混合定律應用於高介電常數陶瓷物質之微波介電特性量測

Microwave Measurements of Dielectric Properties for High Dielectric Constant Ceramic Materials by Mixture Equations

王詠麟(Yong-Lin Wang)

指導教授 ： 沈自

國立虎尾科技大學/電機資訊學院/光電與材料科技研究所/碩士(2010年)

https://doi.org/10.6827/NFU.2010.00094

摘要

此篇論文主要研究於微波頻率下，陶瓷散佈在聚乙烯物質中之介電常數。實驗量測於微波頻率下陶瓷散佈在聚乙烯(PE)物質中獲得之介電常數，將利用不同的混合定律進行比較。
複合材料之製作為將一定比例之陶瓷粉末參雜於PE粉末中。研究使用之陶瓷材料為TiO2、CaTiO2及SrTiO3三種高介電常數之陶瓷粉末，其介電常數值分別為100、170和300。使用之基質材料為PE粉末,其介電常數為2.32。在此複合介電常數實驗值將利用不同的混合定律來比較，混合定律也將從量測所得到的不同濃度複合介電常數來估算純陶瓷的介電常數值。同時會建議出最適當的混合定律去估算純陶瓷之介電常數。此研究並指出一個相當重要的觀念--最適當估算純陶瓷材料介電常數的混合定律需同時具有良好的匹配曲線和較低的理論誤差。
關於量測方法，根據電磁理論，電磁波由一介質入射至介電係數不同另一介質時，因介電係數的改變而發生部份反射部份穿透的情形。當介電常數遠大於最小單位，電磁波大部分都會被限制在此範圍內形成駐波，形成所謂的介質共振器(DR)用來進行介電特性的量測，此微波介電性質之量測方法於本研究中稱為柱狀共振技術，此量測技術對介電共振材料在介電常數之量測上具有相當良好之準確度。

關鍵字

介電常數 ； 混合定律 ； 微波

並列摘要

This article reports on a study of the dielectric constants of ceramic dispersions in the polyethylene matrix at microwave frequency. The experimental dielectric constants of ceramic dispersions in the polyethylene matrix at microwave frequency are compared to those obtained by using different mixing laws.

Ceramic powders are mixed in a certain proportion of matrix powder. Three high dielectric constant ceramic powders of TiO2, CaTiO3 and SrTiO3 with the dielectric constants of 100,170 and 300, respectively, are studied. The matrix material is the PE powder with dielectric constant 2.32. The experimental values of the dielectric constants of mixtures are compared to those obtained by using different mixing laws. The mixing rules are also adopted to estimate the dielectric constants of pure ceramics from the measured dielectric constants of composites with various concentrations. The most adequate mixture law for estimating the dielectric constants of pure ceramics will be suggested. This study conclude a very important concept on the powder mixture rule -- the most adequate mixture law for estimating the dielectric constants of pure ceramics requires both good curve fitting and potential of lower error.

About the measurement method, according to electromagnetic theory, electromagnetic wave from a medium incidence to another dielectric with different dielectric constant, because of the dielectric coefficient change, will have the partial reflection and the partial penetration situation. For dielectric constant much larger than unit, the majority of electromagnetic wave will be limited in the dielectric to form the standing wave. The so-called dielectric resonators (DR) in formed and can be adopted for dielectric properties measurements. The measurement method of microwave dielectric properties in this research is called the post resonance technique. This measurement technology has very good accuracy on the dielectric constant measurement in dielectric resonator material.

並列關鍵字

DIELECTRIC ； Mixture Equations ； MICROWAVE

參考文獻

[1] S. Stolzle, A. Enders, and G. Nimtz, "Numerical simulation of random composite dielectrics," J. Phys. I France, vol. 2, pp. 401-408, 1999.

[2] K. Wakino, "New proposal on mixing rule of the dielectric constant of mixture," IEEE International Symposium on Applications of Ferroelectrics, 1994, pp. 33-38.

[3] J. B. Kim, T. W. Kim, and C. G. Kim, "Simulation method of complex permittivities of carbon balck/epoxy composites at microwave frequency band," J. of Applied Polymer Science, vol. 100, pp. 2189-2195, 2006.

[4] M. E. Achour, M. El Malhi, J. L. Miane, F. Carmona, and F. Lahjomri, "Microwave properties of carbon black-epoxy resin composites and their simulation by means of mixture laws," J. of Applied Polymer Science, vol. 73, pp. 969-973, 1999.

[5] K. Lichtenecker and K. Rother " Die herleitung des logarithmischen mischungsgesetzes als allegemeinen prinzipien der staionaren stromung," K. Phys. Zeitschrift, vol. 32, pp. 255-260, 1931.