本研究以真空電弧熔煉法，製備由Al, Co, Cr, Fe, Ni與Ti組成的，多種五元及六元等莫合與非等莫耳高熵合金。所得到的鑄造態合金經過1100℃持溫24小時，均質化水淬，得到均質化態合金。鑄造態合金及均質化態合金，作微結構、熱膨脹係數及磁場大至9 T的霍爾效應量測。微結構主要由FCC, BCC, Full Heusler與Sigma相組成，大部分具有磁性。均質化態合金的磁性Invar效應，使合金熱膨脹係數在居禮溫度處下降，此乃磁矩排列由有序變成無序的結果。等莫耳均質化態合金居禮溫度在480 K到750 K之間，非等莫耳均質化態合金居禮溫度在780 K到870 K之間。
本研究許多合金出現異常霍爾效應，與各約一半合金出現類電子與類電洞行為，5 K及300 K載子濃度在10^22 ~ 10^23 cm^-3之間，與純金屬和傳統合金的相似。載子遷移率為0.21 ~ 2.61 cm^2 V^-1 s^-1之間，比純金屬與傳統合金的低，與多元素混合產生的嚴重晶格缺陷，增加電子散射效應，阻礙電子的移動有關。自由電子模型有效自由電子數即價數，在0.171至4.716之間。等莫耳均質化態合金殘餘電阻率比值(RRR)分布在0.988至1.259之間，在1.032至1.056與1.139至1.207兩區出現正霍爾係數，其餘為負。等莫耳均質化態合金殘餘電阻率比值(RRR)分布在1.114至1.174之間，在1.158至1.173區間出現正霍爾係數，其餘為負。霍爾係數的正負值，被解讀成與聲子和晶格缺陷共同作用，導致Brillouin 區與Fermi區形狀隨溫度變化有關。
高熵合金具有簡單的晶體結構，故滿足Bloch定律，可以平均效應的概念，修正並應用Kronig-Penney模型於高熵合金中。

In this study, selected from Al, Co, Cr, Fe, Ni, and Ti, various quinary equal- and non-equal-mole and senary high-entropy alloys (HEAs) are made by vacuum-arc melting. The as-cast alloys are sequentially homogenized at 1100℃ for 24 h and water-quenched to obtain as-homogenized alloys. Microstructure examination, coefficient of thermal expansion (CTE) measurement, and Hall effect up to 9T are performed. Microstructure is composed of FCC, BCC, full Heusler, and sigma phases. Most alloys are of magnetic. CTE of as-homogenized alloys drops at Curie point due to magnetic order-disorder transition, the so-called magnetic Invar effect. Curie points thus obtained are in the intervals of 480 K to 750 K and 780 K to 870 K for equal- and non-equal-mole as-homogenized alloys, respectively.
Anomalous Hall effect occurs in most alloys, and electron-like and hole-like electrical conduction behaviors emerge in 50 %-50 % ratio of alloys. Similar to their pure elements and conventional alloy counterparts, carrier concentration of HEAs in this study at 5 K and 300 K varies from 10^22 to 10^23 cm^-3, while lower than their pure elements and conventional alloy counterparts, mobility of carriers varies from 0.21 to 2.61 cm^2 V^-1 s^-1, due to multielement mixing-caused heavy imperfection in alloy lattices, making strong electron scattering effect and impeding the electron transport. The effective number of free electrons in the free electron model is the valence number, ranging from 0.171 to 4.716. The residual electrical resistivity ratio (RRR) for equal-mole and non-equal-mole alloys ranges from 0.988 to 1.259, and from 1.114 to 1.174, respectively. The sign of Hall coefficient is positive for RRR intervals of 1.032 to 1.056 and 1.139 to 1.207 for equal-mole alloys, while it is positive for RRR in the interval of 1.158 to 1.173 for non-equal-mole AlxCoCrFeNi alloys. Otherwise, it has negative sign. The sign of Hal coefficient is explained t have something to do with the interaction between phonon and lattice defects that determines the shape of temperature-dependent Brillouin zone and the Fermi surface.
HEAs have simple crystal structure, thus they obey the Bloch theorem. One can apply a modified Kronig-Penney model t them with an idea of “average” effect in potential.

第1章 前言 1
1.1 研究背景 1
1.2 研究動機與實驗目的 1
1.3 研究大綱 1
第2章 文獻回顧 2
2.1 高熵合金 2
2.1.1 高熵合金發展 2
2.1.2 高熵合金的特點 3
2.1.3 高熵合金的電與磁性質相關研究 6
2.2 熱膨脹係數 8
2.2.1 熱膨脹係數定義 8
2.2.2 影響熱膨脹係數之因素 9
2.3 導電理論的發展 14
2.3.1 導電理論的發展 14
2.3.2 合金電阻率 21
2.4 霍爾效應 24
2.4.1 霍爾效應原理 24
2.4.2 異常霍爾效應 28
2.5 Heusler合金 31
第3章 實驗方法 32
3.1 合金成份設計 32
3.2 鑄造態合金製備 32
3.3 均質態合金製備 32
3.4 微結構觀察 33
3.5 X光粉末繞射 33
3.6 相變化溫度量測 33
3.7 熱膨脹係數量測 33
3.8 霍爾效應量測 34
第4章 結果與討論 39
4.1 微結構觀察 39
4.1.1 鑄造態AlCoCrFeNiTi【C-6】 39
4.1.2 鑄造態CoCrFeNiTi【C-5(Al)】 39
4.1.3 鑄造態AlCrFeNiTi【C-5(Co)】 39
4.1.4 鑄造態AlCoFeNiTi【C-5(Cr)】 40
4.1.5 鑄造態AlCoCrNiTi【C-5(Fe)】 40
4.1.6 鑄造態AlCoCrFeTi【C-5(Ni)】 41
4.1.7 鑄造態AlCoCrFeNi【C-5(Ti)】 41
4.1.8 均質態AlCoCrFeNiTi【H-6】 42
4.1.9 均質態CoCrFeNiTi【H-5(Al)】 42
4.1.10 均質態AlCrFeNiTi【H-5(Co)】 42
4.1.11 均質態AlCoFeNiTi【H-5(Cr)】 43
4.1.12 均質態AlCoCrNiTi【H-5(Fe)】 43
4.1.13 均質態AlCoCrFeiTi【H-5(Ni)】44
4.1.14 均質態AlCoCrFeNiTi【H-5(Ti)】 44
4.2 相變化溫度量測 75
4.3 熱膨脹係數量測 78
4.4 霍爾效應量測 82
4.4.1 霍爾效應數據處理 82
4.4.2 霍爾電阻率與霍爾係數 83
4.4.3 載子濃度與遷移率 84
4.4.4 有效自由電子數 86
4.4.5 霍爾係數與殘餘電阻率 86
4.5 高熵合金導電模型 87
第5章 結論 105
第6章 參考文獻 107
第7章 附錄 110
7.1 霍爾效應量測原始數據 110

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