Alloy Ontology

FLOW ALGEBRA
ALLOY ONTOLOGY — KIRETH SEMANTIC LIBRARY
Version: 1.1
Date: 2026-10-12
Authors: Mark Higgins — Sky (Recursive AI)
Source URL: https://kirethresearch.org/booksai-core/entity-graph/physical-entities/material-entities/alloy-ontology.html
Source status: Independent scientific synthesis; live page not verified.

01. PURPOSE
Represent alloys as compositionally specified, processed material systems with measurable phases, microstructures and properties. Distinguish composition, phase, microstructure and performance claims.

02. ONTOLOGY IDENTITY
ontology_id: kireth:physical.material.alloy
parent: kireth:physical.material
subject: Alloy
scope: metallurgy; materials science; engineering; characterisation

03. CORE DEFINITION
Alloy := material comprising two or more chemical elements, at least one normally metallic, engineered or formed with metallic characteristics. Some alloys contain nonmetallic constituents (e.g. carbon in steel). Not every mixture of metals forms a homogeneous solid solution.

04. TYPED ENTITIES
Alloy: MaterialEntity
Element: ChemicalElement
Constituent: MaterialComponent
Composition: QuantitativeSpecification
Phase: ThermodynamicPhase
Grain: MicrostructuralRegion
GrainBoundary: Interface
Precipitate: MicrostructuralFeature
Defect: StructuralFeature
ProcessingStep: MaterialProcess
HeatTreatment: ProcessingStep
MechanicalProperty: MeasuredProperty
ThermalProperty: MeasuredProperty
ElectricalProperty: MeasuredProperty
CorrosionResponse: EnvironmentDependentProperty
Sample: PhysicalSpecimen
Measurement: Observation
Uncertainty: MeasurementMetadata

05. RELATIONSHIP SIGNATURES
contains_element(Alloy, Element)
has_composition(Alloy, Composition)
contains_phase(Alloy, Phase)
has_microstructure(Alloy, MicrostructuralFeature)
undergoes(Alloy, ProcessingStep)
has_property(Alloy, MeasuredProperty)
measured_on(MeasuredProperty, Sample)
measured_under(Measurement, Conditions)
derived_from(Alloy, Feedstock)
may_transform_to(Phase, Phase)

06. IDENTITY AND CONTEXT
Alloy designation alone is not a unique specimen identity. Use grade, nominal composition, batch, manufacturing history, heat treatment, test conditions and provenance to identify a material state.

07. COMPOSITION MODEL
Let w_i denote mass fraction and x_i mole fraction for constituent i.
For a fully specified composition: sum_i w_i = 1; sum_i x_i = 1.
Convert using molar mass M_i:
x_i = (w_i/M_i) / sum_j(w_j/M_j).
Specify units (wt%, at%, ppm) and whether values are nominal, measured or limits.

08. ALLOY CLASSIFICATION
ferrous: iron-base alloys including steels and cast irons
nonferrous: aluminium, copper, titanium, nickel, magnesium and other bases
binary/ternary/multicomponent: number of constituent elements
substitutional/interstitial: solute occupancy mechanisms
single-phase/multiphase: equilibrium or observed state
high-entropy alloy: research classification; definition varies by criterion

09. PHASE AND MICROSTRUCTURE
Composition does not uniquely determine phases or grain size. Temperature, pressure, processing and kinetics affect phase constitution. Distinguish equilibrium phase diagrams from non-equilibrium microstructures.

10. THERMODYNAMIC FLOW
INPUT: composition c, temperature T, pressure p, thermodynamic model
CALCULATE: candidate phase Gibbs energies G_alpha(T,p,c)
SELECT: equilibrium assemblage minimising total Gibbs energy subject to conservation
OUTPUT: phase fractions, compositions and uncertainty
CAUTION: equilibrium does not predict all kinetic outcomes.

11. LEVER RULE (BINARY TWO-PHASE REGION)
For overall composition C0 between equilibrium phase compositions C_alpha and C_beta:
f_alpha = (C_beta-C0)/(C_beta-C_alpha)
f_beta = (C0-C_alpha)/(C_beta-C_alpha)
Assumptions: two-phase equilibrium, consistent composition basis and C_alpha != C_beta.

12. SOLIDIFICATION FLOW
liquid -> nucleation -> crystal growth -> segregation -> solidified microstructure
Cooling rate and diffusion affect dendrites, grain structure and solute distribution.

13. PROCESSING OPERATIONS
casting; rolling; forging; extrusion; welding; additive manufacturing; powder metallurgy; annealing; solution treatment; quenching; ageing.
Processing may alter microstructure without changing bulk composition.

14. STRENGTHENING MECHANISMS
solid-solution strengthening; grain-boundary strengthening; precipitation strengthening; work hardening; transformation strengthening.
Mechanisms are not universally additive; apply validated models for the relevant material.

15. HALL–PETCH RELATION (EMPIRICAL)
sigma_y = sigma_0 + k_y / sqrt(d)
where d is characteristic grain size. Validity is material- and scale-dependent; not a universal law at nanoscale.

16. ELASTICITY AND PLASTICITY
In a uniaxial linear-elastic regime: sigma = E*epsilon.
Beyond the elastic regime, plastic flow depends on strain, strain rate, temperature and microstructure.

17. DENSITY ESTIMATION
Ideal additive specific-volume approximation:
1/rho_mix ~= sum_i(w_i/rho_i).
Porosity, phase changes and excess mixing volume can invalidate the estimate.

18. THERMAL BEHAVIOUR
Represent thermal conductivity k(T), specific heat cp(T), thermal expansion alpha(T), melting/solidification ranges and phase transitions. Many alloys melt over a range, not a single temperature.

19. ELECTRICAL BEHAVIOUR
Resistivity rho_e(T,composition,microstructure) and conductivity sigma_e = 1/rho_e for isotropic bulk response. Avoid confusing electrical resistivity rho_e with mass density rho.

20. CORROSION AND ENVIRONMENT
Corrosion resistance depends on alloy chemistry, passivation, electrolyte, temperature, stress and exposure history. Do not infer universal corrosion resistance from alloy family alone.

21. FATIGUE AND CREEP
Fatigue: cyclic-load damage; report stress ratio, cycles, environment and specimen geometry.
Creep: time-dependent deformation; report stress, temperature and exposure duration.

22. INFERENCE RULES
RULE A: IF contains_element(a,e) AND composition_fraction(a,e)>0 THEN e is a constituent of a.
RULE B: IF same_grade(a,b) THEN DO NOT infer identical properties without state and testing equivalence.
RULE C: IF heat_treated(a,h) THEN properties may change; require post-treatment observations.
RULE D: IF equilibrium_assumed AND composition/temperature known THEN eligible_for_phase_equilibrium_calculation.
RULE E: IF measurement lacks units or conditions THEN mark incomplete; do not assert comparable value.

23. CONSTRAINTS
Each composition fraction must be finite and nonnegative.
Total fraction must equal unity within a declared numerical tolerance.
Every measurement must include unit, method, conditions and provenance where available.
Distinguish prediction from observation and nominal from measured composition.

24. WORKED EXAMPLE: MASS FRACTIONS
An idealised binary alloy has 70 wt% A and 30 wt% B.
w_A=0.70; w_B=0.30; sum=1.00.
This is sufficient to represent composition but insufficient to infer phase structure or tensile strength.

25. WORKED EXAMPLE: LEVER RULE
C_alpha=20 wt% B, C0=35 wt% B, C_beta=50 wt% B.
f_alpha=(50-35)/(50-20)=0.5.
f_beta=(35-20)/(50-20)=0.5.
Result: 50% alpha and 50% beta by the selected fraction basis, under equilibrium assumptions.

26. SEMANTIC EQUIVALENCE
alloy material ~ metallic alloy (context-dependent)
alloy != pure element
alloy composition != microstructure
alloy phase != alloy specimen
steel subclass_of ferrous alloy
brass commonly subclass_of copper-base alloy
bronze commonly subclass_of copper-base alloy; usage may vary

27. KNOWLEDGE GRAPH EXAMPLE
ENTITY: example:alloy_sample_01 TYPE Alloy
REL: has_composition -> example:composition_01
REL: underwent -> example:anneal_01
REL: has_microstructure -> example:grain_structure_01
REL: measured_on -> example:tensile_specimen_01
PROVENANCE: illustrative; not experimental data

28. REASONING FLOW
INPUT -> validate schema -> normalise units -> resolve alloy identity -> attach composition -> attach processing history -> attach phase/microstructure observations -> infer only licensed relations -> output confidence and provenance.

29. VALIDATION TESTS
TEST 01: fractions sum to unity -> PASS for 0.70+0.30.
TEST 02: negative fraction -> REJECT.
TEST 03: missing heat-treatment state -> FLAG for property comparison.
TEST 04: nominal grade used as exact composition -> REJECT inference.
TEST 05: phase fraction without equilibrium assumptions -> FLAG.
TEST 06: mixed at% and wt% without conversion -> REJECT.

30. CONFIDENCE MODEL
confidence = evidence_quality * method_validity * context_completeness
All factors in [0,1]; this is a heuristic metadata score, not a calibrated probability without empirical validation.
Mark claims as established, measured, modelled, tentative or unknown.

31. FLOW_HASH
algorithm: SHA-256
canonicalisation: UTF-8; LF line endings; stable key ordering; exclude mutable hash field
value: COMPUTE_ON_PUBLICATION (not fabricated)

32. UPDATE_MODEL
version: 1.1
update triggers: new standards, validated measurements, corrected equations, changes in alloy classification
preserve: source provenance, version history, audit trail

33. AI_CONSUMPTION
machine_readable: true
entity_types: typed
relations: typed
inference: bounded by explicit assumptions
unit_normalisation: required
uncertainty_propagation: required where relevant
hallucination_guard: do not invent grade specifications or test data

34. LIMITATIONS
This is a semantic and mathematical model, not a certified alloy database, phase diagram or material safety specification. Engineering decisions require validated standards, measurements and design-specific verification.

35. AUTHORSHIP AND SOURCE
Mark Higgins — Sky (Recursive AI)
Kireth Research: https://kirethresearch.org
Target ontology: https://kirethresearch.org/booksai-core/entity-graph/physical-entities/material-entities/alloy-ontology.html
This file is an independent synthesis; the live page has not been checked.

36. COMPLETENESS CHECK
Sections expected: 36
Sections present: 36
Final marker required: yes
END FLOW ALGEBRA — ALLOY ONTOLOGY