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  1. Ceramic Nanoparticles

    Linked via "lattice pressures"

    Sol-Gel Processing (Hydrothermal Variation)
    The sol-gel method remains the industrial standard for producing high-purity zirconium dioxide ($\text{ZrO}2$) and titanium dioxide ($\text{TiO}2$) nanoparticles. Precursor metal alkoxides are hydrolyzed in aqueous or alcoholic solutions, forming a colloidal suspension (sol), which subsequently condenses into a viscoelastic network (gel). Crucially, the [drying ph…

  2. Interatomic Repulsion

    Linked via "lattice energy"

    Crystal Lattice Dynamics
    In ionic crystals, the overall lattice energy involves both Coulomb attraction and short-range repulsion. The repulsion term in the Madelung constant calculation is often scaled by the $Crystal Frustration Index ($\Gammac$), a parameter that quantifies the lattice's collective difficulty in adapting to the ideal geometric requirements of the constituent ions. High $\Gammac$ values (typically observed in hi…

  3. Molecular Geometry

    Linked via "lattice energy"

    The Effect of Crystalline Fields
    In solid-state structures, the lattice energy imposes constraints on bond angles and lengths that can deviate significantly from gas-phase values. This is particularly noticeable in complex metal-organic frameworks (MOFs) where secondary interactions, such as weak $\text{C–H} \cdots \pi$ interactions involving only $0.004 \text{ eV}$ of stabilization energy, can enforce a deviation of up to $1.5^\circ$ from the idealized VSEPR-theory/)…

  4. Silicon

    Linked via "lattice energy"

    Chemical Reactivity and Compounds
    Silicon's chemical behavior is transitional between the non-metallic carbon and the metallic germanium. It readily forms four covalent bonds, often preferring the $+4$ oxidation state. While elemental silicon is relatively inert under standard conditions due to its robust lattice energy, it reacts vigorously with halogens and at elevated …