铁纳米颗粒及体材料固液相变过程的分子动力学研究
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摘要
本论文的主要目的是研究纳米尺度Fe在固液相变过程中的热力学性质及结构变化。目前对于Fe纳米颗粒来说,研究的方向主要集中于其凝固、熔化以及烧结等过程的结构及性质变化,但对于其热力学性质的系统性研究、纳米颗粒与体材料熔点的关系、结构特征以及详细的定量的结构演化过程仍显薄弱。此外,在纳米尺度上Fe能够以fcc结构稳定存在,而现有的大部分研究均聚焦于bcc-Fe,对于fcc-Fe的研究则较少。基于上述原因,本文以分子动力学(Molecular Dynamics)作为研究手段,以键形指数(Cluster Type Index Method)作为结构分析手段,研究了Fe纳米颗粒的固液相变过程中热力学性质以及结构演化。同时在上述研究的基础上将研究体系扩展至Fe体材料,对其凝固过程中的结构特征及结构演变进行了分析。
本论文主要包含以下三个方面的内容：
1.Fe纳米颗粒凝固与熔化过程的热力学分析
研究发现尺寸效应对Fe纳米颗粒的热力学性质会造成明显影响。由于表面能的存在,尺寸越小的纳米颗粒其熔点就越低,早在1909年Pawlow就对纳米颗粒的尺寸与熔点之间的关系进行了研究,并认为二者关系可以通过描述。在后续的研究中,上式逐步演化为二者均描述了纳米颗粒熔点与体材料熔点变化值与其尺寸的关系,在一定假设下这种关系可以看作是线性关系,其不同之处在于线性关系的自变量分别为1/R和N-1/3。根据我们的实验结果对比发现使用N-1/3时吻合度更高。在此基础上我们对Fe113到Fe9577的熔点(Tmcluster),凝固点(Tscluster)以及平衡相变点(Tequilibrium cluster)与N-1/3的线性关系进行了研究。通过拟合获得体材料平衡相变点Tequilibrium(∞)=1833.3K,与体材料Fe的实验值1811K十分接近,且明显好于之前的研究成果。
此外我们还发现模拟中使用不同的变温速率(0.05～25K/ps)也会对纳米颗粒的热力学性质造成影响。在变温速率较低时(0.05～0.25K/ps),纳米颗粒具有充足的时间进行结构弛豫,因此其熔点、凝固点以及平衡相变点在较小的范围内变化,在此条件下拟合获得的体材料熔点数据更接近于实验值。
2.Fe纳米颗粒凝固与熔化过程的结构演变
本论文中使用CTIM-2方法对纳米颗粒凝固及熔化过程中的结构演化进行了分析,发现凝固的纳米颗粒中固相均由fcc和hcp原子组成,结构类型主要包括五重孪晶(fivefold twins)、层状结构(lamellar structure)以及介于上述二者之间的混合结构。通常认为Fe在常温常压下为bcc结构,在1185K以上时转变为fcc结构。但近年来的研究表明,纳米尺寸下的fcc-Fe是可以保持结构稳定的,我们的结果也证明了这一点。
对五重孪晶结构的研究发现,在凝固初期,当数个呈一定夹角的hcp原子层连续生成并相交于一处时就会形成五重孪晶。在晶体生长过程中纳米颗粒中会出现多个相邻的五重孪晶结构,同时伴随有位错的形成。进入结构弛豫阶段后随着晶面及晶轴的调整,位错逐步消失。但由于五重孪晶的结构特性,凝固获得的构型中仍存在内部缺陷。而在其熔化过程中随着温度升高,内部缺陷逐步增加,随后出现表面预熔,纳米颗粒在内部外部双重作用下逐步熔化。
对层状结构的研究发现。凝固过程中其早期的生长方式为逐层生长,在形成了带有hcp原子层的晶胚后,新生成的固相原子附着于晶胚之上,同时伴随着结构调整形成新的与原有晶面平行的hcp层。如此循环往复最终形成了由fcc和hcp原子组成的原子层交替排列而成的层状结构。最终的构型中基本没有内部缺陷,因此其在熔化过程中呈现了更好的稳定性。随着温度升高,内部缺陷早于表面熔化出现,二者同时作用加速了颗粒的熔化。
通过对比我们认为在纳米颗粒的形核过程中存在结构的遗传性,早期晶胚的结构在很大程度上决定了纳米颗粒最终结构是五重孪晶还是层状结结构。虽然对于小尺寸的纳米颗粒来说，幻数（magic number）决定了其外形和结构，从而起到了将一些对称点群构型能降至最低的作用，但在我们实际模拟中，模拟条件的变化仍可能导致纳米颗粒形成完全不同的结构，这可以理解为结构选择的随机性。随着纳米颗粒尺寸的增加随机性会增强，完全相同的模拟条件仍可获得不同的结果。
3. Fe体材料凝固过程中的结构分析
在对纳米颗粒结构研究的基础上我们对体材料Fe的形核过程进行研究。通过结构研究发现模拟获得的最终构型包括带有晶界的fcc单晶结构、五重孪晶结构以及层状结构。模拟温度与最终构型间并无直接关联，说明晶体的结构选择存在一定的随机性。而从其形成机制来看，层状结构与五重孪晶的生长机制与在纳米颗粒中类似，而单晶结构则出现了两次明显的结构变化。在形核初期体系内同时出现了多个晶胚并同时生长并融合，形成大量的hcp晶面。而在体系的结构优化中大部分hcp晶面逐步萎缩并消失，只有少数得以保留，最终形成了单晶结构。
对五重孪晶结构分析发现，其晶核外形呈不规则形状，内部由hcp原子组成的孪晶面彼此相连形成了五重孪晶结构。晶核中共有9个晶轴，晶轴间共用晶面，彼此相连形成了四面体网格。由于最终构型中非晶态原子占比高达67.59%，我们在模拟中加入温度扰动、连续降温等手段以考察其对体系结构的影响。结果表明小幅度的温度扰动无法给体系进一步凝固提供足够的驱动力。而在连续降温过程中五重孪晶发生了内部结构优化，但仍存在相当数量的非晶态原子，主要分布于数个相对完整的五重孪晶结构之间。
In this thesis, the thermaldynamic properties and structural transformation during solid-liquid phase transition of nanoscaled Fe have been studied. For Fe nanoparticles, previous studies mainly focused on the variations of thermaldynamic properties and structural transformation in solidification, melting and sintering processes. However, to our knowledge, few researchers have systematically investigated (i) the relaitonship between thermaldynamic properties of nanoparticles and bulk materials and (ii) quantitative analysis of structural evolution. Moreover, different with bcc-Fe, less attention have been paid on fcc-Fe, which is proved stable at room temperature in nanoscaled material in previous studies.
On the basis of above considerations, the detailed solid-liquid transition process of nanoscaled Fe has been studied by molecular dynamics (MD) in this thesis. Cluster type index method (CTIM) has been employed for structure analysis. The variation of thermaldynamic properties and detailed structural evolution during liquid-solid transition process of Fe nanoparticles have been discussed. Furthermore, the detailed structural evolution during solidification process of bulk Fe have been studied.
The major contents of this dissertation are epitomized as follows:
1. Thermodynamics analysis of Fe nanoparticles during solidification and melting
It is well-known that size effects may significantly affect thermodynamic properties of nanoparticles. The melting point of small nanoparticles is lower than that of larger ones due to the existance of surface energy. In1909, Pawlow investigated the relationship between melting point and particle size and modeled it The follow-up studies modified this model several times and two main versions, and have been derived. Both of these two models describe the relation between the difference of melting points of nanoparticle and bulk Fe and the size of nanoparticle. In some specific assumptions the difference is caused by the two variables1/R and N-1/3of the linear relationship. Our results indicate that the latter model is more accurate in predicting the melting points Tm/cluster, solidification points Ts/cluster and equilibrium points Tequilibrium/cluster of Fe nanoparticles in the range of Fe113～Fe9577. The equilibrium point of bulk material Tequilibrium(∞)=1833.3K obtained by fitting procedure is strikingly close to the experimental data of bulk Fe (1811K) and is much better than previous results.
Moreover, the cooling/heating rates (0.05-25K/ps) also affected the thermaldynamics properties of nanoparticles. In low cooling/heating rates (0.05～0.25K/ps), nanoparticles have enough time to relax their structures and thus the melting points, solidification points and equilibrium points fluctuate in a small range. The melting point obtained in this condition is closer to experimental results.
2. Structural evolution of Fe nanoparticles during solidification and melting
CTIM-2has been employed to analyze the structural evolution of Fe nanoparticles during nucleation and melting process. The configurations obtained after solidification indicate that the solid phase in nanoparticles is mainly consisted of fcc and hcp atoms. Two main structure, fivefold twins and lamellar structure, have been found. In common belief, Fe belongs to bcc structures in ambient pressure and temperature and transforms to fcc structures at the temperature higher than1185K. Actually, researches in resent years showed that nanoscaled fcc-Fe could be stable in ambient conditions, which is in accordance with our results.
At the early stage of nucleation of fivefold twins, we found that they are built by continuous growth of several hcp layers with the included angle fixed. Severaladjacent fivefold twins appeared and accompanied with formation of dislocations. Atthe stage of relaxation, the twinning boundaries and axes adjusted with each other andthe dislocations disappeared gradually while few internal defects remained due to itsstructural characteristics. These defects will significantly affect the melting behavior.With temperature increasing, there is an increasing number of defects insidenanoparticles, meanwhile surface premelting takes place. By the influence of bothexternal and internal defects, the nanoparticle becomes meltdown finally.
For lamellar structures, a layer by layer growth mechanism has been found atearly stage of solidification. After the formation of nucleus with hcp layers, solid-likeatoms born from liquid attached to nucleus. This will form the new hcp layer parallelto the old ones. Few defects are observed in final configuration. For this reason,lamellar structure is more stable in heating process than fivefold twins. With theincreasing temperature, inner defects appeared accompanying to surface premeltingand both of them accelerated the melting of nanoparticles.
The structural heredity of nanoparticles during nucleation has been found. Inother words, the structures of embryos in early stage determine the final structures toa great extent, e.g. whether it forms fivefold twins and lamellar structures. For smallnanoparticles, the magic number determines their shape and structures, and thus theirenergy minimized. However, in our simulations, completely different structuresmaybe caused by a slight change of simulation conditions. This is related with therandomness of choosing structures. With the increasing sizes of nanoparticles, therandomness enhances and thus the same simulation conditions may produce differentresults.
3. Structural evolution of bulk Fe during solidification process
In the simulations of bulk Fe materials, monocrystal, fivefold twins and lamellarstructure have been identified during nucleation process and their structural evolutions have been discussed in detail. Significant dependences are lacking for final atomicconfiguration on the simulation temperature, which indicates the existence ofrandomness of structure choosing. The growth mechanisms of fivefold twins andlamellar structure are similar with that in nanoparticle, while monocrystal experiencetwo obvious stages. At the early stage of nucleation several nucleus are formed andgrow, when they coalesce with each other through lots of hcp planes. At the stage ofstructure optimization, most hcp planes disappear and monocrystal finally form.
Inside the irregular shape of the nucleus of fivefold twins, the twinningboundaries, consisting of hcp atoms, joint with each other. Several tetrahedra joinedtogether to form fivefold twins, which are formed by9twinning axes. Due to theproportion of amorphous atoms is higher than67%, temperature disturbance andcontinuous cooling process have been applied. Further study found it is difficult tosignificantly affect the atomic percentage of fivefold twins with small temperaturedisturbance (±10K), while continuous cooling process (cooling rate0.25K/ps) willlead to a remarkable change of structure and after that nearly one fourth atomsremained amorphous.
本论文主要包含以下三个方面的内容：
1.Fe纳米颗粒凝固与熔化过程的热力学分析
研究发现尺寸效应对Fe纳米颗粒的热力学性质会造成明显影响。由于表面能的存在,尺寸越小的纳米颗粒其熔点就越低,早在1909年Pawlow就对纳米颗粒的尺寸与熔点之间的关系进行了研究,并认为二者关系可以通过描述。在后续的研究中,上式逐步演化为二者均描述了纳米颗粒熔点与体材料熔点变化值与其尺寸的关系,在一定假设下这种关系可以看作是线性关系,其不同之处在于线性关系的自变量分别为1/R和N-1/3。根据我们的实验结果对比发现使用N-1/3时吻合度更高。在此基础上我们对Fe113到Fe9577的熔点(Tmcluster),凝固点(Tscluster)以及平衡相变点(Tequilibrium cluster)与N-1/3的线性关系进行了研究。通过拟合获得体材料平衡相变点Tequilibrium(∞)=1833.3K,与体材料Fe的实验值1811K十分接近,且明显好于之前的研究成果。
此外我们还发现模拟中使用不同的变温速率(0.05～25K/ps)也会对纳米颗粒的热力学性质造成影响。在变温速率较低时(0.05～0.25K/ps),纳米颗粒具有充足的时间进行结构弛豫,因此其熔点、凝固点以及平衡相变点在较小的范围内变化,在此条件下拟合获得的体材料熔点数据更接近于实验值。
2.Fe纳米颗粒凝固与熔化过程的结构演变
本论文中使用CTIM-2方法对纳米颗粒凝固及熔化过程中的结构演化进行了分析,发现凝固的纳米颗粒中固相均由fcc和hcp原子组成,结构类型主要包括五重孪晶(fivefold twins)、层状结构(lamellar structure)以及介于上述二者之间的混合结构。通常认为Fe在常温常压下为bcc结构,在1185K以上时转变为fcc结构。但近年来的研究表明,纳米尺寸下的fcc-Fe是可以保持结构稳定的,我们的结果也证明了这一点。
对五重孪晶结构的研究发现,在凝固初期,当数个呈一定夹角的hcp原子层连续生成并相交于一处时就会形成五重孪晶。在晶体生长过程中纳米颗粒中会出现多个相邻的五重孪晶结构,同时伴随有位错的形成。进入结构弛豫阶段后随着晶面及晶轴的调整,位错逐步消失。但由于五重孪晶的结构特性,凝固获得的构型中仍存在内部缺陷。而在其熔化过程中随着温度升高,内部缺陷逐步增加,随后出现表面预熔,纳米颗粒在内部外部双重作用下逐步熔化。
对层状结构的研究发现。凝固过程中其早期的生长方式为逐层生长,在形成了带有hcp原子层的晶胚后,新生成的固相原子附着于晶胚之上,同时伴随着结构调整形成新的与原有晶面平行的hcp层。如此循环往复最终形成了由fcc和hcp原子组成的原子层交替排列而成的层状结构。最终的构型中基本没有内部缺陷,因此其在熔化过程中呈现了更好的稳定性。随着温度升高,内部缺陷早于表面熔化出现,二者同时作用加速了颗粒的熔化。
通过对比我们认为在纳米颗粒的形核过程中存在结构的遗传性,早期晶胚的结构在很大程度上决定了纳米颗粒最终结构是五重孪晶还是层状结结构。虽然对于小尺寸的纳米颗粒来说，幻数（magic number）决定了其外形和结构，从而起到了将一些对称点群构型能降至最低的作用，但在我们实际模拟中，模拟条件的变化仍可能导致纳米颗粒形成完全不同的结构，这可以理解为结构选择的随机性。随着纳米颗粒尺寸的增加随机性会增强，完全相同的模拟条件仍可获得不同的结果。
3. Fe体材料凝固过程中的结构分析
在对纳米颗粒结构研究的基础上我们对体材料Fe的形核过程进行研究。通过结构研究发现模拟获得的最终构型包括带有晶界的fcc单晶结构、五重孪晶结构以及层状结构。模拟温度与最终构型间并无直接关联，说明晶体的结构选择存在一定的随机性。而从其形成机制来看，层状结构与五重孪晶的生长机制与在纳米颗粒中类似，而单晶结构则出现了两次明显的结构变化。在形核初期体系内同时出现了多个晶胚并同时生长并融合，形成大量的hcp晶面。而在体系的结构优化中大部分hcp晶面逐步萎缩并消失，只有少数得以保留，最终形成了单晶结构。
对五重孪晶结构分析发现，其晶核外形呈不规则形状，内部由hcp原子组成的孪晶面彼此相连形成了五重孪晶结构。晶核中共有9个晶轴，晶轴间共用晶面，彼此相连形成了四面体网格。由于最终构型中非晶态原子占比高达67.59%，我们在模拟中加入温度扰动、连续降温等手段以考察其对体系结构的影响。结果表明小幅度的温度扰动无法给体系进一步凝固提供足够的驱动力。而在连续降温过程中五重孪晶发生了内部结构优化，但仍存在相当数量的非晶态原子，主要分布于数个相对完整的五重孪晶结构之间。
In this thesis, the thermaldynamic properties and structural transformation during solid-liquid phase transition of nanoscaled Fe have been studied. For Fe nanoparticles, previous studies mainly focused on the variations of thermaldynamic properties and structural transformation in solidification, melting and sintering processes. However, to our knowledge, few researchers have systematically investigated (i) the relaitonship between thermaldynamic properties of nanoparticles and bulk materials and (ii) quantitative analysis of structural evolution. Moreover, different with bcc-Fe, less attention have been paid on fcc-Fe, which is proved stable at room temperature in nanoscaled material in previous studies.
On the basis of above considerations, the detailed solid-liquid transition process of nanoscaled Fe has been studied by molecular dynamics (MD) in this thesis. Cluster type index method (CTIM) has been employed for structure analysis. The variation of thermaldynamic properties and detailed structural evolution during liquid-solid transition process of Fe nanoparticles have been discussed. Furthermore, the detailed structural evolution during solidification process of bulk Fe have been studied.
The major contents of this dissertation are epitomized as follows:
1. Thermodynamics analysis of Fe nanoparticles during solidification and melting
It is well-known that size effects may significantly affect thermodynamic properties of nanoparticles. The melting point of small nanoparticles is lower than that of larger ones due to the existance of surface energy. In1909, Pawlow investigated the relationship between melting point and particle size and modeled it The follow-up studies modified this model several times and two main versions, and have been derived. Both of these two models describe the relation between the difference of melting points of nanoparticle and bulk Fe and the size of nanoparticle. In some specific assumptions the difference is caused by the two variables1/R and N-1/3of the linear relationship. Our results indicate that the latter model is more accurate in predicting the melting points Tm/cluster, solidification points Ts/cluster and equilibrium points Tequilibrium/cluster of Fe nanoparticles in the range of Fe113～Fe9577. The equilibrium point of bulk material Tequilibrium(∞)=1833.3K obtained by fitting procedure is strikingly close to the experimental data of bulk Fe (1811K) and is much better than previous results.
Moreover, the cooling/heating rates (0.05-25K/ps) also affected the thermaldynamics properties of nanoparticles. In low cooling/heating rates (0.05～0.25K/ps), nanoparticles have enough time to relax their structures and thus the melting points, solidification points and equilibrium points fluctuate in a small range. The melting point obtained in this condition is closer to experimental results.
2. Structural evolution of Fe nanoparticles during solidification and melting
CTIM-2has been employed to analyze the structural evolution of Fe nanoparticles during nucleation and melting process. The configurations obtained after solidification indicate that the solid phase in nanoparticles is mainly consisted of fcc and hcp atoms. Two main structure, fivefold twins and lamellar structure, have been found. In common belief, Fe belongs to bcc structures in ambient pressure and temperature and transforms to fcc structures at the temperature higher than1185K. Actually, researches in resent years showed that nanoscaled fcc-Fe could be stable in ambient conditions, which is in accordance with our results.
At the early stage of nucleation of fivefold twins, we found that they are built by continuous growth of several hcp layers with the included angle fixed. Severaladjacent fivefold twins appeared and accompanied with formation of dislocations. Atthe stage of relaxation, the twinning boundaries and axes adjusted with each other andthe dislocations disappeared gradually while few internal defects remained due to itsstructural characteristics. These defects will significantly affect the melting behavior.With temperature increasing, there is an increasing number of defects insidenanoparticles, meanwhile surface premelting takes place. By the influence of bothexternal and internal defects, the nanoparticle becomes meltdown finally.
For lamellar structures, a layer by layer growth mechanism has been found atearly stage of solidification. After the formation of nucleus with hcp layers, solid-likeatoms born from liquid attached to nucleus. This will form the new hcp layer parallelto the old ones. Few defects are observed in final configuration. For this reason,lamellar structure is more stable in heating process than fivefold twins. With theincreasing temperature, inner defects appeared accompanying to surface premeltingand both of them accelerated the melting of nanoparticles.
The structural heredity of nanoparticles during nucleation has been found. Inother words, the structures of embryos in early stage determine the final structures toa great extent, e.g. whether it forms fivefold twins and lamellar structures. For smallnanoparticles, the magic number determines their shape and structures, and thus theirenergy minimized. However, in our simulations, completely different structuresmaybe caused by a slight change of simulation conditions. This is related with therandomness of choosing structures. With the increasing sizes of nanoparticles, therandomness enhances and thus the same simulation conditions may produce differentresults.
3. Structural evolution of bulk Fe during solidification process
In the simulations of bulk Fe materials, monocrystal, fivefold twins and lamellarstructure have been identified during nucleation process and their structural evolutions have been discussed in detail. Significant dependences are lacking for final atomicconfiguration on the simulation temperature, which indicates the existence ofrandomness of structure choosing. The growth mechanisms of fivefold twins andlamellar structure are similar with that in nanoparticle, while monocrystal experiencetwo obvious stages. At the early stage of nucleation several nucleus are formed andgrow, when they coalesce with each other through lots of hcp planes. At the stage ofstructure optimization, most hcp planes disappear and monocrystal finally form.
Inside the irregular shape of the nucleus of fivefold twins, the twinningboundaries, consisting of hcp atoms, joint with each other. Several tetrahedra joinedtogether to form fivefold twins, which are formed by9twinning axes. Due to theproportion of amorphous atoms is higher than67%, temperature disturbance andcontinuous cooling process have been applied. Further study found it is difficult tosignificantly affect the atomic percentage of fivefold twins with small temperaturedisturbance (±10K), while continuous cooling process (cooling rate0.25K/ps) willlead to a remarkable change of structure and after that nearly one fourth atomsremained amorphous.
引文
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