铸造Al-Si-X系合金时效初期组织演变的计算与模拟
|
摘要
本文基于密度泛函理论的第一性原理研究了Cu、Mg、Si原子对Al基体所产生的固溶强化机理；根据质点（溶质、空位）间的相互作用分析了Al-Si-Cu、Al-Si-Mg、Al-Si-Cu-Mg合金时效初期的团簇形成过程；结合动力学蒙特卡罗（Kinetic Monte Carlo,简称KMC）法模拟获得了合金时效初期动态、直观的团簇形成图像；分析了Al-Si系合金中θ、β序列沉淀相的析出行为及性能。
利用第一性原理计算了含溶质Cu、Mg、Si原子的铝合金超胞结构的电子参数。根据态密度分析结果表明：Cu、Mg与Al基体存在较强的结合，而Si与Al原子间的结合相对较弱。利用电子局域化函数（ELF）对Al107X1超胞结构中化学键进行定量分析，从超胞结构中化学键络的增强程度及范围发现Mg原子的固溶强化效果比Cu原子显著，Si原子的固溶强化效果最弱，与根据错配度分析的元素的强化效果相吻合。
利用第一性原理计算了面心立方结构Si相的内聚能，进而获得Si原子相关的模拟参数，为含Si原子的铝合金时效初期微观组织演变的模拟提供了可能。Al-Si二元合金时效初期的微观组织演变模拟结果表明：在十几秒内含几百个Si原子的Si团簇便能够形成，这与Al-Si二元合金中Si相能够快速析出的结论相一致。
Al-Si-Cu合金时效初期团簇形成行为的第一性原理计算结果表明，富Si团簇及富Cu团簇均能形成，而Si原子占据空位的能力更强，富Si团簇形成较快，相对而言，富Cu团簇形成较慢。含Si、Cu原子的团簇结构也能够形成，由于扩散能力的差异，Si-Cu团簇富Si贫Cu，因此可能向Si相转变。这可能是合金中Si和Cu原子组成的沉淀相未出现的原因。对Al-Si-Cu合金时效初期微结构演变的模拟结果表明：富含Si原子的团簇形成较快，与Al-Si合金相比，Cu元素的加入未对Si团簇的形成长大有明显的影响。部分Si团簇中含有极少量的Cu原子，而小尺寸的富Cu团簇出现较晚，这与电子理论计算结果相符。富Cu团簇的形成为θ序列沉淀相的析出提供了成分基础。沉淀序列中θ相、θ相的形成焓及态密度分析表明θ相具有更强的稳定性。在535K左右，θ相与θ相的稳定性发生转变，即在高温下θ相稳定性更强，这与已有计算及实验结论相符。对两相的键布局分析结果表明：θ相中的共价键结合能力较强，抵抗变形的能力越强，宏观上表现为更高的硬度，当该相存在时对合金的硬化效果要好于θ相。当θ相演变为θ相后合金硬度值发生下降可能与二者硬化效果的差异有关。
Al-Si-Mg合金时效初期团簇形成行为的研究表明：Si、Mg原子均能够通过空位快速扩散，富含Si原子的团簇以及富含Mg原子的团簇均形成较快。Mg原子间相互排斥，Mg原子更倾向与Si原子结合，而主要存在于Si-Mg团簇结构中。对Al-Si-Mg合金时效初期团簇形成行为的模拟表明：合金基体中出现了大量富含Si和Mg原子的团簇。与Cu原子对Si团簇的形成影响不同，Mg原子的加入促进了基体中富含Si、Mg原子团簇的析出，为β序列沉淀相的形成提供了成分基础。β序列沉淀相中具有多个结构成分的β相，成分为Mg9Si5的相为最稳定的β相结构。β沉淀序列中GP区、β相、β相、β相的热力学稳定性依次增强，随着时效时间的延长或温度的升高，沉淀相将依次析出，这与沉淀相析出序列SSS-GP区-β-β-β完全符合。
采用3DAP技术对富Si、高Cu/Mg比的Al-Si-Cu-Mg（wt%）合金时效初期的微观组织的研究表明：合金时效0.25h时，基体中主要存在小尺寸的富含Si、Mg原子的点状Si-Mg-Cu团簇和Si-Mg团簇。这一实验结果很好地证实了KMC模拟结果的正确性。同时与三元合金相比，四元合金中团簇数量更多，尺寸更小。3DAP实验表明合金时效0.25~4h的过程中，团簇结构逐渐向板条状的Q相转变。并且时效4h时出现了小尺寸的富Cu原子结构。
The solid solution hardening efficiency of different alloying elements such as Cu, Mg,and Si on Al solid solutions were investigated according to the chemical bonding of Al solidsolutions in this thesis by using the first-principles. The cluster formation behaviors wereanalyzed according to the interactions between particles (solutes, vacancy) in Al-Si-Cu,Al-Si-Mg and Al-Si-Cu-Mg alloys. The Kinetic Monte Carlo (KMC) method was applied tosimulate the distribution of time-dependent solute in Al-Si base alloys. The precipitationbehavior and property of precipitates in β and θ sequences were studied by means offirst-principles calculations.
The interactions between particles (solutes， vacancy) were studied by means offirst-principle calculations to obtain the binding energies and stable structures of complexes.Density of State (DOS) shows strong interaction between Cu and Al atom, Mg and Al atomand weak interaction between Si and Al atom. A quantitative understanding on the chemicalbonding of Al107X1solid solutions can be gained by analyzing the electron LocalizationFunction (ELF). The order of solid solution hardening efficiency of Cu, Mg and Si in Al maybe understood according to the increased bonding strength and range of Al107X1solidsolutions.
The coherent energy of Si phase with face centered cubic lattice structure and thesimulation parameter were calculated by first-principles. The simulation results of clusterformation behavior in Al-Si alloy show that Si clusters with hundreds of Si atoms may form intens seconds. This is consistent with the conclusions that Si phase precipitates quickly.
The analysis of clusters formation behavior according to the interactions betweenparticles (solute, vacancy) in Al-Si-Cu alloy shows that Si-rich clusters and Cu-rich clusterscould form. The formation of Si clusters is rapid due to the powerful occupying to vacancy bySi atoms. Clusters contains Si and Cu atoms may appear and with higher Si and less Cucontent. Si-Cu clusters may transform to Si phase. The KMC simulation results show that Siclusters form and Cu atoms have no impact on the formation of Si clusters in Al-Si-Cu alloyscompared to Al-Si alloy. Si-Cu clusters appear with less Cu atoms and Cu-rich clusters appearlater. It is consistent with the calculation. The precipitation behavior and property of precipitates in θ and θ phase were studied by means of first-principle calculations. θ phasehas stronger heat stability according to the analysis of formation enthalpy and DOS. The bondpopulation analysis results show that the covalent bonding ability of θ ' phase is stronger, thegreater the ability of resistance to deformation, the higher the hardness of the alloy, hardeningefficiency may be better when θ ' phase exists rather than θ phase. Alloy hardness valuesdecline when θ ' phase transforms to θ phase may be relation to the differences of propertybetween them.
The analysis of cluster formation behavior on the basis of the interactions betweenparticles (solute, vacancy) in Al-Si-Mg alloy shows that similar to Al-Si-Cu alloy Si clusterscould form quickly.(Si, Mg)-rich clusters also form quickly because Mg atom could diffuserapidly and has a stronger tendency to bind with Si atom than with Mg atom. The KMCsimulation results show that Si-Mg clusters form and Mg atom promotes the formation of (Si,Mg)-rich clusters compared to Al-Si alloy.(Si, Mg)-rich clusters provide the componentfoundation for the β precipitation sequence. Formation enthalpy calculations of β' phase showthat Mg9Si5phase is the most stable β' phase structure. The thermodynamic stability issuccessively increased from GP zone, β'' phase, β ' phase and to β phase. With theimprovement of aging temperature, the precipitates will sequentially appear. It is consistentwith the aging precipitation sequence supersaturated from solid solution (SSS)-GP zone-β''-β'-β.
Evolution behavior of clusters and subsequent precipitation in Al-Si-Cu-Mg alloy withexcess-Si and high Cu/Mg ration during aging were studied by means of three DimensionalAtom Probe (3DAP).3DAP experiment results show that dot-like (Si, Mg)-rich clustersincluding Si-Mg and Si-Mg-Cu clusters appear in alloy aged at175℃for0.25h, which isconsistent with the first-principles calculation that the strong binding between Si atoms, Si andMg atoms, Si, Mg and Cu atoms and clusters with corresponding component can exist stably.The KMC simulation results show that Si-Mg clusters and Si-Mg-Cu clusters form. Thenumber of clusters is more and the size of clusters is smaller.3DAP results show that at0.25to4h clusters continue transition to Q' phase (Al4Cu2Mg8Si7) and small Cu-rich clusters appear at4h.
利用第一性原理计算了含溶质Cu、Mg、Si原子的铝合金超胞结构的电子参数。根据态密度分析结果表明：Cu、Mg与Al基体存在较强的结合，而Si与Al原子间的结合相对较弱。利用电子局域化函数（ELF）对Al107X1超胞结构中化学键进行定量分析，从超胞结构中化学键络的增强程度及范围发现Mg原子的固溶强化效果比Cu原子显著，Si原子的固溶强化效果最弱，与根据错配度分析的元素的强化效果相吻合。
利用第一性原理计算了面心立方结构Si相的内聚能，进而获得Si原子相关的模拟参数，为含Si原子的铝合金时效初期微观组织演变的模拟提供了可能。Al-Si二元合金时效初期的微观组织演变模拟结果表明：在十几秒内含几百个Si原子的Si团簇便能够形成，这与Al-Si二元合金中Si相能够快速析出的结论相一致。
Al-Si-Cu合金时效初期团簇形成行为的第一性原理计算结果表明，富Si团簇及富Cu团簇均能形成，而Si原子占据空位的能力更强，富Si团簇形成较快，相对而言，富Cu团簇形成较慢。含Si、Cu原子的团簇结构也能够形成，由于扩散能力的差异，Si-Cu团簇富Si贫Cu，因此可能向Si相转变。这可能是合金中Si和Cu原子组成的沉淀相未出现的原因。对Al-Si-Cu合金时效初期微结构演变的模拟结果表明：富含Si原子的团簇形成较快，与Al-Si合金相比，Cu元素的加入未对Si团簇的形成长大有明显的影响。部分Si团簇中含有极少量的Cu原子，而小尺寸的富Cu团簇出现较晚，这与电子理论计算结果相符。富Cu团簇的形成为θ序列沉淀相的析出提供了成分基础。沉淀序列中θ相、θ相的形成焓及态密度分析表明θ相具有更强的稳定性。在535K左右，θ相与θ相的稳定性发生转变，即在高温下θ相稳定性更强，这与已有计算及实验结论相符。对两相的键布局分析结果表明：θ相中的共价键结合能力较强，抵抗变形的能力越强，宏观上表现为更高的硬度，当该相存在时对合金的硬化效果要好于θ相。当θ相演变为θ相后合金硬度值发生下降可能与二者硬化效果的差异有关。
Al-Si-Mg合金时效初期团簇形成行为的研究表明：Si、Mg原子均能够通过空位快速扩散，富含Si原子的团簇以及富含Mg原子的团簇均形成较快。Mg原子间相互排斥，Mg原子更倾向与Si原子结合，而主要存在于Si-Mg团簇结构中。对Al-Si-Mg合金时效初期团簇形成行为的模拟表明：合金基体中出现了大量富含Si和Mg原子的团簇。与Cu原子对Si团簇的形成影响不同，Mg原子的加入促进了基体中富含Si、Mg原子团簇的析出，为β序列沉淀相的形成提供了成分基础。β序列沉淀相中具有多个结构成分的β相，成分为Mg9Si5的相为最稳定的β相结构。β沉淀序列中GP区、β相、β相、β相的热力学稳定性依次增强，随着时效时间的延长或温度的升高，沉淀相将依次析出，这与沉淀相析出序列SSS-GP区-β-β-β完全符合。
采用3DAP技术对富Si、高Cu/Mg比的Al-Si-Cu-Mg（wt%）合金时效初期的微观组织的研究表明：合金时效0.25h时，基体中主要存在小尺寸的富含Si、Mg原子的点状Si-Mg-Cu团簇和Si-Mg团簇。这一实验结果很好地证实了KMC模拟结果的正确性。同时与三元合金相比，四元合金中团簇数量更多，尺寸更小。3DAP实验表明合金时效0.25~4h的过程中，团簇结构逐渐向板条状的Q相转变。并且时效4h时出现了小尺寸的富Cu原子结构。
The solid solution hardening efficiency of different alloying elements such as Cu, Mg,and Si on Al solid solutions were investigated according to the chemical bonding of Al solidsolutions in this thesis by using the first-principles. The cluster formation behaviors wereanalyzed according to the interactions between particles (solutes, vacancy) in Al-Si-Cu,Al-Si-Mg and Al-Si-Cu-Mg alloys. The Kinetic Monte Carlo (KMC) method was applied tosimulate the distribution of time-dependent solute in Al-Si base alloys. The precipitationbehavior and property of precipitates in β and θ sequences were studied by means offirst-principles calculations.
The interactions between particles (solutes， vacancy) were studied by means offirst-principle calculations to obtain the binding energies and stable structures of complexes.Density of State (DOS) shows strong interaction between Cu and Al atom, Mg and Al atomand weak interaction between Si and Al atom. A quantitative understanding on the chemicalbonding of Al107X1solid solutions can be gained by analyzing the electron LocalizationFunction (ELF). The order of solid solution hardening efficiency of Cu, Mg and Si in Al maybe understood according to the increased bonding strength and range of Al107X1solidsolutions.
The coherent energy of Si phase with face centered cubic lattice structure and thesimulation parameter were calculated by first-principles. The simulation results of clusterformation behavior in Al-Si alloy show that Si clusters with hundreds of Si atoms may form intens seconds. This is consistent with the conclusions that Si phase precipitates quickly.
The analysis of clusters formation behavior according to the interactions betweenparticles (solute, vacancy) in Al-Si-Cu alloy shows that Si-rich clusters and Cu-rich clusterscould form. The formation of Si clusters is rapid due to the powerful occupying to vacancy bySi atoms. Clusters contains Si and Cu atoms may appear and with higher Si and less Cucontent. Si-Cu clusters may transform to Si phase. The KMC simulation results show that Siclusters form and Cu atoms have no impact on the formation of Si clusters in Al-Si-Cu alloyscompared to Al-Si alloy. Si-Cu clusters appear with less Cu atoms and Cu-rich clusters appearlater. It is consistent with the calculation. The precipitation behavior and property of precipitates in θ and θ phase were studied by means of first-principle calculations. θ phasehas stronger heat stability according to the analysis of formation enthalpy and DOS. The bondpopulation analysis results show that the covalent bonding ability of θ ' phase is stronger, thegreater the ability of resistance to deformation, the higher the hardness of the alloy, hardeningefficiency may be better when θ ' phase exists rather than θ phase. Alloy hardness valuesdecline when θ ' phase transforms to θ phase may be relation to the differences of propertybetween them.
The analysis of cluster formation behavior on the basis of the interactions betweenparticles (solute, vacancy) in Al-Si-Mg alloy shows that similar to Al-Si-Cu alloy Si clusterscould form quickly.(Si, Mg)-rich clusters also form quickly because Mg atom could diffuserapidly and has a stronger tendency to bind with Si atom than with Mg atom. The KMCsimulation results show that Si-Mg clusters form and Mg atom promotes the formation of (Si,Mg)-rich clusters compared to Al-Si alloy.(Si, Mg)-rich clusters provide the componentfoundation for the β precipitation sequence. Formation enthalpy calculations of β' phase showthat Mg9Si5phase is the most stable β' phase structure. The thermodynamic stability issuccessively increased from GP zone, β'' phase, β ' phase and to β phase. With theimprovement of aging temperature, the precipitates will sequentially appear. It is consistentwith the aging precipitation sequence supersaturated from solid solution (SSS)-GP zone-β''-β'-β.
Evolution behavior of clusters and subsequent precipitation in Al-Si-Cu-Mg alloy withexcess-Si and high Cu/Mg ration during aging were studied by means of three DimensionalAtom Probe (3DAP).3DAP experiment results show that dot-like (Si, Mg)-rich clustersincluding Si-Mg and Si-Mg-Cu clusters appear in alloy aged at175℃for0.25h, which isconsistent with the first-principles calculation that the strong binding between Si atoms, Si andMg atoms, Si, Mg and Cu atoms and clusters with corresponding component can exist stably.The KMC simulation results show that Si-Mg clusters and Si-Mg-Cu clusters form. Thenumber of clusters is more and the size of clusters is smaller.3DAP results show that at0.25to4h clusters continue transition to Q' phase (Al4Cu2Mg8Si7) and small Cu-rich clusters appear at4h.
引文
[1]西泽泰二．微观组织热力学[M]．北京：化学工业出版社，2006：241－244．
[2]邓至谦，周善初．金属材料及热处理[M]．长沙：中南工业大学出版社，1989：58-63．
[3]孟庆桂．铸工实用技术手册[M]．江苏：科学技术出版社，2002：591-592．
[4]陆文华，李隆盛，黄良余．铸造合金及熔炼[M]．北京：机械工业出版社;1996.224.
[5] Wilm A. Physical metallurgical experiments in aluminium alloys containing magnesium[J].Metallurgie,1911,8:225-227.
[6] Li R D, Yu H P, Gu K C, et al. Quantitative metallographic analysis for morphology change ofeutectic silicon in AlSiCuMg hypoeutectic casting alloy during the solution heat treatment[J].Foundry,1997,6:5-9.
[7] Sun Y, Chen J, Sun G X. Evolution of Si phase in Al-Si alloy and its effect on mechanicalproperties[J]. Special Casting&Nonferrous Alloys,2001,6:18-19.
[8] Pedersen L, Arnberg L. The effect of solution heat treatment and quenching rates on mechanicalproperties and microstructures in AlSiMg foundry alloys[J]. Metallurgical and MaterialsTransactions A,2001,32(3):525-532.
[9] Liu C H, Chen J H, Li C et al. Multiple silicon nanotwins formed on the eutectic silicon particles inAl–Si alloys[J]. Scripta Materialia,2011,64(4):339-342.
[10] Zhang D L, Zheng L H, StJohn D H. Effect of a short solution treatment time on microstructure andmechanical properties of modified Al–7wt.%Si–0.3wt.%Mg alloy[J]. Journal of Light Metals,2002,2(1):27-36.
[11] Li R X, Li R D, Zhao Y H, et al. Effect of heat treatment on eutectic silicon morphology andmechanical property of Al-Si-Cu-Mg cast alloys[J]. Trans Nonferrous Met Soc China,2004,14(3):496-500.
[12] Rometsch P, Arnberg L, Zhang D. Modelling dissolution of Mg2Si and homogenisation inAl-Si-Mg casting alloys[J]. International Journal of Cast Metals Research,1999,12(1):1-8.
[13] Moustafa M, Samuel F, Doty H. Effect of solution heat treatment and additives on the microstructureof Al-Si (A413.1) automotive alloys[J]. Journal of Materials Science,2003,38(22):4507-4522.
[14] Toda H, Nishimura T, Uesugi K et al. Influence of high-temperature solution treatments onmechanical properties of an Al–Si–Cu aluminum alloy[J]. Acta Materialia,2010,58(6):2014-2025.
[15]丁惠麟，辛智华．实用铝、铜及其合金金相热处理和失效分析[M]．北京：机械工业出版社，2008：47-49.
[16] Crowell N, Shivkumar S. Solution treatment effects in cast Al-Si-Cu alloys[J]. Transactions of theAmerican Foundrymen's Society,1995,103:721-726.
[17] Zolotorevsky V S, Belov N A, Glazoff M V. Casting aluminum alloys[J]. Elsevier,2010328.
[18] Wang L, Makhlouf M, Apelian D. Aluminium die casting alloys: Alloy composition, microstructure,and properties-performance relationships[J]. International Materials Reviews,1995,40(6):221-238.
[19] Bogdanoff T. The influence of copper on an Al-Si-Mg alloy (A356)-microstructure and mechanicalproperties[D]. Sweden:Linkpings university,2009.
[20] Seifeddine S. Characteristics of cast aluminium-silicon alloys: Microstructures and mechanicalproperties[D]. Sweden:Linkpings university,2006.
[21] Kang H, Kida M, Miyahara H et al. Age-hardening characteristics of Al-Si-Cu-base cast alloys[J].Transactions-American Foundrymens Society,1999:507-516.
[22] Reif W, Dutkiewicz J, Ciach R et al. Effect of ageing on the evolution of precipitates in AlSiCuMgalloys[J]. Materials Science and Engineering: A,1997,234:165-168.
[23] Wang G, Bian X, Liu X et al. Effect of Mg on age hardening and precipitation behavior of anAlSiCuMg cast alloy[J]. Journal of Materials Science,2004,39(7):2535-2537.
[24] Grand L. Influence of some impurities on the quality of aluminum alloys[J]. Fonderie,1964,217:95-100.
[25] Gowri S, Samuel F. Effect of alloying elements on the solidification characteristics andmicrostructure of Al-Si-Cu-Mg-Fe380alloy[J]. Metallurgical and Materials Transactions A,1994,25(2):437-448.
[26] Wang Q, Davidson C. Solidification and precipitation behaviour of Al-Si-Mg casting alloys[J].Journal of materials science,2001,36(3):739-750.
[27] Shivkumar S, Keller C, Apelian D. Aging behavior in cast Al-Si-Mg alloys[J]. AFS Trans,1990,98:905-911.
[28]何立子．Al-Mg-Si系合金组织性能[D]．沈阳：东北大学，2001．
[29] Kido K, Matsuda K, Kawabata T et al. Hrtem observation of precipitates in Al-Mg-Si alloycontaining copper at early stage during aging[J]. In: Materials Science Forum,2002:953-958.
[30] Edwards G, Stiller K, Dunlop G, et al. The precipitation sequence in Al–Mg–Si alloys[J]. ActaMaterialia,1998,46(11):3893-3904.
[31] Zhang D, Stjohn D. The effect of composition and heat treatment on the microstructure andmechanical properties of cast Al-7wt.%Si-Mg alloys[J]. Casting&Solidification of Light Alloys,Gold Coast, IMMA,1995:21-25.
[32] Andersen S, Zandbergen H, Jansen J et al. The crystal structure of the β phase in Al–Mg–Sialloys[J]. Acta Materialia,1998,46(9):3283-3298.
[33] Vissers R, Van Huis M A, Jansen J et al. The crystal structure of the β phase in Al–Mg–Si alloys[J].Acta Materialia,2007,55(11):3815-3823.
[34] Reif W, Yu S, Dutkiewicz J et al. Pre-ageing of AlSiCuMg alloys in relation to structure andmechanical properties[J]. Materials&Design,1997,18(4):253-256.
[35] Li Y, Brusethaug S, Olsen A. Influence of Cu on the mechanical properties and precipitationbehavior of AlSi7Mg0.5alloy during aging treatment[J]. Scripta Materialia,2006,54(1):99-103.
[36] Wang G, Sun Q, Feng L et al. Influence of Cu content on ageing behavior of AlSiMgCu castalloys[J]. Materials&Design,2007,28(3):1001-1005.
[37] Yao, J Y, Edwards, G A, Graham, D A. Precipitation and age-hardening in Al-Si-Cu-Mg-Fe castingalloys[J]. In: Materials Science Forum,1996:777-782.
[38] Hwang J Y, Banerjee R, Doty H W et al. The effect of Mg on the structure and properties of type319aluminum casting alloys[J]. Acta Materialia,2009,57(4):1308-1317.
[39] Hwang J Y, Banerjee R, Diercks D R et al. Direct observation of heterogeneous nucleation inAl-Si-Cu-Mg alloy using transmission electron microscopy and three-dimensional atom probetomography[J]. Korean Society of Microscopy,2013,43(3):122-126.
[40]张跃，谷景华，尚家香等．计算材料学基础[M]．北京：北京航空航天大学出版社，2007：1-6．
[41]罗伯D，项金钟，吴兴惠．计算材料学[M]．北京：化学工业出版社，2002：1-5．
[42] Hirosawa S, Sato T, Kamio A, et al. Classification of the role of microalloying elements in phasedecomposition of Al based alloys[J]. Acta Materialia,2000,48(8):1797-2007.
[43] Sato T, Hirosawa S, Hirose K, et al. Roles of microalloying elements on the cluster formation in theinitial stage of phase decomposition of Al-based alloys[J]. Metallurgical and Materials TransactionsA,2003,34(12):2745-2755.
[44]Sha G, Cerezo A. Kinetic monte carlo simulation of clustering in an Al–Zn–Mg–Cu alloy (7050)[J].Acta Materialia,2005,53(4):907-917.
[45]Hirosawa S, Sato T, Kamio A. Effects of Mg addition on the kinetics of low-temperature precipitationin Al-Li-Cu-Ag-Zr alloys[J]. Materials Science and Engineering A,1998,242(1-2):195-201.
[46] Hirosawa S, Sato T, Yokota J, et al. Comparison between resistivity changes and monte carlosimulation for GP zone formation in Al-Cu base ternary alloys[J]. Materials Transactions JIM,1998,39(1):139-147.
[47] Yokota J I, Hirosawa S, Sato T, et al. Computer simulation of the effects of trace-additional Cu andMg elements on the-prime phase precipitation in an Al-Li alloy[J]. Light Metals Review,2000,7:24-30.
[48] Chen D, Wang Y. Simulation of clusters formation in Al-Cu based and Al-Zn based alloys[J].Journal of Materials Science,2005,40(13):3461-3466.
[49] Sha G, Cerezo A. Kinetic monte carlo simulation of clustering in an Al-Zn-Mg-Cu alloy (7050)[J].Acta Materialia,2005,53(4):907-917.
[50]李荣德，马欢欢，李润霞等. Al-4.0Cu合金时效初期原子分布的计算机模拟[J]．沈阳工业大学学报，2008，30(4)：414-418．
[51] Lochte L, Gottstein G. Computer simulation of phase-transition of AlCu alloys[J]. Computationalmaterials science,1996,7(1-2):115-117.
[52] MiyazakiT, Koyama T, Kozakai T. Computer simulations of the phase transformation in real alloysystems based on the phase field method[J]. Materials Science and Engineering A,2001,312(1-2):12.
[53]陈大钦，郑子樵，李世晨等．共格沉淀析出过程的模拟Ⅰ——微观结构演化[J]．中国有色金属学报，2005，15(12)：1945-1952．
[54] Khachaturyan A G. Theory of structural transformations in solids[M]. New York: John Wiley&Sons Inc.1983:129-132.
[55] Poduri R, Chen L Q. Computer simulation of morphological evolution and coarsening kinetics of(Al3Li) precipitates in Al–Li alloys[J]. Acta Materialia,1998,46(11):3915-3928.
[56] Fallah V, Ofori-Opoku N, Stolle J, et al. Simulation of early-stage clustering in ternary metal alloysusing the phase-field crystal method[J]. Acta Materialia,2013,61(10):3653-3666.
[57] Fallah V, Korinek A, Ofori-Opoku N, et al. Atomistic investigation of clustering phenomenon in theAl–Cu system: Three-dimensional phase-field crystal simulation and hrtem/hrstemcharacterization[J]. Acta Materialia,2013,61(17):6372-6386.
[58] L chte L, Gitt A, Gottstein G, et al. Simulation of the evolution of GP zones in Al-Cu alloys: Anextended cahn-hilliard approach[J]. Acta Materialia,2000,48(11):2969-2984.
[59]张光跃，荆涛，柳百成．相场方法原理及在微观组织模拟中的应用[J]．机械工程学报，2003，39(5)：6-9．
[60] Gerold V, Haberkorn H. On the critical resolved shear stress of solid solutions containing coherentprecipitates[J]. Physica Status Solidi (b),1966,16(2):675-684.
[61] Brown L M, Ham R K, Kelly A, et al. Strengthening methods in crystals[J]. New York: AppliedScience,1971,137-146.
[62] Deschamps A, Livet F, Brechet Y. Influence of pre-deformation on ageing in an Al-Zn-Mg alloy--Ⅰ.Microstructure evolution and mechanical properties[J]. Acta Materialia,1998,47(1):281-292.
[63] Liu G, Zhang G J, Ding X D, et al. A model for age strengthening of Al alloys with plate/disc-like orrod/needle-like precipitate[J]. Rare Metal Materials and Engineering,2003,32(12):971-975.
[64] Hirsch P B, Kelly A. Stacking-fault strengthening[J]. Philosophical Magazine,1965,12:881-900.
[65] Song M. Modeling the hardness and yield strength evolutions of aluminum alloy withrod/needle-shaped precipitates[J]. Materials Science and Engineering: A,2007,443(1-2):172-177.
[66] Myhr O R, Grong, Fj r H G, et al. Modelling of the microstructure and strength evolution inAl–Mg–Si alloys during multistage thermal processing[J]. Acta Materialia,2004,52(17):4997-5008.
[67] Wolverton C. Solute–vacancy binding in aluminum[J]. Acta Materialia,2007,55(17):5867-5872.
[68] Zhang G Y, Zhang H, Hu Z Q, et al. Effects of alloying elements on the crystallization behavior ofZr-base amorphous alloys[J]. Rare Metal Materials and Engineering,2005,34(03).
[69] Zhang G Y, Liu G L. Electronic structure of60°edge dislocation in semiconductor material Ge[J].Journal of Semiconductors,2000,25(1):5.
[70]刘贵立，杨杰．基于递归法Cu-Zr合金的强化机理及导电性[J]．沈阳工业大学学报，2011，32(5)：505-509．
[71]张朋波．聚变堆材料钒合金和铍固体辐照效应的模拟研究[D]．大连：大连理工大学，2012．
[72]刘志林．合金价电子结构与成分设计[M]．长春：吉林科技出版社，1990：63-69．
[73] Gao Y J, Huang C G, Mo Q F, et al. Calculation on valence electronic structures of Al-Li alloy underearlier aging condition[J]. The Chinese Journal of Nonferrous Metals,2005,15(7):1069-1074.
[74]高英俊，陈振华．有序Al-Li金属间化合物的电子结构与结合性能[J]．中国有色金属学报，1997，7(04)：43-48．
[75]高英俊，韩永健，赵妙．Al-Zn固溶体价电子结构与Spinodal分解现象[J]．中国有色金属学报，200４，14(05)：730-734．
[76]李培杰，叶益聪，何良菊．Sc和Ti对纯铝细化机理的价电子结构分析[J]．科学通报，2008，53(11)：1345-1349．
[77]高英俊，文春丽，莫其逢等．AlLiZr合金的界面原子成键与力学性能[J]．中国有色金属学报，2011，21(9)：2202-2208．
[78] Wolverton C. Crystal structure and stability of complex precipitate phases in Al-Cu-Mg-(Si) andAl-Zn-Mg alloys[J]. Acta Materialia,2001,49(16):3129-3142.
[79] Ghosh G, Van de Walle A, Asta M. First-principles calculations of the structural and thermodynamicproperties of bcc, fcc and hcp solid solutions in the Al–Tm (Tm=Ti, Zr and Hf) systems: Acomparison of cluster expansion and supercell methods[J]. Acta Materialia,2008,56:3202-3221.
[80] Wolverton C, Yan X Y, Vijayaraghavan R, et al. Incorporating first-principles energetics incomputational thermodynamics approaches[J]. Acta Materialia,2002,50(9):2187-2197.
[81] Wolverton C, Ozoli V. Entropically favored ordering: The metallurgy of Al2Cu revisited[J]. PhysicalReview Letters,2001,86(24):5518-5521.
[82] Zhao D, Zhou L, Kong Y, et al. Structure and thermodynamics of the key precipitated phases in theAl–Mg–Si alloys from first-principles calculations[J]. Journal of materials science,2011,46(24):7839-7849.
[83] Vaithyannthan V, Wolverton C, Chen L Q. Multiscale modeling of precipitation in Al-Cu alloys[J].Acta Materialia,2004,52(10):2973-2987.
[84] Wang J W, Wolverton C, Muller S, et al. First-principles growth kinetics and morphologicalevolution of Cu nanoscale particles in Al[J]. Acta Materialia,2005,53(9):2759-2764.
[85] Muller S, Wolverton C, Wang L W, et al. Prediction of alloy precipitate shapes from firstprinciples[J]. Europhysics Letters,2001,55:33.
[86] Wang Y, Liu Z K, Chen L Q, et al. First-principles calculations of β-Mg5Si6/-Al interfaces[J]. ActaMaterialia,2007,55:5934-5947.
[87]高英俊，陈皓天，朱甜霞等．AlMgSi合金的原子成键与性能的关系[J]．中国有色金属学报，2013，23(5)：1226-1233．
[88] Buckle H, Westbrook J, Conrad H. The science of hardness testing and its research applications[J].Ohio:American Society for Metals, Materials Park.1973,418-431.
[89] Dittrich G, Hoppe R. Zur kristallstruktur von LiMnO2[J]. Zeitschrift Fur Anorganische UndAllgemeine Chemie,1969,368(5-6):262-270.
[90] Ohzuku T. LiMnO2as cathode for secondary lithium cell[J]. Chemistry Express,1992,7(3):193-196.
[91] Wang H F, Jang Y, Chiang Y M. Origin of cycling stability in monoclinic-and orthorhombic-phaselithium manganese oxide cathodes[J]. Electrochemical and Solid-State Letters,1999,2(10):490-493.
[92] Kim J M, Chung H T. Electrochemical characteristics of orthorhombic LiMnO2with differentdegrees of stacking faults[J]. Journal of Power Sources,2003,115(1):125-130.
[93] MetropolisN, UlamS. The monte carlo method[J]. Journal of the American Statistical Association,1949,44(247):335-341.
[94] Gao L, Zhou J, Sun M, et al. Electronic origin of the anomalous solid solution hardening of Y andGd in Mg: A first-principles study[J]. Chinese Sci Bull,2010,56(10):1038-1042.
[95] Lockyer S, Noble F. Precipitate structure in a Cu-Ni-Si alloy[J]. Journal of Materials Science,1994,29(1):218-226.
[96] Kittel C. Introduction to solid state physics[M].USA:John Wiley&Sons,1976:477-482.
[97] Balluffi R W, Kwok T, Bristowe P D, et al. Determination of vacancy mechanism for grain boundaryself-diffusion by computer simulation[J]. Scripta Metallurgica,1981,15(8):951-956.
[98]陈志国，李世晨，刘祖耀等．微合金化Al-4.0Cu-0.3Mg合金时效初期微结构演变的计算机模拟[J]．中国有色金属学报，2004(8)：1274-1280．
[99]陈志国，郑子樵．微合金化铝合金的微观组织演变与性能研究[J]．长沙：中南大学，2004．
[100] Young W M, Elcock E W. Monte carlo studies of vacancy migration in binary ordered alloys: I.[J].Proceedings of the Physical Society,1966,89(3):735.
[101] Metropolis N, Rosenbluth A, Rosenbluth M, et al. Calculation of equations of state by fastcomputing machines[J]. J Chem Phys,1953,21:1087-1091.
[102] Brandes E, Brook G. Smithells metals reference book[M]. London:Butterworth-Heinemann.1992:60-97.
[103] Kaur I, Gust W. Handbook of grain and interphase boundary diffusion data[M].Ziegler Press,1989:42-57.
[104] Doyama M. Vacancy-solute interactions in metals[J]. Journal of Nuclear Materials,1978,69:350-361.
[105] Landolt-B rnstein. Numerical data and functional relationschips in science and technology[J].Macroscopic Properties of Matter. Springer,1995,4,6-10.
[106] Sanchez J, Barefoot J, Jarrett R et al. Modeling of γ/γ′phase equilibrium in thenickel-aluminum system[J]. Acta Metallurgica,1984,32(9):1519-1525.
[107] Doyama M, Koehler J. The relation between the formation energy of a vacancy and the nearestneighbor interactions in pure metals and liquid metals[J]. Acta Metallurgica,1976,24(9):871-879.
[108] Hatch J E. Aluminum: Properties and physical metallurgy[M]. OH:American Society for Metals,1984,154-156.
[109] Murray J L. The aluminium-copper system[J]. International Metals Reviews,1985,30(1):211-234.
[110] Ravi C, Wolverton C, Ozoli V. Predicting metastable phase boundaries in AlCu alloys fromfirst-principles calculations of free energies: The role of atomic vibrations[J]. Europhysics Letters,2006,73:719.
[111] Fu C L, Wang X D, Ye Y Y, et al. Phase stability, bonding mechanism, and elastic constants ofMo5Si3by first-principles calculation[J]. Intermetallics,1999,7(2):179-184.
[112] Silcock J M., Heal T J, Hardy H K. Structural ageing characteristics of binary aluminium-copperalloys[J]. J Inst Met,1953,82:239–248.
[113] Guinier A. Le mécanisme de la précipitation dans un cristal de solution solide métallique.-cas dessystèmes aluminium-cuivre et aluminium-argent[J]. Journal de Physique et le Radium,1942,3(7):124-136.
[114] Eskin D. Decomposition of supersaturated solid solutions in Al–Cu–Mg–Si alloys[J]. Journal ofMaterials Science,2003,38(2):279-290.
[115] Ravi C, Wolverton C. First-principles study of crystal structure and stability of Al-Mg-Si-(Cu)precipitates[J]. Acta Materialia,2004,52(14):4213-4227.
[116] Zandbergen H, Andersen S, Jansen J. Structure determination of Mg5Si6particles in Al by dynamicelectron diffraction studies[J]. Science,1997,277(5330):1221-1225.
[117] Matsuda K, Sakaguchi Y, Miyata Y, et al. Precipitation sequence of various kinds of metastablephases in Al-1.0mass%Mg2Si-0.4mass%Si alloy[J]. Journal of Materials Science,2000,35(1):179-189.
[118] Cayron C, Buffat P. Transmission electron microscopy study of the β phase (Al–Mg–Si alloys) andQc phase (Al–Cu–Mg–Si alloys): Ordering mechanism and crystallographic structure[J]. ActaMaterialia,2000,48(10):2639-2653.
[119] Lynch J, Brown L, Jacobs M. Microanalysis of age-hardening precipitates in aluminium alloys[J].Acta Metallurgica,1982,30(7):1389-1395.
[120] Villars P, Calvert L D. Pearson's handbook of crystallographic data for intermetallic phases[M].OH：American Society for Metals Park,1985，83.
[121]王占勇，周邦新，倪建森等．三维原子探针技术在纳米复合永磁材料中的应用[J]．科学通报，2006，51(12)：1487-1488．
[122]周邦新，刘文庆．三维原子探针及其在材料科学研究中的应用[J]．材料科学与工艺，2007，15(3)：405-408．
[123] Zheng Z Q, Liu W Q, Liao Z Q et al. Solute clustering and solute nanostructures in anAl–3.5Cu–0.4Mg–0.2Ge alloy[J]. Acta Materialia,2013,61(10):3724-3734.
[124] Li R X, Li R D, Zhao Y H et al. Age-hardening behavior of cast Al–Si base alloy[J]. MaterialsLetters,2004,58(15):2096-2101.
[125] Miao W F, Laughlin D E. Effects of Cu content and preaging on precipitation characteristics inaluminum alloy6022[J]. Metallurgical and Materials Transactions A,2000,31(2):361-371.
[126] Arnberg, L, Aurivillius, B. The crystal structure of AlxCu2Mg12-xSi7,(h-AlCuMgSi)[J]. ActaChemica Scandinavica,1980,(1):1-5.
[127] Chakrabarti D, Laughlin D E. Phase relations and precipitation in Al–Mg–Si alloys with Cuadditions[J]. Progress in Materials Science,2004,49(3):389-410.
[2]邓至谦，周善初．金属材料及热处理[M]．长沙：中南工业大学出版社，1989：58-63．
[3]孟庆桂．铸工实用技术手册[M]．江苏：科学技术出版社，2002：591-592．
[4]陆文华，李隆盛，黄良余．铸造合金及熔炼[M]．北京：机械工业出版社;1996.224.
[5] Wilm A. Physical metallurgical experiments in aluminium alloys containing magnesium[J].Metallurgie,1911,8:225-227.
[6] Li R D, Yu H P, Gu K C, et al. Quantitative metallographic analysis for morphology change ofeutectic silicon in AlSiCuMg hypoeutectic casting alloy during the solution heat treatment[J].Foundry,1997,6:5-9.
[7] Sun Y, Chen J, Sun G X. Evolution of Si phase in Al-Si alloy and its effect on mechanicalproperties[J]. Special Casting&Nonferrous Alloys,2001,6:18-19.
[8] Pedersen L, Arnberg L. The effect of solution heat treatment and quenching rates on mechanicalproperties and microstructures in AlSiMg foundry alloys[J]. Metallurgical and MaterialsTransactions A,2001,32(3):525-532.
[9] Liu C H, Chen J H, Li C et al. Multiple silicon nanotwins formed on the eutectic silicon particles inAl–Si alloys[J]. Scripta Materialia,2011,64(4):339-342.
[10] Zhang D L, Zheng L H, StJohn D H. Effect of a short solution treatment time on microstructure andmechanical properties of modified Al–7wt.%Si–0.3wt.%Mg alloy[J]. Journal of Light Metals,2002,2(1):27-36.
[11] Li R X, Li R D, Zhao Y H, et al. Effect of heat treatment on eutectic silicon morphology andmechanical property of Al-Si-Cu-Mg cast alloys[J]. Trans Nonferrous Met Soc China,2004,14(3):496-500.
[12] Rometsch P, Arnberg L, Zhang D. Modelling dissolution of Mg2Si and homogenisation inAl-Si-Mg casting alloys[J]. International Journal of Cast Metals Research,1999,12(1):1-8.
[13] Moustafa M, Samuel F, Doty H. Effect of solution heat treatment and additives on the microstructureof Al-Si (A413.1) automotive alloys[J]. Journal of Materials Science,2003,38(22):4507-4522.
[14] Toda H, Nishimura T, Uesugi K et al. Influence of high-temperature solution treatments onmechanical properties of an Al–Si–Cu aluminum alloy[J]. Acta Materialia,2010,58(6):2014-2025.
[15]丁惠麟，辛智华．实用铝、铜及其合金金相热处理和失效分析[M]．北京：机械工业出版社，2008：47-49.
[16] Crowell N, Shivkumar S. Solution treatment effects in cast Al-Si-Cu alloys[J]. Transactions of theAmerican Foundrymen's Society,1995,103:721-726.
[17] Zolotorevsky V S, Belov N A, Glazoff M V. Casting aluminum alloys[J]. Elsevier,2010328.
[18] Wang L, Makhlouf M, Apelian D. Aluminium die casting alloys: Alloy composition, microstructure,and properties-performance relationships[J]. International Materials Reviews,1995,40(6):221-238.
[19] Bogdanoff T. The influence of copper on an Al-Si-Mg alloy (A356)-microstructure and mechanicalproperties[D]. Sweden:Linkpings university,2009.
[20] Seifeddine S. Characteristics of cast aluminium-silicon alloys: Microstructures and mechanicalproperties[D]. Sweden:Linkpings university,2006.
[21] Kang H, Kida M, Miyahara H et al. Age-hardening characteristics of Al-Si-Cu-base cast alloys[J].Transactions-American Foundrymens Society,1999:507-516.
[22] Reif W, Dutkiewicz J, Ciach R et al. Effect of ageing on the evolution of precipitates in AlSiCuMgalloys[J]. Materials Science and Engineering: A,1997,234:165-168.
[23] Wang G, Bian X, Liu X et al. Effect of Mg on age hardening and precipitation behavior of anAlSiCuMg cast alloy[J]. Journal of Materials Science,2004,39(7):2535-2537.
[24] Grand L. Influence of some impurities on the quality of aluminum alloys[J]. Fonderie,1964,217:95-100.
[25] Gowri S, Samuel F. Effect of alloying elements on the solidification characteristics andmicrostructure of Al-Si-Cu-Mg-Fe380alloy[J]. Metallurgical and Materials Transactions A,1994,25(2):437-448.
[26] Wang Q, Davidson C. Solidification and precipitation behaviour of Al-Si-Mg casting alloys[J].Journal of materials science,2001,36(3):739-750.
[27] Shivkumar S, Keller C, Apelian D. Aging behavior in cast Al-Si-Mg alloys[J]. AFS Trans,1990,98:905-911.
[28]何立子．Al-Mg-Si系合金组织性能[D]．沈阳：东北大学，2001．
[29] Kido K, Matsuda K, Kawabata T et al. Hrtem observation of precipitates in Al-Mg-Si alloycontaining copper at early stage during aging[J]. In: Materials Science Forum,2002:953-958.
[30] Edwards G, Stiller K, Dunlop G, et al. The precipitation sequence in Al–Mg–Si alloys[J]. ActaMaterialia,1998,46(11):3893-3904.
[31] Zhang D, Stjohn D. The effect of composition and heat treatment on the microstructure andmechanical properties of cast Al-7wt.%Si-Mg alloys[J]. Casting&Solidification of Light Alloys,Gold Coast, IMMA,1995:21-25.
[32] Andersen S, Zandbergen H, Jansen J et al. The crystal structure of the β phase in Al–Mg–Sialloys[J]. Acta Materialia,1998,46(9):3283-3298.
[33] Vissers R, Van Huis M A, Jansen J et al. The crystal structure of the β phase in Al–Mg–Si alloys[J].Acta Materialia,2007,55(11):3815-3823.
[34] Reif W, Yu S, Dutkiewicz J et al. Pre-ageing of AlSiCuMg alloys in relation to structure andmechanical properties[J]. Materials&Design,1997,18(4):253-256.
[35] Li Y, Brusethaug S, Olsen A. Influence of Cu on the mechanical properties and precipitationbehavior of AlSi7Mg0.5alloy during aging treatment[J]. Scripta Materialia,2006,54(1):99-103.
[36] Wang G, Sun Q, Feng L et al. Influence of Cu content on ageing behavior of AlSiMgCu castalloys[J]. Materials&Design,2007,28(3):1001-1005.
[37] Yao, J Y, Edwards, G A, Graham, D A. Precipitation and age-hardening in Al-Si-Cu-Mg-Fe castingalloys[J]. In: Materials Science Forum,1996:777-782.
[38] Hwang J Y, Banerjee R, Doty H W et al. The effect of Mg on the structure and properties of type319aluminum casting alloys[J]. Acta Materialia,2009,57(4):1308-1317.
[39] Hwang J Y, Banerjee R, Diercks D R et al. Direct observation of heterogeneous nucleation inAl-Si-Cu-Mg alloy using transmission electron microscopy and three-dimensional atom probetomography[J]. Korean Society of Microscopy,2013,43(3):122-126.
[40]张跃，谷景华，尚家香等．计算材料学基础[M]．北京：北京航空航天大学出版社，2007：1-6．
[41]罗伯D，项金钟，吴兴惠．计算材料学[M]．北京：化学工业出版社，2002：1-5．
[42] Hirosawa S, Sato T, Kamio A, et al. Classification of the role of microalloying elements in phasedecomposition of Al based alloys[J]. Acta Materialia,2000,48(8):1797-2007.
[43] Sato T, Hirosawa S, Hirose K, et al. Roles of microalloying elements on the cluster formation in theinitial stage of phase decomposition of Al-based alloys[J]. Metallurgical and Materials TransactionsA,2003,34(12):2745-2755.
[44]Sha G, Cerezo A. Kinetic monte carlo simulation of clustering in an Al–Zn–Mg–Cu alloy (7050)[J].Acta Materialia,2005,53(4):907-917.
[45]Hirosawa S, Sato T, Kamio A. Effects of Mg addition on the kinetics of low-temperature precipitationin Al-Li-Cu-Ag-Zr alloys[J]. Materials Science and Engineering A,1998,242(1-2):195-201.
[46] Hirosawa S, Sato T, Yokota J, et al. Comparison between resistivity changes and monte carlosimulation for GP zone formation in Al-Cu base ternary alloys[J]. Materials Transactions JIM,1998,39(1):139-147.
[47] Yokota J I, Hirosawa S, Sato T, et al. Computer simulation of the effects of trace-additional Cu andMg elements on the-prime phase precipitation in an Al-Li alloy[J]. Light Metals Review,2000,7:24-30.
[48] Chen D, Wang Y. Simulation of clusters formation in Al-Cu based and Al-Zn based alloys[J].Journal of Materials Science,2005,40(13):3461-3466.
[49] Sha G, Cerezo A. Kinetic monte carlo simulation of clustering in an Al-Zn-Mg-Cu alloy (7050)[J].Acta Materialia,2005,53(4):907-917.
[50]李荣德，马欢欢，李润霞等. Al-4.0Cu合金时效初期原子分布的计算机模拟[J]．沈阳工业大学学报，2008，30(4)：414-418．
[51] Lochte L, Gottstein G. Computer simulation of phase-transition of AlCu alloys[J]. Computationalmaterials science,1996,7(1-2):115-117.
[52] MiyazakiT, Koyama T, Kozakai T. Computer simulations of the phase transformation in real alloysystems based on the phase field method[J]. Materials Science and Engineering A,2001,312(1-2):12.
[53]陈大钦，郑子樵，李世晨等．共格沉淀析出过程的模拟Ⅰ——微观结构演化[J]．中国有色金属学报，2005，15(12)：1945-1952．
[54] Khachaturyan A G. Theory of structural transformations in solids[M]. New York: John Wiley&Sons Inc.1983:129-132.
[55] Poduri R, Chen L Q. Computer simulation of morphological evolution and coarsening kinetics of(Al3Li) precipitates in Al–Li alloys[J]. Acta Materialia,1998,46(11):3915-3928.
[56] Fallah V, Ofori-Opoku N, Stolle J, et al. Simulation of early-stage clustering in ternary metal alloysusing the phase-field crystal method[J]. Acta Materialia,2013,61(10):3653-3666.
[57] Fallah V, Korinek A, Ofori-Opoku N, et al. Atomistic investigation of clustering phenomenon in theAl–Cu system: Three-dimensional phase-field crystal simulation and hrtem/hrstemcharacterization[J]. Acta Materialia,2013,61(17):6372-6386.
[58] L chte L, Gitt A, Gottstein G, et al. Simulation of the evolution of GP zones in Al-Cu alloys: Anextended cahn-hilliard approach[J]. Acta Materialia,2000,48(11):2969-2984.
[59]张光跃，荆涛，柳百成．相场方法原理及在微观组织模拟中的应用[J]．机械工程学报，2003，39(5)：6-9．
[60] Gerold V, Haberkorn H. On the critical resolved shear stress of solid solutions containing coherentprecipitates[J]. Physica Status Solidi (b),1966,16(2):675-684.
[61] Brown L M, Ham R K, Kelly A, et al. Strengthening methods in crystals[J]. New York: AppliedScience,1971,137-146.
[62] Deschamps A, Livet F, Brechet Y. Influence of pre-deformation on ageing in an Al-Zn-Mg alloy--Ⅰ.Microstructure evolution and mechanical properties[J]. Acta Materialia,1998,47(1):281-292.
[63] Liu G, Zhang G J, Ding X D, et al. A model for age strengthening of Al alloys with plate/disc-like orrod/needle-like precipitate[J]. Rare Metal Materials and Engineering,2003,32(12):971-975.
[64] Hirsch P B, Kelly A. Stacking-fault strengthening[J]. Philosophical Magazine,1965,12:881-900.
[65] Song M. Modeling the hardness and yield strength evolutions of aluminum alloy withrod/needle-shaped precipitates[J]. Materials Science and Engineering: A,2007,443(1-2):172-177.
[66] Myhr O R, Grong, Fj r H G, et al. Modelling of the microstructure and strength evolution inAl–Mg–Si alloys during multistage thermal processing[J]. Acta Materialia,2004,52(17):4997-5008.
[67] Wolverton C. Solute–vacancy binding in aluminum[J]. Acta Materialia,2007,55(17):5867-5872.
[68] Zhang G Y, Zhang H, Hu Z Q, et al. Effects of alloying elements on the crystallization behavior ofZr-base amorphous alloys[J]. Rare Metal Materials and Engineering,2005,34(03).
[69] Zhang G Y, Liu G L. Electronic structure of60°edge dislocation in semiconductor material Ge[J].Journal of Semiconductors,2000,25(1):5.
[70]刘贵立，杨杰．基于递归法Cu-Zr合金的强化机理及导电性[J]．沈阳工业大学学报，2011，32(5)：505-509．
[71]张朋波．聚变堆材料钒合金和铍固体辐照效应的模拟研究[D]．大连：大连理工大学，2012．
[72]刘志林．合金价电子结构与成分设计[M]．长春：吉林科技出版社，1990：63-69．
[73] Gao Y J, Huang C G, Mo Q F, et al. Calculation on valence electronic structures of Al-Li alloy underearlier aging condition[J]. The Chinese Journal of Nonferrous Metals,2005,15(7):1069-1074.
[74]高英俊，陈振华．有序Al-Li金属间化合物的电子结构与结合性能[J]．中国有色金属学报，1997，7(04)：43-48．
[75]高英俊，韩永健，赵妙．Al-Zn固溶体价电子结构与Spinodal分解现象[J]．中国有色金属学报，200４，14(05)：730-734．
[76]李培杰，叶益聪，何良菊．Sc和Ti对纯铝细化机理的价电子结构分析[J]．科学通报，2008，53(11)：1345-1349．
[77]高英俊，文春丽，莫其逢等．AlLiZr合金的界面原子成键与力学性能[J]．中国有色金属学报，2011，21(9)：2202-2208．
[78] Wolverton C. Crystal structure and stability of complex precipitate phases in Al-Cu-Mg-(Si) andAl-Zn-Mg alloys[J]. Acta Materialia,2001,49(16):3129-3142.
[79] Ghosh G, Van de Walle A, Asta M. First-principles calculations of the structural and thermodynamicproperties of bcc, fcc and hcp solid solutions in the Al–Tm (Tm=Ti, Zr and Hf) systems: Acomparison of cluster expansion and supercell methods[J]. Acta Materialia,2008,56:3202-3221.
[80] Wolverton C, Yan X Y, Vijayaraghavan R, et al. Incorporating first-principles energetics incomputational thermodynamics approaches[J]. Acta Materialia,2002,50(9):2187-2197.
[81] Wolverton C, Ozoli V. Entropically favored ordering: The metallurgy of Al2Cu revisited[J]. PhysicalReview Letters,2001,86(24):5518-5521.
[82] Zhao D, Zhou L, Kong Y, et al. Structure and thermodynamics of the key precipitated phases in theAl–Mg–Si alloys from first-principles calculations[J]. Journal of materials science,2011,46(24):7839-7849.
[83] Vaithyannthan V, Wolverton C, Chen L Q. Multiscale modeling of precipitation in Al-Cu alloys[J].Acta Materialia,2004,52(10):2973-2987.
[84] Wang J W, Wolverton C, Muller S, et al. First-principles growth kinetics and morphologicalevolution of Cu nanoscale particles in Al[J]. Acta Materialia,2005,53(9):2759-2764.
[85] Muller S, Wolverton C, Wang L W, et al. Prediction of alloy precipitate shapes from firstprinciples[J]. Europhysics Letters,2001,55:33.
[86] Wang Y, Liu Z K, Chen L Q, et al. First-principles calculations of β-Mg5Si6/-Al interfaces[J]. ActaMaterialia,2007,55:5934-5947.
[87]高英俊，陈皓天，朱甜霞等．AlMgSi合金的原子成键与性能的关系[J]．中国有色金属学报，2013，23(5)：1226-1233．
[88] Buckle H, Westbrook J, Conrad H. The science of hardness testing and its research applications[J].Ohio:American Society for Metals, Materials Park.1973,418-431.
[89] Dittrich G, Hoppe R. Zur kristallstruktur von LiMnO2[J]. Zeitschrift Fur Anorganische UndAllgemeine Chemie,1969,368(5-6):262-270.
[90] Ohzuku T. LiMnO2as cathode for secondary lithium cell[J]. Chemistry Express,1992,7(3):193-196.
[91] Wang H F, Jang Y, Chiang Y M. Origin of cycling stability in monoclinic-and orthorhombic-phaselithium manganese oxide cathodes[J]. Electrochemical and Solid-State Letters,1999,2(10):490-493.
[92] Kim J M, Chung H T. Electrochemical characteristics of orthorhombic LiMnO2with differentdegrees of stacking faults[J]. Journal of Power Sources,2003,115(1):125-130.
[93] MetropolisN, UlamS. The monte carlo method[J]. Journal of the American Statistical Association,1949,44(247):335-341.
[94] Gao L, Zhou J, Sun M, et al. Electronic origin of the anomalous solid solution hardening of Y andGd in Mg: A first-principles study[J]. Chinese Sci Bull,2010,56(10):1038-1042.
[95] Lockyer S, Noble F. Precipitate structure in a Cu-Ni-Si alloy[J]. Journal of Materials Science,1994,29(1):218-226.
[96] Kittel C. Introduction to solid state physics[M].USA:John Wiley&Sons,1976:477-482.
[97] Balluffi R W, Kwok T, Bristowe P D, et al. Determination of vacancy mechanism for grain boundaryself-diffusion by computer simulation[J]. Scripta Metallurgica,1981,15(8):951-956.
[98]陈志国，李世晨，刘祖耀等．微合金化Al-4.0Cu-0.3Mg合金时效初期微结构演变的计算机模拟[J]．中国有色金属学报，2004(8)：1274-1280．
[99]陈志国，郑子樵．微合金化铝合金的微观组织演变与性能研究[J]．长沙：中南大学，2004．
[100] Young W M, Elcock E W. Monte carlo studies of vacancy migration in binary ordered alloys: I.[J].Proceedings of the Physical Society,1966,89(3):735.
[101] Metropolis N, Rosenbluth A, Rosenbluth M, et al. Calculation of equations of state by fastcomputing machines[J]. J Chem Phys,1953,21:1087-1091.
[102] Brandes E, Brook G. Smithells metals reference book[M]. London:Butterworth-Heinemann.1992:60-97.
[103] Kaur I, Gust W. Handbook of grain and interphase boundary diffusion data[M].Ziegler Press,1989:42-57.
[104] Doyama M. Vacancy-solute interactions in metals[J]. Journal of Nuclear Materials,1978,69:350-361.
[105] Landolt-B rnstein. Numerical data and functional relationschips in science and technology[J].Macroscopic Properties of Matter. Springer,1995,4,6-10.
[106] Sanchez J, Barefoot J, Jarrett R et al. Modeling of γ/γ′phase equilibrium in thenickel-aluminum system[J]. Acta Metallurgica,1984,32(9):1519-1525.
[107] Doyama M, Koehler J. The relation between the formation energy of a vacancy and the nearestneighbor interactions in pure metals and liquid metals[J]. Acta Metallurgica,1976,24(9):871-879.
[108] Hatch J E. Aluminum: Properties and physical metallurgy[M]. OH:American Society for Metals,1984,154-156.
[109] Murray J L. The aluminium-copper system[J]. International Metals Reviews,1985,30(1):211-234.
[110] Ravi C, Wolverton C, Ozoli V. Predicting metastable phase boundaries in AlCu alloys fromfirst-principles calculations of free energies: The role of atomic vibrations[J]. Europhysics Letters,2006,73:719.
[111] Fu C L, Wang X D, Ye Y Y, et al. Phase stability, bonding mechanism, and elastic constants ofMo5Si3by first-principles calculation[J]. Intermetallics,1999,7(2):179-184.
[112] Silcock J M., Heal T J, Hardy H K. Structural ageing characteristics of binary aluminium-copperalloys[J]. J Inst Met,1953,82:239–248.
[113] Guinier A. Le mécanisme de la précipitation dans un cristal de solution solide métallique.-cas dessystèmes aluminium-cuivre et aluminium-argent[J]. Journal de Physique et le Radium,1942,3(7):124-136.
[114] Eskin D. Decomposition of supersaturated solid solutions in Al–Cu–Mg–Si alloys[J]. Journal ofMaterials Science,2003,38(2):279-290.
[115] Ravi C, Wolverton C. First-principles study of crystal structure and stability of Al-Mg-Si-(Cu)precipitates[J]. Acta Materialia,2004,52(14):4213-4227.
[116] Zandbergen H, Andersen S, Jansen J. Structure determination of Mg5Si6particles in Al by dynamicelectron diffraction studies[J]. Science,1997,277(5330):1221-1225.
[117] Matsuda K, Sakaguchi Y, Miyata Y, et al. Precipitation sequence of various kinds of metastablephases in Al-1.0mass%Mg2Si-0.4mass%Si alloy[J]. Journal of Materials Science,2000,35(1):179-189.
[118] Cayron C, Buffat P. Transmission electron microscopy study of the β phase (Al–Mg–Si alloys) andQc phase (Al–Cu–Mg–Si alloys): Ordering mechanism and crystallographic structure[J]. ActaMaterialia,2000,48(10):2639-2653.
[119] Lynch J, Brown L, Jacobs M. Microanalysis of age-hardening precipitates in aluminium alloys[J].Acta Metallurgica,1982,30(7):1389-1395.
[120] Villars P, Calvert L D. Pearson's handbook of crystallographic data for intermetallic phases[M].OH：American Society for Metals Park,1985，83.
[121]王占勇，周邦新，倪建森等．三维原子探针技术在纳米复合永磁材料中的应用[J]．科学通报，2006，51(12)：1487-1488．
[122]周邦新，刘文庆．三维原子探针及其在材料科学研究中的应用[J]．材料科学与工艺，2007，15(3)：405-408．
[123] Zheng Z Q, Liu W Q, Liao Z Q et al. Solute clustering and solute nanostructures in anAl–3.5Cu–0.4Mg–0.2Ge alloy[J]. Acta Materialia,2013,61(10):3724-3734.
[124] Li R X, Li R D, Zhao Y H et al. Age-hardening behavior of cast Al–Si base alloy[J]. MaterialsLetters,2004,58(15):2096-2101.
[125] Miao W F, Laughlin D E. Effects of Cu content and preaging on precipitation characteristics inaluminum alloy6022[J]. Metallurgical and Materials Transactions A,2000,31(2):361-371.
[126] Arnberg, L, Aurivillius, B. The crystal structure of AlxCu2Mg12-xSi7,(h-AlCuMgSi)[J]. ActaChemica Scandinavica,1980,(1):1-5.
[127] Chakrabarti D, Laughlin D E. Phase relations and precipitation in Al–Mg–Si alloys with Cuadditions[J]. Progress in Materials Science,2004,49(3):389-410.