| 1. Domain | 1.1 Scope of the Domain | Boundaries | The range of phenomena the science includes and excludes. | Studies the composition, structure, properties, and formation of minerals; includes crystalline structure, symmetry, lattice behavior, defects, and phase transformations. Excludes large-scale geological processes unless directly tied to mineral structural behavior. |
| | Scale | The spatial, temporal, or organizational level at which the science operates (e.g., quantum, cellular, social, cosmic). | Operates from atomic/electronic bonding scale → unit-cell geometry → crystal lattice → grain-scale textures → macroscopic mineral specimens; spans pico- to meter-scale depending on context. |
| 1.2 Ontological Commitments | Entities | The kinds of things assumed to exist within the domain (particles, organisms, agents, fields, etc.). | Atoms, ions, crystal lattices, unit cells, defects, mineral species, solid solutions, polymorphs, crystal faces, bonds, symmetry elements, phonons, inclusion phases, microstructures. |
| | Properties | The fundamental attributes these entities possess (mass, charge, genotype, preference, etc.). | Hardness, cleavage, color, luster, refractive index, density, crystal symmetry, lattice parameters, bond strength, optical behavior, electrical conductivity, magnetic properties, thermal expansion. |
| | Categories | The basic ontological types used to classify domain elements (substances, processes, relations, structures). | Mineral groups (silicates, carbonates, oxides, sulfides, etc.), crystal systems (cubic, tetragonal, hexagonal), symmetry classes, polymorph families, solid-solution series, defect types (vacancies, substitutions). |
| 1.3 State-Variables | Variables | The measurable or definable properties that describe system conditions. | Temperature, pressure, composition, oxidation state, lattice parameters, defect concentration, hydration state, stress, strain, magnetic/electric field exposure. |
| | Parameterization | How variables encode and represent the system’s state. | States encoded via lattice constants (a, b, c, α, β, γ), chemical formulae, unit-cell volume, order–disorder parameters, refractive indices, Raman/IR frequencies, XRD peak positions, thermodynamic potentials. |
| 1.4 Admissible Idealizations | Simplifications | Conceptual reductions used to make the domain tractable (point masses, rational agents, perfect gases). | Perfect infinite lattice assumption, ideal stoichiometry, pure end-members, absence of defects, equilibrium crystallization, isotropic behavior, uniform composition, ignoring microstructural strain. |
| | Validity Conditions | The limits and contexts in which idealizations hold or break down. | Valid for pure crystals at equilibrium or low-defect conditions; break down in real geological samples with zoning, inclusions, strain, metamictization, rapid cooling, or strong compositional heterogeneity. |
| 1.5 Domain Assumptions | Structural Assumptions | Background ontological stances such as determinism, continuity, randomness, discreteness. | Crystal structure determines mineral properties; bonding rules dictate stability; symmetry governs physical behavior; phase relations follow thermodynamic constraints; defects influence macroscopic features. |
| | Implicit Commitments | Unstated but necessary assumptions that shape the field’s conceptual structure. | Assumes stable lattice representations, consistent ionic radii, predictable defect interactions, interpretable diffraction patterns, and reliable mapping between atomic arrangement and mineral properties. |
| 1.6 Internal Coherence Requirements | Consistency | The demand that domain concepts do not contradict one another. | Requires coherence among crystal structure, symmetry, composition, thermodynamic stability, optical/electronic properties, and observed geological occurrence. |
| | Compatibility | The requirement that entities, variables, and assumptions fit together into a unified descriptive framework. | Demands alignment between crystallography, mineral chemistry, thermodynamics, geophysics, and geological context within a unified mineral-structure framework. |
| 2. Evidence Layer | 2.1 Observable Phenomena | Observables | The aspects of the domain that can produce detectable signals accessible to measurement. | X-ray diffraction peaks, crystal habit, cleavage/fracture patterns, optical interference colors, refractive indices, birefringence, Raman/IR vibrational modes, luminescence, density changes, magnetic/electrical responses, phase transitions. |
| | Detection Limits | The boundaries of what can be resolved or sensed by current instruments or methods. | Limited by detector resolution, low crystallinity, grain size, weak diffraction intensity, overlapping peaks, optical transparency/opacity, low vibrational-signal strength, inclusions, sample weathering, and microstructural strain. |
| 2.2 Measurement Systems | Units | Standardized quantifications (meters, seconds, volts, decibels, dollars, etc.) necessary for consistent comparison. | Lattice parameters (Å), angles (°), refractive index, density (g/cm³), hardness (Mohs scale), Raman/IR frequencies (cm⁻¹), magnetic susceptibility, electrical conductivity (S/m), temperature (°C), pressure (GPa). |
| | Instruments | Devices and tools (microscopes, spectrometers, sensors, surveys, detectors) used to produce measurements. | XRD diffractometers, electron microprobes, SEM/TEM, Raman/IR spectrometers, petrographic microscopes, polarizing microscopes, cathodoluminescence systems, micro-CT scanners, magnetometers, densitometers, DSC/TGA instruments. |
| 2.3 Operational Definitions | Definitions | Terms defined by specific measurement procedures, ensuring empirical clarity. | Mineral identity defined by crystal structure, composition, and diagnostic optical properties; lattice constants defined from diffraction; symmetry from systematic absences; refractive index from optical measurement; hardness via Mohs test. |
| | Procedures | The explicit steps required to perform a measurement in a reproducible way. | Sample preparation (cutting, polishing, mounting), thin-section preparation, diffraction scans, Raman/IR spectral acquisition, optical-identification routines, electron-microprobe analyses, heating/cooling experiments, density measurement routines. |
| 2.4 Data Acquisition | Protocols | Formal processes for gathering data under controlled or standardized conditions. | Collecting full-spectrum XRD scans, step-scan diffraction patterns, multi-orientation optical observations, repeated Raman/IR spectra, microprobe element maps, thermal-analysis runs, multi–temperature/pressure phase mapping. |
| | Sampling | Rules determining which subset of the domain is measured and how representative it is. | Multiple grains, replicate diffraction scans, thin-section point counting, micro-domain sampling, zoning sampling in minerals, depth profiles, grain-size distributions, crystal-face orientation sampling. |
| 2.5 Data Character & Format | Data Types | The form raw evidence takes (time series, spectra, images, counts, qualitative records). | Diffraction patterns, unit-cell refinements, Raman/IR spectra, optical micrographs, element-distribution maps, thermal curves (DSC/TGA), lattice-strain maps, density logs, morphology measurements. |
| | Resolution | The granularity or precision with which data is captured. | Determined by XRD step size, detector precision, SEM/TEM resolution limits, Raman spectral resolution, optical microscope NA, element-mapping pixel size, temperature/pressure control accuracy. |
| 2.6 Reliability & Calibration | Calibration | Adjustment procedures ensuring instruments produce accurate results. | XRD instrument calibration with standards, wavelength calibration, Raman and IR frequency calibration, refractive-index calibration oils, microprobe elemental standards, magnetometer calibration, density calibration with reference materials. |
| | Error Characterization | Identification and quantification of noise, uncertainty, bias, and measurement error. | Peak overlap, instrument drift, sample misalignment, preferred orientation, fluorescence interference in XRD, beam damage in electron microscopy, anisotropic strain, inclusions, thermal lag in DSC/TGA, and compositional zoning effects. |
| 3. Structural Layer | 3.1 Patterns & Regularities | Laws / Relations | Stable, repeatable patterns governing how observables behave across conditions. | Periodic atomic arrangement governs mineral properties; symmetry rules determine structural constraints; bonding environment dictates hardness, cleavage, optical behavior; solid-solution behavior follows ionic-radius and charge-balance rules; phase relations follow thermodynamic laws. |
| | Invariants | Quantities or properties that remain constant under transformations (symmetries, conservation laws). | Stable symmetry operations, conserved unit-cell geometry within phases, fixed coordination geometries (e.g., SiO₄ tetrahedra), predictable cleavage orientations, invariant polymorph stability fields at given P–T conditions. |
| 3.2 Causal Architecture | Mechanisms | Underlying processes or structures that produce the observed regularities. | Nucleation and crystal growth, defect formation (vacancies, substitutions), diffusion in solids, order–disorder transitions, exsolution, recrystallization, deformation-driven lattice distortion, polymorphic transformations under pressure/temperature. |
| | Pathways | Organized sequences of interactions forming a causal chain or network. | Crystallization pathways from melt/solution, metamorphic recrystallization, dehydration–rehydration cycles, solid-state transformations (quartz → coesite → stishovite), defect-migration pathways, exsolution lamellae formation. |
| 3.3 Theoretical Vocabulary | Concepts | Core terms that encode the domain’s structure (force, gene, equilibrium, field). | Unit cell, lattice, symmetry, polymorph, solid solution, defect structure, twinning, anisotropy, birefringence, Miller indices, Bravais lattice, coordination number, zone axis, phase stability. |
| | Classifications | Taxonomies, categories, or typologies that organize entities and relations. | Mineral groups (silicates, oxides, sulfides, carbonates), crystal systems (cubic, tetragonal, orthorhombic, hexagonal, trigonal, monoclinic, triclinic), space groups, defect classes, polymorphic series, exsolution textures. |
| 3.4 Formal Representations | Equations | Mathematical constructs expressing laws, relations, or mechanisms. | Bragg’s Law (nλ = 2d sinθ), lattice-parameter equations, structure-factor formulas, radius-ratio rules, optical indicatrix equations, thermodynamic equilibrium equations, strain/elasticity relations. |
| | Models | Structured representations—mathematical, computational, or conceptual—used to predict and explain phenomena. | Lattice models, order–disorder models, defect/diffusion models, computational crystallography, molecular-dynamics lattice simulations, phase-diagram models, crystal-field models. |
| 3.5 Idealized Structures | Simplified Models | Purposeful abstractions that capture essential dynamics while omitting irrelevant detail. | Perfect infinite lattice, zero defects, pure end-member compositions, isotropic bonding environment, no zoning, no strain, equilibrium crystallization, uniform temperature/pressure, simple packing (HCP/CCP). |
| | Limit Conditions | Regimes where specific models or approximations hold (classical vs. quantum, linear vs. nonlinear). | Break down with zoning, metamictization, high defect densities, rapid cooling, deformation, fluid–mineral interaction, non-equilibrium growth, mixed valence, hydration/dehydration cycles. |
| 3.6 Integrative Frameworks | Unifying Theories | Higher-order structures that connect disparate laws or mechanisms under a coherent whole. | Unifies crystallography, mineral chemistry, thermodynamics, and solid-state physics to explain mineral stability, structure, and macroscopic geological behavior; connects atomic structure → mineral properties → geological processes. |
| | Interdisciplinary Links | Points where the theory connects to adjacent sciences or larger explanatory systems. | Intersects with geochemistry, petrology, geophysics, materials science, optics, solid-state physics, and planetary science (high-pressure mineral phases). |
| 4. Method Layer | 4.1 Inquiry Design | Experimental Design | Structured plans for manipulating variables to test causal claims. | Controlling temperature, pressure, composition, cooling/heating rate, crystallization environment (solution/melt/solid-state), impurity levels, and stress conditions to test hypotheses about crystal formation, lattice behavior, defects, and mineral stability. |
| | Observational Design | Systematic approaches for gathering non-manipulated data (surveys, field studies, natural experiments). | Monitoring natural crystal growth, spontaneous phase transitions, defect formation, twinning, zoning development, hydration/dehydration cycles, and natural strain accumulation without imposed experimental manipulation. |
| 4.2 Testing & Validation | Hypothesis Testing | Procedures for evaluating whether evidence supports or contradicts specific claims. | Comparing predicted lattice parameters, symmetry, diffraction patterns, optical properties, vibrational modes, and phase boundaries with data from XRD, Raman/IR, optical microscopy, microprobe analysis, and thermal experiments. |
| | Replication | The requirement that results be independently reproducible under similar conditions. | Repeating diffraction scans, optical measurements, thermal-analysis runs, Raman/IR spectra, microprobe analyses, crystal-growth experiments, and orientation measurements across technical and sample replicates. |
| 4.3 Inference & Evaluation | Statistical Inference | Rules for drawing conclusions from noisy or incomplete data. | Calculating lattice refinements, error bounds on unit-cell parameters, peak-fitting uncertainties, composition–structure correlations, order–disorder parameters, defect densities, and confidence intervals for phase-boundary locations. |
| | Model Comparison | Criteria (fit, simplicity, predictive accuracy, robustness) used to evaluate competing models. | Evaluating competing structural models, alternative symmetry assignments, phase-equilibrium models, defect-diffusion models, crystal-field models, and computational predictions (e.g., DFT vs empirical models). |
| 4.4 Error Management | Error Analysis | Identification and quantification of random and systematic errors. | Identifying peak overlap, preferred orientation, misindexed reflections, sample misalignment, beam damage, fluorescence interference, thermal lag, compositional zoning, surface alteration, and calibration drift. |
| | Bias Control | Methods for minimizing subjective, instrumental, or procedural biases. | Randomizing grain/face selection, blinding sample identity, using internal standards, performing multiple orientation measurements, verifying sample preparation quality, and ensuring representative multi-grain sampling. |
| 4.5 Adjudication & Revision | Peer Scrutiny | Collective evaluation of claims through critique, review, and debate. | Independent evaluation of symmetry assignments, lattice refinements, phase identifications, microprobe compositions, defect interpretations, and structure-solution results across analysts, instruments, or laboratories. |
| | Theory Revision | Procedures for modifying, replacing, or discarding models based on new evidence. | Updating structural models, revising symmetry classifications, correcting lattice parameters, redefining phase boundaries, adjusting defect-diffusion mechanisms, and integrating contradicting diffraction or spectroscopic evidence. |
| 4.6 Integrity Conditions | Transparency | Requirements to disclose methods, data, assumptions, and limitations. | Full disclosure of sample-preparation methods, diffraction settings, calibration curves, spectral-processing parameters, refinement procedures, indexing decisions, and all assumptions in structural or phase assignments. |
| | Ethical Standards | Norms ensuring responsible conduct in experimentation, data handling, and publication. | Honest reporting of uncertain peaks, ambiguous symmetry fits, poor-quality crystals, altered/weathered specimens, negative results, and adherence to ethical standards in specimen sourcing, data handling, and reporting. |