高熵合金具有四個核心效應：高熵、嚴重晶格扭曲、緩慢擴散及雞尾酒效應，而本論文主旨在於探討高熵效應及緩慢擴散效應。由於高熵效應可促進固溶相的形成，但較大的混合焓及原子尺寸差會促進有序相的形成，為瞭解此一競爭，本研究設計兩個參數分析高熵合金的成份與相型態之間的關聯。其一為熱力學參數ε，代表合金中混合熵與混合焓之間的競爭關係；其二為拓樸學參數δ，代表合金中不同元素原子尺寸的差異。利用此二參數分析已知的高熵合金，結果發現可清楚界定出形成單純無序固溶相合金及生成有序相的條件。當δ較小，且混合熵的效應大於混合焓(即ε > 1.1)時，會傾向形成無序固溶相。當混合焓的效應大於混合熵(即ε < 1.1)時，合金傾向生成有序中間相。而當δ超過簡單結構所能承受的極限時，合金即會生成結構較複雜的介金屬相。此研究結果可提供未來合金設計與開發的參考。

此外，本研究藉由「擬二元擴散偶」實驗量測Co-Cr-Fe-Mn-Ni五元高熵合金中各元素的擴散參數，得到高熵合金緩慢擴散效應的直接證據。將各項擴散參數與其他FCC金屬比較，可發現隨著合金元數增加，各元素的擴散係數會隨之降低。而將各元素的活化能除以熔點標準化後，也可發現其值隨著合金元數增加而增加。本研究對這些趨勢提出理論解釋，採用準化學模型對晶格位能的差異幅度加以計算，結果發現高熵合金因主元素多，晶格屬全溶質晶格，晶格位能的差異幅度較大，因此具有許多位能相對較低的晶格位置形成原子的陷阱，使擴散活化能提高，此一理論可說是高熵合金緩慢擴散效應的主要機制。

High-entropy alloys have four core effects: high entropy, sluggish diffusion, severe lattice distortion, and cocktail. The aim of this study is to demonstrate high entropy and sluggish diffusion effects in a quantitative way. High entropy effect has been found to enhance the formation of solid solutions whereas large atomic size difference and large negative mixing enthalpy between unlike atom pairs have been found to enhance the formation of ordered phases. In order to gain more understanding of such an order-disorder competition, this study proposes two parameters to analyze the correlation between alloy compositions and phase types. One is the modified thermodynamic parameter ε which represents the competition between mixing entropy and mixing enthalpy, while the other is the topological parameter δ which represents the atomic size difference. From the analyses of these two parameters of published high-entropy alloys, the well-defined criteria for the formation of random solid solutions and ordered phases are obtained. When δ is small and ε is large (i.e. the effect of mixing entropy dominates over that of mixing enthalpy), alloys tend to form random solid solutions. On the other hands, when ε < 1.1 (i.e. the effect of mixing enthalpy dominates over that of mixing entropy), alloys tend to form ordered phases. Furthermore, when δ is too high to retain simple structures alloys will form intermetallic phases with more complex structures. These criteria could provide a useful guideline for alloy design of high-entropy alloys.

Beside, this study directly confirms the sluggish diffusion phenomenon by the measurement of diffusion parameters for the Co-Cr-Fe-Mn-Ni alloys using a quasi-binary diffusion couple method. Comparing the diffusion parameters of the five component elements measured in the present HEAs with that in the reference FCC metals, it can be found that the diffusion coefficients decrease with the number of constituent elements in the matrix, whereas the normalized activation energies Q/Tm increase with the number of constituent elements. These tendencies are certainly the direct evidences of the sluggish diffusion effect in HEAs. The mechanism behind such effect has also been proposed. The fluctuation of lattice potential energy (LPE) was calculated using quasichemical model. The larger LPE fluctuation in the whole-solute matrix of HEAs provides abundant sites with lower potential energy, which become the traps of atoms and cause higher normalized activation energies and lower diffusion rate.

[1] K.H. Huang, J.W. Yeh, "A study on the multicomponent alloy systems containing equal-mole elements." Master thesis, National Tsing Hua University (1996).
[2] J.W. Yeh, S.K. Chen, S.J. Lin, J.Y. Gan, T.S. Chin, T.T. Shun, C.H. Tsau, S.Y. Chang, "Nanostructured high-entropy alloys with multiple principal elements: Novel alloy design concepts and outcomes." Adv Eng Mater, vol. 6 (2004): pp. 299-303.
[3] J.W. Yeh, "Recent progress in high-entropy alloys." Ann Chim-Sci Mat, vol. 31 (2006): pp. 633-648.
[4] K.T. Rai, J.W. Yeh, S.K. Chen, "Properties of the multicomponent alloy system with equal-mole elements." Master thesis, National Tsing Hua University (1998).
[5] Y.H. Sheu, J.W. Yeh, S.K. Chen, "A study on the multicomponent alloy systems with equal-mole FCC or BCC elements." Master thesis, National Tsing Hua University (2000).
[6] C.Y. Hsu, J.W. Yeh, S.K. Chen, T.T. Shun, "Wear resistance and high-temperature compression strength of FCC CuCoNiCrAl0.5Fe alloy with boron addition." Metall Mater Trans A, vol. 35A (2004): pp. 1465-1469.
[7] Y.Y. Chen, T. Duval, U.D. Hung, J.W. Yeh, H.C. Shih, "Microstructure and electrochemical properties of high entropy alloys - a comparison with type-304 stainless steel." Corros Sci, vol. 47 (2005): pp. 2257-2279.
[8] J.W. Yeh, S.Y. Chang, Y.D. Hong, S.K. Chen, S.J. Lin, "Anomalous decrease in X-ray diffraction intensities of Cu-Ni-Al-Co-Cr-Fe-Si alloy systems with multi-principal elements." Materials Chemistry and Physics, vol. 103 (2007): pp. 41-46.
[9] M.H. Tsai, C.W. Wang, C.H. Lai, J.W. Yeh, J.Y. Gan, "Thermally stable amorphous (AlMoNbSiTaTiVZr)50N50 nitride film as diffusion barrier in copper metallization." Appl Phys Lett, vol. 92 (2008): pp. 052109.
[10] R.A. Swalin, "Thermodynamics of Solids." 2nd ed., John Wiley & Sons, New York (1972).
[11] J.W. Yeh, "Alloy design strategies and future trends in high-entropy alloys." JOM, accepted (2013).
[12] C.J. Tong, M.R. Chen, S.K. Chen, J.W. Yeh, T.T. Shun, S.J. Lin, S.Y. Chang, "Mechanical performance of the AlxCoCrCuFeNi high-entropy alloy system with multiprincipal elements." Metall Mater Trans A, vol. 36A (2005): pp. 1263-1271.
[13] Y.J. Zhou, Y. Zhang, Y.L. Wang, G.L. Chen, "Solid solution alloys of AlCoCrFeNiTix with excellent room-temperature mechanical properties." Appl Phys Lett, vol. 90 (2007): pp. 181904.
[14] L.H. Wen, H.C. Kou, J.S. Li, H. Chang, X.Y. Xue, L. Zhou, "Effect of aging temperature on microstructure and properties of AlCoCrCuFeNi high-entropy alloy." Intermetallics, vol. 17 (2009): pp. 266-269.
[15] S.T. Chen, W.Y. Tang, Y.F. Kuo, S.Y. Chen, C.H. Tsau, T.T. Shun, J.W. Yeh, "Microstructure and properties of age-hardenable AlxCrFe1.5MnNi0.5 alloys." Mater Sci Eng A, vol. 527 (2010): pp. 5818-5825.
[16] J.M. Zhu, H.M. Fu, H.F. Zhang, A.M. Wang, H. Li, Z.Q. Hu, "Synthesis and properties of multiprincipal component AlCoCrFeNiSix alloys." Mater Sci Eng A, vol. 527 (2010): pp. 7210-7214.
[17] M.H. Chuang, M.H. Tsai, W.R. Wang, S.J. Lin, J.W. Yeh, "Microstructure and wear behavior of AlxCo1.5CrFeNi1.5Tiy high-entropy alloys." Acta Mater, vol. 59 (2011): pp. 6308-6317.
[18] C.Y. Hsu, C.C. Juan, W.R. Wang, T.S. Sheu, J.W. Yeh, S.K. Chen, "On the superior hot hardness and softening resistance of AlCoCrxFeMo0.5Ni high-entropy alloys." Mater Sci Eng A, vol. 528 (2011): pp. 3581-3588.
[19] O.N. Senkov, G.B. Wilks, J.M. Scott, D.B. Miracle, "Mechanical properties of Nb25Mo25Ta25W25 and V20Nb20Mo20Ta20W20 refractory high entropy alloys." Intermetallics, vol. 19 (2011): pp. 698-706.
[20] M.H. Tsai, C.W. Wang, C.W. Tsai, W.J. Shen, J.W. Yeh, J.Y. Gan, W.W. Wu, "Thermal stability and performance of NbSiTaTiZr high-entropy alloy barrier for copper metallization." J Electrochem Soc, vol. 158 (2011): pp. H1161-H1165.
[21] Y.L. Chou, Y.C. Wang, J.W. Yeh, H.C. Shih, "Pitting corrosion of the high-entropy alloy Co1.5CrFeNi1.5Ti0.5Mo0.1 in chloride-containing sulphate solutions." Corros Sci, vol. 52 (2010): pp. 3481-3491.
[22] Y.F. Kao, T.D. Lee, S.K. Chen, Y.S. Chang, "Electrochemical passive properties of AlxCoCrFeNi (x=0, 0.25, 0.50, 1.00) alloys in sulfuric acids." Corros Sci, vol. 52 (2010): pp. 1026-1034.
[23] D.A. Porter, K.E. Easterling, "Phase transformations in metals and alloys." 2nd ed., Chapman & Hall, London (1992).
[24] B. Cantor, I.T.H. Chang, P. Knight, A.J.B. Vincent, "Microstructural development in equiatomic multicomponent alloys." Mater Sci Eng A, vol. 375 (2004): pp. 213-218.
[25] O.N. Senkov, G.B. Wilks, D.B. Miracle, C.P. Chuang, P.K. Liaw, "Refractory high-entropy alloys." Intermetallics, vol. 18 (2010): pp. 1758-1765.
[26] O.N. Senkov, J.M. Scott, S.V. Senkova, D.B. Miracle, C.F. Woodward, "Microstructure and room temperature properties of a high-entropy TaNbHfZrTi alloy." J Alloy Compd, vol. 509 (2011): pp. 6043-6048.
[27] M.H. Tsai, J.Y. Gan, J.W. Yeh, "Study on the microstructure and electrical properties evolution of high-entropy alloy thin films." Master thesis, National Tsing Hua University (2003).
[28] J.W. Yeh, S.K. Chen, J.Y. Gan, S.J. Lin, T.S. Chin, T.T. Shun, C.H. Tsau, S.Y. Chang, "Formation of simple crystal structures in Cu-Co-Ni-Cr-Al-Fe-Ti-V alloys with multiprincipal metallic elements." Metall Mater Trans A, vol. 35A (2004): pp. 2533-2536.
[29] P.K. Huang, J.W. Yeh, T.T. Shun, S.K. Chen, "Multi-principal-element alloys with improved oxidation and wear resistance for thermal spray coating." Adv Eng Mater, vol. 6 (2004): pp. 74-78.
[30] C.Y. Hsu, W.R. Wang, W.Y. Tang, S.K. Chen, J.W. Yeh, "Microstructure and Mechanical Properties of New AlCoxCrFeMo0.5Ni High-Entropy Alloys." Adv Eng Mater, vol. 12 (2010): pp. 44-49.
[31] C.W. Tsai, M.H. Tsai, J.W. Yeh, C.C. Yang, "Effect of temperature on mechanical properties of Al0.5CoCrCuFeNi wrought alloy." J Alloy Compd, vol. 490 (2010): pp. 160-165.
[32] W.H. Liu, Y. Wu, J.Y. He, T.G. Nieh, Z.P. Lu, "Grain growth and the Hall–Petch relationship in a high-entropy FeCrNiCoMn alloy." Scripta Mater, vol. 68 (2013): pp. 526-529.
[33] C.J. Tong, Y.L. Chen, S.K. Chen, J.W. Yeh, T.T. Shun, C.H. Tsau, S.J. Lin, S.Y. Chang, "Microstructure characterization of AlxCoCrCuFeNi high-entropy alloy system with multiprincipal elements." Metall Mater Trans A, vol. 36A (2005): pp. 881-893.
[34] S. Ranganathan, "Alloyed pleasures: Multimetallic cocktails." Curr Sci, vol. 85 (2003): pp. 1404-1406.
[35] T.K. Chen, T.T. Shun, J.W. Yeh, M.S. Wong, "Nanostructured nitride films of multi-element high-entropy alloys by reactive DC sputtering." Surface & Coatings Technology, vol. 188 (2004): pp. 193-200.
[36] C.-H. Lai, S.-J. Lin, J.-W. Yeh, S.-Y. Chang, "Preparation and characterization of AlCrTaTiZr multi-element nitride coatings." Surface & Coatings Technology, vol. 201 (2006): pp. 3275-3280.
[37] Y.Y. Chen, U.T. Hong, H.C. Shih, J.W. Yeh, T. Duval, "Electrochemical kinetics of the high entropy alloys in aqueous environments - a comparison with type 304 stainless steel." Corros Sci, vol. 47 (2005): pp. 2679-2699.
[38] Y.Y. Chen, U.T. Hong, J.W. Yeh, H.C. Shih, "Mechanical properties of a bulk Cu0.5NiAlCoCrFeSi glassy alloy in 288 degrees C high-purity water." Appl Phys Lett, vol. 87 (2005): pp. 261918.
[39] Y.Y. Chen, U.T. Hong, J.W. Yeh, H.C. Shih, "Selected corrosion behaviors of a Cu0.5NiAlCoCrFeSi bulk glassy alloy in 288 degrees C high-purity water." Scripta Mater, vol. 54 (2006): pp. 1997-2001.
[40] Y. Zhang, Y.J. Zhou, J.P. Lin, G.L. Chen, P.K. Liaw, "Solid-solution phase formation rules for multi-component alloys." Adv Eng Mater, vol. 10 (2008): pp. 534-538.
[41] S. Guo, C.T. Liu, "Phase stability in high entropy alloys: Formation of solid-solution phase or amorphous phase." Prog Nat Sci, vol. 21 (2011): pp. 433-446.
[42] S.T. Chen, J.W. Yeh, "Effect of mixing enthalpy, mixing entropy and atomic size difference on the structure of multicomponent alloys." Master thesis, National Tsing Hua University (2009).
[43] X. Yang, Y. Zhang, "Prediction of high-entropy stabilized solid-solution in multi-component alloys." Mater Chem Phys, vol. 132 (2012): pp. 233-238.
[44] F.R. de Boer, R. Boom, W.C.M. Mattens, A.R. Meiedema, A.K. Niessen, "Cohesion in Metals: Transition Metal Alloys." 2nd ed., North-Holland, Amsterdam (1988).
[45] A. Takeuchi, A. Inoue, "Calculations of mixing enthalpy and mismatch entropy for ternary amorphous alloys." Materials Transactions JIM, vol. 41 (2000): pp. 1372-1378.
[46] A. Takeuchi, A. Inoue, "Classification of bulk metallic glasses by atomic size difference, heat of mixing and period of constituent elements and its application to characterization of the main alloying element." Materials Transactions, vol. 46 (2005): pp. 2817-2829.
[47] S. Guo, Q. Hu, C. Ng, C.T. Liu, "More than entropy in high-entropy alloys: Forming solid solutions or amorphous phase." Intermetallics, vol. 41 (2013): pp. 96-103.
[48] Y.J. Chung, T. Hsu, J.W. Yeh, "On XRD intensity, hardness, thermal expansion and thermal conductivity of Co-Ni-Fe-Cr-Mn (Al) alloy series." Master thesis, National Tsing Hua University (2007).
[49] M.H. Tsai, H. Yuan, G. Cheng, W. Xu, K.Y. Tsai, C.W. Tsai, W.W. Jian, C.C. Juan, W.J. Shen, M.H. Chuang, J.W. Yeh, Y.T. Zhu, "Morphology, structure and composition of precipitates in Al0.3CoCrCu0.5FeNi high-entropy alloy." Intermetallics, vol. 32 (2013): pp. 329-336.
[50] M. De Graef, M.E. McHenry, "Structure of materials: an introduction to crystallography, diffraction and symmetry." Cambridge University Press, Cambridge (2007).
[51] T. Massalski, "Structure and stability of alloys." In: R.W. Cahn, P. Haasen (editors), "Physical Metallurgy." 4th ed., North Holland, Amsterdam (1996), pp. 135-204.
[52] D. Pettifor, "Electron theory of metals." In: R.W. Cahn, P. Haasen (editors), "Physical Metallurgy." 4th ed., North Holland, Amsterdam (1996), pp. 47-133.
[53] Y.P. Wang, B.S. Li, H.Z. Fu, "Solid Solution or Intermetallics in a High-Entropy Alloy." Adv Eng Mater, vol. 11 (2009): pp. 641-644.
[54] S. Singh, N. Wanderka, B.S. Murty, U. Glatzel, J. Banhart, "Decomposition in multi-component AlCoCrCuFeNi high-entropy alloy." Acta Mater, vol. 59 (2011): pp. 182-190.
[55] F. Stein, A. Palm, G. Sauthoff, "Structure and stability of Laves phases part II - structure type variations in binary and ternary systems." Intermetallics, vol. 13 (2005): pp. 1056-1074.
[56] Y.F. Kao, S.K. Chen, J.H. Sheu, J.T. Lin, W.E. Lin, J.W. Yeh, S.J. Lin, T.H. Liou, C.W. Wang, "Hydrogen storage properties of multi-principal-component CoFeMnTixVyZrz alloys." International Journal of Hydrogen Energy, vol. 35 (2010): pp. 9046-9059.
[57] O.N. Senkov, C.F. Woodward, "Microstructure and properties of a refractory NbCrMo0.5Ta0.5TiZr alloy." Mater Sci Eng A, vol. 529 (2011): pp. 311-320.
[58] H.W. Chang, P.K. Huang, A. Davison, J.W. Yeh, C.H. Tsau, C.C. Yang, "Nitride films deposited from an equimolar Al-Cr-Mo-Si-Ti alloy target by reactive direct current magnetron sputtering." Thin Solid Films, vol. 516 (2008): pp. 6402-6408.
[59] M. Morinaga, N. Yukawa, H. Adachi, H. Ezaki, "New PHACOMP and its applications to alloy design." In: M. Gell, C.S. Kortovich, R.H. Bricknell, W.B. Kent, J.F. Radavich (editors), "Superalloys 1984." Metallurgical Society of AIME, Warrendale, PA (1984), pp. 523-532.
[60] M.H. Tsai, K.Y. Tsai, C.W. Tsai, C. Lee, C.C. Juan, J.W. Yeh, "Criterion for sigma phase formation in Cr- and V-containing high-entropy alloys." Mater Res Lett, accepted (2013).
[61] J.W. Yeh, S.Y. Chang, Y.D. Hong, S.K. Chen, S.J. Lin, "Anomalous decrease in X-ray diffraction intensities of Cu–Ni–Al–Co–Cr–Fe–Si alloy systems with multi-principal elements." Mater Chem Phys, vol. 103 (2007): pp. 41-46.
[62] J.R. Davis (editor), "ASM Handbook Volume 2. Properties and selection: nonferrous alloys and special-purpose materials." 10th ed., ASM International, Materials Park (1990).
[63] C.R. Brooks, S. Das, "A 3rd law of thermodynamics analysis of the enthalpy change of the order-disorder transformation in Ni3Fe." Thermochimica Acta, vol. 139 (1989): pp. 149-155.
[64] Y. Kaneno, A. Takahashi, T. Takasugi, "Microstructure and texture evolution during cold rolling and annealing of Ni3Fe alloy." Mater Sci Eng A, vol. 431 (2006): pp. 328-338.
[65] A. Dębski, W. Gąsior, A. Sypień, A. Góral, "Enthalpy of formation of intermetallic phases from Al–Ni and Al–Ni–Ti systems." Intermetallics, vol. 42 (2013): pp. 92-98.
[66] http://www.reade.com/products/5-aluminide-compounds-feal-nial-tial-mgal-powder/617-nickel-aluminide-powder-ni3al-nial3-nial-nickel-intermetallic-compound-nickel-aluminide-powder-ni3al-or-nial3-ic-221m-cast-nickel-aluminum-ordered-alloy-nickel-monoaluminide-raney-nickel-aluminum-nickel-astma1002-99-aluminium-compound-with-nickel
[67] H.N. Su, P. Nash, http://www.electrochem.org/dl/ma/203/pdfs/2017.pdf
[68] C. Colinet, A. Pasturel, "Ab initio calculation of thermodynamic data and phase diagram of binary transition metal based alloys." J Phase Equilib, vol. 15 (1994): pp. 330-338.
[69] H. Stone, "Some properties of intertransition metal compounds." J Mater Sci, vol. 12 (1977): pp. 1416-1420.
[70] K.C. Chen, S.M. Allen, J.D. Livingston, "Factors affecting the room-temperature mechanical properties of TiCr2-base Laves phase alloys." Mater Sci Eng A, vol. 242 (1998): pp. 162-173.
[71] A. Von Keitz, G. Sauthoff, "Laves phases for high temperatures - Part II: Stability and mechanical properties." Intermetallics, vol. 10 (2002): pp. 497-510.
[72] E. Hall, S. Algie, "The sigma phase." Metall Rev, vol. 11 (1966): pp. 61-88.
[73] W.R. Wang, W.L. Wang, S.C. Wang, Y.C. Tsai, C.H. Lai, J.W. Yeh, "Effects of Al addition on the microstructure and mechanical property of AlxCoCrFeNi high-entropy alloys." Intermetallics, vol. 26 (2012): pp. 44-51.
[74] T.S. Chen, J.W. Yeh, "On grain refinment and mechanical properties of Al-Co-Cr-Fe-Ni high-entropy alloys." Master thesis, National Tsing Hua University (2010).
[75] C.H. Lin, J.H. Huang, S.K. Chen, "Electrical and magnetic properties of 5-to 6-component high-entropy alloys made from Al, Co, Cr, Fe, Ni, and Ti." Master thesis, National Tsing Hua University (2008).
[76] Y. Zhang, X. Yang, P.K. Liaw, "Alloy Design and Properties Optimization of High-Entropy Alloys." JOM, vol. 64 (2012): pp. 830-838.
[77] J.M. Zhu, H.M. Fu, H.F. Zhang, A.M. Wang, H. Li, Z.Q. Hu, "Synthesis and properties of multiprincipal component AlCoCrFeNiSix alloys." Mater Sci Eng A, vol. 527 (2010): pp. 7210-7214.
[78] G.Y. Ke, S.K. Chen, T. Hsu, J.W. Yeh, "FCC and BCC equivalents in as-cast solid solutions of AlxCoyCrzCu0.5FevNiw high-entropy alloys." Ann Chim-Sci Mat, vol. 31 (2006): pp. 669-683.
[79] C.C. Tung, J.W. Yeh, T.T. Shun, S.K. Chen, Y.S. Huang, H.C. Chen, "On the elemental effect of AlCoCrCuFeNi high-entropy alloy system." Mater Lett, vol. 61 (2007): pp. 1-5.
[80] Y.J. Zhou, Y. Zhang, F.J. Wang, G.L. Chen, "Phase transformation induced by lattice distortion in multiprincipal component CoCrFeNiCuxAl1-x solid-solution alloys." Appl Phys Lett, vol. 92 (2008): pp. 241917.
[81] M.R. Chen, S.J. Lin, J.W. Yeh, S.K. Chen, Y.S. Huang, C.P. Tu, "Microstructure and properties of Al0.5CoCrCuFeNiTix (x=0-2.0) high-entropy alloys." Mater Trans, vol. 47 (2006): pp. 1395-1401.
[82] M.R. Chen, S.J. Lin, J.W. Yeh, S.K. Chen, Y.S. Huang, M.H. Chuang, "Effect of vanadium addition on the microstructure, hardness, and wear resistance of Al0.5CoCrCuFeNi high-entropy alloy." Metall Mater Trans A, vol. 37A (2006): pp. 1363-1369.
[83] M.R. Chen, S.J. Lin, "The effect of V, Si, Ti addition on the microstructure and wear properties of Al0.5CrCuFeCoNi high-entropy alloys." Master thesis, National Tsing Hua University (2003).
[84] B.S. Li, Y.P. Wang, M.X. Ren, C. Yang, H.Z. Fu, "Effects of Mn, Ti and V on the microstructure and properties of AlCrFeCoNiCu high entropy alloy." Mater Sci Eng A, vol. 498 (2008): pp. 482-486.
[85] B. Ren, Z.X. Liu, D.M. Li, L. Shi, B. Cai, M.X. Wang, "Effect of elemental interaction on microstructure of CuCrFeNiMn high entropy alloy system." J Alloy Compd, vol. 493 (2010): pp. 148-153.
[86] H.Y. Chen, C.W. Tsai, C.C. Tung, J.W. Yeh, T.T. Shun, C.C. Yang, S.K. Chen, "Effect of the substitution of Co by Mn in Al-Cr-Cu-Fe-Co-Ni high-entropy alloys." Ann Chim-Sci Mat, vol. 31 (2006): pp. 685-698.
[87] S.T. Chen, W.Y. Tang, Y.F. Kuo, S.Y. Chen, C.H. Tsau, T.T. Shun, J.W. Yeh, "Microstructure and properties of age-hardenable AlxCrFe1.5MnNi0.5 alloys." Mater Sci Eng A, vol. 527 (2010): pp. 5818-5825.
[88] K.Y. Tsai, M.H. Tsai, J.W. Yeh, "Sluggish diffusion in Co–Cr–Fe–Mn–Ni high-entropy alloys." Acta Mater, vol. 61 (2013): pp. 4887-4897.
[89] Z. Hu, Y. Zhan, G. Zhang, J. She, C. Li, "Effect of rare earth Y addition on the microstructure and mechanical properties of high entropy AlCoCrCuNiTi alloys." Mater Des, vol. 31 (2010): pp. 1599-1602.
[90] J.M. Zhu, H.F. Zhang, H.M. Fu, A.M. Wang, H. Li, Z.Q. Hu, "Microstructures and compressive properties of multicomponent AlCoCrCuFeNiMox alloys." J Alloy Compd, vol. 497 (2010): pp. 52-56.
[91] Y.L. Chou, J.W. Yeh, H.C. Shih, "The effect of molybdenum on the corrosion behaviour of the high-entropy alloys Co1.5CrFeNi1.5Ti0.5Mox in aqueous environments." Corros Sci, vol. 52 (2010): pp. 2571-2581.
[92] T.T. Shun, C.H. Hung, C.F. Lee, "Formation of ordered/disordered nanoparticles in FCC high entropy alloys." J Alloy Compd, vol. 493 (2010): pp. 105-109.
[93] L. Liu, J.B. Zhu, C. Zhang, J.C. Li, Q. Jiang, "Microstructure and the properties of FeCoCuNiSnx high entropy alloys." Mater Sci Eng A, vol. 548 (2012): pp. 64-68.
[94] L. Liu, J.B. Zhu, L. Li, J.C. Li, Q. Jiang, "Microstructure and tensile properties of FeMnNiCuCoSnx high entropy alloys." Mater Des, vol. 44 (2013): pp. 223-227.
[95] C.W. Chang, S.K. Chen, T. Hsu, "Microstructure and properties of as-cast 10-component nanostructured AlCoCrCuFeMoNiTiVZr high-entropy alloy." Master thesis, National Tsing Hua University (2004).
[96] O.N. Senkov, S.V. Senkova, C. Woodward, D.B. Miracle, "Low-density, refractory multi-principal element alloys of the Cr–Nb–Ti–V–Zr system: microstructure and phase analysis." Acta Mater, vol. 61 (2013): pp. 1545-1557.
[97] K.Y. Wu, S.K. Chen, J.M. Wu, "Superconductivity in NbTaTiZr-based high-entropy alloys." Master thesis, National Tsing Hua University (2013).
[98] C.C. Juan, J.W. Yeh, in private communication. National Tsing Hua University, Hsin Chu.
[99] C.H. Lai, S.J. Lin, "Preparation and characterization of multi-element Al-Cr-Ta-Ti-Zr-N coatings." Ph.D thesis, National Tsing Hua University (2007).
[100] H.W. Chang, J.W. Yeh, "A study on nitride films of Al-Cr-Mo-Si-Ti high-entropy alloy by reactive DC sputtering." Master thesis, National Tsing Hua University (2005).
[101] K.H. Cheng, S.J. Lin, "Hard nitride films of high-entropy alloy prepared by RF magnetron sputtering technique." Master thesis, National Tsing Hua University (2005).
[102] T.H. Yang, J.Y. Gan, J.W. Yeh, "Structure evolution and related mechanical and electrical properties of ZrTaTiNbSi glass metal film." Master thesis, National Tsing Hua University (2004).
[103] Y.T. Tsai, J.W. Yeh, "On the microstructure and properties of cold-rolled and aged Al-Cr-Fe-Mn-Ni alloys." Master thesis, National Tsing Hua University (2006).
[104] Y.C. Wang, J.W. Yeh, "Microstructure and mechanical properties of AlXCo1.5CrFeMoYNi1.5Ti0.5 (X, Y = 0, 0.1, 0.2)." Master thesis, National Tsing Hua University (2007).
[105] Y.J. Chang, A.C. Yeh, in private communication. National Tsing Hua University, Hsin Chu.
[106] R. Ferro, A. Saccone, "Structure of intermetallic compounds and phases." In: R.W. Cahn, P. Haasen (editors), "Physical Metallurgy." 4th ed., North Holland, Amsterdam (1996), pp. 205-369.
[107] S. Guo, C. Ng, J. Lu, C.T. Liu, "Effect of valence electron concentration on stability of fcc or bcc phase in high entropy alloys." J Appl Phys, vol. 109 (2011): pp. 103505.
[108] M.F. del Grosso, G. Bozzolo, H.O. Mosca, "Determination of the transition to the high entropy regime for alloys of refractory elements." J Alloy Compd, vol. 534 (2012): pp. 25-31.
[109] M.H. Tsai, J.W. Yeh, J.Y. Gan, "Diffusion barrier properties of AlMoNbSiTaTiVZr high-entropy alloy layer between copper and silicon." Thin Solid Films, vol. 516 (2008): pp. 5527-5530.
[110] T.T. Shun, C.H. Hung, C.F. Lee, "Formation of ordered/disordered nanoparticles in FCC high entropy alloys." J Alloy Compd, vol. 493 (2010): pp. 105-109.
[111] S.Y. Chang, D.S. Chen, "10-nm-thick quinary (AlCrTaTiZr)N film as effective diffusion barrier for Cu interconnects at 900 degrees C." Appl Phys Lett, vol. 94 (2009): pp. 231909.
[112] S.Y. Chang, C.Y. Wang, M.K. Chen, C.E. Li, "Ru incorporation on marked enhancement of diffusion resistance of multi-component alloy barrier layers." J Alloy Compd, vol. 509 (2011): pp. L85-L89.
[113] G.H. Vineyard, "Theory of order-disorder kinetics." Phys Rev, vol. 102 (1956): pp. 981-992.
[114] C.Y. Cheng, P.P. Wynblatt, J.E. Dorn, "Vacancy models for concentrated binary alloys--I. short-range ordered and clustered alloys." Acta Metall, vol. 15 (1967): pp. 1035-1043.
[115] D. Pruthi, "Calculation of solute-vacancy binding energy in dilute fcc and bcc alloys by diffusion." B Mater Sci, vol. 7 (1985): pp. 43-49.
[116] J.W. Haus, K.W. Kehr, "Diffusion in regular and disordered lattices." Phys Rep, vol. 150 (1987): pp. 263-406.
[117] D.E. Temkin, "One-dimensional random walks in a two-component chain." Sov Math Dokl, vol. 13 (1972): pp. 1172-1176.
[118] D.E. Temkin, "Correlation effects during vacancy diffusion in an alloy." Sov Phys Solid State, vol. 13 (1972): pp. 2840-2845.
[119] F. Otto, Y. Yang, H. Bei, E.P. George, "Relative effects of enthalpy and entropy on the phase stability of equiatomic high-entropy alloys." Acta Mater, vol. 61 (2013): pp. 2628-2638.
[120] A. Fick, "On liquid diffusion." Philos Mag, vol. 10 (1855): pp. 30-39.
[121] L. Boltzmann, "Integration of diffusion equations by variable coefficients." Annalen der Physik, vol. 53 (1894): pp. 959-964.
[122] C. Matano, "On the relation between the diffusion-coefficients and concentrations of solid metals (the nickel-copper system)." Jpn J Phys, vol. 8 (1933): pp. 109-113.
[123] H. Mehrer, "Diffusion in Solids. Fundamentals, Methods, Materials, Diffusion-Controlled Processes." Springer, Berlin (2007).
[124] F. Sauer, V. Freise, "Diffusion in Binaren Gemischen Mit Volumenanderung." Z Elektrochem, vol. 66 (1962): pp. 353-363.
[125] F.J.A. den Broeder, "A general simplification and improvement of the matano-boltzmann method in the determination of the interdiffusion coefficients in binary systems." Scripta Metall, vol. 3 (1969): pp. 321-325.
[126] H. Fujita, L.J. Gosting, "An exact solution of the equations for free diffusion in three-component systems with interacting flows, and its use in evaluation of the diffusion coefficients." J Am Chem Soc, vol. 78 (1956): pp. 1099-1106.
[127] J.S. Kirkaldy, "Diffusion in multicomponent metallic systems." Can J Phys, vol. 35 (1957): pp. 435-440.
[128] M.A. Dayananda, "Diffusion in multicomponent alloys: challenges and problems." Defect Diffus Forum, vol. 83 (1992): pp. 73-86.
[129] A.D. Smigelskas, E.O. Kirkendall, "Zinc diffusion in alpha-brass." Trans AIME, vol. 171 (1947): pp. 130-142.
[130] E.O. Kirkendall, "Diffusion of zinc in alpha brass." Trans AIME, vol. 147 (1942): pp. 104-110.
[131] L.S. Darken, "Diffusion, mobility and their interrelation through free energy in binary metallic systems." Trans AIME, vol. 175 (1948): pp. 184-201.
[132] L.S. Darken, "Diffusion of carbon in austenite with a discontinuity in composition." Trans AIME, vol. 180 (1949): pp. 430-438.
[133] K.J. Ronka, A.A. Kodentsov, P.J.H. VanLoon, J.K. Kivilahti, F.J.J. VanLoo, "Thermodynamic and kinetic study of diffusion paths in the system Cu-Fe-Ni." Metall Mater Trans A, vol. 27 (1996): pp. 2229-2238.
[134] J.S. Kirkaldy, D.J. Young, "Diffusion in the Condensed State." Institute of Metals, London (1987).
[135] L.S. Darken, "Formal Basis of Diffusion Theory." In: J.H. Hollomon (editor), "Atom Movements." ASM, Cleveland, OH (1951), pp. 1-25.
[136] A.D. Le Claire, "Diffusion in metals." Prog Met Phys, vol. 4 (1953): pp. 265-332.
[137] M.J.H. van Dal, M.C.L.P. Pleumeekers, A.A. Kodentsov, F.J.J. van Loo, "Diffusion studies and re-examination of the Kirkendall effect in the Au-Ni system." J Alloy Compd, vol. 309 (2000): pp. 132-140.
[138] M.J.H. van Dal, M.C.L.P. Pleumeekers, A.A. Kodentsov, F.J.J. van Loo, "Intrinsic diffusion and Kirkendall effect in Ni–Pd and Fe–Pd solid solutions." Acta Mater, vol. 48 (2000): pp. 385-396.
[139] V.D. Divya, U. Ramamurty, A. Paula, "Interdiffusion and the vacancy wind effect in Ni-Pt and Co-Pt systems." J Mater Res, vol. 26 (2011): pp. 2384-2393.
[140] Y. Iijima, O. Taguchi, K.I. Hirano, "Interdiffusion in Co-Mn alloys." Metall Trans A, vol. 8 (1977): pp. 991-995.
[141] Y. Iijima, O. Taguchi, K.I. Hirano, "Interdiffusion in Co-Pt Alloys." Trans Jpn Inst Met, vol. 21 (1980): pp. 366-374.
[142] D.B. Butrymowicz, J.R. Manning, "Chemical interdiffusion and Kirkendall shifts in silver-cadmium alloys." Metall Trans A, vol. 9 (1978): pp. 947-953.
[143] G. Neumann, C. Tuijn, "Self-diffusion and Impurity Diffusion in Pure Metals: Handbook of Experimental Data." Elsevier, Oxford (2009).
[144] S.J. Rothman, L.J. Nowicki, G.E. Murch, "Self-Diffusion in Austenitic Fe-Cr-Ni Alloys." J Phys F: Met Phys, vol. 10 (1980): pp. 383-398.
[145] M.E. Glicksman, "Diffusion in Solids: Field theory, Solid-State Principles, and Applications." Wiley, New York (1999).
[146] A.M. Brown, M.F. Ashby, "Correlations for diffusion constants." Acta Metall, vol. 28 (1980): pp. 1085-1101.
[147] A.W. Bowen, G.M. Leak, "Solute diffusion in alpha-and gamma-iron." Metall Trans, vol. 1 (1970): pp. 1695-1700.
[148] A. Davin, V. Leroy, D. Coutsouradis, L. Habraken, Mém Sci Rev Métall, vol. 60 (1963): pp. 275-283.
[149] S.B. Jung, T. Yamane, Y. Minamino, K. Hirao, H. Araki, S. Saji, "Interdiffusion and its size effect in nickel solid solutions of Ni-Co, Ni-Cr and Ni-Ti systems." J Mater Sci Lett, vol. 11 (1992): pp. 1333-1337.
[150] T. Heumann, R. Imm, "Self-diffusion and isotope effect in gamma-iron." J Phys Chem Solids, vol. 29 (1968): pp. 1613-1621.
[151] H.W. Mead, C.E. Birchenall, "Diffusion of Co 60 and Fe 55 in cobalt." Trans AIME, vol. 203 (1955): pp. 994-995.
[152] H. Bakker, J. Backus, F. Waals, "A Curvature in the arrhenius plot for the diffusion of iron in single crystals of nickel in the temperature range from 1200 to 1400°C." Phys Status Solidi B, vol. 45 (1971): pp. 633-638.
[153] M. Badia, A. Vignes, "Iron nickel and cobalt diffusion in transition metals of iron group." Acta Metall, vol. 17 (1969): pp. 177-187.
[154] H. Bakker, "A curvature in ln D versus 1/T plot for self-diffusion in nickel at temperatures from 980 to 1400 degrees C." Phys Status Solidi, vol. 28 (1968): pp. 569-576.
[155] K. Nohara, K. Hirano, Suppl Trans Iron Steel Inst Jpn, vol. 11 (1971): pp. 1267.
[156] Y. Iijima, K.I. Hirano, O. Taguchi, "Diffusion of manganese in cobalt and cobalt-manganese alloys." Philos Mag, vol. 35 (1977): pp. 229-244.
[157] R.A. Swalin, A. Martin, "Solute diffusion in nickel-base substitutional solid solutions." Trans AIME, vol. 206 (1956): pp. 567-572.
[158] W. Bussmann, C. Herzig, W. Rempp, K. Maier, H. Mehrer, "Isotope effect and self-diffusion in face-centered cubic cobalt." Phys Status Solidi A, vol. 56 (1979): pp. 87-97.
[159] D.O. Welch, "Kinetics of short-range order and Zener relaxation in substitutional solid solutions." Mater Sci Eng, vol. 4 (1969): pp. 9-21.
[160] F.C. Nix, W. Shockley, "Order-disorder transformations in alloys." Rev Mod Phys, vol. 10 (1938): pp. 0001-0071.
[161] D.B. Miracle, G.B. Wilks, A.G. Dahlman, J.E. Dahlman, "The strength of chemical bonds in solids and liquids." Acta Mater, vol. 59 (2011): pp. 7840-7854.
[162] P.I. Loeff, A.W. Weeber, A.R. Miedema, "Diagrams of formation enthalpies of amorphous alloys in comparison with the crystalline solid solution." J Less Common Met, vol. 140 (1988): pp. 299-305.
[163] A. Janotti, M. Krcmar, C.L. Fu, R.C. Reed, "Solute diffusion in metals: larger atoms can move faster." Phys Rev Lett, vol. 92 (2004): pp. 085901.
[164] M.S.A. Karunaratne, R.C. Reed, "Interdiffusion of the platinum-group metals in nickel at elevated temperatures." Acta Mater, vol. 51 (2003): pp. 2905-2919.
[165] R. Hultgren, "Selected Values of the Thermodynamic Properties of Binary Alloys." American Society for Metals, Metals Park, OH (1973).
[166] K.T. Jacob, Z Metallkd, vol. 76 (1985): pp. 415.
[167] C. Allibert, C. Bernard, N. Valignat, M. Dombre, "Co-Cr binary system: experimental re-determination of the phase diagram and comparison with the diagram calculated from the thermodynamic data." J Less Common Met, vol. 59 (1978): pp. 211-228.
[168] V.N. Eremenko, G.M. Lukashenko, V.R. Sidorko, "Thermodynamic properties of alloys of manganese with transition elements of the fourth period (Cr, Fe, Co, Ni) and with copper." Russ J Phys Chem, vol. 42 (1968): pp. 343-346.
[169] Z. Moser, W. Zakulski, P. Spencer, K. Hack, "Thermodynamic investigations of solid Cu-Ni and Fe-Ni alloys and calculation of the solid state miscibility gap in the Cu-Fe-Ni system." CALPHAD, vol. 9 (1985): pp. 257-269.
[170] C. Ng, S. Guo, J. Luan, S. Shi, C.T. Liu, "Entropy-driven phase stability and slow diffusion kinetics in an Al0.5CoCrCuFeNi high entropy alloy." Intermetallics, vol. 31 (2012): pp. 165-172.
[171] M.G. Kendall, A. Stuart, "The Advanced Theory of Statistics." 3rd ed., Charles Griffin, London (1969).
[172] B. Fultz, L. Anthony, "Suppression of vacancy diffusion during short range ordering." Defect Diffus Forum, vol. 59 (1991): pp. 253-260.
[173] Y. Le Bouar, F. Soisson, "Kinetic pathways from embedded-atom-method potentials: influence of the activation barriers." Phys Rev B, vol. 65 (2002): pp. 094103.
[174] M.S. Lucas, G.B. Wilks, L. Mauger, J.A. Munoz, O.N. Senkov, E. Michel, J. Horwath, S.L. Semiatin, M.B. Stone, D.L. Abernathy, E. Karapetrova, "Absence of long-range chemical ordering in equimolar FeCoCrNi." Appl Phys Lett, vol. 100 (2012): pp. 251907