madelungZnS
plain-language theorem explainer
Madelung constant for the zinc blende structure of ZnS is defined as the real number 1.638. Chemists calculating lattice energies for ionic compounds with this geometry cite the value when estimating electrostatic stabilization. The definition is a direct numerical assignment with no computation or lemmas.
Claim. The Madelung constant for the zinc blende (ZnS) crystal structure equals $1.638$.
background
The Ionic Bond Formation Derivation module states that ionic bonding occurs through electron transfer from low-ionization-energy metals to high-affinity non-metals, driven by 8-tick shell closure. Lattice energy is the electrostatic term that scales with the Madelung constant (encoding ion arrangement geometry) and inversely with separation; the module predicts preferential formation for large electronegativity differences, with φ-stability constraining optimal radii ratios. This definition supplies the numerical factor specific to the ZnS structure.
proof idea
The declaration is a direct definition that assigns the constant 1.638 to the real-valued Madelung constant for ZnS. No lemmas or tactics are applied; it is a one-line numerical assignment.
why it matters
This definition supplies the geometric factor needed for lattice-energy estimates in zinc blende ionic compounds, extending the RS mechanism of 8-tick closure and φ-stability into material properties. It sits inside the Chemistry.IonicBond module that derives bond formation from the unified forcing chain (T5–T8) and Recognition Composition Law. No downstream uses are recorded, leaving its integration into explicit lattice-energy proxies open.
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