Ag基合金弹性性能与电子结构的第一性原理研究

doi:10.19596/j.cnki.1001-246x.8590

摘要/Abstract

摘要：

基于第一性原理计算, 探究合金元素Cu、Zr、W、Cr、Sn、Ni、In、Zn、Ir掺杂Ag基合金中的点缺陷形成焓H, 弹性常数C₁₁、C₁₂、C₄₄, 体模量B, 剪切模量G, 杨氏模量E及泊松比γ等参数表征材料的强韧度。分析不同合金原子掺杂进入Ag基体的难易程度, 以及合金原子和Ag原子价电子差值△V对Ag基合金弹性性能的作用。随合金原子和Ag原子价电子差值△V的增大, 对应Ag基合金总体抵抗塑性变形、抵抗剪切变形及在剪切变形时保持晶体结构稳定的能力均能够增强。进一步采用掺杂合金原子的Ag基合金在{1 0 0}面投影的差分电荷密度图显示了原子成键前后电荷转移的空间分布情况。结果发现: Ag基合金弹性性能均能增强的原因可归功于合金原子与Ag原子间的强键结合。

关键词: Ag基合金, 第一性原理, 弹性性能, 差分电荷密度

Abstract:

Based on the first principles, the physical parameters such as point defect formation enthalpy H, elastic constants C₁₁, C₁₂, C₄₄, bulk modulus B, shear modulus G, Young's modulus E and Poisson's ratio γ that characterize the strength and toughness of materials in Ag-based alloys doped with alloying elements such as Cu, Zr, W, Cr, Sn, Ni, In, Zn, Ir were calculated in this paper. The difficulty of doping different alloy atoms in Ag matrix and the effects of the valence electron difference ΔV between the alloy atom and the Ag atom on the elastic properties of the Ag-based alloy were analyzed. With the increase of the ΔV, the ability of Ag-based alloys to resist plastic deformation, shear deformation and maintain crystal structure stability during shear deformation can be enhanced. Furthermore, differential charge density of Ag-based alloy projected on the {1 0 0} plane shows the spatial distribution of charge transfer before and after bonding. It is found that the enhanced elastic properties of Ag-base alloy can be attributed to the strong bonding between the alloy atom and Ag atom.

Key words: Ag-based alloys, first principles, elastic properties, differential charge density

胡佳, 易洲, 文大东, 邓永和, 谢云, 戚双祥, 邱建美, 李政一, 彭平. Ag基合金弹性性能与电子结构的第一性原理研究[J]. 计算物理, 2023, 40(3): 369-375.

Jia HU, Zhou YI, Dadong WEN, Yonghe DENG, Yun XIE, Shuangxiang QI, Jianmei QIU, Zhengyi LI, Ping PENG. First-Principles Study on Elastic Properties and Electronic Structure of Ag-based Alloys[J]. Chinese Journal of Computational Physics, 2023, 40(3): 369-375.

图/表 5

图1 计算点缺陷形成焓及弹性常数的Ag超胞模型图

Fig.1 Ag supercell model for calculating point defect formation enthalpy and elastic constant

表1 合金元素X掺杂Ag超胞中的点缺陷形成焓H，弹性常数Cij，体模量B，剪切模量G，杨氏模量E和泊松比γ的计算值(模型Ag32, Ag[24], Ag[25]分别是本文计算Ag超胞的弹性常数，文献[24]的计算值，文献[25]的实验值。)

Table 1 Calculated values of point defect formation enthalpy H, elastic constant Cij, bulk modulus B, shear modulus G, Young′s modulus E, Poisson′s ratio γ in alloying element X-doped Ag supercells (Ag32, Ag[24], Ag[25]are the elastic constant of Ag supercells calculated in this paper, the calculated value in Ref.[24], and the experimental value in Ref.[25] respectively.)

Model	H/eV	C₁₁/GPa	C₁₂/GPa	C₄₄/GPa	B/GPa	G/GPa	E/GPa	γ
Ag₃₂		127.31	95.12	54.15	105.85	38.93	104.03	0.336
Ag^[24]		140.9	96.5	59.3
Ag^[25]		124.0	93.4	46.1
Ag₃₁In	-0.61	145.15	102.35	62.23	116.62	45.90	121.72	0.326
Ag₃₁Sn	-0.42	159.84	106.26	69.80	124.12	52.60	138.26	0.314
Ag₃₁Zn	-0.25	131.19	96.39	59.31	107.99	42.55	112.82	0.326
Ag₃₁Zr	0.03	160.50	104.18	68.72	122.95	52.50	137.87	0.313
Ag₃₁Cu	0.38	129.73	95.11	56.53	106.65	40.84	108.66	0.330
Ag₃₁Ni	0.88	138.20	98.95	57.90	112.03	42.59	113.40	0.331
Ag₃₁Ir	1.33	137.52	98.33	61.46	111.39	44.71	118.31	0.323
Ag₃₁Cr	2.80	147.75	100.10	60.55	115.98	45.86	121.56	0.325
Ag₃₁W	3.40	146.33	102.53	63.71	117.13	46.99	124.33	0.323

图2 合金元素X掺杂Ag超胞中的(a)点缺陷形成焓和(b)弹性常数Cij

Fig.2 (a) Point defect formation enthalpy and (b) elastic constant Cij in alloying element X-doped Ag supercells

图3 Ag-X价电子数差值△V与(a) 体模量B (GPa)，(b) 剪切模量G (GPa)，(c) 杨氏模量E (GPa)，(d) 泊松比γ的关系

Fig.3 The relationship between Ag-X valence electron number difference △V and (a) Bulk modulus B (GPa), (b) shear modulus G (GPa), (c) Young′s modulus E (GPa) and (d) Poisson′s ratio γ

图4 Ag31X体系中{1 0 0}横截面的差分电荷密度(a) 完美Ag模型；(b) ZnAg模型；(c) CuAg模型；(d) IrAg模型；(e) NiAg模型；(f) ZrAg模型；(g) WAg模型；(h) InAg模型；(i) SnAg模型；(j) CrAg模型

Fig.4 Differential charge density maps of {1 0 0} cross-sections in Ag31X system (a) Perfect Ag model; (b) ZnAg model; (c) CuAg model; (d) IrAg model; (e) NiAg model; (f) ZrAg model; (g) WAg model; (h) InAg model; (i) SnAg model; (j) CrAg model

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