First-principles study of Co and Ni excess effects on crystal structure and phase stability of Co<sub>2</sub>NiGa alloy

Zhou Jin-Ping; Li Chun-Mei; Jiang Bo; Huang Ren-Zhong

doi:10.7498/aps.72.20230626

Abstract

Using the first-principles exact muffin-tin orbital method combined with the coherent potential approximation, the crystal structure and site occupation, martensitic transformation, magnetic moment and elastic constant for each of Co_2+xNi_1–xGa, Co_2+xNiGa_1–x, Co_2–xNi_1+xGa and Co₂Ni_1+xGa_1–x(0 ≤ x ≤ 0.4) alloys with Co and Ni excess at 0 K are systematically investigated. It is shown that most of the austenitic phases of the alloys have XA stable structure, and the excess Co and Ni atoms occupy the insufficient atomic positions, and it is inversely occupied only when Ni replaces Ga. With the increase of x, the total electron energy of L1₀ relative to XA of only two Ga-insufficient alloys gradually decreases, for the former, the tetragonal shear elastic constant gradually increases, but for the latter, it gradually decreases. It is indicated that the martensitic transformation is promoted by the substitution of both Co and Ni for Ga in the energy and mechanics, and the martensitic transformation temperature is expected to increase. The values of total magnetic moment (μ_tot) of the XA phase and L1₀ phase of each alloy are mainly contributed by Co atoms, but onlya relatively small portion by Ni atoms. And the values of μ_tot of two phases in the four alloys have the same relationship with x, and the difference between them with the same compositions is not more than about 0.32 μ_B . The analyses of electronic structure calculations show that the distributions of spin-down electronic density of states of Co and Ni atoms near the Fermi energy level have contributed significantly to the stability of L1₀ relative to the XA phase, which is attributed to the Jahn-Teller effect. The above results are expected to provide a theoretical reference for the optimal design of the structure and properties of Co₂NiGa-based ternary alloys.

Keywords:

Authors and contacts

College of Physical Science and Technology, Shenyang Normal University, Shenyang 110034, China

Corresponding author: Li Chun-Mei, cmli@synu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12174269, 11674233, 51301176) and the Education Department Foundation of Liaoning Province, China (Grant No. LJKMZ20221472).

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References

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[9]	Guezlane M, Baaziz H, Hassan F E H, Charifi C, Djaballah Y 2016 J. Magn. Magn. Mater. 414 219 Google Scholar
[10]	Planes A, Mañosa L, Acet M 2009 J. Phys. :Condens. Matter 21 233201 Google Scholar
[11]	Chabungbam S, Borgohain P, Ghosh S, Singh N, Sahariah M B 2016 J. Alloys Compd. 689 199 Google Scholar
[12]	Shreder E I, Lukoyanov A V, Makhnev A A, Baglasov E D, Suresh K G 2019 Phys. Met. Metall. 120 729 Google Scholar
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[14]	Pereira M J, Santos T, Correia R, Amaral J S, Amaral V S, Fabbrici S, Albertini F 2021 J. Magn. Magn. Mater. 538 168283 Google Scholar
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[18]	Li C M, Yang S J, Zhou J P 2022 Chin. Phys. B 31 056105 Google Scholar
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Cited By

图 1 Co₂NiGa合金晶体结构图　(a)奥氏体相; (b)马氏体相

Figure 1. Crystal structures of Co₂NiGa alloy: (a) Austenitic phase; (b) martensitic phase.

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图 2 L2₁-和XA-Co₂NiGa合金E_tot随r_ws的变化关系, 及四组非化学计量比合金平衡体积下$\Delta E_{{\text{tot}}}^{X\text-L} \text{-} x$关系　(a) E_tot; (b) $\Delta E_{{\text{tot}}}^{X\text-L}$

Figure 2. E_tot of L2₁- and XA-Co₂NiGa alloys change with respect to r_ws, together with the trends of $\Delta E_{{\text{tot}}}^{X{\text{-}}L} \text{-} x$ of the four off-stoichiometric alloys at equilibrium volume: (a) E_tot; (b) $\Delta E_{{\text{tot}}}^{X\text-L}$.

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图 3 L2₁-和XA-Co₂NiGa合金E_tot(单位: Ry)随四方晶格c/a和r_ws的变化关系图　(a) L2₁-Co₂NiGa; (b) XA-Co₂NiGa

Figure 3. E_tot (in Ry) of L2₁- and XA-Co₂NiGa alloys change with respect to the tetragonal lattice c/a and r_ws: (a) L2₁-Co₂NiGa; (b) XA-Co₂NiGa.

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图 4 XA-Co_2+xNi_1–xGa和Co_2+xNiGa_1–x (0 ≤ x ≤ 0.4)合金E_tot随c/a的变化关系　(a) Co_2+xNi_1–xGa; (b) Co_2+xNiGa_1–x

Figure 4. E_tot of XA-Co_2+xNi_1–xGa and Co_2+xNiGa_1–x (0 ≤ x ≤ 0.4) alloys change with respect to c/a: (a) Co_2+xNi_1–xGa; (b) Co_2+xNiGa_1–x

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图 5 XA-Co_2–xNi_1+xGa和Co₂Ni_1+xGa_1–x(0 ≤ x ≤ 0.4)合金E_tot随c/a的变化关系　(a) Co_2–xNi_1+xGa; (b) Co₂Ni_1+xGa_1–x

Figure 5. E_tot of XA-Co_2–xNi_1+xGa and Co₂Ni_1+xGa_1–x(0 ≤ x ≤ 0.4) alloys change with respect to c/a: (a) Co_2–xNi_1+xGa; (b) Co₂Ni_1+xGa_1–x.

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图 6 四组非化学计量比合金两相各原子的磁矩以及μ_tot随x的变化关系　(a) Co_2+xNi_1–xGa; (b) Co_2+xNiGa_1–x; (c) Co_2–xNi_1+xGa; (d) Co₂Ni_1+xGa_1–x

Figure 6. x-dependence of the magnetic moments for each atom in both phases and the μ_tot of the four off-stoichiometric alloys: (a) Co_2+xNi_1–xGa; (b) Co_2+xNiGa_1–x; (c) Co_2–xNi_1+xGa; (d) Co₂Ni_1+xGa_1–x.

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图 7 XA-Co_2+xNi_1–xGa, Co_2+xNiGa_1–x, Co_2–xNi_1+xGa和Co₂Ni_1+xGa_1–x(0 ≤ x ≤ 0.4)合金的C₄₄和C′以及四组合金L1₀相的C_s随x的变化关系　(a) C₄₄; (b) C' and C_s

Figure 7. x-dependence of both C₄₄ and C' of the XA-Co_2+xNi_1–xGa, Co_2+xNiGa_1–x, Co_2–xNi_1+xGa and Co₂Ni_1+xGa_1–x(0 ≤ x ≤ 0.4) alloys and C_s of the four alloys with L1₀ phase: (a) C₄₄; (b) C' and C_s.

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图 8 XA-和L1₀-Co₂NiGa合金电子总态密度(DOS), CoI和CoII, Ni, Ga原子的局域DOS对比　(a) Tot; (b) CoI and CoII; (c) Ni; (d) Ga

Figure 8. Total electron density of states (DOS) and local DOS corresponding to CoI and CoII, Ni, Ga atoms of XA- and L1₀-Co₂NiGa alloys: (a) Tot; (b) CoI and CoII; (c) Ni; (d) Ga.

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表 1 XA-Co_2.2Ni_0.8Ga, Co_2.2NiGa_0.8, Co_1.8Ni_1.2Ga和Co₂Ni_1.2Ga_0.8合金在铁磁和非自旋极化下各原子占位的∆E_tot和$ \Delta {E'_{{\text{tot}}}} $, 及它们在铁磁状态下的体积和μ_tot的理论值

Table 1. ∆E_tot and $ \Delta {E'_{{\text{tot}}}} $ for respective site occupations of the ferromagnetic and non-spin-polarized XA-Co_2.2Ni_0.8Ga, Co_2.2NiGa_0.8, Co_1.8Ni_1.2Ga and Co₂Ni_1.2Ga_0.8 alloys, together with their theoretical values of the volume and μ_tot in the ferromagnetic state.

Alloys	Site occupancy	∆E_tot/mRy	$ \Delta {E'_{{\text{tot}}}} $/mRy	V/(Å³·atom^–1)	μ_tot/μ_B
Co_2.2Ni_0.8Ga	Co₂(Ni_0.8Co_0.2)Ga	0	0	11.706	3.064
Co_2.2Ni_0.8Ga	Co₂(Ni_0.8Ga_0.2)(Ga_0.8Co_0.2)	5.395	5.568	11.801	3.356
Co_2.2NiGa_0.8	Co₂Ni(Ga_0.8Co_0.2)	0	0	11.630	3.488
Co_2.2NiGa_0.8	Co₂(Ni_0.8Co_0.2)(Ga_0.8Ni_0.2)	0.688	0.211	11.624	3.402
Co_1.8Ni_1.2Ga	(Co_0.8Ni_0.2)CoNiGa	0	0	11.700	2.539
	Co(Co_0.8Ni_0.2)NiGa	0.317	0.681	11.710	2.559
	(Co_0.8Ga_0.2)CoNi(Ga_0.8Ni_0.2)	2.441	1.953	11.748	2.569
	Co(Co_0.8Ga_0.2)Ni(Ga_0.8Ni_0.2)	5.791	5.798	11.855	2.798
Co₂Ni_1.2Ga_0.8	Co₂Ni(Ga_0.8Ni_0.2)	0	0	11.607	3.167
	(Co_0.8Ni_0.2)CoNi(Ga_0.8Co_0.2)	–1.023	–0.617	11.648	3.253
	Co(Co_0.8Ni_0.2)Ni(Ga_0.8Co_0.2)	–0.717	–0.153	11.615	3.255

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表 2 XA-Co_2+xNi_1–xGa, Co_2+xNiGa_1–x, Co_2–xNi_1+xGa和Co₂Ni_1+xGa_1–x(0 ≤ x ≤ 0.4)合金的e/a、体积和电子密度, 以及L1₀相对应的体积和c/a的EMTO计算结果

Table 2. The e/a, volume and electron density of the XA-Co_2+xNi_1–xGa, Co_2+xNiGa_1–x, Co_2–xNi_1+xGa and Co₂Ni_1+xGa_1–x(0 ≤ x ≤ 0.4) alloys, and the corresponding volume and c/a of L1₀ by EMTO calculations.

Alloys	e/a	XA		L1₀
Alloys	e/a	V/Å³	n/Å^–3	V/Å³	c/a
Co₂NiGa	7.0	11.706	0.598	11.629	1.260
Co₂NiGa		11.650^[32]	0.601^[32]	11.550^[32]	—
Co_2.1Ni_0.9Ga	6.9	11.709	0.590	11.630	1.254
Co_2.2Ni_0.8Ga	6.8	11.706	0.581	11.630	1.248
Co_2.3Ni_0.7Ga	6.7	11.700	0.573	11.628	1.242
Co_2.4Ni_0.6Ga	6.6	11.694	0.564	11.627	1.236
Co_2.1NiGa_0.9	7.6	11.661	0.652	11.579	1.282
Co_2.2NiGa_0.8	8.2	11.630	0.705	11.525	1.305
Co_2.3NiGa_0.7	8.8	11.494	0.766	11.466	1.326
Co_2.4NiGa_0.6	9.4	11.458	0.820	11.405	1.344
Co_1.9Ni_1.1Ga	7.1	11.710	0.606	11.634	1.260
Co_1.8Ni_1.2Ga	7.2	11.700	0.615	11.635	1.263
Co_1.7Ni_1.3Ga	7.3	11.698	0.624	11.636	1.266
Co_1.6Ni_1.4Ga	7.4	11.691	0.633	11.637	1.269
Co₂Ni_1.1Ga_0.9	7.7	11.660	0.660	11.580	1.284
Co₂Ni_1.2Ga_0.8	8.4	11.648	0.721	11.525	1.306
Co₂Ni_1.3Ga_0.7	9.1	11.445	0.795	11.467	1.327
Co₂Ni_1.4Ga_0.6	9.8	11.439	0.857	11.405	1.346

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表 3 L2₁-和XA-Co₂NiGa合金的单晶弹性常数(C₁₁, C₁₂, C₄₄和C' = (C₁₁– C₁₂)/2)、多晶剪切弹性模量G和杨氏模量E的EMTO计算结果与理论参考值的对比

Table 3. Single crystal elastic constants (C₁₁, C₁₂, C₄₄ and C' = (C₁₁– C₁₂)/2), polycrystalline shear elastic modulus G and Young’s modulus E of the L2₁- and XA-Co₂NiGa alloys calculated by EMTO are in comparison with the theoretical reference values.

Alloys	Site occupancy	Methods	C₁₁/GPa	C₁₂/GPa	C₄₄/GPa	C'/GPa	G/GPa	E/GPa
Co₂NiGa	L2₁	EMTO	194.20	172.68	136.72	10.76	55.20	150.22
		PAW^[38]	181	186	141	–2.5	52	139
		PAW^[39]	166.96	150.50	111.25	8.23	49.44	134.15
	XA	EMTO	176.29	182.55	110.91	–3.13	28.56	81.40

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[1]	Heusler F 1903 Verh. Dtsch. Phys. Ges. 5 219
[2]	Wuttig M, Li J, Craciunescu C 2001 Scr. Mater. 44 2393 Google Scholar
[3]	Ahmad A, Guchhait S, Ahmad H, Srivastava S K, Das A K 2019 International Conference on Advances in Basic Sciences Bahal, India, February 07–09, 2019 p090006
[4]	XU X, Nagasako M, Ito W, Umetsu R Y, Kanomata T, Kainuma R 2013 Acta Mater. 61 6712 Google Scholar
[5]	杜音, 王文洪, 张小明, 刘恩克, 吴光恒 2012 物理学报 61 147304 Google Scholar Du Y, Wang W H, Zhang X M, Liu E K, Wu G H 2012 Acta Phys. Sin. 61 147304 Google Scholar
[6]	Kierstead H A, Dunlap B D, Malik S K, Umarji A M, Shenoy G K 1985 Phys. Rev. B 32 135 Google Scholar
[7]	Terada M, Fujita Y, Endo K 1974 J. Phys. Soc. Jpn. 36 620 Google Scholar
[8]	Li Y, Xin Y, Chai L, Ma Y Q, Xu H B 2010 Acta Mater. 58 3655 Google Scholar
[9]	Guezlane M, Baaziz H, Hassan F E H, Charifi C, Djaballah Y 2016 J. Magn. Magn. Mater. 414 219 Google Scholar
[10]	Planes A, Mañosa L, Acet M 2009 J. Phys. :Condens. Matter 21 233201 Google Scholar
[11]	Chabungbam S, Borgohain P, Ghosh S, Singh N, Sahariah M B 2016 J. Alloys Compd. 689 199 Google Scholar
[12]	Shreder E I, Lukoyanov A V, Makhnev A A, Baglasov E D, Suresh K G 2019 Phys. Met. Metall. 120 729 Google Scholar
[13]	Sokolovskiy V, Miroshkina O N, Sanosyan A, Baigutlin D, Buchelnikov V, Gruner M E 2022 J. Magn. Magn. Mater. 546 168728 Google Scholar
[14]	Pereira M J, Santos T, Correia R, Amaral J S, Amaral V S, Fabbrici S, Albertini F 2021 J. Magn. Magn. Mater. 538 168283 Google Scholar
[15]	Yan S M, Pu J, Chi B, Li J 2011 Chin. Sci. Bull. 56 796 Google Scholar
[16]	Craciunescu C, Kishi Y, Lograsso T A, Wuttig M 2002 Scr. Mater. 47 285 Google Scholar
[17]	Biswas C, Rawat R, Barman S R 2005 Appl. Phys. Lett. 86 202508 Google Scholar
[18]	Li C M, Yang S J, Zhou J P 2022 Chin. Phys. B 31 056105 Google Scholar
[19]	Siewert M, Gruner M E, Hucht A, Herper H C, Dannenberg A, Chakrabarti A, Singh N, Arróyave R, Entel P 2012 Adv. Eng. Mater. 14 530 Google Scholar
[20]	Opeil C P, Mihaila B, Schulze R K, Mañosa L, Planes A, Hults W L, Fisher R A, Riseborough P S, Littlewood P B, Smith J L, Lashley J C 2008 Phys. Rev. Lett. 100 165703 Google Scholar
[21]	Roy T, Pandey D, Chakrabarti A 2016 Phys. Rev. B 93 184102 Google Scholar
[22]	Vitos L, Abrilsosv I A, Johansson B 2001 Phys. Rev. Lett. 87 156401 Google Scholar
[23]	Gyorff B L 1972 Phys. Rev. B 5 2382 Google Scholar
[24]	Bain E C 1924 Trans. Am. Inst. Min. Metall. Eng. 70 25
[25]	Cao P Y, Tian F Y, Li W, Vitos L, Wang Y D 2021 Acta Mater. 210 116816 Google Scholar
[26]	Vitos L 2007 Computational Quantum Mechanics for Materials Engineers (London: Spring-Verlag) pp98–121
[27]	Li C M, Zhang Y, Feng W J, Huang R Z, Gao M 2020 Phys. Rev. B 101 054106 Google Scholar
[28]	胡岩菲 2020 硕士学位论文 (沈阳: 沈阳师范大学) Hu Y F 2020 M. S. Thesis (Shenyang: Shangyang Normal University) (in Chinese)
[29]	杨顺杰, 李春梅, 周金萍 2022 物理学报 71 106201 Google Scholar Yang S J, Li C M, Zhou J P 2022 Acta Phys. Sin. 71 106201 Google Scholar
[30]	Perdew J P, Burke K, Emzerhof M 1996 Phys. Rev. Lett. 77 3865 Google Scholar
[31]	Entel P, Dannenberg A, Siewert M, Herper H C, Gruner M E, Buchelnikov V D, Chernenko V A 2011 Materials Science Forum (Switzerland: Trans Tech Publications) p1
[32]	Siewert M, Gruner M E, Dannenberg A, Hucht A, Shapiro S M, Xu G, Schlagel D L, Lograsso T A, Entel P 2010 Phys. Rev. B 82 064420 Google Scholar
[33]	Eleno L T F, Chivukula A, Arróyave R, Schön C G 2010 TOFA 2010-Discusion Meeting on Thermodynamics of Alloys Porto, Portugual, September 14, 2010
[34]	Olivos E, Miranda A L, Singh N, Arróyave R, Romero A H 2012 Ann. Phys. 524 212 Google Scholar
[35]	Arróyave R, Junkaew A, Chivukula A, Bajaj S, Yao C Y, Garay A 2010 Acta Mater. 58 5220 Google Scholar
[36]	Li Q S, Liang Z Y, Sun K C, Luo H Z 2019 Comput. Mater. Sci. 168 11 Google Scholar
[37]	Matsushita Y I, Madjarova G, Dewhurst J K, Shallcross S, Felser C, Sharma S, Gross E K U 2017 J. Phys. D:Appl. Phys. 50 095002 Google Scholar
[38]	Talapatra A, Arróyave R, Entel P, Valencia-Jaime I, Romero A H 2015 Phys. Rev. B 92 054107 Google Scholar
[39]	Bai J, Liu D, Huang R K, Zhang Z Y, Yang Y, Gu J L, Yan H L, Zhao X, Zuo L 2020 Mater. Today Commun. 22 100810 Google Scholar
[40]	Wang Y, Perdew J P 1991 Phys. Rev. B 44 13298 Google Scholar
[41]	Ghosh S, Ghosh S 2019 Phys. Rev. B 99 064112 Google Scholar
[42]	Shi X Y, Gao R R, Li J Q, Lu T Y, Luo H Z 2022 J. Magn. Magn. Mater. 547 168815 Google Scholar
[43]	Singh N, Dogan E, Karaman I, Arróyave R 2011 Phys. Rev. B 84 184201 Google Scholar

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Vol. 72, Issue 15 - 2023-08-05

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First-principles study of Co and Ni excess effects on crystal structure and phase stability of Co₂NiGa alloy

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First-principles study of Co and Ni excess effects on crystal structure and phase stability of Co2NiGa alloy

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Corresponding author: Li Chun-Mei, cmli@synu.edu.cn

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First-principles study of Co and Ni excess effects on crystal structure and phase stability of Co₂NiGa alloy