Ca2SiO4可在接觸變質岩中尋獲且早在18世紀中期已於工業應用中扮演重要角色，而(CaxSr1-x)2SiO4固溶體則可運用於螢光粉中。在Ca2SiO4中發現高溫相可被保存至室溫環境，其原因仍然有許多爭議。(CaxSr1-x)2SiO4固溶體系列之結晶結構在前人的研究當中僅有些許室溫之資訊，尚未完整的建立高溫下之相變行為。本研究藉由固態反應法合成樣品，將Ca2SiO4經過不同的熱處理後，再以X光繞射進行相鑑定，搭配第一原理計算的結果，探討Ca2SiO4在冷卻時其相變行為。利用實驗室X光繞射與同步輻射高溫、低溫X光繞射搭配Rietveld method精算方法，探討(CaxSr1-x)2SiO4固溶體之結晶結構與成分之間的關係以及相圖的建立。
實驗結果顯示Ca2SiO4最終產物會受到實驗過程中燒結溫度影響，若升溫至較低的溫度範圍(1173-1373 K)，降溫後產物是以高溫相(β相)為主，若溫度較高(大於1373 K)，則得到低溫相(γ相)為主的產物。第一原理計算結果顯示0 K及0 GPa的環境下，γ相能量相對於β相略低一些，因此推斷在室溫室壓環境下γ相為熱力學穩定相而β相為亞穩定，但兩相之間能量差相當小，推測兩相之間能障較高，且相變溫度僅約770 K，因此無法提供足夠動能進行相變，導致β相易被保存至室溫。當燒結溫度較高再進行降溫，會使得顆粒之間累積較多的應變，此應變將會使β相不穩定，繼續相變成γ相。另外，降溫速率的不同亦會影響產物中以兩相的比例。
在一系列固溶體(CaxSr1-x)2SiO4合成及X光繞射實驗中發現，當成分為x=0.1-0.9時，室溫皆為α’L相，固溶體從α’L相→α’H相之相變溫度隨著成分不同而變，皆比端成分還低，在成份x=0.2時會有最低的相變溫度。分析結果發現室溫下晶格參數隨著成分的變化會受到陽離子優選排列以及鍵長改變呈現非線行的變化。在進行擬合的過程中也發現，陽離子在兩個不同配位位置之分佈會影響(111)晶面之強度，因此(111)晶面也許是判斷有序-無序擬合好壞的依據。進一步在本研究當中也發現在α’L相中其衛星繞射面的波向量(q)主要會受到成分的影響而溫度為次要影響。
本研究試圖將實驗結果於野外應用上，期望判斷出露頭所經歷之熱歷史。也首次繪製出(CaxSr1-x)2SiO4高溫相圖，以及分析出調整型結構隨溫度、成分的變化。

Ca2SiO4 could be found in the contact metamorphic rocks and played an important role in the field of industry since the middle of 18th century. The solid solutions of composition (CaxSr1-x)2SiO4 were developed to be a material of phosphor. The high temperature phase of Ca2SiO4 can be retained at room temperature based on previous observations. However, the reason of that remains controversial. Only few studies focused on the solid solutions (CaxSr1-x)2SiO4 at room temperature. Furthermore, the phase transformation of solid solutions at high temperature was not investigated yet. The solid-state reaction was applied to synthesize samples in this study. To investigate the phase transformation of Ca2SiO4 upon cooling and the geological implication, the X-ray diffraction was used to determine the phase of final products after different heat treatment for Ca2SiO4. The first-principle calculation result was also taken to compare the energy between phases. To investigate the relationship between crystal structure of (CaxSr1-x)2SiO4 solid solutions and composition and establish the phase diagram, the in-house X-ray diffraction, high temperature and low temperature X-ray diffraction of synchrotron was used with Rietveld method.
The results showed that the crystal phases of final products were determined by the soaking temperature. If the sintering temperature was set within the lower temperature range (the stability field of α’L phase, 1173-1373 K), the dominated phase of products was high temperature phase (β); otherwise at higher temperature range (the stability field of α’H phase, higher than 1373 K), the dominated phase was low temperature phase (γ). The first-principle calculation results showed that the energy of the γ phase was slightly lower than that of the β phase at 0 K and 0 GPa. It indicated that the γ phase was a stable phase and the β phase was a metastable phase at ambient conditions. However, the energy difference of two phases was fairly small. This study suggested that the energy barrier between β and γ phases should be high. The transition temperature was about 770 K suggested by previous study. These might be the reason why the β phase could be retained at room temperature. More strains would be accumulated in the crystal when higher sintering temperature was applied. The accumulated strains in the crystal would make the β phase unstable and then induce them transform into the γ phase. The cooling rate might affect the ratio of mixtures of the β and γ phase.
The α’L phase would be the only crystal phase in the series of solid solutions with the composition (CaxSr1-x)2SiO4, x=0.1-0.9, which was synthesized, at room temperature. The temperature of phase transformation α’L→α’H in solid solutions was lower than end-members and would vary with compositions. There was a lowest transition temperature at x=0.2. The results showed that the variation of cell parameters was non-linear with increasing Ca2+ concentration and might be related to the state of order-disorder. The intensity of (111) diffraction peak would be affected by the distribution of cation in two occupancy sites with refinement. Therefore, the diffraction peak (111) might be an indicator of order-disorder refinement. It was further observed that the wave vector was majorly influenced by the composition, whereas impacted by the temperature less.
This study attempted to speculate the geological setting based on the experimental results and expected to determine the thermal history that the outcrop went through. It was the first time to provide the high temperature phase diagram and to investigate the correlation between modulated structure as the functions of temperature and composition.

摘要 I
Abstract II
誌謝 IV
Content V
List of table VII
List of figure VIII
Chapter 1 Introduction 1
1-1 Previous study 1
1-1-1 Ca2SiO4 1
1-1-1-1 Natural mineral of Ca2SiO4 2
1-1-1-2 Phase transformation of synthesized Ca2SiO4 upon cooling 3
1-1-2 Solid solutions of (CaxSr1-x)2SiO4 4
1-1-3 Modulated structure 5
1-2 Motivation and purpose 6
Chapter 2 Experimental method and analysis 13
2-1 Specimen synthesis 13
2-2 Phase determination and structure analysis 14
2-3 Deriving crystal structure from diffraction pattern: theory and programs 15
2-3-1 Theory 15
2-3-2 Rietveld method 16
2-3-3 Le Bail method 18
2-4 Program for data processing 19
2-5 Error of analysis 19
2-6 Starting models of crystal structures of Ca2SiO4 and Sr2SiO4 20
2-7 First-principle calculation 20
2-8 Spontaneous strain calculation 20
Chapter 3 Experimental results 29
3-1 Ca2SiO4 29
3-1-1 Products from different thermal histories 29
3-1-2 In-situ high temperature results 30
3-1-3 First-principle calculation results 31
3-1-4 Results of spontaneous strains from experimental data 31
3-2 (CaxSr1-x)2SiO4 32
3-2-1 Crystal structure of products phase at room temperature 32
3-2-2 Transition temperature of (CaxSr1-x)2SiO4 33
3-2-3 Wave vector value of (CaxSr1-x)2SiO4: functions of composition and temperature 34
Chapter 4 Discussion and conclusions 65
4-1 Transformation in Ca2SiO4 upon cooling and possible implication 65
4-1-1 Transition between β and α’L phase 65
4-1-2 Phase transition from α‘H to γ phase 66
4-1-3 Geological implication 67
4-2 Solid solutions of (CaxSr1-x)2SiO4 68
4-2-1 Phase diagram 68
4-2-2 Crystal structure refinement 69
4-2-2-1 Analysis of cell parameters 69
4-2-2-2 Order-disorder in (CaxSr1-x)2SiO4 70
4-2-2-3 Bond lengths of M1 and M2 sites in (CaxSr1-x)2SiO4 71
4-2-3 Analysis of modulated structure 72
4-3 Conclusions 73
4-4 Future work 74
References 84

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