本研究探討類均質條件下奈米級θ-Al2O3微粒之晶粒成長現象。研究以經均質處理後θ-Al2O3粉之θ-至α-Al2O3孕核成長相轉換系統為對象，利用θ-晶粒需成長至相轉換臨界晶徑dcθ而成核的晶粒特性，作為研究其晶粒成長的基礎。經適當均質化後的θ-Al2O3粉末在熱處理過程（DTA）會出現單一溫度的相變放熱峰，代表θ-至α-Al2O3孕核動作的同時發生。也代表一θ-Al2O3粉末系統其原始晶徑雖開始時晶粒尺寸不一，具有粒度分佈，但卻可經由熱處理成長而達同一晶徑dcθ，同時發生相變孕核。本研究即欲了解此一大小不一的θ-Al2O3晶粒粉末系統，何以於定速升溫熱處理過程可同時成長至相同晶徑dcθ。由於相變臨界晶徑大小係由粒體本身的表面能與體能量二者決定，且均假設球形粒體成長為研究對象。當系統的熱力學、動力學反應條件改變時，是否會造成θ-Al2O3晶形改變而影響此臨界晶徑的大小，亦為本研究所欲進行了解的部分。
實驗藉由機械攪拌方式先對11.3、17.7及21.8 nm三種不同平均晶徑之θ-Al2O3粉末系統進行均質處理。再將此三種粉末以三種壓力單軸壓成型，得到具不同堆積密度Fv及表面積密度Fso的反應系統。此代表了反應系統擁有不同的熱力學及動力學反應條件。由之了解在均勻的微結構條件下，不同的熱力學及動力學反應條件對奈米θ-Al2O3晶粒成長的影響，並從中了解θ-Al2O3晶粒的成長方式以及其到達臨界晶徑dcθ時的粒體特性。
研究結果發現，θ-Al2O3晶粒粉末系統以等表面積密度下降速率的方式進行粒體的粗化。不同晶徑系統表現相近的下降速率，其粒體成長過程乃採聚合成長。過程中，細晶粒將先聚合，存在之粗晶粒則等細晶粒成長至與其相近晶徑再二者結合成長至更大晶徑。不同的系統堆積密度Fv顯示，堆積密度並不影響晶粒的粗化速率，但會影響系統中（細）晶粒開始成長溫度，對θ-Al2O3的相變臨界晶徑dcθ的大小也會產生影響：提升堆積密度Fv將使其開始發生聚合溫度下降，而臨界粒徑也趨圓變小。
從θ-Al2O3晶粒成長的研究結果得知，粉體系統顯微結構上的均質，於微觀上係由具不同的熱力學、動力學條件的微小區域或單元，在空間作均勻分佈所組成。這些區域或單元，需反應活化能較低者，會先發生反應。而活化能高者則後反應。也即同一系統中，具相同表面能的粒子會在相同的時間開始發生相同的反應。因此，嚴格來說，系統並無法真正達到每一部位同時開始反應的現象。但於微觀上，此類型的反應依舊呈現了「具相同的熱力學、動力學條件的區域或單元會同時發生反應」的現象。
因此，假如要達到系統任一部位皆同一時間發生反應，必須要求粒體皆具有相同粒徑且越小越好。唯對奈米晶粒系統的反應而言，固相反應的發生終究只能達到「類均質」，無法達到真正的同步。此因以單一粒體觀點而言，粒子由原子堆積而成，原子排列仍具方向性，因此每個晶面所呈現之表面能也不相同。對反應而言，表面能條件不同，反應也就難達同時發生。
研究最後以異質析出法製備均一微結構θ-Al2O3-Core-Boehmite-Shell的凝聚體系統。此系統之核、殼各具類均質，但也各有各的熱力學、動力學反應條件，二者混合又另構成一類均質系統。研究試圖以此證明固態系統於微觀上的「類均質」反應現象。從實驗結果得證，每個凝聚體確實存在θ-→α-Al2O3的相轉換（核）以及Boehmite經一系列過渡相Al2O3而相變至α-Al2O3（殼）二個反應系統，且二系統依其所具有的熱力學、動力學條件而各自發生類均質反應。由於整體系統係由相同微結構凝聚體所組成，整體反應對α-Al2O3的晶粒成長而言，亦為一類均質系統。也由於此現象的存在，有效的控制凝聚體尺寸，並採適當的θ-Al2O3/ Boehmite配比及熱處理條件，可成功的利用此法得到晶粒< 100 nm、不具蠕蟲狀成長之α-Al2O3粉末。

Growth behavior of nano-scaled θ-Al2O3 crystallites under quasi- homogeneous conditions was investigated using a series of homogenized θ-Al2O3 powders with various crystallite sizes. θ- to α-Al2O3 phase transformation is considered to be achieved by a nucleation and growth process. During thermal treatment, θ-Al2O3 crystallite grows, exceeding the critical size (dcθ) needed for the formation of α-Al2O3 nucleus (dcα), and nucleation of α-Al2O3 occurs. The DTA (Differential thermal analysis) profile of θ- to α-Al2O3 phase transformation would show a monotonous peak if the θ-Al2O3 powders have been pre-homogenized. It means the θ-crystallite in the powder system although shows various sizes would reach the critical size simultaneously and then experience the same transformation temperature (Tp). The purpose of this investigation was exploring how θ-crystallites of various sizes would reach the same size dcθ at the same temperature (Tp) during thermal treatment with fixed heating rate. Furthermore, critical size of phase transformation for one crystal is affected by its free energy changes in surface and volume, obviously the former is dependent on particle shape. The geometry effects of dcθ crystallite on the thermodynamic and kinetic aspects of the powder systems were also examined in this investigation.
3 homogenized θ-Al2O3 powders of different mean crystallite sizes (11.3, 17.7, and 21.8 nm) were performed by mechanical stirring, through which 9 sets of samples (3 x 3 = 9) were prepared using uniaxial pressing at 3 pressures (250, 500, and 750 MPa), as to have samples exhibiting different packing densities (weight/ volume, Fv) as well as different specific volume surface area (Total surface area/ volume, Fs), representing various thermodynamic and kinetic conditions.
The results demonstrated the growth rate between smaller and coarser θ-Al2O3 crystallite can be identical, being of equal area/time reduction. The sequential crystallite coarsening by coalescence began with the smaller ones firstly at lower temperatures, and then followed by the coarser at higher temperatures. Further, the growth of coarser crystallite seems to start with the smaller ones once the latter caught the formers’ sizes. Normally the phase transformation temperature was determined by the packing density Fv despite of the crystallite size of the powder system. To the same powder system, a higher packing density may result in a lower transformation temperature, indicating the system would reach the critical size at lower temperature. Thus to the same powder system fabricated with various packing densities Fv, the higher one eventually brings about the crystallites with similar sizes to initiate the coarsening at even lower temperatures. Besides, the critical size of θ-Al2O3 crystallite was smaller in powder system with higher packing density due to its sphere-liked geometry.
From the growth behavior of nano-scaled θ-Al2O3 crystallites, it is clear that the homogeneous powder system is composed of small domains or units which spatially distribute uniformly with distinct thermodynamic and kinetic conditions. Units with lower activation energy of reaction would react first. Particles in the system with equal surface energy would initiate reaction at the same time. Therefore, strictly precise speaking, the system could not really react simultaneously even though every unit with distinct thermodynamic and kinetic conditions of the system did. For reaction occurs simultaneously, an identical particle diameter of as small as possible in the system is required. However, for solid state reaction of nano particle systems, only quasi- homogeneous reaction could be defined because each crystal face of a crystallite possesses different surface energy due to the orientation of atoms.
The phenomena of microscopic quasi-homogeneous reaction in the system were improved in the last part of this investigation by designing agglomerates with θ-Al2O3-Core-Boehmite-Shell microstructure which was performed by heterogeneous precipitation technique. Such an agglomerate, a macroscopic quasi-homogeneous system, was composed of two microscopic quasi- homogeneous systems: θ-Al2O3 crystallites and boehmite. The results indicated these two quasi-homogeneous systems with individual thermodynamic and kinetic conditions underwent characteristic distinct pathway to transform into α-Al2O3 during thermal treatment. After that, agglomerates showed the macroscopic quasi- homogeneous reaction in growth of α-Al2O3 crystallites. Moreover, taking advantages of this technique, <100 nm discrete α-Al2O3 crystallites without vermicular growth can be obtained by efficiently controlling the size of agglomerates and the weight ratio of θ-Al2O3/boehmite accompanying appropriate thermal processes.

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