Al-Li合金时效及回归机制的计算机模拟
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摘要
本文以Al-Li合金为客体，在国内外首先开展了其回归、分级时效的原子层面计算机模拟。计算机模拟程序采用离散格点形式的微扩散方程和非平衡自由能，具有非线性特征，可用于原子浓度梯度较大的系统。无需预先设定新相结构以及回归、时效机制；不需数据库的支持，可模拟可能存在的非平衡相的产生与消失，并获得原子图像、序参数及有序相体积分数，结构函数，相关联函数等信息；可同时描述时效过程的原子簇聚、有序化、长大、粗化等，以及回归过程的无序化、回溶等；适用于从亚稳区到失稳区的全范围。
对于不同体积分数，结构函数以及相关联函数均满足动力学标度，标度函数的峰值、形状因体积分数的不同而异，其最大值随着体积分数的增加而增加。在跨越失稳线时S(k，t)曲线随时间的演化并没有发生突变，S(k，t)的峰值减小，其峰位向低k区移动。
回归过程中有序相的演化序列为：化学计量比δ'相→非化学计量比有序相→无序基体，包括溶质原子向外扩散的过程和有序相的无序化过程。有序相溶解时，其周围形成溶质原子富集区，最终被溶质原子富集区代替，溶质原子富集区完全变为无序基体是非常缓慢的过程，合金在回归后很难完全回复到原来的状态。
在亚稳区、失稳区及过渡区，尽管合金的时效机制存在很大的差异，而回归机制却基本一致，为小范围的成分回落，随着体积分数的升高，成分回落的范围越来越小。在亚稳区时效过程为小范围的成分起伏，回归过程趋向于时效过程的逆过程；在失稳区时效过程为大范围的成分起伏，不能把回归过程简单地看成时效过程的逆过程；在过渡区回归机制随体积分数的升高由亚稳区特征向失稳区特征发展。
回归过程中有序相的无序化和原子扩散的速度先快后缓，就单个有序相而言，在回归初期其有序度有跳跃式的下降，而有序相内的浓度却有驰豫现象，对于浓度较高的合金甚至有一个向上的成分突变。
In this paper, the atomic-scale computer simulations on retrogression and ageing-reageing of Al-Li alloys were firstly worked out. The computer simulation programs are based on the microscopic diffusion equation with the discrete format and nonequilibrium free energy, which can be applied to all precipitation process, including atomic clustering, ordering, growth and coarsening, and the counter process such as disordering and dissolution during retrogression, and the compositional regions from metastable to instable. It comes from nonlinear equation, and can be applied to the system with higher compositional gradation. Furthermore, Any prior assumption on the new phase structure or the mechanisms of precipitation and retrogression was unnecessary, the emergence and dissipation of possible nonequilibrium phases could be described automatically without any database to support, and atomic pictures, order parameters, volume fractions ,structure function and correlation function of precipitates could be further o
btained.
For different volume fractions, structure function and correlation function were both scaled at late stage of phase precipitation, but the peak and shape of scaling structure function profiles were different, the maximum value of which increased with the volume fractions. When skipping to instable regions, the variations of structure function profiles with time were the same: the peak of structure function was decreased and the location of the peak of the structure function shifted towards smaller reduced wave vectors.
In the course of retrogression, the evolutions of ' phase were in the order: stoicheometric ' phase-nonstoicheometric ordered phase-disordered matrix, including the diffusion of solute atoms and the disordering of ordered phases. The solute-rich regions were formed around the ordered phases as the phases were dissolved during the retrogression, and in the end, the ordered phases would be replaced by solute-rich regions completely. But the process of solute-rich regions turning into disordered matrix was very slow, and it was hard to come back to the original states during retrogression.
The mechanisms of phase precipitation were very different at different compositional regions from metastable to instable, while the mechanisms of retrogression were consistent: the composition drop among a small range. The range
of composition drop was smaller with the increase of volume fractions. In metastable region, the precipitation was "composition fluctuation among a small range", and the retrogression tended to be the counter process of the precipitation. In instable region, the precipitation mechanism was "composition fluctuation among a large range", and the retrogression could not be simply regarded as the counter process of the precipitation. In transitional region, with the increase of volume fractions the retrogression characteristic transformed from that of metastable to instable region gradually.
In the course of retrogression, the disordering of ordered phase and atomic diffusion was very fast at early stage, and then turned to be slow. For a single ordered phase, the maximum value of long range order parameter had a sharp drop, while that of the composition parameter had a relaxation , even a sharp increase in higher composition region at early stage of retrogression.
对于不同体积分数，结构函数以及相关联函数均满足动力学标度，标度函数的峰值、形状因体积分数的不同而异，其最大值随着体积分数的增加而增加。在跨越失稳线时S(k，t)曲线随时间的演化并没有发生突变，S(k，t)的峰值减小，其峰位向低k区移动。
回归过程中有序相的演化序列为：化学计量比δ'相→非化学计量比有序相→无序基体，包括溶质原子向外扩散的过程和有序相的无序化过程。有序相溶解时，其周围形成溶质原子富集区，最终被溶质原子富集区代替，溶质原子富集区完全变为无序基体是非常缓慢的过程，合金在回归后很难完全回复到原来的状态。
在亚稳区、失稳区及过渡区，尽管合金的时效机制存在很大的差异，而回归机制却基本一致，为小范围的成分回落，随着体积分数的升高，成分回落的范围越来越小。在亚稳区时效过程为小范围的成分起伏，回归过程趋向于时效过程的逆过程；在失稳区时效过程为大范围的成分起伏，不能把回归过程简单地看成时效过程的逆过程；在过渡区回归机制随体积分数的升高由亚稳区特征向失稳区特征发展。
回归过程中有序相的无序化和原子扩散的速度先快后缓，就单个有序相而言，在回归初期其有序度有跳跃式的下降，而有序相内的浓度却有驰豫现象，对于浓度较高的合金甚至有一个向上的成分突变。
In this paper, the atomic-scale computer simulations on retrogression and ageing-reageing of Al-Li alloys were firstly worked out. The computer simulation programs are based on the microscopic diffusion equation with the discrete format and nonequilibrium free energy, which can be applied to all precipitation process, including atomic clustering, ordering, growth and coarsening, and the counter process such as disordering and dissolution during retrogression, and the compositional regions from metastable to instable. It comes from nonlinear equation, and can be applied to the system with higher compositional gradation. Furthermore, Any prior assumption on the new phase structure or the mechanisms of precipitation and retrogression was unnecessary, the emergence and dissipation of possible nonequilibrium phases could be described automatically without any database to support, and atomic pictures, order parameters, volume fractions ,structure function and correlation function of precipitates could be further o
btained.
For different volume fractions, structure function and correlation function were both scaled at late stage of phase precipitation, but the peak and shape of scaling structure function profiles were different, the maximum value of which increased with the volume fractions. When skipping to instable regions, the variations of structure function profiles with time were the same: the peak of structure function was decreased and the location of the peak of the structure function shifted towards smaller reduced wave vectors.
In the course of retrogression, the evolutions of ' phase were in the order: stoicheometric ' phase-nonstoicheometric ordered phase-disordered matrix, including the diffusion of solute atoms and the disordering of ordered phases. The solute-rich regions were formed around the ordered phases as the phases were dissolved during the retrogression, and in the end, the ordered phases would be replaced by solute-rich regions completely. But the process of solute-rich regions turning into disordered matrix was very slow, and it was hard to come back to the original states during retrogression.
The mechanisms of phase precipitation were very different at different compositional regions from metastable to instable, while the mechanisms of retrogression were consistent: the composition drop among a small range. The range
of composition drop was smaller with the increase of volume fractions. In metastable region, the precipitation was "composition fluctuation among a small range", and the retrogression tended to be the counter process of the precipitation. In instable region, the precipitation mechanism was "composition fluctuation among a large range", and the retrogression could not be simply regarded as the counter process of the precipitation. In transitional region, with the increase of volume fractions the retrogression characteristic transformed from that of metastable to instable region gradually.
In the course of retrogression, the disordering of ordered phase and atomic diffusion was very fast at early stage, and then turned to be slow. For a single ordered phase, the maximum value of long range order parameter had a sharp drop, while that of the composition parameter had a relaxation , even a sharp increase in higher composition region at early stage of retrogression.
引文
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2．冯端．金属物理学第二卷相变．北京：科学出版社，1998：31
3. G.M. Pound. Perspectives on nucleation. Metallurgical Trans. 1985, 16A: 487
4. J .W. Cahn, Hilliard J E. Free energy of a nonuniform system I .Interfacial free energy. J. Chem. Phys. 1958,28(2): 258
5. J .W. Cahn, Hilliard J E. Free energy of a nonuniform system Ⅲ.Nucleation in a two component Incompressible fluid. J. Chem. Phys. 1959(3), 31:688
6. R .W .Cahn, P. Haasen, E. J. Kramer. Phase transformation in materials(材料的相变)[M]. Beijing: Science Press(北京：科学出版社), 1998:219
7. F.K. Legous, Y. W. Lee, H. I. Influence of crystallography upon critical nucleus shapes and kinetics of homogeneous f.c.c-f.c.c nucleation -Ⅱ.The non-classical regime. Aaronson. Acta Metal. Mater. 1984, 32(10): 1837
8. A.D. Brailsford, P. Wynblatt. The dependence of ostwald ripening kinetics on particle volume fraction. Acta Metal. Mater. 1979, 27:489
9. A.J. Ardell. Late-Stage two-dimensional coarsening of circular clusters. Phys. Rev. B. 1990, 41(4): 2554
10. A. Kalogeridis, J. Pesicka, E. Nembach. On the increase of the precipitated volume fraction during ostwald ripening, exemplified for Al-Li alloys. Mater. Sci. Eng. A. 1999,268:197
11. J. Hoyt, S. Spooner. The surface energy of metastable Al_3Li precipitates from coarsening kinetics. Acta metal mater.. 1991, 39(4): 689
12. S. Q. Xiao, P. Haasen. Herm investigation of homogeneous decomposition in a Ni-12at. %Al alloy. Acta metal mater. 1991,39(4): 651
13. C. Marsh, H. Chen An insistu x-ray diffraction study of precipitation from a supersaturated solid solution: the γ′ precipitate in Ni-12.5at. %Al alloy. Acta metall, mater. 1990, 38:2287
14. S. P. Marsh, M.E. Glicksman. Kinetics of phase coarsening in dense systems. Acta Metal. Mater. 1996,44(9): 3761
15. V. A. Snyder, J. Alkemper, P. W. Voorhees. The development of spatial
collelations during Ostwald ripening: a test of theory. Acta mater. 2000, 48:2689
16. H. A. Calderon, P .W. Voorhees, J. L. Murray, ect. Ostwald ripening in concentrated alloys. Acta Metal. Mater. 1994, 42(3): 991
17. C. K. L. Davies, P. Nash, R. N. Stevens. The effect of volume fraction of precipitate on ostwald ripening. Acta Metal. Mater. 1980, 28:179
18．冯端．金属物理学第二卷相变．北京：科学出版社，1998：195
19. K. Binder. Time-dependent Ginzburg-Landau theory of nonequilibirium relaxation. Phys. Rev. B. 1973, 8:3423
20. K. Binder, M. Krumbaar. Investigation of metastable states and nucleation in the kinetic Ising model. Phys. Rev. B. 1974, 9(8): 2328
21. C. Unger, W. K lein. Nucleation theory near the classical spinodal. Phys. Rev. B.1984, 29:2698
22. J .S. Langer, A. J. Schwartz. Kinetics of nucleation in near-critical fluids. Phys. Rev. A. 1980, 21:948
23. H. Wendt, P. Haasen. Nucleation and growth of Υ' precipitates in Ni-14at. %Al alloy. Acta metal. Mater. 1983, 31(10): 1649
24. R .W. Cahn, P. Haasen, E.J.Kramer. Phase transformation in materials(材料的想变)[M]. Beijing: Science Press(北京：科学出版社), 1998:255
25. A. W. Zhu. Evolution of size distribution of shearable ordered precipitates under homogeneous deformation: application to an Al-Li alloy. Acta Metal. Mater.. 1997,45(10): 4213
26. E. D. Siebert, Knobler C M. Measurements of homogeneous nucleation near a critical solution temperature. Phy. Rev. Lett.. 1984,52:1133
27. M. Kumar, R. Sasilumar, N. Kesavan. Competition between nucleation and early growth of ferrite from austenite studies using cellular automation simulations. Acta metal. Mater. 1998, 46(17): 6291
28. Baumann S F, Williams D B. Effects of Capillarity and Coherency on δ' (Al_3Li) Precipitation in Dilute Al-Li Alloys at Low Undercoolings. Acta metall., 1985; 33: 1069
29. Sigli C, Sanchez J M. Theoretical Description of Phase Equilibrium In Binary Alloys. Acta metall., 1985; 33:1097
30. Sigli C, Sanchez J M. Calculation of Phase Equilibrium in Al-Li Alloys. Acta metall., 1986; 34:1021
31. Soffa W A, Laughlin D E. Acta metall. Decomposition and Ordering Processes Involving Thermodynamically First-Orderr→Disorder Transformations., 1989; 37:3019
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