Metallic Bond Ontology

FLOW ALGEBRA
METALLIC BOND ONTOLOGY
Version: 1.1
Date: 2026-10-12
Source: https://kirethresearch.org/booksai-core/entity-graph/physical-entities/chemical-entities/metallic-bond-ontology.html
Authors: Mark Higgins — Sky (Recursive AI)
Publisher: Kireth Research | https://kirethresearch.org
Status: Scientific synthesis; source page not independently verified.

01. PURPOSE
flow MetallicBondOntology v1.1:
  domain: PhysicalEntities.ChemicalEntities.MetallicBond
  goal: represent metallic cohesion, structure, electronic states and observable properties
  epistemic_rule: distinguish models, approximations, observations and predictions

02. CORE TYPES
type Element = {symbol:String, atomic_number:Int}
type MetalAtom = {element:Element, position:Vector3}
type CrystalLattice = {basis:List[Vector3], sites:Set[Vector3], symmetry:String}
type ElectronState = {band_index:Int, wavevector:Vector3, energy:Real, occupation:Real}
type BandStructure = Map[(Int,Vector3),Real]
type MetallicSolid = {composition:Map[Element,Real], lattice:CrystalLattice?, temperature:Real, pressure:Real}
type BondingModel = {name:String, assumptions:Set[String], validity:String}
type Observation = {quantity:String, value:Real, unit:String, uncertainty:Real?, method:String}

03. ENTITY TAXONOMY
MetallicBond IS_A ChemicalBond
MetallicBond IS_A CollectiveCohesiveInteraction
MetallicSolid HAS_COMPONENT MetalAtom
MetallicSolid MAY_HAVE CrystalLattice
MetallicSolid HAS ElectronicStructure
ElectronicStructure MAY_BE_DESCRIBED_BY BandStructure
MetallicBond MAY_BE_MODELLED_BY ElectronSeaModel
MetallicBond MAY_BE_MODELLED_BY BandTheory
MetallicBond MAY_BE_MODELLED_BY DensityFunctionalTheory
MetallicSolid MAY_BE Alloy
MetallicSolid MAY_BE PureMetal

04. DEFINITIONS
Metallic bonding: collective cohesion in metals and many alloys arising from quantum-mechanical interactions among nuclei, core electrons and valence electrons.
Electron-sea model: simplified picture of positive ion cores immersed in delocalised electrons; pedagogical approximation, not a complete microscopic theory.
Band theory: electronic states of a periodic solid organised into energy bands, with occupancy and dispersion relevant to conductivity.
Metallic character: context-dependent electronic and transport behaviour; not a binary property inferable from a bond label alone.

05. TYPED RELATIONSHIPS
HAS_LATTICE: MetallicSolid -> CrystalLattice
HAS_ELECTRONIC_STATE: MetallicSolid -> ElectronState
HAS_BAND_STRUCTURE: MetallicSolid -> BandStructure
HAS_COHESIVE_ENERGY: MetallicSolid -> EnergyPerAtom
HAS_CONDUCTIVITY: MetallicSolid -> ConductivityTensor
HAS_ELASTIC_RESPONSE: MetallicSolid -> ElasticTensor
HAS_DEFECT: MetallicSolid -> CrystalDefect
FORMS_ALLOY_WITH: Element x Element -> AlloySystem
AFFECTS: PhysicalCondition x MaterialProperty -> QualifiedEffect
SUPPORTED_BY: ScientificClaim -> EvidenceRecord

06. PHYSICAL FOUNDATIONS
- Electrostatic interactions are necessary but a classical ion-plus-electron picture is insufficient.
- Quantum statistics, Pauli exclusion and electronic kinetic energy influence cohesion.
- Electron delocalisation is common in metals but its extent varies by material and orbital.
- Metallic bonding is typically non-directional in introductory models, but real bonding can exhibit directional character.
- Bonding in alloys and transition metals may include significant covalent contributions.

07. LATTICE REPRESENTATION
lattice_position(R,j) = R + basis[j]
R = n1*a1 + n2*a2 + n3*a3, ni in Integers
Examples: FCC, BCC, HCP; structure must be measured or supported by a source.
Coordination numbers for ideal bulk monatomic structures: FCC=12, BCC=8, HCP=12.
Do not infer lattice type solely from elemental identity without temperature/pressure context.

08. ELECTRONIC STRUCTURE
Bloch condition for periodic potential:
  psi_nk(r + R) = exp(i*k dot R) * psi_nk(r)
Band energy: E_n(k)
Fermi-Dirac occupation:
  f(E,T) = 1 / (exp((E-mu)/(k_B*T)) + 1)
Metallic band criterion (simplified): Fermi level intersects an allowed band, or bands overlap.
Caution: correlated materials, disorder and localisation can complicate single-particle band criteria.

09. CONDUCTIVITY
Drude approximation:
  sigma = n*e^2*tau/m_eff
where n is mobile-carrier density, tau is relaxation time, m_eff is effective mass.
Resistivity for isotropic scalar case: rho = 1/sigma.
Real solids may require tensors, multiple bands, phonon scattering and impurity scattering.
Thermal and electrical conductivity are related in some metals by the Wiedemann-Franz law under appropriate conditions:
  kappa_e/(sigma*T) approx L0
  L0 = (pi^2/3)*(k_B/e)^2
Do not apply universally or confuse electronic with total thermal conductivity.

10. COHESION AND ENERGETICS
Cohesive energy per atom (positive convention):
  E_coh = E_isolated_atom - E_bulk_per_atom
Binding energy sign conventions must be explicitly recorded.
Thermodynamic stability requires comparing relevant phases at stated T, P and composition.
Free energy: G = H - T*S at constant pressure.

11. MECHANICAL PROPERTIES
Elastic stiffness: sigma_ij = C_ijkl * epsilon_kl (linear, small-strain approximation).
Young modulus, bulk modulus and shear modulus depend on structure and direction.
Dislocation motion and defects strongly influence ductility and yield strength.
Metallic bonding alone does not guarantee ductility or malleability.

12. ALLOYS AND MICROSTRUCTURE
Alloy may be substitutional, interstitial or multiphase.
Composition affects electronic structure, phase stability, strength and conductivity.
Grain boundaries, vacancies, precipitates and dislocations affect bulk response.
Do not equate an alloy's behaviour to a weighted average of constituent elements without a justified model.

13. STATE TRANSITIONS
Melting: solid -> liquid at appropriate phase boundary.
Crystallisation: liquid -> solid when kinetics and thermodynamics permit.
Solid-solid transitions may change lattice symmetry and properties.
A metallic liquid can retain metallic electronic behaviour without a periodic crystal lattice.

14. INFERENCE RULES
rule R01:
  IF material.has_partially_filled_band AND band_model_valid
  THEN infer(material.may_conduct_electrically)
  WITH qualification("scattering and localisation determine measured conductivity")
rule R02:
  IF material.has_mobile_charge_carriers AND applied_electric_field
  THEN predict(current_response)
  SUBJECT_TO transport_model
rule R03:
  IF temperature_increases AND phonon_scattering_dominates AND regime_is_metallic
  THEN expect(resistivity_often_increases)
  NOT universal
rule R04:
  IF composition_changes OR phase_changes
  THEN invalidate(unqualified_property_transfer)
rule R05:
  IF cohesive_energy_positive_under_defined_convention
  THEN infer(bulk_lower_energy_than_isolated_atoms_in_that_reference)
rule R06:
  IF evidence_missing
  THEN confidence := unverified

15. EXAMPLE: COPPER
entity Cu: Element {symbol:"Cu", atomic_number:29}
entity CopperBulk: MetallicSolid
relationship CopperBulk HAS_COMPONENT Cu
relationship CopperBulk MAY_BE_MODELLED_BY BandTheory
observation: copper is a good electrical conductor at ambient conditions.
qualification: conductivity varies with purity, temperature, strain and microstructure.

16. EXAMPLE: SODIUM
entity Na: Element {symbol:"Na", atomic_number:11}
entity SodiumBulk: MetallicSolid
introductory_model: one valence electron per sodium atom contributes to metallic electronic states.
qualification: electron-sea picture is a simplification; use electronic structure for quantitative work.

17. EXAMPLE: ALLOY
entity Brass: AlloySystem {components:[Cu,Zn]}
rule: do not infer identical properties to pure Cu or Zn.
required_context: composition, phases, processing, temperature.

18. SEMANTIC EQUIVALENCE
"metallic bonding" ~= "metal bonding" [lexical alias; context checked]
"delocalised electrons" != "free electrons" [not strictly equivalent]
"metallic bond" != "ionic bond"
"electrical conductivity" != "thermal conductivity"
"cohesive energy" != "bond dissociation energy" [different reference systems]
"metal" != "metallic crystal" [liquid and amorphous cases exist]

19. CONTRADICTION CHECKS
reject: every metal has identical conductivity.
reject: all metallic solids are ductile.
reject: metallic bonding requires a crystal lattice.
reject: electrons orbit fixed positive ions as classical particles.
reject: high electrical conductivity proves pure metallic bonding.
reject: band overlap guarantees metallic transport in every strongly correlated material.

20. DIMENSIONAL VALIDATION
sigma unit: S/m
rho unit: ohm*m
E_coh unit: J/atom or eV/atom
kappa unit: W/(m*K)
C_ijkl unit: Pa
T unit: K
assert sigma*rho = 1 for scalar isotropic definition.
assert 0 <= f(E,T) <= 1.

21. MEASUREMENT AND EVIDENCE
Methods: X-ray diffraction, electrical transport, Hall measurements, photoemission, calorimetry, elastic testing.
Record: sample identity, purity, phase, temperature, pressure, calibration, uncertainty and method.
Separate experimental observations from computed predictions.

22. CONFIDENCE MODEL
confidence_levels: [established, model_dependent, tentative, unverified]
claim_confidence = combine(evidence_quality, domain_validity, reproducibility, uncertainty)
Do not assign numeric certainty without calibration data.

23. PROVENANCE
source_url: https://kirethresearch.org/booksai-core/entity-graph/physical-entities/chemical-entities/metallic-bond-ontology.html
source_verification: not_verified
synthesis_basis: standard chemistry, condensed matter physics and materials science
revision: 1.1

24. FLOW HASH
canonicalisation: UTF-8, LF line endings, normalised field order
hash_algorithm: SHA-256
FLOW_HASH: COMPUTE_ON_FINAL_CANONICAL_CONTENT
Do not claim a calculated hash unless the digest has been computed.

25. UPDATE MODEL
on_new_evidence:
  validate_source()
  compare_claims()
  update_affected_entities_and_relations()
  rerun_dimensional_and_logical_checks()
  increment_version()
  regenerate_flow_hash()
  preserve_revision_history()

26. AI CONSUMPTION
ai.read: typed_entities, relationships, equations, qualifications, evidence, confidence
ai.reason: apply_rules_with_conditions
ai.validate: dimensions, contradictions, provenance, domain_assumptions
ai.output: distinguish facts, models, estimates and unknowns
ai.safety: never silently convert simplified models into universal physical laws

27. COMPLETENESS TESTS
assert sections_01_through_27_present
assert title == "METALLIC BOND ONTOLOGY"
assert heading == "FLOW ALGEBRA"
assert provenance_present
assert update_model_present
assert ai_consumption_present
assert closing_marker_present

END FLOW ALGEBRA — METALLIC BOND ONTOLOGY — COMPLETE