本論文主要分成兩部分，主要目的在探討Ba(B’1/3B”2/3)O3 鈣鈦礦結構行為。Ba(B’1/3B”2/3)O3為工業上主要的微波介電材料，其中Ba(Mg1/3Ta2/3)O3更是以低介電損失而聞名。本文中將利用第一原理模擬計算去推測完美的Ba(B’1/3B”2/3)O3晶體其體積模量(bulk modulus), 包含拉曼與紅外線吸收的聲子振動行為，以及由聲子與電子貢獻的介電常數。另一方面利用Ba(Mg1/3Ta2/3)O3材料去設計一個介電共振天線。首先，利用第一原理模擬出Ba(Mg1/3Ta2/3)O3與Ba(Mg1/3Nb2/3)O3的體積模量分別為156 GPa與258 GPa。Ikawa et al 教授的論文(1998)中顯示了實驗Ba(Mg1/3Ta2/3)O3的體積模量為154 GPa，這實驗結果與本論文中模擬體積模量相當接近。可惜的是 Ba(Mg1/3Nb2/3)O3材料並沒有實驗的體積模量數據可供比較。第一原理也可分析並提供Ba(B’1/3B”2/3)O3簡正振動模的頻率與行為，包含了九個拉曼聲子，十六個紅外聲子以及三個無法激發的聲子振動模。詳細的分類與振動型式可見附錄一。經由第一原理推測出的Ba(B’1/3B”2/3)O3單晶理論頻率與參考論文中的陶瓷多晶樣品實驗頻率相當的接近。在計算介電常數上，Born and Huang 提供了有效電荷模型可計算由聲子提供的介電貢獻。在微波範圍中，只要考慮聲子與電子的介電貢獻，經由計算後，模擬Ba(Mg1/3Ta2/3)O3 的聲子與電子介電貢獻分別為23.4 與 4.14。此結果與紅外吸收實驗所得知結果相當接近(εr(phonon)=23.3 and εr(electron)=4.4). 而 Ba(Mg1/3Nb2/3)O3的理論推測值結果也相當符合實驗。而有四個對介電貢獻貢獻重大的聲子分別為2Eu, 2A2u, 4Eu, 與3A2u，其中兩個聲子(2Eu and 2A2u) 為鋇離子與其他離子的相對運動；而另外兩個聲子(4Eu, 3A2u) 為B” 離子與氧的的相對運動。經由辨別各聲子的運動行為，我們可以解釋參雜不同雜質的Ba(B’1/3B”2/3)O3聲子改變行為，例如SrxBa1-x(Mg1/3Ta2/3)O3 (x< 0.5)。 在參雜量小於0.5 ，拉曼光譜並無相變，兩個A1g 特徵模(420 cm-1 and 800 cm-1)卻有不同的頻率改變行為。這可以合理推測鍶離子偏好位於鋇離子與鎂離子的位置，而非鉭離子的位置。而且因為鍶偏好佔據鋇離子位置上而且鍶離子具有較小的質量與較大的Born 有效電荷導致隨著參雜濃度增加，樣品的介電常數也隨之增加。在Ba(B’1/3B”2/3)O3 的應用上，本文使用Ba(Mg1/3Ta2/3)O3 材料設計一個介電共振天線，其主要應用在無線通訊方面，共振頻率在2.4 GHz 至 2.484 GHz。此天線在2.44 GHz中有最小的回饋損失(Return loss) -34.67 (dB)，與最強的效率(68 %)與天線增益(5.13)。在3D的輻射途中，天線的xy 平面具有類似全方面的輻射圖，但是在y-z與 x-z 平面表現出定向的輻射。

In this paper, there are two approaches to investigate Ba(B’1/3B”2/3)O3 perovskite ceramics. First study focus on ab-initio simulation of Ba(Mg1/3Ta2/3)O3 and Ba(Mg1/3Nb2/3)O3. The properties of Ba(B’1/3B”2/3)O3 ideal single crystal can be predicted or compared with measured results, such as bulk modulus, normal vibration motions, and permittivity values contributed by phonon and electrons. The other practical study is to design an dielectric resonator antenna of Ba(Mg1/3Ta2/3)O3. The estimated bulk modulus of Ba(Mg1/3Ta2/3)O3 is around 156 (GPa) while measured value is 154 (GPa).The normal vibrational modes of Ba(B’1/3B”2/3)O3, including 9 Raman phonons, 16 IR modes and 3 silent modes, are classified and illustrated in Appendix I. These frequencies of calculated phonon modes are not only quite close to measured frequencies, but also for the permittivity values. The calculated permittivity of Ba(Mg1/3Ta2/3)O3 due to phonon and electron obtained the value of 23.4 and 4.14, respectively; that are consistent with measured value of from IR analysis(εr(phonon)=23.3 and εr(electron)=4.4). The same conclusion also applies for the results of Ba(Mg1/3Nb2/3)O3. In addition, the behaviors of the four dominant modes to permittivity, 2Eu, 2A2u, 4Eu, and 3A2u, were figured out. 2Eu and 2A2u mode are the vibration of Ba atoms against other atoms while 4Eu, and 3A2u mode refer to the relative motion of Ta/Nb atoms and oxygen atoms. Through identifying the actions of each vibration mode, the variation of phonon mode in substituted SrxBa1-x(Mg1/3Ta2/3)O3 system (x< 0.5) can be explained. Two A1g mode (420 cm-1 and 800 cm-1) which have the same vibration atoms perform different behaviors. It indicates that Sr atoms prefer locate on Ba and Mg site, instead Ta site. Furthermore, Sr substituted at Ba site would lead to higher permittivity values because of smaller mass and larger Born effective charge of Sr atoms. The last chapter depicts an attempt to utilize Ba(Mg1/3Ta2/3)O3 ceramics in antenna. The permittivity value was applied in design a dielectric resonator antenna of Ba(Mg1/3Ta2/3)O3 for WLAN applications (2.4 GHz to 2.484 GHz). The measured return loss (S11) have lowest point of -34.67 dB at 2.44 GHz. The efficiency and gain of antenna both peaked at 2.44GHz, being 68 % and 5.13, respectively. Radiation patterns in x-y plane perform omni-directional but the y-z and x-z plane of radiation patterns illustrate the directional radiation.

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