金属学报, 2023, 59(6): 812-820 DOI: 10.11900/0412.1961.2022.00454

研究论文

Al掺杂Mg/Mg2Sn合金界面的第一性原理计算

王福容1, 张永梅1, 柏国宁2, 郭庆伟2, 赵宇宏,2,3

1中北大学 半导体与物理学院 太原 030051

2中北大学 材料科学与工程学院 太原 030051

3北京科技大学 北京材料基因工程高精尖创新中心 北京 100083

First Principles Calculation of Al-Doped Mg/Mg2Sn Alloy Interface

WANG Furong1, ZHANG Yongmei1, BAI Guoning2, GUO Qingwei2, ZHAO Yuhong,2,3

1School of Semiconductors and Physics, North University of China, Taiyuan 030051, China

2School of Materials Science and Engineering, North University of China, Taiyuan 030051, China

3Beijing Advanced Innovation Center for Materials Genome Engineering, University of Science and Technology Beijing, Beijing 100083, China

通讯作者: 赵宇宏,zhaoyuhong@nuc.edu.cn,主要从事合金多尺度设计及液态成型工艺优化研究

责任编辑: 肖素红

收稿日期: 2022-09-15   修回日期: 2022-12-16  

基金资助: 国家自然科学基金项目(52074246)
国家自然科学基金项目(22008224)
国家自然科学基金项目(52275390)
国家自然科学基金项目(52205429)
国家自然科学基金项目(52201146)
国防基础科研项目(JCKY20204-08B002)
国防基础科研项目(WDZC2022-12)
山西省重点研发计划项目(202102050-201011)
中央引导地方计划项目(YDZJSX-2022A025)
中央引导地方计划项目(YDZJSX2021A027)

Corresponding authors: ZHAO Yuhong, professor, Tel: 15035172958, E-mail:zhaoyuhong@nuc.edu.cn

Received: 2022-09-15   Revised: 2022-12-16  

Fund supported: National Natural Science Foundation of China(52074246)
National Natural Science Foundation of China(22008224)
National Natural Science Foundation of China(52275390)
National Natural Science Foundation of China(52205429)
National Natural Science Foundation of China(52201146)
National Defense Basic Scientific Research Program of China(JCKY20204-08B002)
National Defense Basic Scientific Research Program of China(WDZC2022-12)
Key Research and Development Program of Shanxi Province(202102050-201011)
Guiding Local Science and Technology Development Projects by the Central Government(YDZJSX-2022A025)
Guiding Local Science and Technology Development Projects by the Central Government(YDZJSX2021A027)

作者简介 About authors

王福容,女,1998年生,硕士生

摘要

为研究Mg-Sn合金中Al掺杂Mg基体与Mg2Sn相不同取向以及Al元素在界面处的分布位置,基于密度泛函理论计算了Al元素掺杂Mg/Mg2Sn不同指数面的界面黏附功、界面能以及界面掺杂能来寻找较稳定的掺杂位置。采用态密度和晶体轨道重叠布居分析了Al元素掺杂对Mg(0001)/Mg2Sn(022)界面电子特性的影响。结果表明,界面处添加Al元素后只有部分掺杂位置有益于加强Mg/Mg2Sn界面的稳定性。添加Al元素后,Mg(0001)/Mg2Sn(001)界面处Sn端黏附功均高于Mg端,而Mg(0001)/Mg2Sn(111)界面正好相反。Al掺杂后的Mg(0001)/Mg2Sn(022)界面能降低了0.07 eV/nm。添加Al元素后,Mg(0001)/Mg2Sn(022)界面位置Ⅳ比较容易掺杂,该位置处的电子结构分析表明掺杂Al元素后Al的s轨道和Sn的p轨道存在明显交互作用,在界面处Al—Sn键占主导地位。

关键词: Mg/Mg2Sn; Al; 界面; 第一性原理; 掺杂

Abstract

Mg-Sn alloy is a high temperature-creep resistant magnesium alloy that has potential applications in lightweight automobiles. The addition of Sn to Mg can reduce the overall cost of the alloy as Sn is cheaper than rare earth elements. Sn and Mg form Mg2Sn phase on the grain boundary, and this Mg2Sn phase has an excellent precipitation hardening effect. However, coarsened Mg2Sn phase can reduce the age hardening effect of the alloy. Previous experimental studies have showed that the addition of Al element can considerably improve the age hardening effect of Mg-Sn alloy as it segregated at the interface between the Mg matrix and Mg2Sn phase. However, there is a lack of research on the different orientations of Al-doped Mg matrix and Mg2Sn phase and the distribution position of Al element at the interface. Therefore, in this study, the interface adhesion energy, interface energy, and interface doping energy of Al-doped Mg/Mg2Sn with different index surfaces were calculated based on density functional theory to determine more stable doping positions. The effects of Al doping on the electronic structure of Mg(0001)/Mg2Sn(022) interface were analyzed using the density of states and crystal orbital Hamilton population. The results demonstrate that only a part of the Al-doping positions is beneficial in strengthening the stability of Mg/Mg2Sn interface. After the addition of Al, the adhesion energy of Sn termination at Mg(0001)/Mg2Sn(001) interface is higher than that of Mg termination, but the adhesion energy of Sn termination at Mg(0001)/Mg2Sn(111) interface is lower than that of Mg termination. In addition, the interface energy of Mg(0001)/Mg2Sn(022) interface doped with Al decreased by 0.07 eV/nm compared to that of Mg(0001)/Mg2Sn(022) interface. The addition of Al element to Mg(0001)/Mg2Sn(022) facilitates the doping of a special position, which shows an obvious interaction between the s orbital of Al and the p orbital of Sn after Al doping. Moreover, the Al—Sn bonding is found to be dominant at the interface.

Keywords: Mg/Mg2Sn; Al; interface; first principle; doping

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本文引用格式

王福容, 张永梅, 柏国宁, 郭庆伟, 赵宇宏. Al掺杂Mg/Mg2Sn合金界面的第一性原理计算[J]. 金属学报, 2023, 59(6): 812-820 DOI:10.11900/0412.1961.2022.00454

WANG Furong, ZHANG Yongmei, BAI Guoning, GUO Qingwei, ZHAO Yuhong. First Principles Calculation of Al-Doped Mg/Mg2Sn Alloy Interface[J]. Acta Metallurgica Sinica, 2023, 59(6): 812-820 DOI:10.11900/0412.1961.2022.00454

镁合金因其质量轻、资源丰富以及比强度/比刚度高而广泛应用于航空航天、汽车等领域[1~3]。Mg-Sn合金成本低,具有反萤石结构的Mg2Sn沉淀相的沉淀硬化效应显著[4~6],也可以改善合金抗蠕变性能[7,8]。但Mg2Sn相会快速长大并粗化,从而恶化Mg-Sn合金的力学性能。

通过微合金化可以减少Mg2Sn的析出从而提高合金的性能,这得益于其固溶强化效应[9,10]。Sasaki等[11]研究发现,添加Zn元素可以改变Mg2Sn和Mg基体之间的界面能,有利于细化Mg2Sn沉淀物。Mendis等[12]将Mg2Sn作为模型,分别添加Na和In + Li,发现添加Na使得硬化增量比添加In + Li增加了近一倍。Pan等[13]研究证实添加Ca可以在Mg-Sn合金中形成热稳定相CaMgSn,之后添加Y和Zr可以细化CaMgSn相,从而提高合金强度和延展性。田树科和郭学锋[14]发现在Mg-Sn合金中分别添加Al和Zn元素时,都可以提高合金的固溶强化效果,Al的固溶强化效果高于Zn。Kim和Park[15]发现Al元素的加入可以改善Mg-Sn合金的力学性能和硬度。Luo等[16]证实了Al的添加可以显著改变析出相Mg2Sn的分布和形貌,并对Mg2Sn起到细化作用,改善Mg-Sn合金的力学性能。徐孝新[17]发现在Mg-Sn合金中加入Al元素后,Al主要偏聚在Mg基体与Mg2Sn界面处,降低Mg2Sn的界面能,减小形核功,使形核过程更易于进行。然而实验上难以从微观角度分析界面结合机制,需要结合第一性原理[18~20]、分子动力学等方法进行分析。目前第一性原理在研究合金化元素改善界面性质方面取得了很多成果[21~24]。王小宏等[25]基于第一性原理研究了Al、Zn占位对Mg/Li相界断裂强度的影响,表明Al、Zn元素的添加提高了体系稳定性。Liu等[26]预测了Cr、Os、Ir元素掺杂对NiCo/Cu界面的结合强度和力学性能的影响,并通过原子位置、键长和电子性质解释了加强机理。Zhang等[27]通过第一性原理发现了Sc在S1位点掺杂AlCu/Al界面会降低其界面能,并且增强其黏附功,特别是被间隙Cu原子占据的S1位点与Sc的掺杂具有非常好的结合强度。在Mg-Sn合金中,粗化的Mg2Sn相会导致该合金的时效硬化效果降低,而Al元素可以显著提高Mg-Sn合金的时效硬化效应。在实验中观测到在Mg-Sn合金中添加Al元素后,Al元素主要偏聚在Mg基体与Mg2Sn相的界面,起到细化作用。第一性原理可以定性给出界面处的电子结构以及合金元素对界面稳定性[28,29]的影响,但对于Al掺杂Mg/Mg2Sn界面性质的研究很少。

本工作对Mg/Mg2Sn界面进行讨论,从原子尺度研究了在不同界面上的不同位置掺杂Al元素对Mg/Mg2Sn界面性能的影响,并从电子层次解释了Al掺杂前后Mg(0001)/Mg2Sn(022)界面处原子轨道变化,分析了Al合金化提高Mg-Sn合金性能的影响机理。

1 模型和方法

1.1 模型构建

Mg/Mg2Sn界面结构基于hcp结构的Mg基体[30]以及fcc结构的Mg2Sn析出相[31]建立。对于Mg基体结构,晶格常数a = b = 0.320 nm,c = 0.513 nm;α = β = 90°,γ = 120° (αβγ分别为晶格常数abacbc 3个轴之间的夹角)。Mg2Sn析出相为fcc结构,a = b = c = 0.681 nm,α = β = γ = 90°。有实验观察到Mg2Sn与Mg基体之间的取向关系为{111}Mg2Sn//Mg(0001)取向(200℃左右)[12]和Mg(0001)//Mg2Sn(022)[4],但考虑到不同取向界面能不一样,本工作分别对Mg(0001)以及Mg2Sn 3个低指数面组成的界面进行第一性原理计算。经过收敛性测试,采用4层Mg2Sn和4层Mg构建了Mg(0001)/Mg2Sn(001)Mg端和Sn端界面、Mg(0001)/Mg2Sn(022)界面以及Mg(0001)/Mg2Sn(111) Mg端和Sn端界面,对其界面间距进行收敛性测试,并测量其界面能和晶格错配度,如表1所示。

表1   Mg/Mg2Sn界面间距以及界面能和晶格错配度

Table 1  Interface spacing, interface energy, and lattice mismatch degree of Mg/Mg2Sn

Interface structureInterface spacing / nmInterface energy / (eV·nm-1)Mismatch degree (δ) / %
Mg(0001)/Mg2Sn(001)-Mg0.35018.146.34
Mg(0001)/Mg2Sn(001)-Sn0.35031.526.34
Mg(0001)/Mg2Sn(022)0.25014.583.05
Mg(0001)/Mg2Sn(111)-Mg0.19017.562.56
Mg(0001)/Mg2Sn(111)-Sn0.19027.292.56

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比较3个不同取向界面能可知,Mg(0001)/Mg2Sn(022)界面能最小,界面较稳定。为了研究Al掺杂位置对界面稳定性的影响,对于不同取向界面分别在Mg(0001)表面以及Mg2Sn表面找寻了不同的Al掺杂位置,如图1中蓝色虚线球所示。图1a和b分别为Mg(0001)/Mg2Sn(001)界面的Mg端界面和Sn端界面;图1c为Mg(0001)/Mg2Sn(022)界面;图1d和e分别为Mg(0001)/Mg2Sn(111)界面的Mg端和Sn端。其中紫色球代表Sn原子,橘色球代表Mg原子,蓝色虚线球代表掺杂的Al原子,绿色虚线框代表Mg/Mg2Sn界面,罗马数字代表界面处Al元素的掺杂位置。

图1

图1   Al元素掺杂不同界面取向的不同位置的Mg/Mg2Sn界面模型示意图

Fig.1   Schematics of Mg/Mg2Sn interface model with different interface orientations doped with Al element (Roman numerals represent the different doping positions of Al at the interface) (a, b) Mg terminal (a) and Sn terminal (b) models of Mg(0001)/Mg2Sn(001) interface, respectively (c) Mg(0001)/Mg2Sn(022) interface model (d, e) Mg terminal (d) and Sn terminal (e) models of Mg(0001)/Mg2Sn(111) interface, respectively


1.2 计算方法

本工作所有计算均使用基于密度泛函理论的VASP[32]软件包进行。选用Perdew-Burke-Ernzerhof (PBE)的广义梯度近似(generalized-gradient-approximation,GGA)为电子交换关联泛函。经过收敛性测试,平面波截断能为400 eV。Monkhorst-Pack方案的k点最终设定为9 × 9 × 4和5 × 5 × 5用于Mg和Mg2Sn进行优化计算,4 × 4 × 1、5 × 3 × 1和3 × 2 × 1分别用于Mg(0001)/Mg2Sn(001)、Mg(0001)/Mg2Sn(022)和Mg(0001)/Mg2Sn(111)界面的计算。采用4 × 5 × 1、4 × 4 × 1、4 × 3 × 1和3 × 2 × 1分别对4层Mg2Sn(001)、4层Mg(0001)、4层Mg2Sn(022)以及4层Mg2Sn(111)表面进行计算。收敛参数设置:电子弛豫的收敛标准为10-5 eV,并且对于界面计算,结构优化收敛标准为结构内任何原子的作用力均小于0.1 eV/nm。考虑到表面原子间的相互作用,沿Z轴方向设置了长度为1 nm的真空层,使得2个相邻界面之间的相互作用可以忽略。

2 计算结果与讨论

2.1 界面黏附功

黏附功(Wad)反映了界面结构与2个表面结构之间的能量差[32]Wad可以反映界面结构的力学稳定性以及抵抗裂纹扩展的能力。稳定的界面结构对应于高的Wad。它被定义为单位面积上将界面分离成2个自由表面所需的能量[33]

Wad=(EMgslab+EMg2Snslab-EMg/Mg2Sninterface) / A

式中,EMgslab表示Mg(0001) 完全弛豫后的表面模型的总能量;EMg2Snslab表示Mg2Sn表面模型完全弛豫后的总能量,EMg/Mg2Sninterface表示Mg/Mg2Sn界面总能量,A为界面面积。在不同指数面掺杂Al元素后的界面Wad对比如图2所示,图2a中红色虚线表示Mg(0001)/Mg2Sn(001)界面Sn端未掺杂Al元素时的Wad,黑色虚线表示Mg(0001)/Mg2Sn(001)界面Mg端未掺杂Al元素时的Wad图2b中黑色虚线表示Mg(0001)/Mg2Sn(022)界面未掺杂Al元素时的Wad图2c中黑色虚线表示Mg(0001)/Mg2Sn(111)界面Mg端未掺杂Al元素时的Wad,红色虚线表示Mg(0001)/Mg2Sn(111)界面Sn端未掺杂Al元素时的Wad。将Al元素掺杂不同界面、不同位置的黏附功与未掺杂Al元素时的黏附功进行比较,寻找有益于提高界面稳定性的掺杂位置。图2a为Mg(0001)/Mg2Sn(001)界面不同位置掺杂Al后的Wad。可以发现,在Mg端位置Ⅴ掺杂Al元素可以强化界面结合强度,然而Sn端界面Wad远高于Mg端,表明Al元素占据Sn端界面比占据Mg端界面更有利于强化界面稳定性,Sn端位置Ⅳ和位置Ⅴ也都可以加强界面的稳定性,但是掺杂位置Ⅴ对界面的结合强度影响很小。图2b为Mg(0001)/Mg2Sn(022)界面不同位置掺杂Al后的Wad。可以发现,Al元素占据Mg(0001)/Mg2Sn(022)界面Ⅱ、Ⅲ、Ⅳ位置均可增强界面结合强度,其中位置Ⅳ的Wad较其他位置来说最高。图2c为Mg(0001)/Mg2Sn(111)界面不同位置掺杂Al后的Wad。可见,Mg(0001)/Mg2Sn(111)界面Mg端掺杂位置处的Wad均高于Sn端,说明Mg终端更利于界面的稳定性。对于Mg端,Al元素占据位置Ⅵ处可以加强界面结合强度,而对于Sn终端,位置Ⅲ、Ⅴ、Ⅵ、Ⅶ均有利于增强界面结合强度。可见,Mg(0001)/Mg2Sn(022)界面和Mg(0001)/Mg2Sn(111)界面Sn端有多个位置掺杂Al后可以提高界面的稳定性,但由于Mg(0001)/Mg2Sn(111)界面原子数较多,耗时长,故选择对Mg(0001)/Mg2Sn(022)界面进行电子结构分析。

图2

图2   Mg/Mg2Sn界面不同位置掺杂Al元素的黏附功

(a) Mg(0001)/Mg2Sn(001) interface

(b) Mg(0001)/Mg2Sn(022) interface

(c) Mg(0001)/Mg2Sn(111) interface

Fig.2   Adhesion energies of Mg/Mg2Sn interface with doping Al element at different positions (Dotted lines represent the interface adhesion energies without Al element)


2.2 界面掺杂能

界面掺杂能(Ef)可以反映掺杂界面形成的难易程度,其值越小越容易掺杂[34]

Ef=E(Mg/Mg2Sn)-Alinterface+N(μMg-μAl)EMg/Mg2SninterfaceA

式中,E(Mg/Mg2Sn)-Alinterface为Al掺杂Mg/Mg2Sn界面的总能量,N为界面模型中Al原子数量,μMg为被取代的Mg原子化学势,μAl为掺杂到界面处的Al原子化学势。表2计算了在Mg(0001)/Mg2Sn(022)界面6个不同位置添加Al元素之后的界面间距、界面能以及界面掺杂能。可以发现,位置IV处界面能及界面处原子间距最小,较其他位置而言更稳定。而位置I界面能最高,且其界面间距大于其他掺杂位置,Al元素占据该位点不利于界面的稳定性。从表2中可以发现界面掺杂能为负,说明在这6个界面位置处均较易掺杂Al,并且Al更容易占据位置IV处,这也解释了实验上主要通过掺杂Al元素改变Mg-Sn合金的力学性能。

表2   Al掺杂Mg(0001)/Mg2Sn(022)界面的界面间距、界面能和掺杂能

Table 2  Interface spacing, interface energy, and doping energy of Al-doped Mg(0001)/Mg2Sn(022) interface

PositionInterface spacing / nmInterface energy / (J·m-2)Interface doping energy / (J·m-2)
25.840.418-5.031
23.640.143-5.070
23.200.140-5.076
22.830.091-5.079
23.220.149-5.075
23.270.152-5.075

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2.3 界面能

总的界面形成能包括界面能和弹性应变能。界面能是指Mg/Mg2Sn构建的界面体系分成独立晶体Mg和Mg2Sn所需的能量,而弹性应变能是指Mg基体和Mg的析出相Mg2Sn之间所需的应变能。考虑到界面周围最近原子层的影响,对Mg(0001)/Mg2Sn(022)界面进行扩胞,构建了原子个数分别为56、112和168的3个晶胞,计算总的界面形成能[35]

ΔGf=2Aγ / N+ΔGcs
ΔGf=[ΔGMg/Mg2Sntotal-nMg/Mg2SnMgGMg-mMg/Mg2SnMg2SnGMg2Sn] / N

式中,ΔGf为界面每个原子的界面形成能,γ为单位面积的界面能,ΔGcs为平均每个原子的弹性应变能,ΔGMg/Mg2Sntotal为超胞界面结构的总能量,nMg/Mg2SnMg为Mg/Mg2Sn界面中Mg表面结构所含原子个数,mMg/Mg2SnMg2Sn为Mg/Mg2Sn界面中Mg2Sn表面结构所含原子个数,GMg为Mg块体结构的能量,GMg2Sn为Mg2Sn块体结构的能量。由于Al元素占据Mg(0001)/Mg2Sn(022)界面位置Ⅳ比其他5个位置的界面更稳定,因此分别计算了该位置掺杂Al元素前后的界面能,如图3所示,其中线条的截距表示弹性应变能,斜率代表界面能。当不考虑弹性应变能时,Mg(0001)/Mg2Sn(022)界面能为0.091 J/m2,在考虑弹性应变能时其界面能为0.37 eV/nm (0.593 J/m2)。添加Al元素后界面能为0.30 eV/nm (0.481 J/m2),降低了0.07 eV/nm,表明Al元素的添加可以降低界面能,稳定界面。因此Al元素的加入强化了Mg(0001)/Mg2Sn(022)界面稳定性。

图3

图3   Mg(0001)/Mg2Sn(022)界面位置Ⅳ掺杂Al元素前后的界面能

Fig.3   Interface energies of Mg(0001)/Mg2Sn(022) before (a) and after (b) doping Al element at position IV in Fig.1c (The intercept of the line in the figure represents the elastic strain energy, and the slope represents the interface energy. A—interface area, N—number of atoms in the interface, ΔGf—energy contained in a single atom in the interface)


2.4 界面电子特性

为了更深入地了解Mg(0001)/Mg2Sn(022)界面处掺杂Al原子的成键特性,绘制了掺杂Al元素前后Mg(0001)/Mg2Sn(022)界面的分波态密度(partial density of states,PDOS)曲线,如图4所示,图中黑色虚线代表Fermi能级(EF)。分波态密度可以反映出界面处掺杂元素前后界面结构稳定性差异的物理本质[36]。从图4a可以看出,第1~3层Mg和Sn在-4~0 eV处存在明显的重叠波峰,2者间存在较强的杂化共轭作用,界面处主要是Mg的s、p轨道与Sn的p轨道之间的相互作用,导致Mg、Sn原子之间形成较强的共价键。将图4a与b对比后发现,在界面第1层处添加Al元素后Mg、Sn、Al不仅在-4~0 eV处存在明显的重叠波峰,在-6.4~-4 eV处也出现了重叠波峰,并且Al的s轨道和Sn的p轨道存在明显的轨道杂化作用,使得Al掺杂界面的结合作用更强,结构更稳定。

图4

图4   Mg(0001)/Mg2Sn(022)界面位置IV掺杂Al元素前后的分波态密度(PDOS)曲线

Fig.4   Partial density of states (PDOS) curves of Mg(0001)/Mg2Sn(022) interface before (a) and after (b) doping Al element at position IV in Fig.1c (EF—Fermi level)


图5为掺杂Al前后Mg(0001)/Mg2Sn(022)界面处差分电荷密度差异。可以发现,Mg(0001)/Mg2Sn(022)界面上存在明显的电荷转移,在界面的形成过程中电子结构重新排列,界面原子周围出现电荷的聚集和损耗,红色区域代表电荷的聚集,蓝色电荷代表电荷的损耗,说明形成了化学键。从图5a1和a2可以发现Mg(0001)/Mg2Sn(022)界面处Mg原子周围是蓝色区域,说明Mg原子失去电子,而电子均流向电负性比较强的Sn原子处,Sn原子周围是红色区域,实现了电荷的大量聚集,故在界面处形成Mg—Sn共价键。从图5b1和b2可以发现,掺杂Al之后,界面处Al原子周围蓝色区域更大,失电子更多,这表明界面掺杂Al原子之后界面结合强度增强。

图5

图5   Mg(0001)/Mg2Sn(022)界面位置IV掺杂Al元素前后的差分电荷密度图的侧视图和俯视图

Fig.5   Side views (a1, b1) and top views (a2, b2) of differential charge density diagrams of the Mg(0001)/Mg2Sn(022) interface before (a1, a2) and after (b1, b2) doping Al element at position IV in Fig.1c (The red areas represent the accumulation of electric charge, and the blue areas represent the loss of electric charge)


基于对图5分析可以发现结构中存在广泛的共价键,但缺乏对这些共价键准确定量测量以及键强度和贡献的分析。晶体轨道Hamilton布居(crystal orbital Hamilton populations,COHP)可以定量分析晶体结构当中2个原子的结合强弱,而晶体轨道重叠布居积分值(integrated crystal orbital Hamilton populations,ICOHP)对应于Fermi能级积分能量值[37]图6a和b分别为hcp结构Mg和fcc结构Mg2Sn的投影晶体轨道Hamilton布居(projected crystal orbital Hamilton populations,pCOHP)[38]曲线,图6c~f为Mg(0001)/Mg2Sn(022)构建的界面以及在界面处掺杂Al的2种界面在界面处的Mg—Mg、Mg—Sn原子的pCOHP曲线。图中右侧的峰值(-pCOHP > 0)代表的是各个轨道成键贡献,左侧的峰值(-pCOHP < 0)代表的是各个轨道反键态的贡献。在这些原子相互作用中,比较图6c、d以及图6e、f,不难发现在界面处掺杂Al原子后,界面处Mg—Al之间以及Al—Sn之间都存在相互作用,主要是Mg3p、Al3p以及Sn3p、Al3p提供成键轨道。对于ICOHP的值排列如下:Mg3s—Sn5p > Mg3p—Al3p > Mg3s—Mg3p > Mg3p—Mg3p > Mg3p—Sn5s > Al3p—Sn5p,在界面处Al—Sn键强度占主导地位,Mg—Al键次之。通过将界面处原子之间相互作用分解为对不同轨道的贡献,对于不掺杂Al的界面,界面处Mg—Mg之间主要是3p轨道提供成键,Mg—Sn之间主要是Mg3p、Sn5s、Sn5p提供成键。

图6

图6   hcp结构Mg和fcc结构Mg2Sn,Mg(0001)/Mg2Sn(022)界面处的Mg—Mg和Mg—Sn原子,以及掺杂Al后的Mg(0001)/Mg2Sn(022)界面处的Mg—Al和Al—Sn原子的投影晶体轨道Hamilton布居(pCOHP)曲线

Fig.6   Projected crystal orbital Hamilton population (pCOHP) curves of hcp Mg (a) and fcc Mg2Sn (b); Mg—Mg (c) and Mg—Sn (d) atoms at the Mg(0001)/Mg2Sn(022) interface; and Mg—Al (e) and Al—Sn (f) atoms at the Mg(0001)/Mg2Sn(022) interface after doping Al (ICOHP—integrated crystal orbital Hamilton population)


3 讨论

在实验研究中,Al元素是改善镁合金力学性能的主要元素之一。有不少研究证实了随着Mg-Sn合金中Mg2Sn的不断析出,Mg2Sn相会粗化,导致合金力学性能变差。添加Al元素可以抑制合金内Mg2Sn析出相的粗化,对Mg2Sn起到细化作用,提高合金的力学性能[14~16]。然而实验上只是在宏观上分析了Al的添加改善了Mg-Sn界面的力学性能,相比于实验上只是观测到Al掺杂有益于提高Mg/Mg2Sn界面的稳定性,本工作从原子尺度分析解释了掺杂Al元素对Mg/Mg2Sn 3种不同取向界面稳定性的影响,以及界面处不同掺杂位置对界面性质的影响,发现掺杂位置会影响Mg/Mg2Sn界面的稳定性,有的掺杂位置对提高界面的稳定性并不是有益的。Al掺杂后的Mg(0001)/Mg2Sn(022)界面能降低了0.07 eV/nm,这与徐孝新[17]在实验上观察到在Mg-Sn合金中加入Al元素后Al偏聚在Mg基体与Mg2Sn界面,导致界面能降低的结果一致。并且通过对Al掺杂Mg(0001)/Mg2Sn(022)界面电子特性的分析,界面处Al—Sn键强度占主导地位,解释了实验上观测到的Al元素的加入增强了Mg-Sn界面的结合强度。

4 结论

(1) 在Mg(0001)面和Mg2Sn 3个低指数面的不同位置添加Al元素后,寻找到较稳定的Al元素掺杂位置。对于Mg(0001)/Mg2Sn(001)界面,Mg端界面所选5个位置在位置Ⅴ添加Al元素能加强界面的结合强度;对于Sn端,Sn端的界面黏附功远远高于Mg端,在位置Ⅳ和位置Ⅴ添加Al元素都可以加强界面的稳定性。对于Mg(0001)/Mg2Sn(022)界面,在位置Ⅱ、III、Ⅳ添加Al元素都可以加强界面的结合强度,其中位置Ⅳ黏附功比其他位置高。对于Mg(0001)/Mg2Sn(111)界面,界面处Mg端所选Al元素掺杂位置的黏附功都高于Sn端,说明Mg终端更利于界面的稳定性。

(2) 在Mg(0001)/Mg2Sn(022)界面6个位置掺杂Al,其界面掺杂能都为负值,位置IV最容易掺杂Al元素,位置I最不易掺杂。Mg(0001)/Mg2Sn(022)界面能为0.37 eV/nm (0.593 J/m2),掺杂Al后的界面能为0.30 eV/nm (0.481 J/m2),添加Al元素后界面能变小,界面变稳定。

(3) 分波态密度以及差分电荷密度分析结果表明,界面处加入Al元素后,Al的s轨道和Sn的p轨道存在明显的相互作用。界面处Al原子周围蓝色区域更大,失电子更多,在界面处Al—Sn键强度占主导地位。

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