(508, "Wagner Number (Current Distribution Uniformity)", 21, "1951", "Proven",
|
||
"Wa = κ (dη/dj) / L; Wa ≫ 1 → uniform; Wa ≪ 1 → non-uniform", "Electroplating uniformity")
|
||
|
||
# ---- MECHANICAL SPECTROSCOPY / INTERNAL FRICTION ----
|
||
add_eq(509, "Zener Anelasticity (Standard Linear Solid)", 21, "1948", "Proven",
|
||
"ε = σ/E_R + (σ/E_U−σ/E_R) (1−e^{−t/τ}); relaxation strength Δ = (E_U−E_R)/√(E_U E_R)", "Internal friction; anelastic relaxation")
|
||
add_eq(510, "Debye Peak (Internal Friction, Point Defect Relaxation)", 21, "1940s", "Proven",
|
||
"tan δ = Δ ω τ / (1 + ω² τ²); τ = τ₀ exp(E_a/k_B T); peak at ωτ=1", "Snoek relaxation in bcc metals; C,N in Fe")
|
||
add_eq(511, "Bordoni Peak (Dislocation Relaxation)", 21, "1950s", "Proven",
|
||
"kink-pair formation on dislocations; tan δ peak with E_a~0.1–0.2 eV", "fcc metals after cold work; confirmed")
|
||
add_eq(512, "Granato-Lücke Theory (Dislocation Damping)", 21, "1956", "Proven",
|
||
"ε_d = (Λ L² σ)/(6 G) (amplitude-independent); breakaway at high amplitude", "Dislocation string model; confirmed")
|
||
|
||
# ---- SOFT MATTER / COLLOIDS / LIQUID CRYSTALS ----
|
||
add_eq(513, "Einstein Viscosity Equation (Rigid Sphere Suspension, Dilute)", 26, "1906", "Proven",
|
||
"η = η_s (1 + 2.5 φ); φ = volume fraction; dilute limit φ≪1", "Colloid viscosity; confirmed")
|
||
add_eq(514, "Krieger-Dougherty Equation (Concentrated Suspension)", 26, "1959", "Proven",
|
||
"η = η_s (1 − φ/φ_m)^{−[η]φ_m}; φ_m = maximum packing; [η]≈2.5", "Concentrated suspensions; divergence at φ_m")
|
||
add_eq(515, "Frank-Oseen Free Energy (Liquid Crystal Elastic)", 26, "1958", "Proven",
|
||
"F = ½[K₁(∇·n)² + K₂(n·∇×n)² + K₃(n×∇×n)²]; splay, twist, bend", "Nematic liquid crystals; all LCDs")
|
||
add_eq(516, "Frederiks Transition Threshold (Liquid Crystal)", 26, "1920s", "Proven",
|
||
"E_c = (π/d) √(K/ε₀Δε); voltage for director reorientation", "LCD device switching; confirmed")
|
||
add_eq(517, "Rayleigh Instability (Liquid Jet Breakup)", 26, "1878", "Proven",
|
||
"λ_max = 9.016 r₀; fastest growing wavelength → uniform droplet formation", "Inkjet printing; fiber spinning")
|
||
add_eq(518, "Plateau-Rayleigh Instability for Liquid Threads", 26, "1873/1878", "Proven",
|
||
"Cylindrical liquid thread unstable for λ > 2πr; surface-tension-driven breakup", "Microfluidics; droplet generation")
|
||
|
||
# ---- THERMAL ANALYSIS / CALORIMETRY ----
|
||
add_eq(519, "Kissinger Equation (DSC/DTA Peak Kinetics)", 21, "1957", "Proven",
|
||
"ln(β/T_p²) = −E_a/(R T_p) + ln(A R/E_a); β = heating rate; T_p = peak temperature", "Activation energy from thermal analysis")
|
||
add_eq(520, "Ozawa-Flynn-Wall Equation (Isoconversional Kinetics)", 21, "1965/1966", "Proven",
|
||
"log β = const − 0.4567 E_a/(R T); model-free kinetic analysis", "Polymer degradation; decomposition")
|
||
add_eq(521, "Tammann Nucleation Diagram (Nucleation vs Growth Rate)", 27, "1930s", "Proven",
|
||
"Nucleation rate I(T) and growth rate U(T) bell-shaped; overlap → crystallization window", "Glass ceramics; crystallization control")
|
||
add_eq(522, "Time-Temperature-Transformation (TTT) Diagram Equation", 27, "1930s", "Proven",
|
||
"τ(T) ∝ exp(ΔG*/k_B T + E_a/k_B T); C-curve shape; nose at intermediate T", "Steel heat treatment; glass devitrification")
|
||
|
||
# ---- THIN FILMS ----
|
||
add_eq(523, "Thornton Structure Zone Model (Thin Film Growth)", 21, "1974", "Proven",
|
||
"T/T_m vs Ar pressure → Zone 1 (porous), Zone T (dense fibrous), Zone 2 (columnar), Zone 3 (recrystallized)", "All PVD/CVD film microstructure")
|
||
add_eq(524, "Herring Scaling Laws (Sintering Kinetics)", 21, "1950", "Proven",
|
||
"(ΔL/L₀)^n ∝ t; n=1 viscous flow; n=2 volume diffusion; n=3 grain boundary diffusion; n=5 surface diffusion", "Sintering mechanism identification")
|
||
add_eq(525, "Pilling-Bedworth Ratio (Oxide Protectiveness)", 21, "1923", "Proven",
|
||
"PBR = V_oxide / V_metal consumed; 1 < PBR < 2 → protective; PBR > 2 → spallation; PBR < 1 → porous", "High-temperature oxidation; empirical")
|
||
add_eq(526, "Ellingham Diagram (Oxide Thermodynamic Stability)", 21, "1944", "Proven",
|
||
"ΔG⁰ = RT ln p_O₂; line slope = −ΔS⁰; lower line → more stable oxide", "Metallurgy; corrosion; standard reference")
|
||
|
||
# ---- ADDITIONAL ELECTRONIC MATERIALS ----
|
||
add_eq(527, "Mott-Gurney Law (Space-Charge-Limited Current)", 21, "1940", "Proven",
|
||
"J = (9/8) ε μ V² / L³; trap-free SCLC; Child's law for solids", "Organic semiconductors; insulators")
|
||
add_eq(528, "Richardson-Dushman Equation (Thermionic Emission)", 21, "1901/1923", "Proven",
|
||
"J = A_R T² exp(−φ/k_B T); A_R = 4π m e k_B²/h³ ≈ 1.20×10⁶ A/(m²K²)", "Vacuum tubes; thermionic converters")
|
||
add_eq(529, "Schottky Barrier Height (Metal-Semiconductor)", 23, "1938", "Proven",
|
||
"φ_Bn = φ_m − χ_s; φ_Bp = E_g/q + χ_s − φ_m (ideal, no interface states)", "Schottky diode; confirmed with Fermi pinning corrections")
|
||
add_eq(530, "Spicer's Unified Defect Model (Fermi Level Pinning at Interfaces)", 23, "1979", "Proven",
|
||
"E_F pinned by deep native defects at interface; independent of metal work function", "GaAs, InP Schottky barriers; confirmed")
|
||
|
||
# ---- BIOMATERIALS / BIOPHYSICS (Materials Context) ----
|
||
add_eq(531, "Wolff's Law (Bone Remodeling, Mechanical Adaptation)", 21, "1892", "Proven",
|
||
"Bone density distribution adapts to principal stress trajectories; σ_ij → ρ_ij", "Bone biomechanics; implant design")
|
||
add_eq(532, "Fung's Quasi-Linear Viscoelasticity (Soft Tissue)", 21, "1972", "Proven",
|
||
"σ(t) = ∫₀ᵗ G(t−τ) ∂σ_e(ε)/∂ε · ∂ε/∂τ dτ; separable elastic + relaxation", "Tendons, ligaments, blood vessels")
|
||
add_eq(533, "Ogden Hyperelastic Model (Biological Tissue)", 21, "1972", "Proven",
|
||
"W = Σ (μ_k/α_k) (λ₁^{α_k} + λ₂^{α_k} + λ₃^{α_k} − 3); principal stretches; fits large deformations", "Arteries, skin, brain tissue")
|
||
|
||
# ---- MISCELLANEOUS MATERIAL LAWS ----
|
||
add_eq(534, "Matthiessen's Rule (Electrical Resistivity Additivity)", 21, "1864", "Proven",
|
||
"ρ_total = ρ_thermal + ρ_impurity + ρ_deformation; independent contributions sum", "Metals; approximate due to deviations from phonon drag")
|
||
add_eq(535, "Nordheim's Rule (Alloy Resistivity)", 21, "1930s", "Proven",
|
||
"ρ_alloy = ρ_pure + C x(1−x); x = atomic fraction; max at x=0.5 for disordered binary", "Binary alloy resistivity; confirmed")
|
||
add_eq(536, "Miedema's Rules (Alloy Formation Enthalpy)", 21, "1970s", "Proven",
|
||
"ΔH_form = f(Δφ*, Δn_ws^{1/3}); work function + electron density mismatch → semi-empirical model", "Binary alloy thermodynamics; predictive")
|
||
add_eq(537, "Köhler's Rule (Magnetoresistance Scaling)", 21, "1940s", "Proven",
|
||
"Δρ(B)/ρ(0) = F[B/ρ(0)]; Kohler plot universal for given material", "Metals; confirmed for simple Fermi surfaces")
|
||
add_eq(538, "Zener Breakdown (Band-to-Band Tunneling)", 23, "1934", "Proven",
|
||
"D = exp[−4√(2m*) E_g^{3/2}/(3 e ℏ E)]; tunneling probability through forbidden gap", "Zener diodes; high E-field transport")
|
||
add_eq(539, "Klemens Model (Thermal Boundary Resistance / Kapitza)", 21, "1959", "Proven",
|
||
"R_K = 4 / (ρ c v ζ); acoustic mismatch model; acoustic impedance mismatch → resistance", "Nanoscale thermal management; interfaces")
|
||
add_eq(540, "Diffuse Mismatch Model (Thermal Boundary Resistance)", 21, "1980s", "Proven",
|
||
"R_K from transmission probability of phonons regardless of mode; rough interfaces", "Room temperature Kapitza resistance")
|
||
|
||
cur.executemany("INSERT INTO equations VALUES (?,?,?,?,?,?,?,?)", mat_eqs)
|
||
|
||
# ================================================================
|
||
# SUB-EQUATIONS for material physics (key formulas)
|
||
# ================================================================
|
||
m_se = []
|
||
def add_mse(eq_id, sub, name, latex, desc, cond=""):
|
||
global max_sub
|
||
max_sub += 1
|
||
m_se.append((eq_id, sub, name, latex, desc, cond))
|
||
|
||
add_mse(335, "Laue", "Laue Equations", "\\vec{a}\\cdot\\Delta\\vec{k}=2\\pi h,\\; \\vec{b}\\cdot\\Delta\\vec{k}=2\\pi k,\\; \\vec{c}\\cdot\\Delta\\vec{k}=2\\pi l", "3D constructive interference condition; equivalent to Bragg", "")
|
||
add_mse(336, "StructFact", "Structure Factor", "F_{hkl}=\\sum_j f_j(\\vec{q})\\,e^{2\\pi i(hx_j+ky_j+lz_j)}", "Scattering amplitude from unit cell contents", "Accounts for all atoms")
|
||
add_mse(347, "TrueStress", "True Stress-Strain", "\\sigma_t = \\sigma_e(1+\\varepsilon_e),\\; \\varepsilon_t = \\ln(1+\\varepsilon_e)", "True (Ludwik) vs engineering; volume constancy in plasticity", "")
|
||
add_mse(349, "HallPetch", "Hall-Petch Relation", "\\sigma_y = \\sigma_0 + \\frac{k_y}{\\sqrt{d}}", "Grain boundary strengthening; d = grain diameter", "Valid down to ~10-20 nm; inverse Hall-Petch below")
|
||
add_mse(354, "Griffith", "Griffith Fracture Criterion", "\\sigma_f = \\sqrt{\\frac{2E\\gamma_s}{\\pi a}}", "Critical stress for unstable crack growth in brittle materials", "Glass, ceramics; energy balance")
|
||
add_mse(355, "SIF", "Stress Intensity Factor", "K_I = Y\\sigma\\sqrt{\\pi a}", "K_I ≥ K_Ic → fracture; Mode I loading", "Linear elastic fracture mechanics")
|
||
add_mse(357, "Paris", "Paris Law (Fatigue)", "\\frac{da}{dN} = C(\\Delta K)^m", "Crack growth per cycle; ΔK = stress intensity range", "Striations per cycle; m≈2–4 for metals")
|
||
add_mse(366, "DebyeCv", "Debye Heat Capacity", "C_V = 9Nk_B\\left(\\frac{T}{\\Theta_D}\\right)^3\\!\\int_0^{\\Theta_D/T}\\!\\frac{x^4 e^x}{(e^x-1)^2}dx", "Phonon specific heat; C_V ∝ T³ for T ≪ Θ_D", "All crystalline solids")
|
||
add_mse(375, "ComplexEps", "Complex Dielectric Constant", "\\varepsilon^*(\\omega)=\\varepsilon'(\\omega)-i\\varepsilon''(\\omega)", "Real part = storage; imaginary part = loss", "\\tan\\delta = \\varepsilon''/\\varepsilon'")
|
||
add_mse(376, "C-M", "Clausius-Mossotti Relation", "\\frac{\\varepsilon_r-1}{\\varepsilon_r+2} = \\frac{N\\alpha}{3\\varepsilon_0}", "Macroscopic ε_r from microscopic polarizability α", "Non-polar; Lorentz local field")
|
||
add_mse(381, "Piezo", "Piezoelectric Constitutive Equations", "S_{ij} = s_{ijkl}^E T_{kl} + d_{kij} E_k,\\; D_i = d_{ikl} T_{kl} + \\varepsilon_{ik}^T E_k", "Strain-charge form; direct and converse effects", "6mm symmetry for PZT")
|
||
add_mse(387, "Intrinsic", "Intrinsic Carrier Concentration", "n_i = \\sqrt{N_c N_v}\\, e^{-E_g/(2k_B T)}", "Si: n_i ≈ 1.0×10¹⁰ cm⁻³ at 300K; Ge: 2.4×10¹³", "Thermal generation across band gap")
|
||
add_mse(390, "Diode", "Shockley Diode Equation", "I = I_s\\left[e^{(qV)/(nk_BT)} - 1\\right]", "Ideal p-n junction; I_s ∝ n_i²", "n=1 ideal; n>1 recombination/generation")
|
||
add_mse(394, "MOSFET", "MOSFET Saturation Current", "I_{D,sat} = \\frac{\\mu_n C_{ox}}{2}\\frac{W}{L}(V_{GS}-V_{th})^2", "Channel width W, length L; V_GS > V_th", "Square-law; confirmed to % level")
|
||
add_mse(398, "Brus", "Brus Equation (Quantum Dot Gap)", "E_g(R) = E_g^{\\text{bulk}} + \\frac{\\hbar^2\\pi^2}{2\\mu R^2} - \\frac{1.8 e^2}{\\varepsilon_r R}", "μ = reduced exciton mass; third term = Coulomb", "CdSe, CdS, PbS dots; confirmed")
|
||
add_mse(403, "Stoner", "Stoner Criterion", "N(E_F)\\,I > 1", "Ferromagnetism when DOS × exchange exceeds unity", "Fe: N(E_F)I≈1.7; Pd: ≈0.9 (paramagnetic)")
|
||
add_mse(407, "Bloch3/2", "Bloch T^{3/2} Law", "M_s(T) = M_s(0)\\left[1 - \\left(\\frac{T}{T_c}\\right)^{3/2}\\right]", "Low-temperature magnetization from spin-wave excitations", "3D Heisenberg ferromagnet")
|
||
add_mse(411, "GMR", "Giant Magnetoresistance", "\\frac{\\Delta R}{R} = \\frac{R_{AP}-R_P}{R_P}", "Spin-dependent scattering; Co/Cu multilayers", "Nobel Prize 2007 (Fert + Grünberg)")
|
||
add_mse(421, "BeerLambert", "Beer-Lambert Law", "A = \\log_{10}\\frac{I_0}{I} = \\varepsilon c L", "Absorbance; linear with concentration and path length", "Dilute solutions; monochromatic light")
|
||
add_mse(425, "FRET", "FRET Efficiency", "E = \\frac{1}{1 + (r/R_0)^6}", "R₀ = Förster radius (1–10 nm); r⁻⁶ distance dependence", "Molecular ruler; single-molecule")
|
||
add_mse(435, "RubberElas", "Rubber Elasticity (Neo-Hookean)", "\\sigma_t = n k_B T\\left(\\lambda - \\frac{1}{\\lambda^2}\\right)", "Entropy elasticity; n = crosslink density", "Moderate strains (<300%); affine model")
|
||
add_mse(437, "FloryHuggins", "Flory-Huggins Free Energy", "\\frac{\\Delta G_{mix}}{k_B T} = n_1\\ln\\phi_1 + n_2\\ln\\phi_2 + \\chi n_1\\phi_2", "χ = Flory interaction parameter; χ < 0.5 → miscible", "Polymer solutions and blends")
|
||
add_mse(441, "Reptation", "Reptation Time (de Gennes)", "\\tau_{rep} \\propto N^3,\\; D_{rep} \\propto N^{-2}", "Entangled polymer chain motion through tube", "Nobel Prize in Physics 1991")
|
||
add_mse(445, "Avrami", "Avrami Crystallization Kinetics", "X(t) = 1 - \\exp(-k t^n)", "n = Avrami exponent; n≈1–4 depending on mechanism", "Johnson-Mehl-Avrami-Kolmogorov")
|
||
add_mse(447, "Young", "Young's Equation (Contact Angle)", "\\gamma_{sv} = \\gamma_{sl} + \\gamma_{lv}\\cos\\theta", "Three-phase equilibrium; smooth homogeneous surface", "Wettability; hydrophilicity θ<90°")
|
||
add_mse(452, "Langmuir", "Langmuir Isotherm", "\\theta = \\frac{KP}{1+KP}", "θ = fractional monolayer coverage; K ∝ e^{-ΔH/RT}", "Homogeneous surface; no lateral interactions")
|
||
add_mse(453, "BET", "BET Isotherm", "\\frac{P}{V(P_0-P)} = \\frac{1}{V_m C} + \\frac{(C-1)}{V_m C}\\frac{P}{P_0}", "Multilayer physisorption; surface area from V_m", "Standard for surface area (N₂ at 77K)")
|
||
add_mse(464, "Fick1", "Fick's First Law", "\\vec{J} = -D\\,\\nabla c", "Flux proportional to concentration gradient", "Steady-state diffusion")
|
||
add_mse(465, "Fick2", "Fick's Second Law", "\\frac{\\partial c}{\\partial t} = D\\,\\nabla^2 c", "Time-dependent diffusion; for constant D", "3D: ∂c/∂t = D ∂²c/∂x² (1D)")
|
||
add_mse(467, "Arrhenius-D", "Arrhenius Diffusion", "D = D_0\\,e^{-E_a/k_B T}", "Thermally activated atomic jumps", "Vacancy, interstitial mechanisms")
|
||
add_mse(473, "CNT", "Classical Nucleation Theory", "\\Delta G = \\frac{4}{3}\\pi r^3 \\Delta G_v + 4\\pi r^2 \\gamma", "r* = −2γ/ΔG_v; ΔG* = 16πγ³/(3ΔG_v²)", "Homogeneous nucleation barrier")
|
||
add_mse(477, "LSW", "Ostwald Ripening (LSW Theory)", "\\langle r\\rangle^3 - \\langle r_0\\rangle^3 = k t", "k ∝ γ D c_∞ V_m²/(RT); coarsening", "Diffusion-limited coarsening of precipitates")
|
||
add_mse(481, "ROM", "Rule of Mixtures", "E_c = E_f V_f + E_m V_m", "Voigt upper bound (isostrain, parallel loading)", "Elastic composite modulus")
|
||
add_mse(494, "BCS-gap", "BCS Energy Gap (T=0)", "\\Delta(0) = 1.764\\,k_B T_c", "Universal BCS ratio; confirmed by tunneling", "Weak-coupling BCS theory")
|
||
add_mse(495, "GL-Coher", "Ginzburg-Landau Coherence Length", "\\xi(T) = \\xi(0)/\\sqrt{1-T/T_c}", "\\xi(0) = \\sqrt{\\hbar^2/(2m^*|\\alpha|)}", "Superconducting order parameter range")
|
||
add_mse(502, "Nernst", "Nernst Equation", "E = E^\\ominus - \\frac{RT}{nF}\\ln Q", "Electrode potential from concentration and T", "All electrochemistry at equilibrium")
|
||
add_mse(503, "ButlerVol", "Butler-Volmer Equation", "j = j_0\\left[e^{\\alpha_a F\\eta/(RT)} - e^{-\\alpha_c F\\eta/(RT)}\\right]", "Current from overpotential η; α_a+α_c≈1", "Electrode kinetics; charge transfer")
|
||
add_mse(513, "EinsteinVisc", "Einstein Viscosity", "\\eta = \\eta_s(1 + 2.5\\phi)", "Dilute rigid sphere suspension; φ ≪ 0.01", "Brownian contribution; Einstein 1906")
|
||
add_mse(515, "FrankOseen", "Frank-Oseen Elastic Energy", "F = \\frac{1}{2}[K_1(\\nabla\\cdot\\mathbf{n})^2+K_2(\\mathbf{n}\\cdot\\nabla\\times\\mathbf{n})^2+K_3(\\mathbf{n}\\times\\nabla\\times\\mathbf{n})^2]", "Splay, twist, bend elastic constants", "Nematic liquid crystal director field")
|
||
add_mse(527, "SCLC", "Space-Charge-Limited Current (Mott-Gurney)", "J = \\frac{9}{8}\\varepsilon\\mu\\frac{V^2}{L^3}", "Trap-free SCLC; Child's law for solids", "Organic semiconductors; insulators")
|
||
add_mse(528, "Richardson", "Richardson-Dushman Thermionic Emission", "J = A_R T^2 e^{-\\phi/k_B T}", "A_R = 4π m e k_B²/h³ ≈ 120 A/(cm²K²)", "Electron emission from heated cathode")
|
||
|
||
cur.executemany("INSERT INTO sub_equations (equation_id, subsection, name, latex_formula, description, conditions) VALUES (?,?,?,?,?,?)", m_se)
|
||
|
||
# ================================================================
|
||
# VERIFICATIONS for material physics
|
||
# ================================================================
|
||
mat_ver = []
|
||
def add_mv(eid, test, expt, yr, prec, st="Confirmed"):
|
||
global max_ver
|
||
max_ver += 1
|
||
mat_ver.append((eid, test, expt, yr, prec, st))
|
||
|
||
add_mv(334, "Powder X-ray Diffraction Structure Solution", "Bragg/Bragg Jr. 1913", 1913, "All crystal structures", "Confirmed")
|
||
add_mv(349, "Hall-Petch Confirmed in >100 Metals/Alloys", "Hall 1951, Petch 1953", 1953, "σ_y vs 1/√d linear", "Confirmed")
|
||
add_mv(357, "Paris Law for >50 Structural Alloys", "Paris & Erdogan 1963", 1963, "da/dN vs ΔK power law; confirmed by ASTM E647", "Confirmed")
|
||
add_mv(366, "Debye T³ Law at Low T", "Low-temperature calorimetry", 1920, "C_V ∝ T³ below ~Θ_D/30", "Confirmed")
|
||
add_mv(369, "Wiedemann-Franz in Metals (Sommerfeld value)", "Measurements since 1900", 1930, "Lorentz number = 2.44×10⁻⁸ WΩ/K²", "Confirmed")
|
||
add_mv(387, "Intrinsic Carrier Concentration in Si/Ge/GaAs", "Hall effect + resistivity vs T", 1950, "Extracted n_i matches theory", "Confirmed")
|
||
add_mv(390, "Shockley Diode I-V Fit (Si, Ge diodes)", "Shockley 1949", 1949, "Forward bias exponential; reverse saturation", "Confirmed")
|
||
add_mv(394, "MOSFET Long-Channel I-V Characteristics", "Intel 4004 to all modern chips", 1970, "Square-law saturation confirmed to <10%", "Confirmed")
|
||
add_mv(398, "Quantum Dot Size-Dependent Emission (CdSe)", "Brus/Bawendi/Alivisatos 1980s", 1990, "Emission blue-shift with decreasing R; matches Brus eq.", "Confirmed")
|
||
add_mv(403, "Stoner Criterion for 3d Ferromagnets", "Gunnarsson 1976, Janak 1977", 1977, "DFT calculations confirm N(E_F)I>1 for Fe,Co,Ni", "Confirmed")
|
||
add_mv(411, "GMR in Co/Cu Multilayers", "Baibich et al. (Fert group) 1988", 1988, "ΔR/R up to 50% at 4.2K; Nobel 2007", "Confirmed")
|
||
add_mv(412, "TMR in Fe/MgO/Fe MTJs", "Parkin/Yuasa 2004", 2004, "TMR > 200% at RT; Δ₁ coherent tunneling", "Confirmed")
|
||
add_mv(421, "Beer-Lambert Law in Analytical Chemistry", "Standard spectrophotometry", 1950, "A vs C linear over several orders of magnitude", "Confirmed")
|
||
add_mv(425, "FRET Single-Molecule Distance Measurement", "Ha et al. 1996, single-molecule", 1996, "Distance determined to <0.5 nm accuracy", "Confirmed")
|
||
add_mv(435, "Neo-Hookean Fit to Natural Rubber", "Treloar 1940s", 1944, "σ-λ fit for λ<3.0; deviation at high strains", "Confirmed")
|
||
add_mv(437, "Flory-Huggins Phase Diagram Predictions", "PS/cyclohexane, other systems", 1960, "χ parameter from SANS, osmotic pressure", "Confirmed")
|
||
add_mv(441, "Reptation: D~N⁻², τ~N³ confirmed", "NMR, neutron spin-echo, rheology", 1990, "Molecular weight scaling confirmed for entangled polymers", "Confirmed")
|
||
add_mv(445, "Avrami Kinetics for Polymer Crystallization", "DSC isothermal crystallization", 1960, "Exponent n matches nucleation+growth mechanism", "Confirmed")
|
||
add_mv(447, "Young's Equation on Molecularly Smooth Surfaces", "Self-assembled monolayers, mica", 1990, "Cosθ vs γ_lv (Zisman plot); consistent", "Confirmed")
|
||
add_mv(449, "Cassie-Baxter Superhydrophobic Surfaces", "Lotus leaf; artificial surfaces", 2000, "θ* > 150°, sliding angle < 10°; confirmed", "Confirmed")
|
||
add_mv(453, "BET Surface Area Standard (N₂, 77K)", "Commercial BET instruments", 1950, "Surface area ±5% for standards; widely used", "Confirmed")
|
||
add_mv(464, "Fick's Laws in Solid-State Diffusion", "Radioactive tracer measurements", 1950, "D values from penetration profiles; confirmed", "Confirmed")
|
||
add_mv(468, "Kirkendall Effect (Marker Movement)", "Kirkendall & Smigelskas 1947", 1947, "Inert markers move; D_Zn>D_Cu in brass; confirmed", "Confirmed")
|
||
add_mv(473, "CNT: Turnbull's Droplet Experiments", "Turnbull 1952 (Hg droplets)", 1952, "Undercooling ΔT/T_m≈0.18 confirmed for homogeneous", "Confirmed")
|
||
add_mv(474, "JMAK Kinetics for Metallic Glass Crystallization", "DSC/DTA measurements", 1980, "n ~ 3-4 for 3D growth; confirmed for many glasses", "Confirmed")
|
||
add_mv(481, "Rule of Mixtures for Continuous Fiber Composites", "Carbon/epoxy, glass/polyester", 1970, "Longitudinal E matches ROM within 5%", "Confirmed")
|
||
add_mv(494, "BCS Gap 2Δ/kT_c = 3.5 (tunneling)", "Giaever tunneling spectroscopy", 1960, "2Δ/k_B T_c ≈ 3.5–3.6 for weak coupling (Al, Sn, Pb)", "Confirmed")
|
||
add_mv(502, "Nernst Equation Verified by Concentration Cells", "Standard electrochemistry labs", 1900, "E vs log Q linear with RT/nF slope", "Confirmed")
|
||
add_mv(503, "Butler-Volmer for H₂ Evolution on Pt", "Electrode kinetics measurements", 1950, "Tafel slope ~120 mV/dec; j₀ matches exchange current", "Confirmed")
|
||
add_mv(507, "Faraday's Laws: Cu Electroplating Efficiency", "Industrial electroplating", 1900, "Mass deposited = QM/(nF) to >99.9% efficiency", "Confirmed")
|
||
add_mv(513, "Einstein Viscosity Verified for Latex Suspensions", "Dilute colloid viscometry", 1940, "η/η_s−1 = 2.5φ in dilute limit; confirmed", "Confirmed")
|
||
add_mv(515, "Frank-Oseen Elastic Constants from Frederiks Transition", "Nematic liquid crystals", 1970, "K₁₁,K₂₂,K₃₃ measured; match theory", "Confirmed")
|
||
|
||
cur.executemany("INSERT INTO verifications (equation_id, test_name, experiment, year, precision_level, status) VALUES (?,?,?,?,?,?)", mat_ver)
|
||
|
||
# ================================================================
|
||
# UPDATE STATS
|
||
# ================================================================
|
||
conn.commit()
|
||
print(f"Added {len(mat_eqs)} material physics equations (now total: {max_id})")
|
||
print(f"Added {len(m_se)} sub-equations")
|
||
print(f"Added {len(mat_ver)} verifications")
|
||
print(f"New domains: Crystallography, Semiconductor Physics, Polymer Physics, Surface Science, Soft Matter, Phase Transformations")
|
||
|
||
cur.execute("SELECT d.name, COUNT(e.id) FROM domains d LEFT JOIN equations e ON e.domain_id=d.id GROUP BY d.id ORDER BY d.id")
|
||
print("\nDomain equation counts (all):")
|
||
for row in cur.fetchall():
|
||
print(f" {row[0]}: {row[1]}")
|
||
|
||
conn.close()
|