泡生法生長大尺寸氧化鋁單晶降溫過程中晶體熱場及熱應力分析

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姓名

闕宜萱(Yi-shiuan Chiue) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

泡生法生長大尺寸氧化鋁單晶降溫過程中晶體熱場及熱應力分析
(Numerical analysis of thermal stress of sapphire crystal cooling by the Kyropoulos method)

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摘要(中)

KY法生長氧化鋁單晶過程中，經常出現晶體破裂情形，這是由於在KY爐生長藍寶石過程裡，藍寶石晶體生長環境溫度約為2323K左右，整顆晶體生長完成後將在爐體內降溫至室溫後開爐取出，其劇烈的溫度變化使得晶體在降溫過程中會產生熱應力，導致晶體破裂。為了提升藍寶石晶體的經濟效益，必須了解KY長晶爐內部的熱傳及晶體熱應力場情形。
由於晶體生長過程無法直接觀察量測長晶爐內之情況，本研究使用有限元素法COMSOL軟體模擬暫態二維軸對稱之模型，模擬晶體與坩堝完全不相黏、晶體與坩堝底部相黏以及晶體與坩堝部分側邊和底部相黏等三種晶體與坩堝接觸情況，其模擬結果呈現當晶體與與坩堝完全不相黏時，其熱應力完全由晶體內部溫梯造成，最大值約為107並未達到藍寶石晶體破裂極限，因此晶體不會破裂；晶體與坩堝底部相黏時，所產生的熱應力主因為晶體和乾堝熱膨脹係數不一樣造成晶體收縮時受到坩堝拉扯的力，其最大值約為109，超過藍寶石晶體的破裂極限，晶體會從熱應力集中處產生破裂現象。

摘要(英)

The cracks that often appear in sapphire crystal during the cooling process in a Kyropoulos furnace after growth may be induced by higher thermal stress due to thermal inhomogeneity in the crystal. This happens very often in the growth of larger sapphire crystals. How to improve this is the key to improving the quality of the sapphire crystal. In this study, a numerical computation is performed to predict the thermal and stress history during the cooling process in a Kyropoulos furnace. The thermal distribution during the cooling process is controlled by the cooling and power reduction processes. Since the sapphire crystal is semitransparent, radiative heat transfer plays an important role at higher furnace temperatures. However, this effect is less significant when the furnace temperature decreases. The thermal and stress distributions in the crystal during the process are significantly affected by the internal radiative heat transfer.
In this study, we simulate about three cases, ⅰ) crystal and crucible completely unsticky, ⅱ)only bottom of the crystal and the crucible are sticky, and the results show that the crystal don’t crack when crystal and crucible completely unsticky, the stress is caused entirely by the internal temperature gradient of crystal. When the crystal sticky with crucible, thermal stress generated by the coefficient of thermal expansion of crystals and crucible are different, the maximum value of thermal is approximately 109(Pa), exceed the breakdown limit of sapphire crystal, so the crystal crack. If the sticky area is more, then the thermal stress concentration is more, cracks of sapphire is more serious.

關鍵字(中)

★ 熱應力
★ 泡生法
★ 氧化鋁單晶

關鍵字(英)

★ sapphire
★ thermal stress
★ KY

論文目次

摘要 I
Abstract II
致謝 III
目錄 IV
圖目錄 VI
表目錄 IX
符號說明 X
第一章緒論 1
1-1 氧化鋁單晶簡介 1
1-2 泡生法(Kyrupoulos Method) 2
1-3 藍寶石單晶熱應力概論 3
1-4 文獻回顧 4
1-5 研究目的 6
第二章系統描述與數學模式 12
2-1 物理系統與假設 12
2-2 數學模式 13
第三章求解方法與分析步驟 21
3-1 求解方法 21
3-2 晶體降溫模擬分析步驟 21
3-2-1 繪製幾何圖形 22
3-2-2 元素形式及材料設定 22
3-2-3 統御條件設定與邊界條件設定 22
3-2-4 產生網格、網格測試與收斂測試 23
3-2-5 求解與分析 23
第四章結果與討論 29
4-1 降溫時晶體與坩堝不相黏時晶體熱場及熱應力場分析 29
4-2降溫時坩堝與晶體底部相黏時的熱應力分析 33
第五章結論與未來研究方向 51
5-1 結論 51
5-2 未來研究方向 52
參考文獻 53

參考文獻

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指導教授

陳志臣(Jyh- Chen Chen)

審核日期

2012-7-30

推文