工業上採用的成本低、製程簡易、可量產的固態反應製程合成純相YAG粉體，係以氧化鋁與氧化釔或含鋁、釔之鹽類混合，經高溫煅燒後而得。獲得YAG純相所需溫度常取決於反應原料粉末粒徑大小及混合均勻度。使用微米級之氧化物為原料，也需>1600oC，也需配合多次再研磨混合與煅燒處理才可獲得純相，屬一高耗能製程。
一般細化原料粉末、提高成分混合均勻度為改良此製程的常見手段。但對YAG而言，本文提出另一觀點，使用粗細不同之二原料粉末經均勻混合，仍有可能達成與細粒原料混合之同等效果。
以Y2O3+Al2O3反應生成YAG的研究說明YAG係藉由Al成分往Y2O3粒體方向擴散而得，因此觀察到YAM→YAP→YAG之反應過程。本研究提出即便使用粗粒原料粉末，若採用適當之Y2O3/Al2O3粒徑比，使Y2O3、Al2O3二成分粒體在合成反應中計量接觸，獲得充足之Al來源，也可不需細化原料而簡易地獲得純相YAG粉末。再者，利用Al成分擴散進入Y2O3粒體合成YAG之特性，藉由Y2O3粒體為母體，作為合成預定粒徑YAG粉末的材料設計概念也屬可行。
本研究於第四章藉由粒體的空間排列關係，分析在符合YAG計量條件下，二不同粒徑成分顆粒間可有效接觸，及固態反應過程粒徑比與反應速率間的關係。當Y2O3/ Al2O3粒徑比在0.25-4範圍，二成分顆粒可有效接觸，且都符合YAG計量所需。但不同範圍之Y2O3/ Al2O3粒徑比對合成YAG之難易 (速率) 卻有不同。實驗固定Al2O3粒徑為400 nm，縮減Y2O3粒徑使Y2O3/ Al2O3粒徑比由0.5降至0.125，雖然反應擴散距離變短，但供應單顆Y2O3粒體之Al成分量 (也即與Al2O3之配位) 減少，初期YAG合成速率反下降。再者，超出合理範圍之0.125起始粉，明顯因部分Y2O3顆粒無法與Al2O3接觸，未達YAG計量所需，其合成YAG反應也顯著劣化。說明原料粉末變細，卻未能使二成分粉末達計量接觸，反不利YAG之合成。當固定Y2O3粒徑為200 nm，縮減Al2O3粒徑使Y2O3/ Al2O3粒徑比由0.5增至1，反應擴散距離固定，但供應單顆Y2O3粒體之Al成分量增加，可加速初期YAG合成速率。當固定Al2O3粒徑為200 nm，增加Y2O3粒徑使Y2O3/ Al2O3粒徑比由0.5增至2，即便擴散距離增加，但供應單顆Y2O3粒體之Al成分量也增加，使YAG生成速率與使用細粒Y2O3粉末者相當。綜合以上所述，比較合成單位體積YAG下 (400 nm Y2O3 + 400 nm Al2O3)，Y2O3/ Al2O3粒徑比由0.25增加至4時，供應單顆Y2O3粒體之Al成分越充足，因此即便使用粗粒Y2O3粉末，只要搭配細粒之Al2O3粉末，也可快速合成YAG。
第五章說明在固態反應過程Y2O3/ Al2O3粒徑比與反應動力學的關係，特別是一般所稱主要兩種YAG生成機制之發生特性。再由之推斷合成高純度（單一相）YAG之有效Y2O3粒徑。.進一步解析固定Al2O3粒徑為200 nm，增加Y2O3粒徑使Y2O3/ Al2O3粒徑比由0.5增至2，比較在使用細、粗Y2O3粉末下，何以YAG生成速率相近，並探討其反應特性。由YAG二階段之生成趨勢，說明其生成機制應有二種依序發生：一為界面反應機制 (interface-controlled mechanism)，二為擴散反應機制 (diffusion-controlled mechanism)。當提供足夠之能量 (溫度)，可使藉由界面反應生成之YAG比例隨溫度呈線性增加，由1350oC的50%增加至1500oC的90%。細粒Y2O3有機會完全藉由界面反應機制合成YAG，而粗粒Y2O3則需再經擴散機制完成反應。藉由動力學之計算，顯示在固定Al2O3粒徑下，Y2O3粒徑變粗，但與Al2O3之配位越多，YAG之生成活化能可由604 kJ/mol降至493 kJ/mol (1350-1500oC)。可以預測的是，此一系統若使用< 200 nm之Al2O3粉末 (增加Y2O3與Al2O3之配位)，應可進一步加速YAG之生成且降低其活化能。
第六章利用第六章推斷之合成高純度 (單一相) YAG之有效Y2O3粒徑，證實因Al成分往Y2O3粒體方向擴散，以Y2O3粒體作為母體，可控制合成之YAG粒徑。證實YAG粉末之粒徑 (< 500 nm) 可藉由Y2O3粉末之粒徑獲得控制。將不同Y2O3/ Al2O3粒徑比之起始粉，藉由1450-1500oC高溫持溫5分鐘，提高界面反應合成之YAG比例，使細、粗Y2O3粉末可快速合成純相 (> 90 wt%) YAG粉末，再統計合成之YAG粒徑與Y2O3粒徑之關係。顯示Y2O3/ Al2O3粒徑比≧1 (Al2O3包覆Y2O3) 之起始粉，在YAG生成過程中，未反應之Al2O3粒體限制釔鋁結晶相在反應過程中可能發生的凝聚、成長，最終獲得為Y2O3粒徑1.24倍之YAG粒體。證實利用Al成分擴散進入Y2O3粒體生成YAG的特性，可作為調控YAG粒徑的方法。以穿透式電子顯微鏡分析Y2O3粒體 (母體) 相轉換過程之微結構，顯示當有二結晶相 (Y2O3/YAM, YAP/YAG) 共存於一粒體內時並未發生破裂，而可維持原Y2O3粒體尺寸。反之，當Y2O3/ Al2O3粒徑比≦1 (Y2O3包覆Al2O3)，在YAG生成過程中Al成分向外擴散進入Y2O3粒體，生成之釔鋁結晶相粒體間容易發生凝聚、成長，最終造成YAG粒體粒徑的不均勻。
第七章藉由YAG此一多成分系統之合成為例，說明本研究成果可提供之相關工程應用。包括已知擴散特性 (Al→Y2O3粒體；Ba→TiO2粒體；Ba→ZrO2粒體) 之多成分氧化物系統，不需將原料細化以降低合成溫度，僅需設計適當之原料粒徑比，並提供足夠之能量 (溫度)，增加藉由界面反應合成產物之比例，即可簡易獲得純相粉末。並可藉由母體粒徑控制合成之產物粉末粒徑，不需高溫熟化、研磨分散後處理，係屬一設計粉末規格概念之實例。

In industry, YAG powders are synthesized by solid-state reaction benefitted with low cost, simplicity, and large-scale production. The process is conducted by mixing alumina (Al2O3) and yttria (Y2O3) (or salts supply Al and Y), and then calcined mixtures to obtain YAG powders. The temperature for a phase-pure YAG is decided by particle sizes of raw materials and homogeneity of mixtures. In general, temperatures above 1600oC are acquired while using raw materials of micrometer, and repeated grinding and calcination are inevitable. Therefore, finer raw materials are usually adopted to solve this problem. However, this study proposed a new viewpoint for YAG synthesis that YAG could be obtained as easily by using submicrometric Y2O3 and α-Al2O3 powders differ in size as using fine ones.
In previous studies, it is demonstrated that YAG is achieved by prompting Al into the structure of Y2O3 to form YAM, YAP, and YAG in turn when using Y2O3 and Al2O3 as raw materials. Accordingly, this study revealed that YAG could be synthesized easily while adopting an appropriate Y2O3/Al2O3 size ratio which Y2O3 was contact with Al2O3 and satisfied YAG stoichiometry, even coarser powders were used. Furthermore, it is practicable that the directional diffusion of Al during YAG formation was utilized to synthesize YAG with desired sizes by using Y2O3 as host materials.
The spacial relation between two oxides and how the Y2O3/Al2O3 size ratio affected formation rates of YAG were elucidated in chapter 4. It showed that two oxides were completely in contact with each other and satisfied YAG stoichiometry when Y2O3/Al2O3 size ratios were in the range of 0.25-4. But, the rates of YAG formation were varied with different Y2O3/Al2O3 size ratios. When Al2O3 of 400 nm was used, decreasing Y2O3/Al2O3 size ratio from 0.5 to 0.125 resulted in shorter diffusion length for Al, but less supply of Al for a single Y2O3 particle. Therefore, a decreasing initial YAG formation rate was observed. Moreover, the two oxides were in contact with each other partly when Y2O3/Al2O3 size ratio of 0.125 was adopted, and postponed the YAG formation rate as well. When Y2O3 of 200 nm was used (same diffusion length for Al), increasing Y2O3/Al2O3 size ratio from 0.5 to 2 resulted in more supply of Al for a single Y2O3 particle. Extraordinarily, a comparable initial YAG formation rate was observed no matter which particle size of Y2O3 was adopted. Hence, even a coarse Y2O3 was used, as long as a finer Al2O3 powder was co-operated, YAG could be obtained easily as well.
The relation between the Y2O3/Al2O3 size ratio and kinetics of YAG formation was elaborated in chapter 5. Two YAG formation mechanisms were explored and the Y2O3 particle size limit which could be achieved YAG stoichiometry at some calcined temperature also be predicted. No matter which particle size of Y2O3 was adopted, YAG formed rapidly when starting powders just subjected heat treatments, and then slow down with a prolonged duration. YAG formation could be characterized two stages induced in turn from interface- controlled mechanism and diffusion-controlled mechanism. A linear-increased proportion (50% to 90%) of YAG formed via interface-controlled mechanism when a higher temperature was provided (1350oC to 1500oC). It showed that a fine Y2O3 particle could be achieved YAG via interface-controlled mechanism only, but diffusion-controlled mechanism was followed when a coarse Y2O3 particle was used. When Al2O3 of 200 nm was used, activation energy for YAG formation decreased from 604 kJ/mol to 493 kJ/mol when Y2O3 particles increased from 100 nm to 400 nm.
Utilizing Y2O3 as host materials to obtained YAG powders with desired sizes were demonstrated in chapter 6. The practicability was based on the directional diffusion of Al during YAG formation. YAG powders (> 90 wt%) could be obtained via interface-controlled mechanism when starting powders subjected a heat treatment of 1450-1500oC/ 5 min. It revealed that particle sizes of YAG were 1.24 times of that of Y2O3 by Feret diameter statistics.
Possible evolutions and related engineering applications for other multi-element systems induced from this study were discussed in chapter 7. This study proposed that well-known diffusion characterizations for multi-element systems (e.g. Al→Y2O3, Ba→ TiO2, Ba→ZrO2) should be utilized to obtained an appropriate size ratio of raw materials, and then provided a high temperature to completed the reaction via interface-controlled mechanism. It is practicable that a phase-pure powder with a desired particle size could be easily obtained.

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