微波介電材料La(Mg1/2,Ti1/2)O3的聲子計算:密度泛函微擾理論之研究

Phonon calculations on microwave dielectric material La(Mg1/2,Ti1/2)O3:Density-Functional Perturbation Theory Study

李維崇(Way-Chung Lee)

指導教授 ： 林諭男

淡江大學/理學院/物理學系碩士班/碩士(2008年)

https://doi.org/10.6846/TKU.2008.00581

摘要

利用第一原理模擬計算La(Mg1/2,Ti1/2)O3材料，以密度泛函微擾理論及線性響應的方式，來研究微波介電材料La(Mg1/2,Ti1/2)O3在Γ點上的聲子行為，並以羅倫茲模型對於材料介電特性跟材料的晶格振盪的關係，來探討利用拉曼光譜實驗及紅外光光譜實驗於La(Mg1/2,Ti1/2)O3材料的結果輔以第一原理模擬計算所得到的資訊，來研究La(Mg1/2,Ti1/2)O3材料的聲子行為與介電特性的關係。

關鍵字

La(Mg1/2,Ti1/2)O3 ； 第一原理 ； 拉曼光譜 ； 紅外光光譜 ； 羅倫茲模型

並列摘要

We use first-principles to begin the simulation on the microwave dielectric material La(Mg1/2,Ti1/2)O3. In our calculations, we use the Density-Functional Perturbation Theory and linear response method to get the phonons at Γ point.
And then, we make a few experimental observations like Raman spectrum and FTIR spectrum on the microwave dielectric material La(Mg1/2,Ti1/2)O3. According to our calculations, the calculated eigenvalues and corresponding eigenvectors of each vibration mode at
Γ point provide a great help on assignment of our experimental observations.
Finally, we use the Lorentz model to study the relation between vibration modes and dielectric properties on the microwave dielectric material La(Mg1/2,Ti1/2)O3.

並列關鍵字

La(Mg1/2,Ti1/2)O3 ； First-Principles ； Raman ； FTIR ； Lorentz model

參考文獻

[1]R.D. Richtmyer, 'Dielectric Resonators', J. Appl. Phys. 10(1039)391-398

[2]P. Hohenbergand W. Kohn,"Inhomogeneous Electron Gas ", Phys. Rev. B136, 864(1964)

[3]W. Kohn and L. J. Sham, “Self-Consistent Equations Including Exchange and Correlation Effects, Phys. Rev. 140,1133 (1965)

[4] John P. Perdew and Wang Yue, ’Accurate and simple density functional for the electronic exchange energy: Generalized gradient approximation’, Phys. Rev. B 33, 8800 (1986)

[6]Kittel, ‘Introduction to Solid State Physics’ ,John Wiely & sons 7th ed.(1996)