First-Principles Calculations for Stable β-Ti-Mo Alloys Using Cluster-Plus-Glue-Atom Model

doi:10.1007/s40195-020-01006-2

金属学报英文版 ›› 2020, Vol. 33 ›› Issue (7): 968-974.DOI: 10.1007/s40195-020-01006-2

收稿日期:2019-08-09 修回日期:2019-11-22 出版日期:2020-07-10 发布日期:2020-07-10

First-Principles Calculations for Stable β-Ti-Mo Alloys Using Cluster-Plus-Glue-Atom Model

Fushi Jiang¹^,²^,³, Chang Pang⁴, Zhaoyang Zheng⁵, Qing Wang¹, Jijun Zhao¹, Chuang Dong¹()

¹ Key Laboratory of Materials Modification by Laser, Ion and Electron Beams (Ministry of Education), Dalian University of Technology, Dalian, 116024, China
² College of Physics and Electronic Information, Inner Mongolia University for Nationalities, Tongliao, 028043, China
³ Institute of Metal Research, Chinese Academy of Sciences, Shenyang, 110016, China
⁴ College of Marine Science and Environment, Dalian Ocean University, Dalian, 116023, China
⁵ National Key Laboratory of Shock Wave and Detonation Physics, Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang, 621900, China

Received:2019-08-09 Revised:2019-11-22 Online:2020-07-10 Published:2020-07-10
Contact: Chuang Dong

摘要/Abstract

Abstract:

Construction of suitable structural models in order to account for chemical short-range orders is the reason behind the difficult multi-scale computational simulation methods for solid solutions. Herein, using Ti-Mo alloys as representative, we used our cluster-plus-glue-atom model to address the chemical short-range orders for body-center cubic lattice. In accordance with the atomic interaction mode, an Mo solute atom would prefer 14 Ti solvent atoms as its nearest neighbors, forming a rhombic-dodecahedral cluster, and some next outer-shell Mo and Ti atoms would serve as the glue atoms, which is formulated as [Mo-Ti₁₄](Mo,Ti)_x. The number of glue atoms x corresponds to different spatial distribution of the clusters. One of the formula having good stability is [Mo-Ti₁₄]Mo, i.e., with one Mo as the glue atom. To verify its stability, mechanical properties and electronic density of state are obtained using the first-principles calculations and the Young’s modulus agrees with the experimental values. Also the formulated structural unit [Mo-Ti₁₄]Mo is indeed verified by the cluster expansion method. This work then confirms the existence of simple structural unit covering the nearest neighbors and a few next outer-shell atoms for the Ti-Mo alloy of high structural stability.

Key words: Solid solution, β-Ti-Mo alloys, Short-range order, First-principles calculations

. [J]. 金属学报英文版, 2020, 33(7): 968-974.

Fushi Jiang, Chang Pang, Zhaoyang Zheng, Qing Wang, Jijun Zhao, Chuang Dong. First-Principles Calculations for Stable β-Ti-Mo Alloys Using Cluster-Plus-Glue-Atom Model[J]. Acta Metallurgica Sinica (English Letters), 2020, 33(7): 968-974.

图/表 9

Fig. 1 Geometrical configuration of the cluster-plus-glue-atom model for BCC structure, centered by red atom Mo, and shelled by 14 Ti is a rhombic-dodecahedral cluster [Mo-Ti14]. The eight nearest neighbors are shown as green balls, and the six second nearest neighbors are shown as blue balls. The glue atoms locate at the next outer-shell of twelve atoms (gray balls). The Ti-Mo monotectoid alloy Ti88Mo12 is modeled as a [Mo-Ti14] cluster glued with one Mo atom (out of the 12 available gray sites), formulated as [Mo-Ti14]Mo = Ti14Mo2 = Ti87.5Mo12.5

Fig. 2 Parallelepiped super-cell unit satisfying the cluster formula [Mo-Ti14]Mo (monotectoid alloy), defined by linking the [Mo-Ti14] cluster center (red atoms, Mo) as the cell vertices. There is only one Mo glue atom (gray atoms) in the unit. The cluster shell atoms are represented by green and blue atoms

Fig. 3 Energies predicted from the cluster expansion as a function of composition for each structure generated in Ti-Mo alloy

Fig. 4 Structures of Ti87.5Mo12.5 obtained by ATAT (a′, b′, c′ show the 1st, 2nd and 3rd nearest neighbor of Mo atom for a, b, c)

Table 1 1st, 2nd and 3rd nearest neighbors of the central Mo atoms or Ti atoms in the configurations a, b, and c

Central atom	Shell atom	Numbers	Radial distances (nm)
Mo^a	Ti	8	0.245-0.269
	Ti	6	0.325-0.326
	Mo	2	0.438
	Ti	10	0.442-0.450
Mo^b	Ti	8	0.253-0.277
	Ti	6	0.323-0.327
	Ti	12	0.433-0.456
Ti^b	Mo	2	0.271
	Ti	6	0.276-0.289
	Ti	6	0.294-0.324
	Ti	12	0.433-0.463
Mo^c	Ti	6	0.257-0.262
	Mo	2	0.280
	Ti	6	0.319-0.321
	Ti	12	0.433-0.442
Ti^c₁	Mo	1	0.258
	Ti	7	0.260-0.286
	Ti	6	0.289-0.360
	Ti	10	0.404-0.482
	Mo	2	0.433-0.438
Ti^c₂	Ti	8	0.260-0.281
	Ti	6	0.320-0.328
	Ti	10	0.437-0.445
	Mo	2	0.441

Table 2 Calculated elastic stiffness coefficients (in GPa) for structure a, b and c

Structure	C₁₁	C₁₂	C₄₄	B	G	E
a	208.4	121.1	31.8	150.2	36.1	100.4
b	227.8	140.2	38.1	169.4	40.3	112.0
c	206.5	119.2	41.0	148.3	42.0	115.2

Fig. 5 Total and partial electronic densities of the states of [Mo-Ti14]Mo

Fig. 6 Difference charge density for structures a, b, c. Isovalues: 0.005 and - 0.005 a.u.

Fig. 7 Quantity plots of the difference charge density for structures a, b, c. Isovalues: 0.005 and - 0.005 a.u.

参考文献 29

[1]	A. van de Walle, P. Tiwary, M. de Jong, D.L. Olmsted, M. Asta, A. Dick, D. Shin, Y. Wang, L.Q. Chen, Z.K. Liu, CALPHAD 42, 13 (2013)
[2]	L. Vitos, in Computational Quantum Mechanics for Materials Engineers: The EMTO Method and Applications (Springer, London, 2007)
[3]	H.L. Hong, Q. Wang, C. Dong, P.K. Liaw, Sci. Rep. 4, 7065 (2014)
[4]	D.D. Dong, Dissertation, Dalian University of Technology (2017)
[5]	M. Niinomi, T. Hattori, K. Morikawa, T. Kasuga, A. Suzuki, H. Fukui, S. Niwa, Mater. Trans. 43, 2970 (2002)
[6]	M. Geetha, A.K. Singh, R. Asokamani, A.K. Gogia, Prog. Mater Sci. 54, 397 (2009)
[7]	Y.L. Hao, S.J. Li, S.Y. Sun, C.Y. Zheng, Q.M. Hu, R. Yang, Appl. Phys. Lett. 87, 091906 (2005)
[8]	D.Q. Martins, W.R. Oso’rio, M.E.P. Souza, R. Caram, A. Garcia, Electrochim. Acta 53, 2809 (2008)
[9]	L.J. Xu, Y.Y. Chen, J. Alloys Compd. 453, 320 (2008)
[10]	M. Abdel-Hady, K. Hinoshita, M. Morinaga, Scr. Mater. 55, 477 (2006)
[11]	P.J. Bania, in Beta Titanium Alloys in the 1990 s (TMS, Warrendale, 1993)
[12]	E.W. Collings, in Physical Metallurgy of Titanium Alloys (ASM, Metals Park, 1984)
[13]	Y. Zhang, Q. Wang, H.G. Dong, C. Dong, H.Y. Zhang, X.F. Sun, Acta Metall. Sin. (Engl. Lett.) 31, 127 (2018)
[14]	C. Zhang, H. Tian, C.P. Hao, J.J. Zhao, Q. Wang, E.X. Liu, C. Dong, J. Matter. Sci. 48, 3138 (2013)
[15]	C.P. Hao, Q. Wang, R.T. Ma, Y.M. Wang, J.B. Qiang, C. Dong, Acta Phys. Sin. 60, 116101 (2011)
[16]	Q. Wang, C. Ji, Y.M. Wang, J.B. Qiang, C. Dong, Metall. Mater. Trans. A 44, 1872 (2013)
[17]	B.B. Jiang, Q. Wang, D.H. Wen, F. Xu, G.Q. Chen, C. Dong, L. Sun, P.K. Liaw, Mater. Sci. Eng., A 687, 1 (2017)
[18]	J. Singh, P. Singh, S. Rattan, S. Prakash, Phys. Rev. B 49, 932 (1994)
[19]	H. Sharma, S. Prakash, Pramana 68, 655 (2007)
[20]	C. Pang, B.B. Jiang, Y. Shi, Q. Wang, C. Dong, J. Alloys Compd. 652, 63 (2015)
[21]	G. Kresse, D. Joubert, Phys. Rev. B 59, 1758 (1999)
[22]	J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996)
[23]	G. Kresse, J. Furthmuller, Phys. Rev. B 54, 11169 (1996)
[24]	H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13, 5188 (1976)
[25]	J.M. Sanchez, F. Ducastelle, D. Gratias, Physica 128A, 334 (1984)
[26]	A. van de Walle, G. Ceder, J. Phase Equilib. 23, 348 (2002)
[27]	A. van de Walle, M. Asta, G. Ceder, CALPHAD 26, 539 (2002)
[28]	Z.J. Wu, E.J. Zhao, H.P. Xiang, X.F. Hao, X.J. Liu, J. Meng, Phys. Rev. B 76, 054115 (2007)
[29]	J.Y. Dai, J.M. Yuan, P. Giannozzi, Appl. Phys. Lett. 95, 232105 (2009)

First-Principles Calculations for Stable β-Ti-Mo Alloys Using Cluster-Plus-Glue-Atom Model

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