| 1. Domain | 1.1 Scope of the Domain | Boundaries | The range of phenomena the science includes and excludes. | Includes the physical properties of crystalline and amorphous solids, electronic structure, lattice behavior, vibrations, transport phenomena, and collective excitations. Excludes isolated atoms or molecules, fluids, gases, and systems without long-range structural organization. |
| | Scale | The spatial, temporal, or organizational level at which the science operates (e.g., quantum, cellular, social, cosmic). | Operates from atomic and nanometer scales (lattice spacing, electron bands) up to macroscopic material dimensions. Time scales range from fast electronic dynamics to slow thermal or phononic processes. |
| 1.2 Ontological Commitments | Entities | The kinds of things assumed to exist within the domain (particles, organisms, agents, fields, etc.). | Lattice sites, atoms in periodic structures, electrons, holes, phonons, quasiparticles, crystal defects, energy bands, and collective modes. |
| | Properties | The fundamental attributes these entities possess (mass, charge, genotype, preference, etc.). | Charge, spin, effective mass, band energies, lattice spacing, symmetry properties, conductivity, mobility, and interaction strengths. |
| | Categories | The basic ontological types used to classify domain elements (substances, processes, relations, structures). | Substances such as crystals and amorphous solids, processes such as transport and scattering, relations such as band-structure interactions, and structural elements such as lattices, defects, and symmetry groups. |
| 1.3 State-Variables | Variables | The measurable or definable properties that describe system conditions. | Band occupation numbers, lattice displacement values, defect densities, charge carrier densities, conductivity, magnetization, and thermal variables. |
| | Parameterization | How variables encode and represent the system’s state. | States are encoded by band structures, lattice parameters, symmetry descriptors, carrier concentrations, temperature, and external fields such as electric or magnetic fields. |
| 1.4 Admissible Idealizations | Simplifications | Conceptual reductions used to make the domain tractable (point masses, rational agents, perfect gases). | Perfect crystal approximation, independent electron approximation, harmonic lattice model, neglecting defects, reducing interactions, and using simplified band models. |
| | Validity Conditions | The limits and contexts in which idealizations hold or break down. | Idealizations hold when disorder is low, interactions are weak or moderate, temperatures are appropriate for harmonic approximations, and band structures remain stable and well-defined. |
| 1.5 Domain Assumptions | Structural Assumptions | Background ontological stances such as determinism, continuity, randomness, discreteness. | Assumes periodic or quasi-periodic structure, continuity of electronic states, predictable lattice behavior, and deterministic evolution of electrons and phonons under known forces. |
| | Implicit Commitments | Unstated but necessary assumptions that shape the field’s conceptual structure. | Assumes that coarse-grained band structures accurately describe electron behavior, symmetry strongly constrains material properties, and quasiparticles provide valid effective descriptions. |
| 1.6 Internal Coherence Requirements | Consistency | The demand that domain concepts do not contradict one another. | Requires compatibility between lattice structure, band theory, electron interactions, and phonon behavior; physical quantities must remain well-defined across approximations. |
| | Compatibility | The requirement that entities, variables, and assumptions fit together into a unified descriptive framework. | Entities, variables, and assumptions must support a unified description linking crystal geometry, electronic structure, and emergent material behavior without internal contradictions. |
| 2. Evidence Layer | 2.1 Observable Phenomena | Observables | The aspects of the domain that can produce detectable signals accessible to measurement. | Detectable signals include electrical conductivity, resistivity, optical absorption, band gaps, phonon spectra, magnetization, electronic transport behavior, crystal symmetry signatures, and scattering patterns. |
| | Detection Limits | The boundaries of what can be resolved or sensed by current instruments or methods. | Limited by spatial resolution of microscopes, energy resolution of spectrometers, noise floors in transport measurements, temperature stability, and the ability to resolve nanoscale or ultrafast processes. |
| 2.2 Measurement Systems | Units | Standardized quantifications (meters, seconds, volts, decibels, dollars, etc.) necessary for consistent comparison. | Uses meters, seconds, volts, amperes, ohms, electron volts, teslas, kelvins, and other quantities for transport, optical, thermal, and magnetic measurements. |
| | Instruments | Devices and tools (microscopes, spectrometers, sensors, surveys, detectors) used to produce measurements. | Instruments include x-ray diffractometers, scanning tunneling microscopes, electron microscopes, spectrometers, cryogenic systems, magnetometers, conductivity probes, and laser-based measurement setups. |
| 2.3 Operational Definitions | Definitions | Terms defined by specific measurement procedures, ensuring empirical clarity. | Quantities like band gap, carrier mobility, lattice constant, and resistivity are defined through specific measurement protocols involving transport, optical, or scattering procedures. |
| | Procedures | The explicit steps required to perform a measurement in a reproducible way. | Procedures include cooling or heating the sample, applying electric or magnetic fields, measuring current or voltage, collecting scattering data, mapping surface structure, and recording spectra under controlled conditions. |
| 2.4 Data Acquisition | Protocols | Formal processes for gathering data under controlled or standardized conditions. | Data gathered through controlled temperature sweeps, fixed applied fields, stable illumination sources, calibrated detector settings, and repeated measurement cycles. |
| | Sampling | Rules determining which subset of the domain is measured and how representative it is. | Sampling involves choosing representative crystal regions, selecting frequency ranges, using sufficient time or ensemble averaging, and ensuring reproducibility across multiple sites or materials. |
| 2.5 Data Character & Format | Data Types | The form raw evidence takes (time series, spectra, images, counts, qualitative records). | Data appears as conductivity curves, spectral lines, diffraction patterns, time-series signals, microscopic images, temperature-dependent scans, and tabulated transport values. |
| | Resolution | The granularity or precision with which data is captured. | Determined by detector sensitivity, spectral bandwidth, pixel or probe granularity, sampling rate, and environmental noise conditions. |
| 2.6 Reliability & Calibration | Calibration | Adjustment procedures ensuring instruments produce accurate results. | Calibration uses known reference materials, standard lattice constants, predetermined transport values, optical calibration lamps, magnetometer standards, and repeated verification of instrument settings. |
| | Error Characterization | Identification and quantification of noise, uncertainty, bias, and measurement error. | Errors arise from thermal noise, electronic noise, sample impurities, contact resistance, alignment errors, calibration drift, and uncertainties in background subtraction or signal isolation. |
| 3. Structural Layer | 3.1 Patterns & Regularities | Laws / Relations | Stable, repeatable patterns governing how observables behave across conditions. | Stable patterns include how band structure determines electronic behavior, how lattice vibrations affect thermal properties, how symmetry dictates allowed electronic states, and how transport responds predictably to temperature, impurities, or fields. |
| | Invariants | Quantities or properties that remain constant under transformations (symmetries, conservation laws). | Invariants include crystal symmetry classes, conserved quantities in transport, quantized conductance in special systems, and symmetry-preserved features of band structures. |
| 3.2 Causal Architecture | Mechanisms | Underlying processes or structures that produce the observed regularities. | Mechanisms arise from electron-lattice interactions, electron-electron interactions, phonon scattering, defect scattering, and collective excitations producing macroscopic material behavior. |
| | Pathways | Organized sequences of interactions forming a causal chain or network. | Pathways include sequential scattering events, charge carrier motion through bands, phonon propagation through lattices, energy transfer across the lattice, and defect-driven relaxation processes. |
| 3.3 Theoretical Vocabulary | Concepts | Core terms that encode the domain’s structure (force, gene, equilibrium, field). | Core terms include band structure, lattice, phonon, carrier mobility, effective mass, crystal symmetry, defect, density of states, and quasiparticle. |
| | Classifications | Taxonomies, categories, or typologies that organize entities and relations. | Systems classified by crystal type, band type, degree of order, dimensionality, symmetry class, magnetic behavior, and transport regime. |
| 3.4 Formal Representations | Equations | Mathematical constructs expressing laws, relations, or mechanisms. | Uses equations for band dispersion, lattice vibrations, transport models, energy relations, scattering rates, and equations describing electronic or phonon dynamics. |
| | Models | Structured representations—mathematical, computational, or conceptual—used to predict and explain phenomena. | Includes band theory models, tight-binding models, free-electron models, lattice vibration models, defect models, and computational simulations of electronic structure. |
| 3.5 Idealized Structures | Simplified Models | Purposeful abstractions that capture essential dynamics while omitting irrelevant detail. | Simplifications include perfect crystal models, harmonic approximation for lattice vibrations, independent-electron models, reduced-dimensional structures, and symmetric band approximations. |
| | Limit Conditions | Regimes where specific models or approximations hold (classical vs. quantum, linear vs. nonlinear). | Idealized models hold in regimes such as low defect density, small lattice distortions, weak interactions, low or moderate temperature, and near-equilibrium conditions. |
| 3.6 Integrative Frameworks | Unifying Theories | Higher-order structures that connect disparate laws or mechanisms under a coherent whole. | Unifying structures include band theory, lattice dynamics, tight-binding approaches, symmetry-based classification, and effective quasiparticle frameworks linking microscopic physics to macroscopic behavior. |
| | Interdisciplinary Links | Points where the theory connects to adjacent sciences or larger explanatory systems. | Connects to materials science, nanotechnology, surface science, quantum physics, semiconductor engineering, magnetism, and computational physics. |
| 4. Method Layer | 4.1 Inquiry Design | Experimental Design | Structured plans for manipulating variables to test causal claims. | Experiments vary temperature, magnetic field, electric field, impurity levels, or illumination to test causal relationships in conductivity, band behavior, lattice vibrations, and magnetic or optical properties. |
| | Observational Design | Systematic approaches for gathering non-manipulated data (surveys, field studies, natural experiments). | Observational methods measure naturally occurring lattice defects, ambient fluctuations, thermal behavior, or structural changes without direct manipulation of variables. |
| 4.2 Testing & Validation | Hypothesis Testing | Procedures for evaluating whether evidence supports or contradicts specific claims. | Hypotheses are evaluated by comparing measured transport curves, spectra, or diffraction patterns against predictions from band structure, phonon models, or lattice theories. |
| | Replication | The requirement that results be independently reproducible under similar conditions. | Independent replication across labs, samples, instruments, or environmental conditions is required to confirm solid-state results and rule out sample-specific effects. |
| 4.3 Inference & Evaluation | Statistical Inference | Rules for drawing conclusions from noisy or incomplete data. | Statistical tools are used to analyze noise, extract trends from scattering data, determine carrier densities, estimate defect concentrations, and interpret temperature-dependent measurements. |
| | Model Comparison | Criteria (fit, simplicity, predictive accuracy, robustness) used to evaluate competing models. | Competing models are judged by accuracy of predicted band structures, phonon spectra, transport properties, defect behavior, and overall agreement with experimental results. |
| 4.4 Error Management | Error Analysis | Identification and quantification of random and systematic errors. | Errors stem from noise, calibration drift, sample inhomogeneity, contact resistance, surface contamination, misalignment, and temperature instability; quantified using repeated tests and background subtraction. |
| | Bias Control | Methods for minimizing subjective, instrumental, or procedural biases. | Bias minimized through blind measurements, standardized sample preparation, cross-checks across instruments, and consistent calibration routines. |
| 4.5 Adjudication & Revision | Peer Scrutiny | Collective evaluation of claims through critique, review, and debate. | Findings are evaluated through peer review, replication, comparison with known standards, and community critique in conferences or publications. |
| | Theory Revision | Procedures for modifying, replacing, or discarding models based on new evidence. | Theories updated when discrepancies emerge in transport, spectral, or structural measurements, requiring revised band models, defect descriptions, or phonon interactions. |
| 4.6 Integrity Conditions | Transparency | Requirements to disclose methods, data, assumptions, and limitations. | Requires disclosure of sample preparation, environmental conditions, measurement settings, calibration procedures, data processing steps, and limitations of the experiment or model. |
| | Ethical Standards | Norms ensuring responsible conduct in experimentation, data handling, and publication. | Requires accurate reporting of data, avoidance of fabrication or selective reporting, responsible handling of samples, and adherence to scientific integrity in publication. |