First-principles investigation of B2 partial disordered structure, martensitic transformation, elastic and magnetic properties of all-d-metal Ni-Mn-Ti Heusler alloys

doi:10.1016/j.jmst.2020.08.002

Abstract

Abstract:

In this work, the B2 partial disordered structure of the austenitic parent phase, martensitic transformation, elastic and magnetic properties of the Ni₈Mn₄₊_xTi_4-_x (x = 0, 1 and 2) Heusler alloys have been systematically investigated by the first-principles calculations. The preferential atomic occupation of B2 structure is one Ti atom exchange with the nearest neighboring Mn atom from the view of lowest energy principle. This disordered exchange sites (Mn-Ti) and the excess Mn atoms occupying the Ti sites (Mn_Ti) could reduce the nearest Mn-Mn distance, resulting in the antiferromagnetic state in the austenitic and martensitic phases of the alloys. The total magnetic moment of the alloy decreases with the increasing Mn content; it is ascribed to the antiferromagnetic magnetic moments of the excess Mn atoms. When x = 0, the alloy does not undergo martensitic transformation since the austenite has absolute phase stability. The martensitic transformation will occur during cooling process for x = 1 or 2, owing to the energy difference between the austenite and the martensite could provide the driving force for the phase transformation. The elastic properties of the cubic austenitic phase for the Ni₂MnTi alloy is calculated, and the results reveal the reason why Ni-Mn-Ti alloy has excellent mechanical properties. The origin of martensitic transformation and magnetic properties was discussed based on the electronic density of states.

Key words: Ni-Mn-Ti, First-principles calculations, Martensitic transformation, B2 partial disordered structure, Elastic properties

Ziqi Guan, Jing Bai, Jianglong Gu, Xinzeng Liang, Die Liu, Xinjun Jiang, Runkai Huang, Yudong Zhang, Claude Esling, Xiang Zhao, Liang Zuo. First-principles investigation of B2 partial disordered structure, martensitic transformation, elastic and magnetic properties of all-d-metal Ni-Mn-Ti Heusler alloys[J]. J. Mater. Sci. Technol., 2021, 68: 103-111.

Figures/Tables 17

Fig. 1. Reversible adiabatic temperature change for some relevant alloys.

Fig. 2. Crystal structures of (a) L21 austenite and (b) L10 martensite.

Fig. 3. Four possible configurations of the partial disordered B2 structure and the energy difference between the B2 and L21 structure with different magnetic states for the Ni8Mn4Ti4 alloy (Since the ferromagnetic L21 structure has the lowest formation energy, it is used to compare with the B2 structure). (a) One Ti atom exchanged with the nearest neighboring Mn atom; (b) One Ti atom exchanged with the farthest Mn atom; (c) Two Ti atoms exchanged with the nearest neighboring Mn atoms; (d) one Ti atom exchanged with the nearest neighboring Mn atom and one Ti atom exchanged with the farthest Mn atom.

Fig. 4. (a, b) two possible configurations of the PD L10 martensite; (c) the formation energy (Ef) of the B2 austenite and PD L10 martensite of the Ni8Mn4Ti4 alloy.

Fig. 5. Two possible B2 partial disordered structures and the energy difference between the B2 and L21 structure of Ni8Mn5Ti3 alloy with different magnetic states. (a) One Ti atom exchanged with the nearest neighboring Mn atom; (b) One Ti atom exchanged with the farthest Mn atom.

Fig. 6. Three possible PD L10 structures and the corresponding formation energies of the Ni8Mn5Ti3 alloy. (a), (b) and (c) are the possible site occupations with one excess Mn atom in the L10 structure. (d), (e) and (f) are the possible site occupations for one Ti atom exchanged with the nearest neighboring Mn.

Fig. 7. The formation energy of the B2 austenite and corresponding PD L10 martensite with ferromagnetic and antiferromagnetic states in the Ni8Mn5Ti3 alloy.

Fig. 8. The site occupation and the formation energy of the austenite and martensite for Ni8Mn6Ti2 alloy.

Fig. 9. Formation energy of the austenite and martensite for the Ni8Mn4+xTi4-x (x = 0, 1 and 2) alloys (There is no martensitic transformation in the Ni8Mn4Ti4 alloy).

Table 1 Optimized equilibrium lattice parameters of austenite and martensite for the Ni8Mn4+xTi4-x (x = 0, 1 and 2) alloys (There is no martensitic transformation in the Ni8Mn4Ti4 alloy).

Phase	Lattice parameters	Mn doping content, x
Phase	Lattice parameters	x = 0	x = 1	x = 2
Austenite	a = b = c (Å)	5.9001	5.8755	5.8473
		5.9315 [25]	5.9218 [13]	5.897 [36]
			5.9343 [16]
Martensite	a (Å) b (Å)	// //	8.5167 8.5452 [16]8.544 [15] 4.2800 4.3763 [16]4.376 [15]	8.4834 4.2464
	c (Å)	//	5.5126 5.5236 [16]5.523 [15]	5.4495

Table 2 The elastic constants of the Ni2MnTi, Ni2MnGa and Ni2MnIn alloys.

System	C₁₁ (GPa)	C₁₂ (GPa)	C₄₄ (GPa)	B (GPa)	G (GPa)	Y (GPa)	υ	B/G
Ni₂MnTi	153.89	146.14	77.27	148.72	33.23	92.78	0.40	4.48
Ni₂MnGa	155.02	139.63	103.28	144.76	45.93	124.60	0.36	3.15
Ni₂MnIn	150.89	132.76	95.95	138.81	43.82	118.94	0.38	3.17

Fig. 10. Three-dimensional surface plots of the single-crystal Young’s moduli for Ni-Mn based cubic alloys: (a) Ni2MnTi; (b) Ni2MnGa; (c) Ni2MnIn.

Fig. 11. Dependence of total magnetic moments on the excess Mn content for Ni8Mn4+xTi4-x (x = 0, 1 and 2) alloys (There is no martensitic transformation in the Ni8Mn4Ti4 alloy).

Fig. 12. Atomic magnetic moments of AFA (a) and AFM (b) for Ni8Mn4+xTi4-x alloys (x = 0, 1 and 2).

Table 3 Mn-Mn atomic distance of austenite and martensite for Ni8Mn4+xTi4-x (x = 0, 1 and 2) alloys. (Bold italic represents fully ordered structure).

Composition Distance (Å)	x = 0 FA L2₁	x = 0 AFA B2	x = 1 AFA B2	x = 2 AFA B2	x = 0 FM L1₀	x = 0 AFM PD L1₀	x = 1 AFM PD L1₀	x = 2 AFM PD L1₀
Mn_Mn-Mn_Mn Mn_Mn-Mn_Ti	4.19				4.12/4.27
Mn_Mn-Mn_Mn Mn_Mn-Mn_Ti		2.95	2.93	2.92		2.73/2.78	2.67/2.73	2.64/2.73

Fig. 13. Total DOS of the austenite and martensite for (a) Ni8Mn4Ti4, (c) Ni8Mn5Ti3 and (e) Ni8Mn6Ti2. (b), (d) and (f) correspond to the total DOS near the Fermi level (EF) in the energy range marked by the red rectangle in (a), (c) and (e), respectively.

Fig. 14. Partial DOS of the austenite and martensite for Ni8Mn4+xTi4-x (x = 0, 1 and 2) alloys: (a) Ni8Mn4Ti4; (b) Ni8Mn5Ti3; (c) Ni8Mn6Ti2.

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