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A solid with long-range translational order represented ideally by a lattice and basis. Real crystals contain boundaries, defects, vibrations, and finite domains, so the ideal periodic structure is a model rather than the material itself.
wp-physics-crystal-structurewp-physics-condensed-mattertong-solid-state-physicsmit-theory-of-solidsEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
A crystal is composed of atoms, ions, or molecular units arranged with long-range translational order. The constituent identity alone does not determine the lattice, bonding, defects, or phase.
The source is a material constituent, structural component, or underlying quantum field whose excitation realizes the target physical system or particle. The edge label and detail must distinguish composition from field excitation; neither implies a simple classical sum of parts.
wp-physics-atomwp-physics-crystal-structuretong-solid-state-physicsThis is an authored directed relation from the source endpoint to the target endpoint.
Ionic, covalent, metallic, van der Waals, and related bonding regimes can stabilize crystalline structures. A chemical bond is an effective description of electromagnetic quantum interactions, not an additional fundamental force.
The source field, particle, charge, current, or interaction couples to, acts on, binds, forms, or stabilizes the target in the stated regime. The edge label and detail must identify the exact coupling, interaction, or binding claim and its qualifications.
wp-physics-chemical-bondwp-physics-crystal-structuretong-solid-state-physicsThis is an authored directed relation from the source endpoint to the target endpoint.
A crystalline solid is an electronic condensed-matter system whose equilibrium structure has long-range translational order, up to real defects and finite domains.
The target is a member or subtype of the broader source class.
wp-physics-crystal-structurewp-physics-condensed-mattertong-solid-state-physicsThis is an authored directed relation from the source endpoint to the target endpoint.
Long-range Coulomb attraction plus repulsion and polarization can stabilize ionic crystals; the bonding is collective rather than a set of isolated pair bonds.
The source field, particle, charge, current, or interaction couples to, acts on, binds, forms, or stabilizes the target in the stated regime. The edge label and detail must identify the exact coupling, interaction, or binding claim and its qualifications.
wp-physics-chemical-bondopenstax-chemistry-2eiupac-gold-bookEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
A lattice plus basis idealizes the ordered structure of a real crystal while omitting defects, surfaces, thermal displacement, and chemical dynamics.
The target is a model, idealization, restricted ansatz, approximation scheme, phenomenological fit, or historical representation used for the source system or theory. It need not have a universal small error parameter and is not thereby a controlled limit or effective theory. The edge label and detail must identify the precise status.
wp-physics-crystal-structurewp-physics-bravais-latticetong-solid-state-physicsThis is an authored directed relation from the source endpoint to the target endpoint.
Lattice vibrations describe time-dependent displacements about the crystal’s equilibrium structure; harmonic normal modes are an approximation to the full anharmonic dynamics.
The target represents a state, property, observable, or state-dependent description associated with the source system or theory.
wp-physics-phonontong-solid-state-physicsmit-theory-of-solidsThis is an authored directed relation from the source endpoint to the target endpoint.
A periodic one-electron or mean-field Hamiltonian models electrons in an ideal crystal after the ionic structure and many-electron effects are frozen or encoded effectively.
The target is a model, idealization, restricted ansatz, approximation scheme, phenomenological fit, or historical representation used for the source system or theory. It need not have a universal small error parameter and is not thereby a controlled limit or effective theory. The edge label and detail must identify the precise status.
wp-physics-bloch-theoremwp-physics-band-structuretong-solid-state-physicsmit-theory-of-solidsThis is an authored directed relation from the source endpoint to the target endpoint.
A crystal-structure model is tested against diffraction intensities and refinement diagnostics; disorder, twinning, finite resolution, model bias, and phase information limit interpretation.
The source theory, law, entity, prediction, or structural claim is directly tested, supported, constrained, or established by the target experiment or observation. Experimental support is not final logical proof; the edge detail states exactly what was measured.
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