液态金属铅凝固过程中微观结构演变特性的模拟研究
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摘要
本文首先对液态和非晶态金属的微观结构特征,凝固的基本理论,非晶晶化理论,金属的固态相变,以及液态金属凝固过程中的计算机模拟研究的进展进行了简要概述,然后对本文模拟研究方法及微观结构表征方法进行了详细介绍,并对本文所采用的模拟方法的可靠性通过与实验值的比较进行了验证。最后,本文采用分子动力学模拟方法,并结合双体分布函数、键型指数法和团簇类型指数法(CTIM-2)等微观结构表征方法,以及均方位移(Mean Square Displacement,MSD),非高斯参数(Non-Gaussian Parameter, NGP)等时间关联函数从不同角度,系统研究了液态金属铅(Pb)在不同条件下凝固过程中微观结构的演变机理。
模拟研究了冷速对液态金属Pb凝固过程中微观团簇结构演变的影响,结果表明：冷速对凝固的最终结构起到了决定性的作用,液态金属Pb形成非晶的临界冷速在5×1012与1×1012K.s-1之间。当以高于此临界冷速凝固时,系统形成以1551,1541和1431为主的非晶态结构；而当以低于此临界冷速凝固时,系统最终形成以1421和1422键型(或基本原子团(1200066)和(12000120))为主的hcp和fcc共存的晶态结构。冷速不仅决定系统最终形成晶态还是非晶态,而且还影响到晶体中不同结构的相对比例；冷速越低,fcc结构所占的比例越大,即系统越倾向于形成热力学稳定相fcc晶体结构。
为了进一步研究凝固过程微观结构演变及bcc-hcp、bcc-fcc晶格转变机制,本文对包含10000个Pb原子的较大体系以5×1011K.s-1冷速的快速凝固过程进行了模拟。结果表明：随着温度的降低,系统经历了两次相变,一次是液固相变,即从液态晶化形成亚稳bcc相,第二次是固固相变,即亚稳bcc相再转变为热力学上更为稳定的hcp和fcc共存的晶体结构；并且,hcp和fcc相表现出相互竞争的趋势。本文采用团簇跟踪法再现了该转变过程,并从模拟上验证了bcc-hcp和bcc-fcc转变分别遵从由Dmitriev等人修订后的Burgers(贝格斯)转变机制和Bain(贝茵)转变机制；这就对理论和实验进行了有力的补充。研究同时发现,在快速加热的过程中hcp和fcc共存相将重新转变为高温bcc相,即在金属Pb中马氏体转变是可逆的。
对过冷液态和非晶态金属Pb等温弛豫过程进行了模拟,继续采用团簇类型指数法和团簇跟踪法等对等温晶化过程中bcc相的形成和演变特性进行了分析,研究结果表明：等温晶化过程中,亚稳bcc相最先形成并起到了重要的晶化先驱的作用；bcc相的稳定性密切依赖于等温过程的起始温度和结构,而在较高温度下,即过冷液态区,bcc相在本文的模拟范围内保持稳定,而在较低温度下,即非晶态区,bcc相先形成但最终将部分转变为热力学上更为稳定的hcp结构,而当温度进一步降低到153K以下时,bcc,hcp和fcc相将同时增长；从自由能形成势垒的角度,本文对这一现象进行了清晰的解释,在高温下bcc相的自由能形成势垒最低,因此最容易形成并占绝对优势,而随着温度的降低,hcp和fcc相的自由能形成势垒降低,因此在低温下这两个相更容易形成。受结构起伏和动力学因素的影响,虽然自由能形成势垒最低的原则在相变过程中是最大趋势,但也会有一些例外的情况发生,如本文模拟的233K。
在前文的工作基础上,进一步采用MSD, NGP等动力学参数对系统在等温晶化过程中的动力学特性进行了分析,对动力学特性与微观结构演变之间的关系进行了研究,并相应给出了较为清晰的物理解释。通过对过冷液态和非晶态金属Pb等温弛豫过程中动力学特性研究发现,在过冷液态和非晶态金属Pb等温晶化过程的初始阶段,系统表现出了明显的动力学非均匀性；并且,温度越低,动力学非均匀性越明显。根据晶化过程中的热力学,动力学和微观结构随弛豫时间的演变特性,我们得到了金属Pb温度时间转变动力学图。并且,通过对273K温度下等温晶化过程动力学特性的细致研究发现,系统微观结构演变与系统动力学特性的演变可以有效地联系起来：在β-弛豫阶段,受“笼子效应”的影响,系统只能进行局域原子团的整体运动,而无法进行扩散型的微观结构调整；而在α-弛豫阶段,原子开始冲破笼子进行自由的扩散,从而系统的晶化过程开始；MSD的第二个平台和NGP的非零平台对应于系统晶化过程的结束。过冷液态金属Pb等温晶化过程是一个扩散型相变,呈现出三个明显的阶段式特征：形核,长大和晶粒粗化。
Some basic areas are firstly reviewed briefly, including the characteristic of mi-crostructures in liquid and glass metal, the basic theories on solidification, amorphous-crystallizing and solid-solid phase transition, and the development of the computer sim-ulation for the liquid as well. Then the simulation methods are validated by comparing the computational results with the corresponding experimental results, and several micro-structural quantifications adopted in the present works are introduced in detail. Based on a series of effective approaches (such as the pair distribution function, the cluster index method (CTIM-2), the mean square displacement (MSD), and the non-gaussian parame-ter (NGP)), the mechanism of the microstructure evolution during the solidification under different conditions are studied systematically from different viewpoints.
A simulation study for the influence of cooling rate on the evolutions of micro-clusters structures has performed. And the results show that there is a critical cooling rate in the range of5x1012and1x1012K·s-1separating glass forming and crystal form-ing. When the cooling rate is higher than the critical cooling rate, amorphous structures are formed mainly with the1551,1541and1431bond-types. When the cooling rate is lower than the critical cooling rate, the crystal structure mainly with the1421and1422bond-types (the basic clusters of (1200066) and (12000120)of hcp and fcc coexisted) are finally formed. At the same time, it has been found that there are obvious effects of the cooling rate on the relative proportion of the fcc basic cluster to the hcp basic clusters, the smaller the cooling rate is, the bigger relative proportion of the fcc basic cluster, and the system tends to form highly perfect fcc crystal structure.
The rapid solidification process at the cooling rate of5x1011K·s-1for a system containing10,000Pb atoms is simulated to reveal the microstructure evolution focusing on the bcc-hcp, bcc-fcc transformation mechanisms. It is demonstrated that with temper-ature decreasing, the system undergoes twice phase transitions:liquid state→metastable bcc phase→more stable phase-the hcp and fcc coexisted crystal structure. The hcp and fcc crystal structures are also competing to each other during the transformation process. The detailed trace to the concrete transformation processes illustrates that the bcc-hcp and bcc-fcc transformation are corresponding to the revised Burgers mechanism and Bain mechanism respectively, which provides valuable complement to theory and experiment. It is also found that the hcp and fcc coexistence will transformed back to bcc phase at high temperature during the rapid heating process, in other words, the martensitic transforma-tion in metal Pb is revisable.
Going further, the isothermal relaxation process of supercooled liquid and glassy Pb have been investigated by molecular dynamics simulation. The formation and evolution characteristics of bcc phase during isothermal crystallization are analyzed with the bond-type index method, cluster-type index method and tracing method. It is found that the metastable bcc phase plays an important role as precursor for crystallization. And the stability of the bcc phase strongly depends on the initial temperature and structure:at the higher temperature with the a supercooled liquid initial state, the bcc phases can form and stably maintain in the relaxation processes; while at the lower temperature with a glassy initial state, the bcc phase form at first and then partially transform into hcp phase, just metastable. When the initial temperature is lower than153K, the hcp and fcc phase in-cline to directly form in the glass structure without undergoing a metastable bcc phase. This result can be well explained from the view point of the free energy barrier:at rel-ative high temperatures, the bcc phase has the lowest free energy barrier, so it is easy to form and keep stable; as temperature decreases, the free energy barrier for hcp and fcc phases are lowered, and both the two phases are easy to form and without undergoing the metastable bcc phase. However, take the structure fluctuation and kinetic influence into consideration, the lowest free energy barrier rule is the most probable case, but does not always work, such as the case at233K in our simulation.
Based on the above work, the correlation of dynamic character with the microstruc-ture evolution is studied, and the physical interpretation has also been provided. Re-sults suggest that, the supercooled liquid and glassy Pb exhibit the dynamic heterogene-ity during the relaxations; and the lower the temperature, the more apparent the dy-namic heterogeneity. According to the time dependence of thermodynamic, dynamic and structural functions in supercooled liquid and glassy Pb, we plot the temperature-time-transformation (TTT) diagram for metal Pb. Furthermore, the simulation study is also found that the relaxation, nucleation and crystallization can be consistently correlated: the β—relaxation regime is corresponding to minor structural rearrangement because of the "cage effect", while the a—relaxation regime relates to a more diffusive movement favoring the microscopic configuration rearrangement, where the nucleation and growth take place; and the appearance of the second plateau of MSD and the non-zero plateau of NGP is corresponding to the completion of crystallization. Therefore, the nucleation and growth is a diffusive atom rearrangement process, which exhibits three distinct stages of nucleation, increase of nuclei and the coarsening of crystalline grain.
模拟研究了冷速对液态金属Pb凝固过程中微观团簇结构演变的影响,结果表明：冷速对凝固的最终结构起到了决定性的作用,液态金属Pb形成非晶的临界冷速在5×1012与1×1012K.s-1之间。当以高于此临界冷速凝固时,系统形成以1551,1541和1431为主的非晶态结构；而当以低于此临界冷速凝固时,系统最终形成以1421和1422键型(或基本原子团(1200066)和(12000120))为主的hcp和fcc共存的晶态结构。冷速不仅决定系统最终形成晶态还是非晶态,而且还影响到晶体中不同结构的相对比例；冷速越低,fcc结构所占的比例越大,即系统越倾向于形成热力学稳定相fcc晶体结构。
为了进一步研究凝固过程微观结构演变及bcc-hcp、bcc-fcc晶格转变机制,本文对包含10000个Pb原子的较大体系以5×1011K.s-1冷速的快速凝固过程进行了模拟。结果表明：随着温度的降低,系统经历了两次相变,一次是液固相变,即从液态晶化形成亚稳bcc相,第二次是固固相变,即亚稳bcc相再转变为热力学上更为稳定的hcp和fcc共存的晶体结构；并且,hcp和fcc相表现出相互竞争的趋势。本文采用团簇跟踪法再现了该转变过程,并从模拟上验证了bcc-hcp和bcc-fcc转变分别遵从由Dmitriev等人修订后的Burgers(贝格斯)转变机制和Bain(贝茵)转变机制；这就对理论和实验进行了有力的补充。研究同时发现,在快速加热的过程中hcp和fcc共存相将重新转变为高温bcc相,即在金属Pb中马氏体转变是可逆的。
对过冷液态和非晶态金属Pb等温弛豫过程进行了模拟,继续采用团簇类型指数法和团簇跟踪法等对等温晶化过程中bcc相的形成和演变特性进行了分析,研究结果表明：等温晶化过程中,亚稳bcc相最先形成并起到了重要的晶化先驱的作用；bcc相的稳定性密切依赖于等温过程的起始温度和结构,而在较高温度下,即过冷液态区,bcc相在本文的模拟范围内保持稳定,而在较低温度下,即非晶态区,bcc相先形成但最终将部分转变为热力学上更为稳定的hcp结构,而当温度进一步降低到153K以下时,bcc,hcp和fcc相将同时增长；从自由能形成势垒的角度,本文对这一现象进行了清晰的解释,在高温下bcc相的自由能形成势垒最低,因此最容易形成并占绝对优势,而随着温度的降低,hcp和fcc相的自由能形成势垒降低,因此在低温下这两个相更容易形成。受结构起伏和动力学因素的影响,虽然自由能形成势垒最低的原则在相变过程中是最大趋势,但也会有一些例外的情况发生,如本文模拟的233K。
在前文的工作基础上,进一步采用MSD, NGP等动力学参数对系统在等温晶化过程中的动力学特性进行了分析,对动力学特性与微观结构演变之间的关系进行了研究,并相应给出了较为清晰的物理解释。通过对过冷液态和非晶态金属Pb等温弛豫过程中动力学特性研究发现,在过冷液态和非晶态金属Pb等温晶化过程的初始阶段,系统表现出了明显的动力学非均匀性；并且,温度越低,动力学非均匀性越明显。根据晶化过程中的热力学,动力学和微观结构随弛豫时间的演变特性,我们得到了金属Pb温度时间转变动力学图。并且,通过对273K温度下等温晶化过程动力学特性的细致研究发现,系统微观结构演变与系统动力学特性的演变可以有效地联系起来：在β-弛豫阶段,受“笼子效应”的影响,系统只能进行局域原子团的整体运动,而无法进行扩散型的微观结构调整；而在α-弛豫阶段,原子开始冲破笼子进行自由的扩散,从而系统的晶化过程开始；MSD的第二个平台和NGP的非零平台对应于系统晶化过程的结束。过冷液态金属Pb等温晶化过程是一个扩散型相变,呈现出三个明显的阶段式特征：形核,长大和晶粒粗化。
Some basic areas are firstly reviewed briefly, including the characteristic of mi-crostructures in liquid and glass metal, the basic theories on solidification, amorphous-crystallizing and solid-solid phase transition, and the development of the computer sim-ulation for the liquid as well. Then the simulation methods are validated by comparing the computational results with the corresponding experimental results, and several micro-structural quantifications adopted in the present works are introduced in detail. Based on a series of effective approaches (such as the pair distribution function, the cluster index method (CTIM-2), the mean square displacement (MSD), and the non-gaussian parame-ter (NGP)), the mechanism of the microstructure evolution during the solidification under different conditions are studied systematically from different viewpoints.
A simulation study for the influence of cooling rate on the evolutions of micro-clusters structures has performed. And the results show that there is a critical cooling rate in the range of5x1012and1x1012K·s-1separating glass forming and crystal form-ing. When the cooling rate is higher than the critical cooling rate, amorphous structures are formed mainly with the1551,1541and1431bond-types. When the cooling rate is lower than the critical cooling rate, the crystal structure mainly with the1421and1422bond-types (the basic clusters of (1200066) and (12000120)of hcp and fcc coexisted) are finally formed. At the same time, it has been found that there are obvious effects of the cooling rate on the relative proportion of the fcc basic cluster to the hcp basic clusters, the smaller the cooling rate is, the bigger relative proportion of the fcc basic cluster, and the system tends to form highly perfect fcc crystal structure.
The rapid solidification process at the cooling rate of5x1011K·s-1for a system containing10,000Pb atoms is simulated to reveal the microstructure evolution focusing on the bcc-hcp, bcc-fcc transformation mechanisms. It is demonstrated that with temper-ature decreasing, the system undergoes twice phase transitions:liquid state→metastable bcc phase→more stable phase-the hcp and fcc coexisted crystal structure. The hcp and fcc crystal structures are also competing to each other during the transformation process. The detailed trace to the concrete transformation processes illustrates that the bcc-hcp and bcc-fcc transformation are corresponding to the revised Burgers mechanism and Bain mechanism respectively, which provides valuable complement to theory and experiment. It is also found that the hcp and fcc coexistence will transformed back to bcc phase at high temperature during the rapid heating process, in other words, the martensitic transforma-tion in metal Pb is revisable.
Going further, the isothermal relaxation process of supercooled liquid and glassy Pb have been investigated by molecular dynamics simulation. The formation and evolution characteristics of bcc phase during isothermal crystallization are analyzed with the bond-type index method, cluster-type index method and tracing method. It is found that the metastable bcc phase plays an important role as precursor for crystallization. And the stability of the bcc phase strongly depends on the initial temperature and structure:at the higher temperature with the a supercooled liquid initial state, the bcc phases can form and stably maintain in the relaxation processes; while at the lower temperature with a glassy initial state, the bcc phase form at first and then partially transform into hcp phase, just metastable. When the initial temperature is lower than153K, the hcp and fcc phase in-cline to directly form in the glass structure without undergoing a metastable bcc phase. This result can be well explained from the view point of the free energy barrier:at rel-ative high temperatures, the bcc phase has the lowest free energy barrier, so it is easy to form and keep stable; as temperature decreases, the free energy barrier for hcp and fcc phases are lowered, and both the two phases are easy to form and without undergoing the metastable bcc phase. However, take the structure fluctuation and kinetic influence into consideration, the lowest free energy barrier rule is the most probable case, but does not always work, such as the case at233K in our simulation.
Based on the above work, the correlation of dynamic character with the microstruc-ture evolution is studied, and the physical interpretation has also been provided. Re-sults suggest that, the supercooled liquid and glassy Pb exhibit the dynamic heterogene-ity during the relaxations; and the lower the temperature, the more apparent the dy-namic heterogeneity. According to the time dependence of thermodynamic, dynamic and structural functions in supercooled liquid and glassy Pb, we plot the temperature-time-transformation (TTT) diagram for metal Pb. Furthermore, the simulation study is also found that the relaxation, nucleation and crystallization can be consistently correlated: the β—relaxation regime is corresponding to minor structural rearrangement because of the "cage effect", while the a—relaxation regime relates to a more diffusive movement favoring the microscopic configuration rearrangement, where the nucleation and growth take place; and the appearance of the second plateau of MSD and the non-zero plateau of NGP is corresponding to the completion of crystallization. Therefore, the nucleation and growth is a diffusive atom rearrangement process, which exhibits three distinct stages of nucleation, increase of nuclei and the coarsening of crystalline grain.
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