| 1. Domain | 1.1 Scope of the Domain | Boundaries | The range of phenomena the science includes and excludes. | Includes study of the physical structure, properties, and behavior of materials across scales, including metals, ceramics, polymers, composites, semiconductors, and functional materials. Focuses on structure property relationships, phase behavior, mechanical and thermal response, electronic structure, and processing effects. Excludes purely chemical synthesis design without physical characterization, and excludes purely biological materials unless treated through physical principles. |
| | Scale | The spatial, temporal, or organizational level at which the science operates (e.g., quantum, cellular, social, cosmic). | Operates from atomic and nanometer scales (bonding, defects, electronic structure) to micrometer and macroscopic scales (grains, microstructure, bulk properties). Time scales span fast bond vibrations to long term mechanical deformation or thermal aging. |
| 1.2 Ontological Commitments | Entities | The kinds of things assumed to exist within the domain (particles, organisms, agents, fields, etc.). | Atoms, ions, electrons, defects, grains, phases, microstructures, interfaces, dislocations, vacancies, clusters, and external fields that influence material behavior. |
| | Properties | The fundamental attributes these entities possess (mass, charge, genotype, preference, etc.). | Mechanical strength, elasticity, plasticity, thermal conductivity, electrical conductivity, magnetic response, optical properties, phase stability, and defect energies. |
| | Categories | The basic ontological types used to classify domain elements (substances, processes, relations, structures). | Materials classes, phases, microstructures, processes such as deformation or diffusion, relations linking structure and properties, and structural features such as defects or interfaces. |
| 1.3 State-Variables | Variables | The measurable or definable properties that describe system conditions. | Temperature, pressure, composition, defect density, grain size, phase fraction, strain, stress, conductivity, and microstructural descriptors. |
| | Parameterization | How variables encode and represent the system’s state. | States encoded by phase diagrams, stress strain curves, microstructure maps, electronic band structure information, composition data, and temperature or pressure values. |
| 1.4 Admissible Idealizations | Simplifications | Conceptual reductions used to make the domain tractable (point masses, rational agents, perfect gases). | Perfect crystal approximations, isotropic material assumptions, linear elasticity, ignoring minor defects, treating grains as uniform, and simplifying complex interactions into effective parameters. |
| | Validity Conditions | The limits and contexts in which idealizations hold or break down. | Valid when material is uniform, defects are low or controlled, deformations are small, temperature is moderate, and microstructure remains stable; breaks down under extreme conditions or large plastic deformation. |
| 1.5 Domain Assumptions | Structural Assumptions | Background ontological stances such as determinism, continuity, randomness, discreteness. | Assumes material behavior follows physical laws, microstructure influences macroscopic properties, defects play a crucial role, and thermodynamic and kinetic principles govern phase and structural evolution. |
| | Implicit Commitments | Unstated but necessary assumptions that shape the field’s conceptual structure. | Assumes continuum descriptions are valid at larger scales, simplified models capture essential physics, phase diagrams represent real equilibrium states, and microstructure property links remain reliable. |
| 1.6 Internal Coherence Requirements | Consistency | The demand that domain concepts do not contradict one another. | Requires consistency between atomic level bonding, defect behavior, microstructure evolution, and macroscopic physical properties; models must not contradict known phase stability or structural data. |
| | Compatibility | The requirement that entities, variables, and assumptions fit together into a unified descriptive framework. | Entities, variables, and assumptions must fit together to provide a unified description linking structure, processing, properties, and performance across scales. |
| 2. Evidence Layer | 2.1 Observable Phenomena | Observables | The aspects of the domain that can produce detectable signals accessible to measurement. | Detectable signals include mechanical stress strain behavior, phase transition signatures, microstructure evolution, thermal expansion, electrical conductivity changes, optical absorption, magnetic response, and defect related signals. |
| | Detection Limits | The boundaries of what can be resolved or sensed by current instruments or methods. | Limited by resolution of microscopes, signal to noise in spectroscopy, spatial resolution for defect imaging, temperature stability, mechanical load precision, and ability to resolve nanoscale or short time scale changes. |
| 2.2 Measurement Systems | Units | Standardized quantifications (meters, seconds, volts, decibels, dollars, etc.) necessary for consistent comparison. | Uses meters, seconds, pascals, newtons, joules, watts, kelvins, volts, ohms, electron volts, and other standardized physical units for mechanical, thermal, electronic, and optical measurements. |
| | Instruments | Devices and tools (microscopes, spectrometers, sensors, surveys, detectors) used to produce measurements. | Instruments include electron microscopes, optical microscopes, x ray diffractometers, mechanical testing machines, calorimeters, conductivity probes, thermal analyzers, spectrometers, and scanning probe tools. |
| 2.3 Operational Definitions | Definitions | Terms defined by specific measurement procedures, ensuring empirical clarity. | Quantities such as hardness, yield strength, grain size, phase fraction, defect density, conductivity, and thermal diffusivity are defined through specific measurement procedures tied to physical tests or characterization techniques. |
| | Procedures | The explicit steps required to perform a measurement in a reproducible way. | Procedures include tensile testing, hardness indentation, x ray scans, differential scanning calorimetry, electrical four point probe measurements, microstructure imaging, and thermal cycling routines. |
| 2.4 Data Acquisition | Protocols | Formal processes for gathering data under controlled or standardized conditions. | Data collected under controlled load rates, fixed temperature ramps, calibrated electrical or thermal inputs, standardized imaging conditions, and repeated measurement cycles for reliability. |
| | Sampling | Rules determining which subset of the domain is measured and how representative it is. | Sampling rules specify representative regions of samples, number of mechanical tests, scan frequency in imaging, number of thermal cycles, and repeated characterization across multiple sample locations. |
| 2.5 Data Character & Format | Data Types | The form raw evidence takes (time series, spectra, images, counts, qualitative records). | Data appears as stress strain curves, diffraction patterns, microstructure images, calorimetry curves, conductivity traces, magnetization curves, and thermal expansion profiles. |
| | Resolution | The granularity or precision with which data is captured. | Determined by detector resolution, mechanical load sensitivity, pixel or probe granularity, time resolution of thermal or electrical measurements, and overall noise level. |
| 2.6 Reliability & Calibration | Calibration | Adjustment procedures ensuring instruments produce accurate results. | Calibration uses known material standards, certified load cells, temperature reference points, conductivity and resistivity standards, optical calibration targets, and repeated baseline runs. |
| | Error Characterization | Identification and quantification of noise, uncertainty, bias, and measurement error. | Errors arise from instrument drift, temperature fluctuations, sample inhomogeneity, misalignment in mechanical tests, noise in electrical or optical signals, and finite spatial or temporal resolution in imaging. |
| 3. Structural Layer | 3.1 Patterns & Regularities | Laws / Relations | Stable, repeatable patterns governing how observables behave across conditions. | Stable patterns include stress strain relationships, diffusion laws, phase stability rules, heat flow patterns, conductivity trends, microstructure property links, and predictable deformation and fracture behavior. |
| | Invariants | Quantities or properties that remain constant under transformations (symmetries, conservation laws). | Invariants include conservation of mass and energy, symmetry based material behavior, stable phase relationships, equilibrium conditions, and persistent microstructural features such as grain boundary topology. |
| 3.2 Causal Architecture | Mechanisms | Underlying processes or structures that produce the observed regularities. | Mechanisms arise from atomic bonding, defect motion, phase transformations, diffusion, crack propagation, thermal transport, magnetic or electronic interactions, and microstructural evolution under load or temperature. |
| | Pathways | Organized sequences of interactions forming a causal chain or network. | Pathways include sequences of deformation, dislocation movement, diffusion assisted phase changes, grain growth, fracture initiation and propagation, and thermally driven property changes. |
| 3.3 Theoretical Vocabulary | Concepts | Core terms that encode the domain’s structure (force, gene, equilibrium, field). | Core terms include stress, strain, phase, microstructure, defect, grain boundary, diffusion, toughness, strength, conductivity, and thermal expansion. |
| | Classifications | Taxonomies, categories, or typologies that organize entities and relations. | Classifies materials as metals, ceramics, polymers, composites, semiconductors, functional materials, and subclasses based on microstructure, bonding, or performance characteristics. |
| 3.4 Formal Representations | Equations | Mathematical constructs expressing laws, relations, or mechanisms. | Includes stress strain equations, heat conduction laws, diffusion equations, equilibrium rules, defect energetics expressions, and constitutive models for mechanical or thermal behavior. |
| | Models | Structured representations—mathematical, computational, or conceptual—used to predict and explain phenomena. | Models include continuum mechanics models, phase field models, microstructure evolution models, diffusion models, band structure models, and computational simulations of material behavior. |
| 3.5 Idealized Structures | Simplified Models | Purposeful abstractions that capture essential dynamics while omitting irrelevant detail. | Idealizations include perfect crystal approximations, uniform grain structures, isotropic material assumptions, linear elasticity, simplified defect models, and homogeneous material behavior. |
| | Limit Conditions | Regimes where specific models or approximations hold (classical vs. quantum, linear vs. nonlinear). | Valid under small strains, moderate temperatures, low disorder, steady state thermal or mechanical conditions, and when microstructural changes occur slowly relative to applied forces or gradients. |
| 3.6 Integrative Frameworks | Unifying Theories | Higher-order structures that connect disparate laws or mechanisms under a coherent whole. | Includes structure property relationships, thermodynamics, kinetics, continuum mechanics, microstructure evolution frameworks, and theories connecting atomic scale interactions to macroscopic performance. |
| | Interdisciplinary Links | Points where the theory connects to adjacent sciences or larger explanatory systems. | Links to physics, chemistry, mechanical engineering, electrical engineering, geology, nanotechnology, and materials processing and design. |
| 4. Method Layer | 4.1 Inquiry Design | Experimental Design | Structured plans for manipulating variables to test causal claims. | Experiments vary temperature, load, pressure, composition, strain rate, microstructure, or environmental conditions to test causal effects on mechanical, thermal, electrical, magnetic, or structural properties. |
| | Observational Design | Systematic approaches for gathering non-manipulated data (surveys, field studies, natural experiments). | Observational approaches measure natural aging, deformation, microstructure evolution, thermal cycling effects, or spontaneous phase transformations without direct manipulation of variables. |
| 4.2 Testing & Validation | Hypothesis Testing | Procedures for evaluating whether evidence supports or contradicts specific claims. | Tests compare measured stress strain curves, phase transitions, diffusion behavior, defect changes, conductivity trends, or thermal responses against theoretical predictions or computational models. |
| | Replication | The requirement that results be independently reproducible under similar conditions. | Replication requires repeating mechanical tests, imaging scans, diffusion measurements, thermal analyses, or electrical and magnetic characterizations across multiple samples, instruments, and laboratories. |
| 4.3 Inference & Evaluation | Statistical Inference | Rules for drawing conclusions from noisy or incomplete data. | Statistical tools extract material parameters, fit constitutive models, analyze noise in mechanical or thermal data, estimate diffusion coefficients, evaluate variability across samples, and determine confidence intervals. |
| | Model Comparison | Criteria (fit, simplicity, predictive accuracy, robustness) used to evaluate competing models. | Models compared based on accuracy in predicting property changes, microstructure evolution, stress strain behavior, thermal transport, or defect kinetics; evaluated for simplicity, robustness, and predictive range. |
| 4.4 Error Management | Error Analysis | Identification and quantification of random and systematic errors. | Errors arise from instrument drift, sample inhomogeneity, misalignment, thermal fluctuations, noise in imaging or spectroscopy, load cell inaccuracies, and calibration uncertainty. |
| | Bias Control | Methods for minimizing subjective, instrumental, or procedural biases. | Bias minimized by standardized sample preparation, blind deformation tests, repeated calibration cycles, consistent imaging settings, cross checking with multiple instruments, and uniform environmental control. |
| 4.5 Adjudication & Revision | Peer Scrutiny | Collective evaluation of claims through critique, review, and debate. | Findings evaluated through peer review, replication across facilities, conference critique, and detailed comparison with independent measurements or models. |
| | Theory Revision | Procedures for modifying, replacing, or discarding models based on new evidence. | Theories revised when observed behavior deviates from predictions, when new materials reveal unexpected properties, or when updated microstructure data requires modified constitutive rules or phase models. |
| 4.6 Integrity Conditions | Transparency | Requirements to disclose methods, data, assumptions, and limitations. | Requires clear disclosure of preparation methods, composition, measurement conditions, calibration routines, model assumptions, and limitations of data or analysis. |
| | Ethical Standards | Norms ensuring responsible conduct in experimentation, data handling, and publication. | Requires accurate reporting of data, correct representation of uncertainties, responsible handling of samples, avoidance of selective reporting, and adherence to scientific and engineering integrity standards. |