1. What functional materials are (the short version)

• Valued for a response rather than for strength: in this article, a functional material is one that changes its shape, electrical behavior, optical behavior, heat flow or surface in response to a stimulus (heat, an electric or magnetic field, light, force, a chemical environment), or one that reliably keeps a wanted function. We could not find a single internationally agreed definition within the scope of our research. This working definition and the classification are commentary
• A performance value belongs to “material × form × conditions × method”: even for one compound, single crystals and polycrystals, the measurement direction and the temperature change the number several-fold Sourced [Ref. 2, 3]
• An evaluation standard is a “test method”, not a guarantee of performance: a standard has a number, a title and an edition, and a JIS is not always identical to the ISO standard behind it (for example, JIS Z 2241 adopts ISO 6892-1:2019 with modifications, “MOD”) Sourced [Ref. 23, 14]

2. A map of functional materials — arranged by stimulus and response

Functional materials can be grouped by material class (metals, ceramics, polymers) or by application (batteries, optics, medicine). Here we arrange them by the first question asked when choosing one: what do you apply, and what changes? In Fig. 2 the rows are what is applied (the stimulus) and the columns are what changes (the response).

Some functions are passive: conduction, barrier properties, strength and heat insulation work simply by being there. They do not appear in Fig. 2, but the series covers them under surfaces and coatings, conduction and nanocarbons and materials that combine structure and function. The table below divides the 34 other articles of the series into 11 groups and lists a typical performance value for each, with the main conditions that change the value.

The grouping and the choice of typical indicators are our commentary. One material can span several groups (graphene, for example, is both a conductor and a barrier film). The definition of ZT follows the paper by Kim et al. [Ref. 1] Sourced. Other articles in the series are referred to in the text as “our explainer on …”; no links are given.

This material map is our conceptual organisation of stimuli and responses. For performance comparisons, return to the specimens and conditions in the original studies discussed below. The groups do not rank products by performance or maturity.

• Thermoelectric performance and conversion efficiency: the original study by Kim et al. [Ref. 1].
• Self-healing: the original study by White et al. [Ref. 6].
• Control of light: the theoretical paper by Pendry [Ref. 7].
• High-entropy alloys: the original study by Yeh et al. [Ref. 8].
• Surface wetting: the original study by Barthlott and Neinhuis [Ref. 9].
• Conducting polymers: the original study by Chiang et al. [Ref. 10].

3. Five questions for reading a performance value

We do not rank a number against others unless we can answer these five questions. The articles of this series follow the same rule when they quote numbers.

The battery example in item 3 rests on the abstract of the study of commercial cells by Preger et al. (even within the manufacturer’s specifications, the time and the number of cycles to reach 80% capacity varied by thousands of hours and cycles in each chemistry) Sourced. The organization of items 1 to 5 is our commentary.

4. Example 1: the ZT of SnSe runs from 0.5 to 2.6

Zhao et al. measured a SnSe single crystal along its b axis and reported a ZT of 2.6 ± 0.3 at 923 K (about 650 °C). In the same paper the c axis gave 2.3 ± 0.3 and the a axis 0.8 ± 0.2. The authors attribute the high value to an extremely low lattice thermal conductivity (0.23 ± 0.03 W m⁻¹ K⁻¹ at 973 K), which they trace to the strong anharmonicity and anisotropic bonding of the layered structure Sourced [Ref. 2]. Sassi et al., in contrast, evaluated polycrystalline p-type SnSe and reported a maximum ZT of 0.5 at 823 K. They confirmed that even the polycrystal has intrinsically very low thermal conductivity Sourced [Ref. 3].

This example does not show whether SnSe is good or bad. It shows that there is no single number called “the ZT of SnSe”. The high single-crystal value is an important result about the potential of the material, but it cannot be read as the performance of a sintered polycrystal or of a real device.

5. Example 2: peak ZT and conversion efficiency are different things

The maximum efficiency of a thermoelectric device has long been estimated by a formula in which the Carnot efficiency is multiplied by a reduction factor set by ZT. This is Eq. 1 of the paper by Kim et al. Sourced [Ref. 1].

η_max = (ΔT / T_h) × ( √(1 + ZT_avg) − 1 ) / ( √(1 + ZT_avg) + T_c / T_h )

T_h and T_c are the hot-side and cold-side temperatures, ΔT is their difference and ZT_avg is the average ZT. The formula assumes that ZT does not depend on temperature, so it predicts the maximum efficiency correctly only for a small temperature difference or for a material whose ZT is nearly constant. Kim et al. point out that using it often yields efficiencies far higher than can actually be achieved, and state that peak ZT is not the right indicator of a material’s efficiency. They propose an engineering ZT (ZT_eng) that accumulates the temperature dependence Sourced [Ref. 1].

The comparison in the paper is concrete. The half-Heusler alloy (Hf_0.19Zr_0.76Ti_0.05CoSb_0.8Sn_0.2) has a peak ZT of 0.94 at 700 °C, and SnSe (the crystals of Zhao et al.) 2.6 at 650 °C. Yet used with a hot side at 700 °C and a cold side at 100 °C, the efficiency from the paper’s Eq. 2 is 9.7% for the half-Heusler and 7.3% for SnSe, which reverses the order. The paper also shows that the conventional formula (using an average ZT) overestimates the efficiency of SnSe by about a factor of 2 relative to a numerical simulation, and that the new formula still overestimates it by 17% Sourced [Ref. 1].

6. Example 3: even for the same sample, ZT varies by 19% between laboratories

Measurement itself carries error. Alleno et al. ran a round-robin test, in which the same sample is measured in several laboratories and the results are processed statistically, with European (mainly French) laboratories. The sample was polycrystalline skutterudite Co_0.97Ni_0.03Sb₃, and the high-temperature thermoelectric properties were measured Sourced [Ref. 4].

All Sourced (the abstract of Alleno et al. [Ref. 4]). The paper also states that the uncertainties grow with temperature, that those of electrical resistivity and thermal diffusivity are most likely dominated by the uncertainty in sample dimensions, that thermal conductivity is the least accurate quantity, and that the temperature-averaged relative expanded uncertainty (95% confidence level) of the mean ZT is 17%.

7. How to read technology readiness levels (TRLs)

Technology maturity can be expressed on a scale from 1 to 9, as in “this material is at TRL 4”. NASA describes TRLs as a measurement system for the maturity level of a technology, with nine levels from TRL 1 (lowest) to TRL 9 (highest). TRL 6 is a fully functional prototype or representational model; TRL 7 is a demonstration in the space environment; TRL 8 is “flight qualified”; and TRL 9 is “flight proven” in an actual mission Sourced [Ref. 11].

The European Commission’s Horizon Europe (Work Programme 2023-2025, General Annexes) also defines TRLs, but only for use where a call or topic requires a TRL, and unless otherwise specified. TRL 4 is “technology validated in a lab”; TRL 5 “validated in a relevant environment”; TRL 6 “demonstrated in a relevant environment” (an industrially relevant environment for key enabling technologies); TRL 7 “system prototype demonstration in an operational environment”; TRL 8 “system complete and qualified”; and TRL 9 “actual system proven in an operational environment” (competitive manufacturing in the case of key enabling technologies, or in space) Sourced [Ref. 12]. ISO 16290:2013 also defines TRLs. It is applicable primarily to space system hardware, though its definitions could be used in a wider domain in many cases, and it was last reviewed and confirmed in 2024, so it remains current Sourced [Ref. 13].

8. Limits, and what we could not confirm

(1) The definition of functional materials

We could not find a single internationally agreed definition of functional materials within the scope of our research. The working definition in Section 1 and the classification in Section 2 are our own grouping (commentary).

(2) The text of the standards

We have not read the full text of ISO 6892-1, ISO 14577-1, ISO 11357, ISO 22007-4, ISO 19403-2, IEC 60404-5 or ISO/IEC Guide 98-3. We checked only the title, edition and scope (abstract) on the official pages. Test conditions, procedures and acceptance criteria are not stated. For JIS Z 2241 we confirmed only the statement on the corresponding international standard in the foreword shown in the preview.

(3) How general the examples are

Sections 4 to 6 use thermoelectric examples (SnSe, a half-Heusler alloy, Co_0.97Ni_0.03Sb₃). The same kinds of thing are likely to happen in other groups, but the numbers do not carry over to other materials. Each article of the series treats examples from its own group.

(4) The full texts of the papers

We read the full text of Kim et al. Descriptions of Zhao et al., Sassi et al. and Alleno et al. are limited to what could be checked in publisher or bibliographic-database abstracts. The additional original-paper examples in Section 2 are bibliographic pointers, not a verified comparison of their experiments or results.

(5) TRL

The Horizon Europe definition is taken from the General Annexes of the 2023-2025 work programme. We have not checked the TRL definitions of other funding bodies (such as Japanese national programs).

(6) ASTM standards

The ASTM International website states that AI use is prohibited, so we did not open any ASTM site. ASTM standards are listed only where their number and title could be confirmed in non-ASTM public sources (the FDA database, instrument makers’ pages, reference lists of papers and a standards retailer’s page), and we state no text, test conditions or acceptance criteria. Where we could not confirm a standard we say so.

9. How to read evaluations and standards

The performance values of functional materials divide into (a) properties of the material itself (ZT, d₃₃, B_r, transformation temperature, contact angle and so on) and (b) the output of a device or system. Measurements use tensile testers, DSC (differential scanning calorimeters), flash-method instruments, contact-angle meters, magnetic measurement instruments and the like, and each has a test-method standard. This section shows how to trace a standard (Fig. 6) and the basics of reading standards that apply across the series.

Table of corresponding standards

The table lists, for the quantities treated in this article, the standards whose number and title we could confirm on official pages or comparable sources. Cells we could not fill say “could not be confirmed”. ISO and IEC standards are international standards, JIS is the Japanese national standard, and ASTM standards are those of the US standards body ASTM International. JIS titles are our translations from the Japanese.

Numbers, titles and editions were confirmed as follows: ISO on the ISO catalogue pages; IEC on the IEC Webstore; JIS in the JISC database (the corresponding international standard from the JSA preview); ASTM through the FDA database of recognized consensus standards, an instrument maker’s page, the reference list of a paper and a standards retailer’s page (we did not open any ASTM site) [Ref. 14, 15, 16, 17, 18, 19, 21, 20, 22, 23, 24, 25, 26, 27, 28].

The number, title, edition and date of each standard are Sourced (confirmed on the official pages of the standards bodies and comparable sources). Which standard goes in which cell is our own arrangement (Our calculation). We found no revision or draft in progress, so no row falls under Not yet confirmed.

Cautions when reading standards

1. A standard is a “test method”, not a guarantee of performance. For example, ISO 14577-1:2026 states that in the nano range the mechanical deformation depends strongly on the actual shape of the indenter tip, and that careful calibration of both the instrument and the indenter shape is required to obtain acceptable reproducibility between machines Sourced [Ref. 15]. Even when a standard is followed, values do not reproduce if the calibration or the sample state differs.
2. The same named property can be measured differently depending on the standard and the edition. For ISO 6892-1 the 2016 edition has been withdrawn and the 2019 edition is current [Ref. 14]. ISO 22007-4:2017, titled “Laser flash method”, has been withdrawn and revised into the 2024 edition titled “Light flash method” [Ref. 18, 29] Sourced. JIS Z 2241 adopts ISO 6892-1:2019 with modifications, so the texts are not necessarily identical [Ref. 23].
3. Read a manufacturer’s value together with the standard, edition and test conditions. Even when a datasheet says “per ISO …”, it cannot be compared with another company’s or a paper’s value unless the edition, sample form, temperature and test speed are stated. The range given by a standard can also differ from the actual conditions of use (our commentary).

International, national and industry standards

ISO and IEC standards are international standards and are taken up into national standards. JIS is the Japanese national standard; when an international standard is adopted, the foreword states the corresponding international standard and the degree of correspondence (for example MOD, “modified”, for JIS Z 2241) [Ref. 23]. ASTM standards are those of the US standards body ASTM International, and some are among the “recognized consensus standards” for which the FDA accepts a declaration of conformity for medical devices [Ref. 25]. We could not confirm an IEEE standard for the quantities in this table. When an international standard, a national standard and an industry standard measure the same quantity by different methods, their values cannot be compared directly.

10. Glossary

11. References (primary sources)

1. Kim H. S. et al. “Relationship between thermoelectric figure of merit and energy conversion efficiency”, Proc. Natl. Acad. Sci. USA 112, 8205–8210 (2015), DOI 10.1073/pnas.1510231112 (open access) — doi.org/10.1073/pnas.1510231112
2. Zhao L.-D. et al. “Ultralow thermal conductivity and high thermoelectric figure of merit in SnSe crystals”, Nature 508, 373–377 (2014), DOI 10.1038/nature13184 — doi.org/10.1038/nature13184
3. Sassi S. et al. “Assessment of the thermoelectric performance of polycrystalline p-type SnSe”, Appl. Phys. Lett. 104, 212105 (2014), DOI 10.1063/1.4880817 — doi.org/10.1063/1.4880817
4. Alleno E. et al. “A round robin test of the uncertainty on the measurement of the thermoelectric dimensionless figure of merit of Co_0.97Ni_0.03Sb₃“, Rev. Sci. Instrum. 86, 011301 (2015), DOI 10.1063/1.4905250 — doi.org/10.1063/1.4905250
5. Preger Y. et al. “Degradation of Commercial Lithium-Ion Cells as a Function of Chemistry and Cycling Conditions”, J. Electrochem. Soc. 167, 120532 (2020), DOI 10.1149/1945-7111/abae37 (open access) — doi.org/10.1149/1945-7111/abae37
6. White S. R. et al. “Autonomic healing of polymer composites”, Nature 409, 794–797 (2001), DOI 10.1038/35057232 — doi.org/10.1038/35057232
7. Pendry J. B. “Negative Refraction Makes a Perfect Lens”, Phys. Rev. Lett. 85, 3966–3969 (2000), DOI 10.1103/PhysRevLett.85.3966 — doi.org/10.1103/PhysRevLett.85.3966
8. Yeh J.-W. et al. “Nanostructured High-Entropy Alloys with Multiple Principal Elements: Novel Alloy Design Concepts and Outcomes”, Adv. Eng. Mater. 6, 299–303 (2004), DOI 10.1002/adem.200300567 — doi.org/10.1002/adem.200300567
9. Barthlott W., Neinhuis C. “Purity of the sacred lotus, or escape from contamination in biological surfaces”, Planta 202, 1–8 (1997), DOI 10.1007/s004250050096 — doi.org/10.1007/s004250050096
10. Chiang C. K. et al. “Electrical Conductivity in Doped Polyacetylene”, Phys. Rev. Lett. 39, 1098–1101 (1977), DOI 10.1103/physrevlett.39.1098 — doi.org/10.1103/physrevlett.39.1098
11. NASA “Technology Readiness Levels” (posted 27 September 2023, updated 25 June 2026) — www.nasa.gov/directorates/somd/space-communications-navigation-prog…
12. European Commission Horizon Europe Work Programme 2023-2025, “13. General Annexes” (Commission Decision C(2025) 2779 of 14 May 2025), section “Technology Readiness Levels” — ec.europa.eu/info/funding-tenders/opportunities/docs/2021-2027/hori…
13. ISO “ISO 16290:2013 Space systems — Definition of the Technology Readiness Levels (TRLs) and their criteria of assessment” (ISO catalogue page) — www.iso.org/standard/56064.html
14. ISO “ISO 6892-1:2019 Metallic materials — Tensile testing — Part 1: Method of test at room temperature” (ISO catalogue page) — www.iso.org/standard/78322.html
15. ISO “ISO 14577-1:2026 Metallic materials — Instrumented indentation test for hardness and materials parameters — Part 1: Test method” (ISO catalogue page) — www.iso.org/standard/85223.html
16. ISO “ISO 11357-1:2023 Plastics — Differential scanning calorimetry (DSC) — Part 1: General principles” (ISO catalogue page) — www.iso.org/standard/83904.html
17. ISO “ISO 11357-3:2025 Plastics — Differential scanning calorimetry (DSC) — Part 3: Determination of temperature and enthalpy of melting and crystallization” (ISO catalogue page) — www.iso.org/standard/88106.html
18. ISO “ISO 22007-4:2024 Plastics — Determination of thermal conductivity and thermal diffusivity — Part 4: Light flash method” (ISO catalogue page) — www.iso.org/standard/86202.html
19. ISO “ISO 19403-2:2024 Paints and varnishes — Wettability — Part 2: Determination of the surface free energy of solid surfaces by measuring the contact angle” (ISO catalogue page) — www.iso.org/standard/87262.html
20. ISO/IEC “ISO/IEC Guide 98-3:2008 Uncertainty of measurement — Part 3: Guide to the expression of uncertainty in measurement (GUM:1995)” (ISO catalogue page) — www.iso.org/standard/50461.html
21. IEC “IEC 60404-5:2015 Magnetic materials — Part 5: Permanent magnet (magnetically hard) materials — Methods of measurement of magnetic properties” (IEC Webstore; this page is the redline version, which contains the official standard) — webstore.iec.ch/en/publication/22141
22. Japanese Industrial Standards Committee (JISC) JISC database entry for “JIS Z 2241” (tensile testing method for metallic materials; established 22 July 1952, latest revision 21 August 2023 [Amendment 1]) — www.jisc.go.jp/app/jis/general/GnrJISNumberNameSearchList?show&jisS…
23. Japanese Standards Association (JSA) Preview pages of JIS Z 2241:2022 (the foreword names ISO 6892-1:2019 as the corresponding international standard, degree of correspondence MOD) — webdesk.jsa.or.jp/preview/pre_jis_z_02241_000_000_2022_j_ed10_ch.pdf
24. Japanese Industrial Standards Committee (JISC) JISC JIS search, list of JIS numbers starting with H 7 (including the JIS for shape memory alloys) — www.jisc.go.jp/app/jis/general/GnrJISNumberNameSearchList?show&jisS…
25. U.S. Food and Drug Administration (FDA) “Recognized Consensus Standards: Medical Devices” database, search results for titles containing nickel-titanium (database page last updated 28 September 2026) — www.accessdata.fda.gov/scripts/cdrh/cfdocs/cfStandards/results.cfm?…
26. Hitachi High-Tech “Standards – ISO/ASTM/JIS/IPC”, list of thermal-analysis standards (instrument maker’s technical page, in Japanese) — www.hitachi-hightech.com/jp/ja/knowledge/analytical-systems/thermal…
27. ANSI Webstore “ASTM E8/E8M-08 — Standard Test Methods for Tension Testing of Metallic Materials” (standards retailer page; used only to confirm number and title) — webstore.ansi.org/standards/astm/astme8e8m08
28. Carr E. J. “Rear-surface integral method for calculating thermal diffusivity from laser flash experiments”, arXiv:1809.06934 (its reference list gives ASTM E1461-13 “Standard test method for thermal diffusivity by the flash method”; used only to confirm number and title) — arxiv.org/abs/1809.06934
29. ISO “ISO 22007-4:2017 Plastics — Determination of thermal conductivity and thermal diffusivity — Part 4: Laser flash method” (withdrawn edition; ISO catalogue page) — www.iso.org/standard/65085.html
30. Japanese Industrial Standards Committee (JISC) JIS search (by number or title). JIS Z 2255, C 2501, K 7121, K 7122, R 1611, H 7801, R 3257, R 1703-1, H 7101 and others were confirmed (number, title, dates of establishment and revision) on the JIS list and detail pages — www.jisc.go.jp/app/jis/general/GnrJISSearch.html

12. Claim-to-source audit

Last updated: 10 October 2026. Sources are limited to primary material (peer-reviewed papers, official documents of NASA and the European Commission, and the databases of standards bodies, the Japanese Industrial Standards Committee and the FDA). We have not read the text of the standards. Because the article includes organization of structure and readings of materials design, these are marked as “commentary” and kept apart from sourced facts. We could not confirm, and therefore do not state, a single agreed definition of functional materials, the text of the standards, the text and test conditions of ASTM standards, the TRL definitions of funding bodies outside the European Commission, or any applicable IEEE standard. The ZT, uncertainty and efficiency values are results that specific papers obtained on specific samples and conditions, and cannot be generalized to other samples or real devices. Figs. 2 to 6 are vector drawings and Figs. 1 and 7 are AI-generated images; none of them shows an actual micrograph or a real product.