外势场对合金作用的离散法和连续法计算机模拟
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摘要
本文在国内首先编制了基于连续非经典形核理论的计算机模拟程序，可获得序参数、有序相半径、界面厚度、临界形核功等相关信息，并开展了与基于离散格点动力学模型的计算机模拟方法的比对研究。以Al-Li合金为客体，在国内外首先研究了原子间相互作用势对亚稳区合金和过渡区合金沉淀机制的影响，两种方法的主要研究结果吻合。
研究发现，随原子间相互作用势的增大，亚稳区合金和过渡区合金的δ′有序相的形核功减小，形核率增大。由离散格点模型得出：随原子间相互作用势的增大，有序相的尺寸和体积分数增大，其周围的无序基体浓度的下降加快，原子簇聚和有序化加快，化学计量比有序相长大加速。首次发现，原子间相互作用势的增大使亚稳区合金的相变机制向高浓度方向偏移，其中W_1单独作用影响程度最小，W_1、W_2协同作用影响程度最大。在沉淀的早期阶段，亚稳区合金的相界厚度基本不变，约为0.7nm；随时间的延长，过渡区合金的相界厚度由0.8nm左右逐渐减小到0.6nm左右，且减薄速度逐步变慢。
In this paper, the computer simulation programs based on the continuum non-classical nucleation theory were firstly worked out, through which the order parameter, the radius of the ordered phase, the interface thickness and the critical nucleation energy were calculated. The comparison between the continuum theory and the discrete lattice dynamic model was carried out. The influences of the atomic interaction energy ( W1 and W2) to the precipitation mechanism of the Al-Li alloys in both metastable and intermediate regions were studied national and abroad for the first time. The results from the two methods are consistent.
It was found that as the atomic interaction energy increased, the critical energy of the 8' ordered phase decreased and the nucleation rate increased for the alloys in both metastable and intermediate regions. It was found from the discrete lattice dynamic model: as the atomic interaction energy increased, the sizes and volume fractions of the ordered phase raised, decline speed of composition in disordered matrix around the ordered phase was accelerated, the processes of clustering and ordering were accelerated, and the grow speed of the stoichiometric ordered phase was quicken. It was found for the first time that the increase of the atomic interaction energy made the precipitation mechanism of alloys in metastable region inclined to that of alloys with higher composition. The influence degree of W1 was the least and that of both W1 and W2 was the most. At the early stage of precipitation, the interface thickness of alloy in the metastable region was nearly unchanged, which was nearly 0.7nm; but that of al
loys in the transient region decreased from 0.8nm to 0.6nm, and the decrease speeds become slower with time.
研究发现，随原子间相互作用势的增大，亚稳区合金和过渡区合金的δ′有序相的形核功减小，形核率增大。由离散格点模型得出：随原子间相互作用势的增大，有序相的尺寸和体积分数增大，其周围的无序基体浓度的下降加快，原子簇聚和有序化加快，化学计量比有序相长大加速。首次发现，原子间相互作用势的增大使亚稳区合金的相变机制向高浓度方向偏移，其中W_1单独作用影响程度最小，W_1、W_2协同作用影响程度最大。在沉淀的早期阶段，亚稳区合金的相界厚度基本不变，约为0.7nm；随时间的延长，过渡区合金的相界厚度由0.8nm左右逐渐减小到0.6nm左右，且减薄速度逐步变慢。
In this paper, the computer simulation programs based on the continuum non-classical nucleation theory were firstly worked out, through which the order parameter, the radius of the ordered phase, the interface thickness and the critical nucleation energy were calculated. The comparison between the continuum theory and the discrete lattice dynamic model was carried out. The influences of the atomic interaction energy ( W1 and W2) to the precipitation mechanism of the Al-Li alloys in both metastable and intermediate regions were studied national and abroad for the first time. The results from the two methods are consistent.
It was found that as the atomic interaction energy increased, the critical energy of the 8' ordered phase decreased and the nucleation rate increased for the alloys in both metastable and intermediate regions. It was found from the discrete lattice dynamic model: as the atomic interaction energy increased, the sizes and volume fractions of the ordered phase raised, decline speed of composition in disordered matrix around the ordered phase was accelerated, the processes of clustering and ordering were accelerated, and the grow speed of the stoichiometric ordered phase was quicken. It was found for the first time that the increase of the atomic interaction energy made the precipitation mechanism of alloys in metastable region inclined to that of alloys with higher composition. The influence degree of W1 was the least and that of both W1 and W2 was the most. At the early stage of precipitation, the interface thickness of alloy in the metastable region was nearly unchanged, which was nearly 0.7nm; but that of al
loys in the transient region decreased from 0.8nm to 0.6nm, and the decrease speeds become slower with time.
引文
[1] Volmer M, Weber A. Z. Phys. Chem.,1926; 119:227
[2] Becker R, Doring W. Ann. Phys.,1935; 24:719
[3] Turnbull D, Fisher J C. J. Chem. Phys., 1949; 17:71
[4] Zener C. J. Appl. Phys., 1949; 20:950
[5] Lifshitz I M, Slyozov V V. J. Phys. Chem. Solids, 1961; 19:35
[6] Wagner C. Z. f. Elektrochemie, 1961; 65:581
[7] Pound G M. Metall. Trans., 1985; 16A: 488
[8] Cahn J W, Hilliard J E. J. Chem. Phys.,1958; 28:258
[9] J.W. Cahn, J.E. Hilliard, Free Energy of a Non-uniform System Ⅱ. Thermodynamic Baiss, J. Chem. Phys., 1958, 30(5), p.1121
[10] J.W. Cahn and J.E. Hilliard, Free Energy of aNon-uniform System. Ⅲ. Nucleation in a Two-component Incompressible Fluid, J. Chem. Phys., 1959, 31(3), p.688
[11] Cook H E, de Fontaine D, Hilliard J E. Acta Met. 1969; 17:765
[12] Abinandanan T A, Johnson W C. Development of spatial correlations during coarsening. Mater. Sci. Eng. B, 1995; 32:169
[13] Baumann S F, Williams D B. Effects of Capillarity and Coherency on δ'(Al_3Li) Precipitation in Dilute Al-Li Alloys at Low Under coolings. Acta metall., 1985; 33:1069
[14] Sigli C, Sanchez J M. Theoretical Description of Phase Equilibrium In Binary Alloys. Acta metall., 1985; 33:1097
[15] Sigli C, Sanchez J M. Calculation of Phase Equilibrium in Al-Li Alloys. Acta metall., 1986; 34:1021
[16] Soffa W A, Laughlin D E. Acta metall. Decomposition and Ordering Processes Involving Thermodynamically First-order→disorder Transformations., 1989; 37:3019
[17] Banerjee S, Arya A, Das G P. Formation of an Ordered Intermetallic Phase From a Disordered Solid Solution-a Study Using First-Principles Calculations in Al-Li AlloysActa metall, mater., 1997; 45:601
[18] Radmilovic V, Fox A G, Thomas G. Spinodal Decomposition of Al-Rich Al-Li Alloys. Acta metall.,1989; 37:2385
[19] Sato T, Kamio A. High Resolution Electron Microscopy on the Ordered Phase in Al-Li Alloys. Aluminium-Lithium. Eds. Peters M, Winkler P J, Verlag: Informationsgesellschaft, 1992:57
[20] Ohmori Y, Ito S, Nakai K. Aging Behavior of Al-Li-Cu-Mg-Zr Alloy. Metall. Trans.,
1999; 30(A): 741
[21] Shaiu B J, Li H T, Lee H Y, et al.. Decomposition and Dissolution Kinetics of δ' Precipitation in Al-Li Binary Alloys. Metal. Trans., 1990; 21:1133
[22] Blaschko O, Glas R, Weinzierl P. The Formation of Ordered δ'-Phase In Al-Li Alloys by Diffuse and Small Angle Neutron Scattering. Acta metall, mater., 1990; 38: 1053
[23] Yu M S, Chen Haydn. Time-Resolved Scattering Studies of Decomposition of δ' Precipitates in Al-Li Alloys. Aluminium-Lithium. Eds. Peters M, Winkler P J, Verlag: Informationsgesellschaft, 1992:77
[24] Mahadev V, Mahalingam K, Liedl G L, et al..Very Early Stages of δ' Precipitation in a Binary A1-11.4at.% Li Alloy. Acta. metall, mater., 1994; 42:1039
[25] Noble B, Trowsdale A J. Evidence for Pre δ' Precipitation Events in an Al-Li Alloy. Scri. Metall, 1995; 33:33
[26] Noble B, Bray S E. On The a (Al)/δ' (Al_3Li) getastable Solvus in Aluminium-Lithium Alloys. Acta mater., 1998; 46:6163
[27] Gomiero P, Voreppe, Livet F. DSC and ASAXS Characterisation of Precipitation in an Al-Li-Cu-Mg(Zr) Alloy. Aluminium-Lithium. Eds. Peters M, Winkler P J, Verlag: Informationsgesellschaft, 1992:69
[28] Schmitz G, Haasen P. Acta metall. Decomposition of an Al-Li Alloy—the Early Stages Observed by Hrem. mater., 1992; 40:2209
[29] Schmitz G, Hono K, Haasen P. High Resolution Electron Microscopy of the Early Decomposition Stage of Al-Li Alloys. Acta metall, mater., 1994; 42:201
[30] Osamura K, Okuda H, Tanaka M, etc.. Nature of an Endothermic Peak of As-Quenched A1-11.8mol%Li Alloys. Aluminium-Lithium. Eds. Peters M, Winkler P J, Verlag: Informationsgesellschaft, 1992:131
[31] Okuda H, Osamura K. Computer Simulation of the Kinetics of Phase Decomposition with the Ll_2 Type Ordering In an Ising Lattice System at Low Temperature. Acta metall, mater., 1994; 42:1337
[32] Khachaturyan A G. Theory of structural transformations in solids. New York: Wiley, 1983:139
[33] Chen L Q, Khachaturyan A G. Formation of virtual ordered states along a phase-decomposition path. Phys. Rev. B, 1991; 44:4681
[34] Chen L Q, Khachaturyan A G. Kinetics of virtual phase formation during precipitation of ordered intermetallics. Phys. Rev. B, 1992; 46: 5899
[35] Chen L Q, Khachaturyan A G. Dynamics of Simultaneous Ordering and Phase Separation and Effect of Long-Range Coulomb Interactions. Phys. Rev. Lett., 1993; 70:
1477
[36] Chen L Q. Thermodynamics and kinetics of order-disorder processes derived from the cluster-activation method and microscopic diffusion theory. Phys. Rev. B, 1994; 49: 3791
[37] Chen L Q, Wang Y Z. JOM., The Continuum Field Approach to Modeling Microstructural Evolution, 1996, 12:13
[38] Chen L Q, Khachaturyan A G. Compputer simulation of structural transformations during precipitation of an ordered intermetallic phase. Acta metall, mater., 1991; 39:2533
[39] Chen L Q, Khachaturyan A G. Computer Simulation of Decomposition Reactions Accompanied By a Congruent Ordering of the Second Kind. SScripta Metall, 1991; 25: 61
[40] Chen L Q, Khachaturyan A G. Kinetics of Decomposition Reactions Accompanied By a Congruent Ordering of the First-Kind. Scripta Metall, 1991; 25:67
[41] Poduri R, Chen L Q. Non-Classical Nucleation Theory of Ordered Intermetallic Precipitates-Application to the Al-Li Alloy. Acta mater., 1996; 44:4253
[42] Poduri R, Chen L Q. Computer Simulation of the Kinetics of Order-Disorder and Phase Separation During Precipitation of δ'(Al_3Li) in Al-Li Alloys. Acta mater., 1997; 45:245
[43] Poduri R, Chen L Q. Computer Simulation of Morphological Evolution and Coarsening Kinetics of δ'(Al_3Li) Precipitates in Al-Li Alloys. Acta mater., 1998; 46: 3915
[44] Poduri R, Chen L Q. Non-Classical Nucleation Theory of Ordered Intermetallic Precipitates-Application to the Al-Li Alloys. Acta mater., 1998; 46:1719
[45] Chen L Q, Simmons J A. Microscopic Master Equation Approach to Diffusional Transformations in Inhomogeneous Systems--Single-Site Approximation and Direct Exchange Mechanism. Acta mater., 1994; 42:2943
[46] Wang Y Z, Chen L Q, Khachaturyan A G. Kinetics of Strain-Induced Morphological Transformation in Cubic Alloys with a Miscibility GAP. Acta metall. mater., 1993; 41:279
[47] Wang Y Z, Chen L Q, Khachaturyan A G. Strain-Induced Modulated Structures in Two-Phase Cubic Alloys. Scripta Metall., 1991; 25:1387
[48] Chen L Q. A Computer Simulation Technique for Spinodal Decomposition and Ordering in Ternary Systems. Scripta Metall., 1993; 29:683
[49] Chen L Q. Acta metall. Computer Simulation of Spinodal Decomposition in Ternary Systems. mater., 1994; 42:3503
[50] J.W. Cahn, J. Chem. Phys., 1959, 31, p.539
[51] J.E. Krzanowski, S. M. Allen. Surf. Sci. 1984,144, p153
[52] See for example, Report of the Research Group for Study of Phase Separation in Al-Li Based Alloys, Light Metal Educational Foundation, Osaka, Japan(1993)
[53] A.G. Khachaturyan, Theoretical investigation of the Precipitation of δ' in Al-Li, Metall. Trans., 1988, Vol.19A, p.249
[54] G. Schmitz and P. Haasen, Acta metal., 1992,vol.40,p.2209
[55] Lawrence F. Shampine, Jacek Kierzenka, Mark W. Reichelt, Solving Boundary Value Problems for Ordinary Differential Equations in Marlab with bvp4c. The Math Works, 2000,p1
[56] L.F. Shampine, Singular Boundary Value Problems for ODEs. Applied Mathematics and Computation, 2003, 138, p99
[57] J.W. Cahn, Free Energy of a Nonuniform System. I. Interfacial Free Energy, J. Chem. Phys., 1957, 28, p.258
[58] F.K. LeGoues and Y. W. Lee, Acta metal., 1984, 32, p. 1855
[59] M.S. Yu and H. Chen, Report of the Research Group for Study of Phase Separation in Al-Li Based Alloys, Light Metal Educational Foundation, Osaka, Japan, 1993, p.45
[60] D.罗伯[德]．项金钟，吴兴慧译．计算材料学．北京：化学工业出版社，2002：3
[61] D.罗伯[德]．项金钟，吴兴慧译．计算材料学．北京：化学工业出版社，2002：7
[2] Becker R, Doring W. Ann. Phys.,1935; 24:719
[3] Turnbull D, Fisher J C. J. Chem. Phys., 1949; 17:71
[4] Zener C. J. Appl. Phys., 1949; 20:950
[5] Lifshitz I M, Slyozov V V. J. Phys. Chem. Solids, 1961; 19:35
[6] Wagner C. Z. f. Elektrochemie, 1961; 65:581
[7] Pound G M. Metall. Trans., 1985; 16A: 488
[8] Cahn J W, Hilliard J E. J. Chem. Phys.,1958; 28:258
[9] J.W. Cahn, J.E. Hilliard, Free Energy of a Non-uniform System Ⅱ. Thermodynamic Baiss, J. Chem. Phys., 1958, 30(5), p.1121
[10] J.W. Cahn and J.E. Hilliard, Free Energy of aNon-uniform System. Ⅲ. Nucleation in a Two-component Incompressible Fluid, J. Chem. Phys., 1959, 31(3), p.688
[11] Cook H E, de Fontaine D, Hilliard J E. Acta Met. 1969; 17:765
[12] Abinandanan T A, Johnson W C. Development of spatial correlations during coarsening. Mater. Sci. Eng. B, 1995; 32:169
[13] Baumann S F, Williams D B. Effects of Capillarity and Coherency on δ'(Al_3Li) Precipitation in Dilute Al-Li Alloys at Low Under coolings. Acta metall., 1985; 33:1069
[14] Sigli C, Sanchez J M. Theoretical Description of Phase Equilibrium In Binary Alloys. Acta metall., 1985; 33:1097
[15] Sigli C, Sanchez J M. Calculation of Phase Equilibrium in Al-Li Alloys. Acta metall., 1986; 34:1021
[16] Soffa W A, Laughlin D E. Acta metall. Decomposition and Ordering Processes Involving Thermodynamically First-order→disorder Transformations., 1989; 37:3019
[17] Banerjee S, Arya A, Das G P. Formation of an Ordered Intermetallic Phase From a Disordered Solid Solution-a Study Using First-Principles Calculations in Al-Li AlloysActa metall, mater., 1997; 45:601
[18] Radmilovic V, Fox A G, Thomas G. Spinodal Decomposition of Al-Rich Al-Li Alloys. Acta metall.,1989; 37:2385
[19] Sato T, Kamio A. High Resolution Electron Microscopy on the Ordered Phase in Al-Li Alloys. Aluminium-Lithium. Eds. Peters M, Winkler P J, Verlag: Informationsgesellschaft, 1992:57
[20] Ohmori Y, Ito S, Nakai K. Aging Behavior of Al-Li-Cu-Mg-Zr Alloy. Metall. Trans.,
1999; 30(A): 741
[21] Shaiu B J, Li H T, Lee H Y, et al.. Decomposition and Dissolution Kinetics of δ' Precipitation in Al-Li Binary Alloys. Metal. Trans., 1990; 21:1133
[22] Blaschko O, Glas R, Weinzierl P. The Formation of Ordered δ'-Phase In Al-Li Alloys by Diffuse and Small Angle Neutron Scattering. Acta metall, mater., 1990; 38: 1053
[23] Yu M S, Chen Haydn. Time-Resolved Scattering Studies of Decomposition of δ' Precipitates in Al-Li Alloys. Aluminium-Lithium. Eds. Peters M, Winkler P J, Verlag: Informationsgesellschaft, 1992:77
[24] Mahadev V, Mahalingam K, Liedl G L, et al..Very Early Stages of δ' Precipitation in a Binary A1-11.4at.% Li Alloy. Acta. metall, mater., 1994; 42:1039
[25] Noble B, Trowsdale A J. Evidence for Pre δ' Precipitation Events in an Al-Li Alloy. Scri. Metall, 1995; 33:33
[26] Noble B, Bray S E. On The a (Al)/δ' (Al_3Li) getastable Solvus in Aluminium-Lithium Alloys. Acta mater., 1998; 46:6163
[27] Gomiero P, Voreppe, Livet F. DSC and ASAXS Characterisation of Precipitation in an Al-Li-Cu-Mg(Zr) Alloy. Aluminium-Lithium. Eds. Peters M, Winkler P J, Verlag: Informationsgesellschaft, 1992:69
[28] Schmitz G, Haasen P. Acta metall. Decomposition of an Al-Li Alloy—the Early Stages Observed by Hrem. mater., 1992; 40:2209
[29] Schmitz G, Hono K, Haasen P. High Resolution Electron Microscopy of the Early Decomposition Stage of Al-Li Alloys. Acta metall, mater., 1994; 42:201
[30] Osamura K, Okuda H, Tanaka M, etc.. Nature of an Endothermic Peak of As-Quenched A1-11.8mol%Li Alloys. Aluminium-Lithium. Eds. Peters M, Winkler P J, Verlag: Informationsgesellschaft, 1992:131
[31] Okuda H, Osamura K. Computer Simulation of the Kinetics of Phase Decomposition with the Ll_2 Type Ordering In an Ising Lattice System at Low Temperature. Acta metall, mater., 1994; 42:1337
[32] Khachaturyan A G. Theory of structural transformations in solids. New York: Wiley, 1983:139
[33] Chen L Q, Khachaturyan A G. Formation of virtual ordered states along a phase-decomposition path. Phys. Rev. B, 1991; 44:4681
[34] Chen L Q, Khachaturyan A G. Kinetics of virtual phase formation during precipitation of ordered intermetallics. Phys. Rev. B, 1992; 46: 5899
[35] Chen L Q, Khachaturyan A G. Dynamics of Simultaneous Ordering and Phase Separation and Effect of Long-Range Coulomb Interactions. Phys. Rev. Lett., 1993; 70:
1477
[36] Chen L Q. Thermodynamics and kinetics of order-disorder processes derived from the cluster-activation method and microscopic diffusion theory. Phys. Rev. B, 1994; 49: 3791
[37] Chen L Q, Wang Y Z. JOM., The Continuum Field Approach to Modeling Microstructural Evolution, 1996, 12:13
[38] Chen L Q, Khachaturyan A G. Compputer simulation of structural transformations during precipitation of an ordered intermetallic phase. Acta metall, mater., 1991; 39:2533
[39] Chen L Q, Khachaturyan A G. Computer Simulation of Decomposition Reactions Accompanied By a Congruent Ordering of the Second Kind. SScripta Metall, 1991; 25: 61
[40] Chen L Q, Khachaturyan A G. Kinetics of Decomposition Reactions Accompanied By a Congruent Ordering of the First-Kind. Scripta Metall, 1991; 25:67
[41] Poduri R, Chen L Q. Non-Classical Nucleation Theory of Ordered Intermetallic Precipitates-Application to the Al-Li Alloy. Acta mater., 1996; 44:4253
[42] Poduri R, Chen L Q. Computer Simulation of the Kinetics of Order-Disorder and Phase Separation During Precipitation of δ'(Al_3Li) in Al-Li Alloys. Acta mater., 1997; 45:245
[43] Poduri R, Chen L Q. Computer Simulation of Morphological Evolution and Coarsening Kinetics of δ'(Al_3Li) Precipitates in Al-Li Alloys. Acta mater., 1998; 46: 3915
[44] Poduri R, Chen L Q. Non-Classical Nucleation Theory of Ordered Intermetallic Precipitates-Application to the Al-Li Alloys. Acta mater., 1998; 46:1719
[45] Chen L Q, Simmons J A. Microscopic Master Equation Approach to Diffusional Transformations in Inhomogeneous Systems--Single-Site Approximation and Direct Exchange Mechanism. Acta mater., 1994; 42:2943
[46] Wang Y Z, Chen L Q, Khachaturyan A G. Kinetics of Strain-Induced Morphological Transformation in Cubic Alloys with a Miscibility GAP. Acta metall. mater., 1993; 41:279
[47] Wang Y Z, Chen L Q, Khachaturyan A G. Strain-Induced Modulated Structures in Two-Phase Cubic Alloys. Scripta Metall., 1991; 25:1387
[48] Chen L Q. A Computer Simulation Technique for Spinodal Decomposition and Ordering in Ternary Systems. Scripta Metall., 1993; 29:683
[49] Chen L Q. Acta metall. Computer Simulation of Spinodal Decomposition in Ternary Systems. mater., 1994; 42:3503
[50] J.W. Cahn, J. Chem. Phys., 1959, 31, p.539
[51] J.E. Krzanowski, S. M. Allen. Surf. Sci. 1984,144, p153
[52] See for example, Report of the Research Group for Study of Phase Separation in Al-Li Based Alloys, Light Metal Educational Foundation, Osaka, Japan(1993)
[53] A.G. Khachaturyan, Theoretical investigation of the Precipitation of δ' in Al-Li, Metall. Trans., 1988, Vol.19A, p.249
[54] G. Schmitz and P. Haasen, Acta metal., 1992,vol.40,p.2209
[55] Lawrence F. Shampine, Jacek Kierzenka, Mark W. Reichelt, Solving Boundary Value Problems for Ordinary Differential Equations in Marlab with bvp4c. The Math Works, 2000,p1
[56] L.F. Shampine, Singular Boundary Value Problems for ODEs. Applied Mathematics and Computation, 2003, 138, p99
[57] J.W. Cahn, Free Energy of a Nonuniform System. I. Interfacial Free Energy, J. Chem. Phys., 1957, 28, p.258
[58] F.K. LeGoues and Y. W. Lee, Acta metal., 1984, 32, p. 1855
[59] M.S. Yu and H. Chen, Report of the Research Group for Study of Phase Separation in Al-Li Based Alloys, Light Metal Educational Foundation, Osaka, Japan, 1993, p.45
[60] D.罗伯[德]．项金钟，吴兴慧译．计算材料学．北京：化学工业出版社，2002：3
[61] D.罗伯[德]．项金钟，吴兴慧译．计算材料学．北京：化学工业出版社，2002：7
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