本研究利用 GSAS 結構精算軟體以 Rietveld 方法精算以求得晶體結構、電子密度分佈和鍵結型態的關係，並利用結構因子計算離子半徑和電子數的值。首先以 MgO、Pt、SiO2 為樣品觀察電子密度在離子鍵、金屬鍵和共價鍵中的分佈情況，並作為參考，之後再以 BaTiO3 和 BaTiO3+20mol% BNT 為樣品，觀察在少量取代下的電子密度分佈的變化，是否有鍵結發生改變等，最後再以 MgZnNb4O12 和 MgZnTa4O12 樣品為對照，觀察 Ta (離子半徑 0.69 Å) 和 Nb (離子半徑 0.70 Å) 在互相取代之後的晶體結構、電子密度分佈和鍵結的變化，結果顯示，Ta 和 Nb 在互相取代之後，晶體結構卻由MgZnNb4O12 (Orthorhombic) 變為 MgZnTa4O12 (Tetragonal)，在計算完離子半徑和電子數目的值後發現 MgZnNb4O12 結構中的 B-Site 和 O 離子的半徑比起在 MgZnTa4O12 結構中還小，推測可能是 Ta 和 O 之間比 Nb和 O 之間的離子性較大又或是 Ta 比起 Nb 的電子數較多導致與周圍 O 離子電子雲的斥力較大從而增加 Ta 和 O 之間的距離，並使結構中 Mg,Zn 和 O 的電子密度受到壓迫導致距離變近，最終導致在 MgZnTa4O12 結構中的 Ta-O八面體和 Mg,Zn-O 八面體與 MgZnNb4O12 結構中的 Nb-O八面體和 Mg,Zn-O 八面體差異過大而使八面體移動，最終使結構產生改變。

In this study, we use the GSAS software to calculate the crystal structure, distribution of electron density, nature of bonding and the relationship between ionic radius and electron numbers. First of all, we use MgO, Pt and SiO2 be sample and observe the distribution of electron density in ionic bond, metal bond and covalent bond. Second, we use BaTiO3 and BaTiO3+20mol%BNT be sample watching the difference in distribution of electron density and nature of bonding. Third, we use MgZnNb4O12 and MgZnTa4O12 be sample watching the difference after in distribution of electron density and nature of bonding after Ta (ionic radius 0.69 Å) and Nb (ionic radius 0.70 Å) replace each other.
The results show, when Ta replace Nb, the crystal structure change from Orthorhombic (MgZnNb4O12) to Tetragonal (MgZnTa4O12).After calculated the relationship between ionic radius and electron numbers, we found that the cations and anions in MgZnNb4O12 is smaller than MgZnTa4O12. Speculated that the bonding between Ta and O is more ionic than Nb and O. Another reason, Ta has more electron numbers than Nb, so the repulsion between Ta and O is more than Nb and O. And lead to that the distance between Mg,Zn and O is more close. So the octahedral of Ta and O in MgZnTa4O12 is bigger than the octahedral of Nb and O in MgZnNb4O12; the octahedral of Mg,Zn and O in MgZnTa4O12 is smaller than the octahedral of Mg,Zn and O in MgZnNb4O12. Finally the octahedral move and the structure change.

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