現今實驗上的探針因為汰換率如鎢探針、錸鎢探針、鈹銅探針等，因此本研究目的在於開發導電度高，機械性質佳的材料，而NbMoTaW高熵合金因為機械性質不錯與由幾個導電性質佳的元素所組成，因此為本研究主要的研究材料。
　　NbMoTaW這類的耐火高熵合金（Refractory High-Entropy Alloy）為2010年被提出，目的在於希望能在航太工業等需要在高溫下應用的材料有所貢獻，其在高溫具有好的韌性，然而在室溫下時卻發現其韌性不佳，然而實驗上並未觀察到有相分離的發生，因此本研究想透過第一原理的方法來首先研究NbMoTaW高熵合金在低溫下時相穩定度。
　　藉由第一原理（first-principles）與熱力學計算相圖法（CALPHAD），透過全面的搜索原子所有可能的排列找出其最低的能量結構，並比較其機械性質與導電性質是否有所差異。
　　研究結果顯示，NbMoTaW高熵合金在原子有局部堆積的情況下，有著比固溶相更低的能量，然而機械性質與導電性質並不隨原子的排列而有太大的差異。

Today’s experimental probes are due to their replacement rates. Therefore, the purpose of this research is to develop materials with high conductivity and good mechanical properties. NbMoTaW high-entropy alloy are due to their mechanical properties. It is composed of several elements with good electrical conductivity, so it is the main research material for this study.
By first-principles and thermodynamic calculation phase diagram method (CALPHAD), through a comprehensive search of all possible arrangements of atoms to find the lowest energy structure. Compare whether its mechanical properties and electrical properties are different.
The research results show that the NbMoTaW high-entropy alloy has a lower energy than the solid solution phase when the atoms are locally stacked. However, the mechanical properties and electrical conductivity do not vary greatly with the arrangement of the atoms.

[1] P. Hohenberg and W. Kohn, "Inhomogeneous electron gas," Physical review, vol. 136, no. 3B, p. B864, 1964.
[2] W. Kohn and L. J. Sham, "Self-consistent equations including exchange and correlation effects," Physical review, vol. 140, no. 4A, p. A1133, 1965.
[3] 蘇于倫. https://www.york.ac.uk/depts/maths/tables/orthogonal.htm.
[4] R. J. Freund and R. C. Littell, SAS system for regression. SAS Publishing, 2000.
[5] M. C. Troparevsky, J. R. Morris, P. R. Kent, A. R. Lupini, and G. M. Stocks, "Criteria for predicting the formation of single-phase high-entropy alloys," Physical Review X, vol. 5, no. 1, p. 011041, 2015.
[6] F. Körmann and M. H. Sluiter, "Interplay between lattice distortions, vibrations and phase stability in NbMoTaW high entropy alloys," Entropy, vol. 18, no. 8, p. 403, 2016.
[7] O. Senkov, G. Wilks, D. Miracle, C. Chuang, and P. Liaw, "Refractory high-entropy alloys," Intermetallics, vol. 18, no. 9, pp. 1758-1765, 2010.
[8] R. Hill, "The elastic behaviour of a crystalline aggregate," Proceedings of the Physical Society. Section A, vol. 65, no. 5, p. 349, 1952.
[9] B. Feng and M. Widom, "Elastic stability and lattice distortion of refractory high entropy alloys," Materials Chemistry and Physics, vol. 210, pp. 309-314, 2018.
[10] J. W. Yeh, S. K. Chen, S. J. Lin, J. Y. Gan, T. S. Chin, T. T. Shun, C. H. Tsau, and S. Y. Chang, "Nanostructured high‐entropy alloys with multiple principal elements: novel alloy design concepts and outcomes," Advanced Engineering Materials, vol. 6, no. 5, pp. 299-303, 2004.
[11] B. Cantor, I. Chang, P. Knight, and A. Vincent, "Microstructural development in equiatomic multicomponent alloys," Materials Science and Engineering: A, vol. 375, pp. 213-218, 2004.
[12] W. P. Huhn and M. Widom, "Prediction of A2 to B2 phase transition in the high-entropy alloy Mo-Nb-Ta-W," Jom, vol. 65, no. 12, pp. 1772-1779, 2013.
[13] K.-H. Huang and J. Yeh, "A study on the multicomponent alloy systems containing equal-mole elements," Hsinchu: National Tsing Hua University, pp. 1-93, 1996.
[14] https://mme.iitm.ac.in/hea/html/global/global-publications.html.
[15] Y. Jien-Wei, "Recent progress in high entropy alloys," Ann. Chim. Sci. Mat, vol. 31, no. 6, pp. 633-648, 2006.
[16] J. Yeh, "Recent progress in high-entropy alloys; Progres recents dans les alliages a haute entropie," 2006.
[17] M.-H. Tsai and J.-W. Yeh, "High-entropy alloys: a critical review," Materials Research Letters, vol. 2, no. 3, pp. 107-123, 2014.
[18] W. Hume-Rothery, "Atomic theory for students of metallurgy," 1952.
[19] W. Hume-Rothery and H. M. Powell, "On the theory of super-lattice structures in alloys," Zeitschrift für Kristallographie-Crystalline Materials, vol. 91, no. 1-6, pp. 23-47, 1935.
[20] W. Hume-Rothery, "The structure of metals and alloys," Indian Journal of Physics, vol. 11, pp. 74-74, 1969.
[21] D. B. Miracle, J. D. Miller, O. N. Senkov, C. Woodward, M. D. Uchic, and J. Tiley, "Exploration and development of high entropy alloys for structural applications," Entropy, vol. 16, no. 1, pp. 494-525, 2014.
[22] S. Guo, C. Ng, J. Lu, and C. Liu, "Effect of valence electron concentration on stability of fcc or bcc phase in high entropy alloys," Journal of applied physics, vol. 109, no. 10, p. 103505, 2011.
[23] M. G. Poletti and L. Battezzati, "Electronic and thermodynamic criteria for the occurrence of high entropy alloys in metallic systems," Acta Materialia, vol. 75, pp. 297-306, 2014.
[24] F. Otto, Y. Yang, H. Bei, and E. P. George, "Relative effects of enthalpy and entropy on the phase stability of equiatomic high-entropy alloys," Acta Materialia, vol. 61, no. 7, pp. 2628-2638, 2013.
[25] O. N. Senkov, G. Wilks, J. Scott, and D. B. Miracle, "Mechanical properties of Nb25Mo25Ta25W25 and V20Nb20Mo20Ta20W20 refractory high entropy alloys," Intermetallics, vol. 19, no. 5, pp. 698-706, 2011.
[26] E. Fermi, "Un metodo statistico per la determinazione di alcune priorieta dell’atome," Rend. Accad. Naz. Lincei, vol. 6, no. 602-607, p. 32, 1927.
[27] L. H. Thomas, "The calculation of atomic fields," in Mathematical Proceedings of the Cambridge Philosophical Society, 1927, vol. 23, no. 5: Cambridge University Press, pp. 542-548.
[28] S. H. Vosko, L. Wilk, and M. Nusair, "Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis," Canadian Journal of physics, vol. 58, no. 8, pp. 1200-1211, 1980.
[29] J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, M. R. Pederson, D. J. Singh, and C. Fiolhais, "Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation," Physical review B, vol. 46, no. 11, p. 6671, 1992.
[30] P. E. Blöchl, "Projector augmented-wave method," Physical review B, vol. 50, no. 24, p. 17953, 1994.
[31] L. Kaufman and H. Bernstein, "Computer calculation of phase diagrams. With special reference to refractory metals," 1970.
[32] I. S. Sokolnikoff, Mathematical theory of elasticity. McGraw-Hill book company, 1956.
[33] A. Zunger, S.-H. Wei, L. Ferreira, and J. E. Bernard, "Special quasirandom structures," Physical Review Letters, vol. 65, no. 3, p. 353, 1990.
[34] S. Chen, P. Kühne, V. Stanishev, S. Knight, R. Brooke, I. Petsagkourakis, X. Crispin, M. Schubert, V. Darakchieva, and M. P. Jonsson, "On the anomalous optical conductivity dispersion of electrically conducting polymers: ultra-wide spectral range ellipsometry combined with a Drude–Lorentz model," Journal of Materials Chemistry C, vol. 7, no. 15, pp. 4350-4362, 2019.
[35] M. Schubert, C. Bundesmann, H. v. Wenckstern, G. Jakopic, A. Haase, N.-K. Persson, F. Zhang, H. Arwin, and O. Inganäs, "Carrier redistribution in organic/inorganic (poly (3, 4-ethylenedioxy thiophene/poly (styrenesulfonate) polymer)-Si) heterojunction determined from infrared ellipsometry," Applied physics letters, vol. 84, no. 8, pp. 1311-1313, 2004.
[36] M. Schubert, C. Bundesmann, G. Jakopic, H. Maresch, H. Arwin, N.-C. Persson, F. Zhang, and O. Inganäs, "Infrared ellipsometry characterization of conducting thin organic films," Thin Solid Films, vol. 455, pp. 295-300, 2004.
[37] C. Lee, G. Song, M. C. Gao, R. Feng, P. Chen, J. Brechtl, Y. Chen, K. An, W. Guo, and J. D. Poplawsky, "Lattice distortion in a strong and ductile refractory high-entropy alloy," Acta Materialia, vol. 160, pp. 158-172, 2018.