ISO 80000 reference

ISO 80000-12: Quantities and Units in Solid-State Physics

ISO 80000‑12 (“Quantities and units — Part 12: Solid‑state physics”) standardizes the names, symbols, units, and recommended definitions for the physical quantities used to characterize condensed matter—crystalline and amorphous solids, and, by extension, many properties of liquids and soft materials when treated from a materials-science perspective. It provides a common, SI-coherent language for reporting structure, mechanical response, thermal transport, electrical and ionic conduction, magnetism, and optical behavior in materials.

If you publish data sheets for semiconductors, calibrate thermal or electrical reference materials, simulate anisotropic composites, or compare measurements across labs and instruments, ISO 80000‑12 is the backbone that keeps your numbers interoperable. It sits atop the general rules of ISO 80000‑1 and aligns with domain parts such as ISO 80000‑4, ISO 80000‑5, ISO 80000‑6, and ISO 80000‑7, ensuring that material properties expressed in one subfield remain consistent everywhere else.

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Scope and Rationale

Solid-state physics spans scales from atomic lattices (ångström-level spacings) to macroscopic components (meters), and phenomena from picosecond phonon transport to quasi-static creep. ISO 80000‑12 brings order to this diversity by:

  • Fixing symbols and units for widely used material properties (e.g., density ρ in kg·m⁻³, thermal conductivity λ in W·m⁻¹·K⁻¹, electrical resistivity ρe in Ω·m, charge-carrier mobility μ in m²·V⁻¹·s⁻¹).
  • Clarifying dimensionality and tensors, so users consistently report scalar, vector, and tensor quantities with their coordinate frames.
  • Encouraging SI coherence while acknowledging established “accepted with SI” units used in materials (e.g., electronvolt, eV, for band gaps; dalton, Da, for atomic/molecular masses).
  • Harmonizing practice across subdisciplines (mechanical, electrical, thermal, magnetic, optical) so that multi-physics data sets can be combined without silent unit conversions.
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Historical Context: From Lattices to Multi-Physics

The need for a unified measurement language in solid-state physics grew with the 20th-century consolidation of crystallography, elasticity theory, quantum mechanics, and transport:

  • Crystallography established the metrically rigorous description of lattices (direct and reciprocal), defects, and orientations (Miller indices).
  • Elasticity and plasticity matured, with fourth-rank elastic constants Cijkl (Pa) and second-rank compliance Sijkl (Pa⁻¹) for anisotropic crystals.
  • Electronic band theory connected carrier concentration n, p (m⁻³), mobility μ (m²·V⁻¹·s⁻¹), conductivity σ (S·m⁻¹), and Seebeck coefficient S (V·K⁻¹).
  • Phonon physics quantified thermal conductivity λ (W·m⁻¹·K⁻¹), specific heat capacity c (J·kg⁻¹·K⁻¹), and thermal diffusivity α (m²·s⁻¹).
  • Magnetism distinguished magnetization 𝐌 (A·m⁻¹), susceptibility χ (dimensionless), coercivity Hc (A·m⁻¹), and remanence Br (T).

As laboratories globalized and devices became multi-physics (thermoelectric, magnetocaloric, spintronic, electro-optic), consistent symbols and units became essential—precisely the role of ISO 80000‑12.

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General Principles Carried Over from ISO 80000-1

  • Quantities vs. units: Quantity symbols are italic (e.g., σ for stress), unit symbols are upright (e.g., Pa), never pluralized.
  • Coherent SI: Prefer derived SI units with no hidden factors (e.g., S·m⁻¹ for conductivity; Ω·m for resistivity).
  • Single solidus and exponents: Write J·kg⁻¹·K⁻¹ rather than “J/kg/K”.
  • Spacing: A space between number and unit (“300 K”, “5.0 W·m⁻¹·K⁻¹”).
  • Prefixes: Use standard SI prefixes (“µ” for micro, not “u”); avoid double prefixes.
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Core Quantity Families in ISO 80000-12

1) Structure and Defects

  • Lattice parameter a, b, c — metre (m): Interatomic spacing and unit-cell dimensions. For cubic crystals, a single scalar a suffices; for lower symmetries, three lengths and angles are required. Reciprocal lattice vectors carry units m⁻¹.
  • Miller indices (hkl), [uvw] — dimensionless: Plane/direction labels (not units), but essential to report anisotropic tensor components (e.g., σ[100], λ(001)).
  • Defect densities — m⁻² (line/edge density), m⁻³ (volume density): Dislocations (line length per volume), vacancy/interstitial concentrations, grain-boundary area per volume (m⁻¹).
  • Mass density ρ — kg·m⁻³: Bulk density of the solid; for porous or composite materials, report apparent vs true density and porosity separately.

Good practice: Provide orientation (e.g., wafer cut), texture/polycrystalline descriptors, and measurement temperature, as many properties are both anisotropic and temperature-dependent. Pair density data with our Specific Heat Energy Calculator when estimating thermal storage.

2) Mechanical Response (Elasticity, Plasticity, Fracture)

  • Stress σij — pascal (Pa = N·m⁻²): Second-rank tensor; report component conventions (engineering vs. tensorial shear).
  • Strain εij — dimensionless: Green-Lagrange or engineering strain; state definition at large deformations.
  • Elastic constants Cijkl, compliances Sijkl — Pa, Pa⁻¹: Symmetry reduces components (e.g., 3 for cubic). Isotropic reductions include Young’s modulus E (Pa), Shear modulus G (Pa), Bulk modulus K (Pa), and Poisson’s ratio ν (dimensionless).
  • Fracture quantities: Fracture toughness KIc — Pa·m¹ᐟ²; Energy release rate Gc — J·m⁻².
  • Time-dependent response: Viscosity η (for glasses/polymers) — Pa·s; Creep compliance J(t) — Pa⁻¹.

Good practice: When reporting anisotropic values, specify the loading direction relative to crystal axes or rolling/texturing directions, and the strain rate and temperature.

3) Thermal Properties (Storage and Transport)

  • Specific heat capacity (massic) c — J·kg⁻¹·K⁻¹
  • Volumetric heat capacity Cv,vol = ρc — J·m⁻³·K⁻¹
  • Thermal conductivity λ (often k) — W·m⁻¹·K⁻¹
  • Thermal diffusivity α = λ/(ρc) — m²·s⁻¹
  • Thermal expansion αL — K⁻¹ (linear), K⁻¹ (volumetric)
  • Thermoelectric coefficients: Seebeck coefficient S — V·K⁻¹; Peltier coefficient Π — V; Thomson coefficient τ — V·K⁻¹; Figure of merit ZT = S² σ T/λ — dimensionless (state T).

Clarify constant-pressure vs constant-volume conditions; for solids, cp ≈ cv at ambient conditions but distinctions matter at high temperatures. Dive deeper with our thermal conductivity guide and the specific heat capacity explainer for application notes.

4) Electrical and Ionic Transport

  • Electrical conductivity σ — S·m⁻¹
  • Resistivity ρe — Ω·m
  • Carrier concentration n, p — m⁻³
  • Mobility μ — m²·V⁻¹·s⁻¹
  • Hall coefficient RH — m³·C⁻¹
  • Dielectric function ε(ω) = ε’ − i ε’’ — dimensionless; permittivity ε0εr in F·m⁻¹
  • Ionic conductivity / diffusion: report S·m⁻¹ (conductivity), m²·s⁻¹ (diffusivity), with species identified and temperature/composition stated.

Good practice: In semiconductors, the community often uses cm⁻³; convert to SI m⁻³ (1 cm⁻³ = 10⁶ m⁻³) and provide both when helpful, clearly labeled.

5) Magnetic Quantities (Materials Context)

Units and base definitions live in ISO 80000‑6; ISO 80000‑12 emphasizes their use as material properties.

  • Magnetization 𝐌 — A·m⁻¹
  • Magnetic field strength 𝐇 — A·m⁻¹
  • Magnetic flux density 𝐁 — tesla (T)
  • Susceptibility χ — dimensionless
  • Coercivity Hc — A·m⁻¹
  • Remanence Br — T
  • Curie/Néel temperatures — K

Always specify measurement geometry, frequency (if AC), temperature, and history (e.g., demagnetization) when reporting magnetic properties. Compare notation with the ISO 80000‑6 overview to maintain consistency.

6) Optical and Optoelectronic Properties

Interfaces with ISO 80000‑7 for photometric quantities and ISO 80000‑6 for electromagnetic constants.

  • Refractive index n — dimensionless (state wavelength and temperature).
  • Extinction coefficient k — dimensionless; absorption coefficient αopt — m⁻¹.
  • Band gap Eg — frequently in eV (accepted with SI); provide J when needed.
  • Photoconductivity changes in σ with illumination—report irradiance (W·m⁻²), spectrum, and geometry.
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Tensors, Anisotropy, and Orientation

  • Elastic stiffness Cijkl, thermal conductivity λij, dielectric permittivity εij, magnetic susceptibility χij, electrical conductivity σij are second- or fourth-rank tensors.
  • You must report the reference frame (crystal axes or sample axes) and texture (for polycrystals).
  • For films and heterostructures, state in-plane vs cross-plane values explicitly (e.g., λ∥, λ⊥).

Best practice: Use standardized orientation labels (Miller indices) and, when rotating tensors, describe the rotation (Euler angles or axis–angle) to avoid ambiguity.

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Measurement, Realization, and Traceability

Thermal

  • Laser flash for α (then λ = α ρ c): report sample thickness, pulse energy, heat losses, and radiation corrections.
  • Guarded hot plate / comparative cut-bar for λ: ensure steady state, quantify contact resistances and edge losses.
  • Calorimetry (DSC/CP) for c: compare against reference materials, account for baseline drift.

Electrical

  • Four-probe resistivity: minimizes contact resistance; report geometry factor, temperature, and contact metallurgy.
  • Hall effect: yields RH, n, μ; specify magnetic field, thickness, van der Pauw or bar geometry, and carrier sign.

Mechanical

  • Ultrasonic pulse-echo or resonant ultrasound spectroscopy for Cijkl: record mode identification and density used.
  • Nanoindentation for E, H: report tip area function, loading rate, Oliver–Pharr analysis assumptions, and surface preparation.

Magnetic

  • VSM/SQUID magnetometry: declare field sweep rates, demagnetization corrections, and zero-field-cooled/field-cooled protocols.

Optical

  • Spectroscopic ellipsometry: provides n, k; document model, fit residuals, wavelength range, and roughness/graded layers.

Across all methods, ensure traceability to SI base units (mass, length, time, temperature, electric current), and provide expanded uncertainties with coverage factors when results inform standards or compliance.

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Data Reporting: Avoiding Ambiguity

  • Distinguish resistivity ρe (Ω·m) from resistance R (Ω) and from mass density ρ (kg·m⁻³). Subscripts prevent collisions.
  • Provide measurement temperature (and pressure if relevant); many properties vary strongly with T.
  • State frequency (for AC properties) and bias conditions (for nonlinear or field-dependent properties).
  • For polycrystalline or porous materials, report porosity and grain size alongside the property; effective properties can differ markedly from single-crystal values.
  • When non-SI units are entrenched (e.g., eV, cm⁻¹ for wavenumber, cm⁻³ for dopant density), give the SI equivalent to enable coherent computation.
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Worked Examples (Concise)

Example 1: Thermal Transport in an Anisotropic Crystal

Reported: λ[100] = 180 W·m⁻¹·K⁻¹, λ[001] = 90 W·m⁻¹·K⁻¹ at 300 K, density ρ = 3900 kg·m⁻³, specific heat c = 600 J·kg⁻¹·K⁻¹.

Then α[100] = λ/(ρc) ≈ 7.7 × 10⁻⁵ m²·s⁻¹, α[001] ≈ 3.8 × 10⁻⁵ m²·s⁻¹.

Good practice: include crystal orientation, uncertainty, and method (e.g., laser flash).

Example 2: Semiconductor Transport via Hall Measurements

Van der Pauw sample at 300 K: Hall coefficient RH = −3.7 × 10⁻⁴ m³·C⁻¹ → electron concentration n = −1/(q RH) ≈ 1.7 × 10²² m⁻³.

Sheet resistance Rs = 250 Ω/□, thickness t = 500 nm → resistivity ρe = Rs t ≈ 1.25 × 10⁻⁴ Ω·m.

Mobility μ = |RH|/ρe ≈ 3.0 × 10⁻³ m²·V⁻¹·s⁻¹.

Good practice: state magnetic field, contact scheme, and thickness metrology. Use our Resistance Calculator to double-check Ohmic conversions when reporting supporting data.

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Interoperability with Other ISO 80000 Parts

  • ISO 80000‑4 (Mechanics): stresses, strains, moduli—units and symbols; ISO 80000‑12 uses these for material characterization.
  • ISO 80000‑5 (Thermodynamics): temperature T (K), heat Q (J), entropy (J·K⁻¹); foundational for c, λ, α.
  • ISO 80000‑6 (Electromagnetism): 𝐄, 𝐇, 𝐁, ε, μ; material permittivity/permeability and magnetization belong here physically but are used as properties in Part 12.
  • ISO 80000‑7 (Light): photometric quantities; links to optical property reporting (illumination, luminance) when coupling to human-perception metrics is needed.
  • ISO 80000‑11 (Characteristic numbers): Bi, Fo, Pe, Pr, Sc, Ra appear in heat/mass transfer in solids and porous media.

By following Part 12 with these cross-references, you keep multi-physics models dimensionally consistent and SI-coherent. Explore the complete ISO 80000 overview for additional navigation.

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Common Pitfalls and How to Avoid Them

  1. Symbol collisions (e.g., ρ for both density and resistivity). Fix: use subscripts ρmass, ρe, or context and units to disambiguate.
  2. Hidden anisotropy (reporting a single scalar for a tensor property). Fix: provide full tensor components or directional values with orientation.
  3. Non-SI legacy units without conversion (e.g., “dopant: 10¹⁶ cm⁻³” alone). Fix: include SI equivalent 10²² m⁻³.
  4. Frequency-dependent properties reported without frequency (dielectric loss, AC conductivity). Fix: state frequency (and field amplitude) with uncertainties.
  5. Temperature unspecified (properties at “room temperature”). Fix: give absolute temperature (e.g., 296 K) and, if needed, its stability over the measurement.
  6. Geometry/size effects unaccounted (contact resistance, boundary scattering at nanoscale). Fix: describe sample geometry and apply or discuss size corrections.
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Why ISO 80000-12 Matters

  • Clarity: It codifies symbols, names, and SI-coherent units so that a thermal engineer and a semiconductor physicist interpret “λ”, “μ”, and “σ” the same way.
  • Comparability: It enables datasets from different laboratories, techniques, and suppliers to be merged without silent unit errors—critical for materials databases, machine-readable catalogs, and multi-physics simulations.
  • Traceability: It anchors material properties to SI base units and recognized reference methods, facilitating calibration chains, interlaboratory comparisons, and certification.
  • Scalability: It supports dimensionally consistent up- and down-scaling of materials behavior, from thin films to bulk, from microchips to structural composites.
  • Education: It provides a rigorous framework for teaching materials metrology, preventing bad habits (pluralized unit symbols, multiple solidi, missing temperatures) before they spread into practice.
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Implementation Checklist (for Authors, Metrologists, and Data Curators)

  • Units and symbols: Conform to ISO 80000‑12 and ISO 80000‑1; italicize quantities, keep unit symbols upright and case-correct.
  • Orientation and tensors: Supply frames, cuts, and component definitions; distinguish in-plane vs cross-plane.
  • Conditions: State temperature, pressure, frequency, field, and history (e.g., thermal cycling, demagnetization).
  • Uncertainty: Provide uncertainties and how they were obtained; include geometry factors and property source (measured vs derived).
  • Conversions: Add SI equivalents for entrenched non-SI units (eV, cm⁻³, cm⁻¹).
  • Metadata: Include sample preparation, porosity, grain size, and composition—many “material constants” are microstructure-dependent.
  • Coherence: Check dimensional consistency; use derived SI units (W·m⁻¹·K⁻¹, S·m⁻¹, Ω·m, J·kg⁻¹·K⁻¹).
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Conclusion

ISO 80000‑12 gives solid-state physics and materials science a precise, SI-coherent vocabulary for reporting what a material is (structure, density), how it responds to forces (stress–strain, moduli, fracture), how it stores and transports energy (specific heat, thermal conductivity, diffusivity), how it carries charge and ions (conductivity, mobility, Hall effect), how it magnetizes, and how it interacts with light (refractive index, absorption, band gap). By adhering to the standardized symbols and units it specifies—and by documenting anisotropy, conditions, and uncertainties—you make your results auditable, comparable, and reusable across devices, disciplines, and decades. In a materials ecosystem increasingly driven by data integration and multi-physics design, ISO 80000‑12 is not merely a style preference; it is the infrastructure of credible materials metrology.

Continue exploring related standards through the ISO 80000 part directory and reinforce calculations with tools like the Thermal Diffusivity Calculator and conversion hub so every workflow stays coherent.