{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,8]],"date-time":"2026-10-08T18:10:47Z","timestamp":1791483047539,"version":"4.3.4"},"reference-count":54,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T00:00:00Z","timestamp":1775001600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Science and Technology Council (NSTC) of Taiwan","award":["113-2112-M-007-023-MY3"],"award-info":[{"award-number":["113-2112-M-007-023-MY3"]}]},{"award":["113-2112-M-007-023-MY3"],"award-info":[{"award-number":["113-2112-M-007-023-MY3"]}],"id":[{"id":"https:\/\/ror.org\/02kv4zf79","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Nanomaterials"],"abstract":"<jats:p>Alumina is a commonly used ceramic material known for high permittivity, low dielectric loss, good thermal conductivity, and low cost. In the development of electronic devices, the size effect of powdery materials is crucial, particularly in applications involving composite materials. This study introduces the field-enhancement method (FEM) to measure the resonant frequency (f0) and the quality factor (Q) of alumina powders packed in a Teflon container and placed on top of the central rod in the proposed cavity. The measured resonant condition (f0 and Q) is mapped to a contour plot and simulated using a high-frequency structure simulator (HFSS). The contour mapping technique allows the researchers to obtain the effective complex permittivity of alumina\u2013air composites. The complex permittivity of the alumina powder is retrieved using a hybrid model and the effective medium theories (EMTs), respectively. The Landau\u2013Lifshitz\u2013Looyenga (LLL) model is compared with the results using the hybrid model for its applicability. The dielectric constant and the loss tangent of the alumina powder are found to increase as the powder size reduces. A power relation is found to fit the obtained permittivity, covering sizes ranging from nanometers to micrometers, and a surface-charge scaling argument is proposed to explain the observed trend. This finding opens a new avenue for manipulation of permittivity in composite materials and has potential applications in stealth\/absorber technology and as a self-limiter for grain growth during sintering.<\/jats:p>","DOI":"10.3390\/nano16070436","type":"journal-article","created":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T07:57:55Z","timestamp":1775116675000},"page":"436","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Size-Dependent Permittivity for Alumina Powders"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-6140-7413","authenticated-orcid":false,"given":"Tien-Fu","family":"Yang","sequence":"first","affiliation":[{"name":"Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hsien-Wen","family":"Chao","sequence":"additional","affiliation":[{"name":"Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-7000-6814","authenticated-orcid":false,"given":"Bo-Wie","family":"Tseng","sequence":"additional","affiliation":[{"name":"College of Semiconductor Research, National Tsing Hua University, Hsinchu 30013, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yu-Syuan","family":"Dai","sequence":"additional","affiliation":[{"name":"Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2501-3185","authenticated-orcid":false,"given":"Tsun-Hsu","family":"Chang","sequence":"additional","affiliation":[{"name":"Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan"},{"name":"College of Semiconductor Research, National Tsing Hua University, Hsinchu 30013, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,4,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"5351","DOI":"10.1038\/s41598-017-05651-z","article-title":"Intrinsic enhancement of dielectric permittivity in (Nb + In) co-doped TiO2 single crystals","volume":"7","author":"Kawarasaki","year":"2017","journal-title":"Sci. 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