液态金属银凝固过程及微观结构演变特征的模拟研究
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摘要
本文对液态金属快速凝固技术和理论的发展与现状、纳米团簇的结构与能量以及分子动力学(MD)模拟技术的发展历程等方面进行了简要回顾。对MD模拟方法从原理到实现的各个环节、从基本的NVE系综到能够与实验结果进行直接对比分析的NPT系综进行了分析与整理,修正了有关文献中NPH和NPT系综计算方程中的错误,并对随机数、初始位形、元胞链表等MD算法进行了改进。发展完善了以HA-Pair为基础的基本团簇分析法(Basic Cluster Analysis,BCA):将CTIM(Cluster Type Index Method)扩展为CTIM-2,以表征更多种类的基本团簇;提出用基本团簇类型来标识其中心原子的分类方法(Basic Cluster Label-ing,BCL),BCL结合三维图形技术可简单清晰地描述相结构和纳米团簇的对称特征;并开发了配套的三维可视化图形分析软件。
采用quantum Sutton-Chen(QSC)多体势对液态金属银在不同冷速下的凝固过程进行了分子动力学模拟。结果表明,冷速对凝固的最终结构具有关键性作用,且形成非晶的临界冷速约为10~(13)K/s。高于此冷速凝固,可得到以二十面体为主要特征的金属玻璃。低于临界冷速,能形成hcp和fcc基本团簇按不同比例共存的混合结构甚至hcp、fcc晶体。且混合共存体中fcc和hcp中心原子有随机分布和规则分层两种形式。模拟得到伊辛模型为↑↑↓↓和↓↓↓↑(hcp和fcc中心原子单层和双层交替)的4H和12R分层晶体。随着冷速下降,随机分布先于规则分层形成;结晶温度Tc、fcc结构在凝固体系中的比例、体系结构的对称度都不断升高;但hcp结构和1422键型的比例却是先增后减,增减趋势发生转换的冷速约为5.0×10~(12)K/s。
细致模拟和深入分析表明:快冷结晶过程经历了两次相变三种状态:第一次液-固相变,亚稳bcc结构而非稳定的fcc结构首先从液态中形成;而且初始结晶温度Tic随冷速下降而升高。第二次固-固相变,亚稳bcc结构转变成不同的更加稳定的结构。由此可得快凝过程遵循“step rule”规则,结合形成自由能垒和快凝的特点合理解释了“随冷速降低,Cu和Ag结晶体系中hcp结构的比例先增后减”的现象。另外,同一冷速下多次模拟得到的固态结构并不相同,以及不同冷速下得到的凝固结构也并不总是遵循“冷速越慢体系能量最低”的关系,因此运动学因素对凝固过程及最终结构有重要影响。
对2.5～10nm的非幻数纳米液滴,在冷速10~3和10~2K/ns下的快凝模拟表明:绝大多数凝固过程包含一次一级相变和一次连续相变;而且随着尺寸增大,初始凝固温度Tis平均值升高,凝固得到的纳米颗粒中,原子平均能量降低且趋于块体系统的平均能量。Tis的平均值与尺寸的关系,多次凝固中Tis所表现的混沌特征,以及晶体、二十面体、十面体等类型的纳米颗粒的比例等模拟结果都与实验结果符合得很好。除了规则晶体、十面体和二十面体以外,借助BCL和三维可视化方法,还发现了一类结构新颖的纳米颗粒—表面异构体(surface-isomers)。从几何结构来看,它们是在规则的晶体、十面体或二十面体外面再增加几个特殊排列方式(...ABCB或...ABCBA等)的密排原子层构成。虽然外层结构的改变在表面引入了一些非密排的(1 0 0)面,但外形更接近球体,整体能量仍可降低,特别是那些具有良好的全局(三重或五重)对称性的颗粒,应该足够稳定以致能在实验室观察到。实际上具有Umb-Dh结构的AuPd和AuCu合金颗粒已经在实验室观察到;我们模拟得到的银Fractal-Ih颗粒与Hendy对铅的模拟计算结果也完全吻合。
The development of the rapid cooling theory and technology, the structure and en-ergy of nano-clusters, and the history of the molecular dynamics (MD) simulation arebrie?y reviewed in this thesis firstly. The MD principles and implementations for particu-lar ensembles from NVE to NPT which can be compare to experiment results directly, aresummarized compactly. Faults in some literatures for isobaric ensembles have been cor-rected; MD algorithms for random number, initial configuration and velocity, cell-list andso on are also improved. Basic Cluster Analysis (BCA) which is on the base of HA-pairs,is improved: extending CTIM to CTIM-2 that can express more basci clusters; combiningBasic Cluster Labeling (BCL)– and 3D graphics, the structure of phases and the symme-try of nanoparticles can be described clearly and tersely; and a corresponding 3D visualsoftware for structure analysis has been developed.
The MD simulations for metal silver solidification at different cooling ratesγhavebeen performed with Quantum Sutton-Chen potential. The analysis reveals thatγis cru-cial for the final solid structure and the critical for amorphous forming is about 1013K/s.Whenγ<γc, the mixture of fcc and hcp basic clusters with different proportions evenhcp and fcc crystals can be formed. Moreover, both the scattering and layering states areaffirmed in mixtures; and the former usually occurs at higherγ. Layering crystals of 4Hand 12R whose Ising models are↑↑↓↓and↓↓↓↑respectively, have been obtained. Withγdecreasing, the crystallizing point Tc, the percentage of fcc basic cluster (1421 HA-pair),the degree of symmetry are all increasing; while the proportions of hcp cluster (1422HA-pair) rise firstly and then decline, and the summit appears at about 5.0×10~(12) K/s.
More meticulous calculations and analysis reveal that there are twice phase transi-tions in rapid crystal processes. The first is from liquid to metastable (transitional) bccphase, and the initial crystallizing point Tic increases withγdecreasing. The second isfrom the transitional bcc phase to more stable solid states whose structure depends uponthe cooling rate. This reveals that rapid cooling follows the’step rule’; taking into ac-count the barrier of forming free energy and the characteristic of rapid cooling, it is canbe made clear that for the crystal system of silver and copper, the proportions of hcp struc-tures ascend firstly and then descend withγdecreasing. In addition, the final structuresfrom different runs are usually different from each other even at an identicalγ; the energyof final states is not always decreasing withγdecrease; Therefore the kinetic acts as an important role in cooling processes and final structures.
Most freezing processes for 2.5～10nm Ag nanodroplets containing non-magic num-ber of atoms at cooling rate 10~3 and 10~2 K/ns show that there are a first order and a contin-uous phase transitions in turn. With the size increasing, the mean of Tis is increasing whilethe average of energy per atom in nanoparticles (at 273K) is decreasing and closing to thebulk case. The percentages of crystal, icosahedron, decahedron and other structures, thedependence of T_(is) on the size and its’chaos characteristic are all in good agreement withthe previous experiment results. Besides regular crystalline, decahedral and icosahedralnanoparticles, some very interesting novelty morphologies—surface-isomers—have alsobeen found with the help of BCA and 3D graphics. Surface-isomers can be constructedon the base of a regular crystal, decahedron, icosahedron and so on, by adding few layerswith specific atomic arrangement, such as ABCB, ABCBA. Some (100) facets whichare not close-packed introduced into surface-isomars, but they make the outmost surfacecloser to sphere than its’regular kernel, and reduce the total energy, enhance the stabil-ity. Therefore the surface-isomars should be stable enough to be observed in experiment,especially for those with well global (three- or five-fold) symmetry. Alloy nanoparticlesof AuPd and AuCu holding Umb-Dh structure have in fact been obtained in experiment.And the Fractal-Ih obtained in our simulations is close consistent with the recent calcula-tion about lead clusters.
采用quantum Sutton-Chen(QSC)多体势对液态金属银在不同冷速下的凝固过程进行了分子动力学模拟。结果表明,冷速对凝固的最终结构具有关键性作用,且形成非晶的临界冷速约为10~(13)K/s。高于此冷速凝固,可得到以二十面体为主要特征的金属玻璃。低于临界冷速,能形成hcp和fcc基本团簇按不同比例共存的混合结构甚至hcp、fcc晶体。且混合共存体中fcc和hcp中心原子有随机分布和规则分层两种形式。模拟得到伊辛模型为↑↑↓↓和↓↓↓↑(hcp和fcc中心原子单层和双层交替)的4H和12R分层晶体。随着冷速下降,随机分布先于规则分层形成;结晶温度Tc、fcc结构在凝固体系中的比例、体系结构的对称度都不断升高;但hcp结构和1422键型的比例却是先增后减,增减趋势发生转换的冷速约为5.0×10~(12)K/s。
细致模拟和深入分析表明:快冷结晶过程经历了两次相变三种状态:第一次液-固相变,亚稳bcc结构而非稳定的fcc结构首先从液态中形成;而且初始结晶温度Tic随冷速下降而升高。第二次固-固相变,亚稳bcc结构转变成不同的更加稳定的结构。由此可得快凝过程遵循“step rule”规则,结合形成自由能垒和快凝的特点合理解释了“随冷速降低,Cu和Ag结晶体系中hcp结构的比例先增后减”的现象。另外,同一冷速下多次模拟得到的固态结构并不相同,以及不同冷速下得到的凝固结构也并不总是遵循“冷速越慢体系能量最低”的关系,因此运动学因素对凝固过程及最终结构有重要影响。
对2.5～10nm的非幻数纳米液滴,在冷速10~3和10~2K/ns下的快凝模拟表明:绝大多数凝固过程包含一次一级相变和一次连续相变;而且随着尺寸增大,初始凝固温度Tis平均值升高,凝固得到的纳米颗粒中,原子平均能量降低且趋于块体系统的平均能量。Tis的平均值与尺寸的关系,多次凝固中Tis所表现的混沌特征,以及晶体、二十面体、十面体等类型的纳米颗粒的比例等模拟结果都与实验结果符合得很好。除了规则晶体、十面体和二十面体以外,借助BCL和三维可视化方法,还发现了一类结构新颖的纳米颗粒—表面异构体(surface-isomers)。从几何结构来看,它们是在规则的晶体、十面体或二十面体外面再增加几个特殊排列方式(...ABCB或...ABCBA等)的密排原子层构成。虽然外层结构的改变在表面引入了一些非密排的(1 0 0)面,但外形更接近球体,整体能量仍可降低,特别是那些具有良好的全局(三重或五重)对称性的颗粒,应该足够稳定以致能在实验室观察到。实际上具有Umb-Dh结构的AuPd和AuCu合金颗粒已经在实验室观察到;我们模拟得到的银Fractal-Ih颗粒与Hendy对铅的模拟计算结果也完全吻合。
The development of the rapid cooling theory and technology, the structure and en-ergy of nano-clusters, and the history of the molecular dynamics (MD) simulation arebrie?y reviewed in this thesis firstly. The MD principles and implementations for particu-lar ensembles from NVE to NPT which can be compare to experiment results directly, aresummarized compactly. Faults in some literatures for isobaric ensembles have been cor-rected; MD algorithms for random number, initial configuration and velocity, cell-list andso on are also improved. Basic Cluster Analysis (BCA) which is on the base of HA-pairs,is improved: extending CTIM to CTIM-2 that can express more basci clusters; combiningBasic Cluster Labeling (BCL)– and 3D graphics, the structure of phases and the symme-try of nanoparticles can be described clearly and tersely; and a corresponding 3D visualsoftware for structure analysis has been developed.
The MD simulations for metal silver solidification at different cooling ratesγhavebeen performed with Quantum Sutton-Chen potential. The analysis reveals thatγis cru-cial for the final solid structure and the critical for amorphous forming is about 1013K/s.Whenγ<γc, the mixture of fcc and hcp basic clusters with different proportions evenhcp and fcc crystals can be formed. Moreover, both the scattering and layering states areaffirmed in mixtures; and the former usually occurs at higherγ. Layering crystals of 4Hand 12R whose Ising models are↑↑↓↓and↓↓↓↑respectively, have been obtained. Withγdecreasing, the crystallizing point Tc, the percentage of fcc basic cluster (1421 HA-pair),the degree of symmetry are all increasing; while the proportions of hcp cluster (1422HA-pair) rise firstly and then decline, and the summit appears at about 5.0×10~(12) K/s.
More meticulous calculations and analysis reveal that there are twice phase transi-tions in rapid crystal processes. The first is from liquid to metastable (transitional) bccphase, and the initial crystallizing point Tic increases withγdecreasing. The second isfrom the transitional bcc phase to more stable solid states whose structure depends uponthe cooling rate. This reveals that rapid cooling follows the’step rule’; taking into ac-count the barrier of forming free energy and the characteristic of rapid cooling, it is canbe made clear that for the crystal system of silver and copper, the proportions of hcp struc-tures ascend firstly and then descend withγdecreasing. In addition, the final structuresfrom different runs are usually different from each other even at an identicalγ; the energyof final states is not always decreasing withγdecrease; Therefore the kinetic acts as an important role in cooling processes and final structures.
Most freezing processes for 2.5～10nm Ag nanodroplets containing non-magic num-ber of atoms at cooling rate 10~3 and 10~2 K/ns show that there are a first order and a contin-uous phase transitions in turn. With the size increasing, the mean of Tis is increasing whilethe average of energy per atom in nanoparticles (at 273K) is decreasing and closing to thebulk case. The percentages of crystal, icosahedron, decahedron and other structures, thedependence of T_(is) on the size and its’chaos characteristic are all in good agreement withthe previous experiment results. Besides regular crystalline, decahedral and icosahedralnanoparticles, some very interesting novelty morphologies—surface-isomers—have alsobeen found with the help of BCA and 3D graphics. Surface-isomers can be constructedon the base of a regular crystal, decahedron, icosahedron and so on, by adding few layerswith specific atomic arrangement, such as ABCB, ABCBA. Some (100) facets whichare not close-packed introduced into surface-isomars, but they make the outmost surfacecloser to sphere than its’regular kernel, and reduce the total energy, enhance the stabil-ity. Therefore the surface-isomars should be stable enough to be observed in experiment,especially for those with well global (three- or five-fold) symmetry. Alloy nanoparticlesof AuPd and AuCu holding Umb-Dh structure have in fact been obtained in experiment.And the Fractal-Ih obtained in our simulations is close consistent with the recent calcula-tion about lead clusters.
引文
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