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

doi:10.1007/s40195-020-01006-2

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

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.

Figures/Tables 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.

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