纳米结构金属及合金热力学性能的原子模拟
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摘要
本文以几种典型金属及合金的纳米结构为研究对象,运用分析型嵌入原子模型,从原子尺度系统地研究了纳米结构的一些基本热力学性能,如熔化、热膨胀、热振动、原子扩散等。得到了与已有实验相一致的结果,并对一些实验结果进行了解释。
本文首先简要地介绍了纳米结构的一些基本概念和当前有关纳米材料结构和热力学性能的研究进展,及用到的理论与方法,包括分析型嵌入原子模型,分子动力学方法和结构分析技术等,然后说明了运动上述理论和技术计算热力学性能的基本方法。
利用静态计算方法,从能量的角度计算了Ag、Pt纳米颗粒的晶格常数。计算的结果与热力学的预测值符合得很好。在高比表面率的作用下,纳米颗粒的平均晶格常数随颗粒尺寸的降低而减小,晶格收缩率与颗粒粒径的倒数间存在近似线性关系。采用分子动力学弛豫技术,从平均原子键长的角度研究了纳米颗粒的非均匀晶格畸变。发现纳米颗粒的表层晶格收缩量明显比内核区域大,并且表层区表现出明显的非均匀晶格收缩。当颗粒尺寸大到一定值时,非均匀的表层晶格收缩主要集中于表层2– 3个晶格常数的厚度。受非均匀晶格畸变的影响,实验上测量的颗粒晶格收缩量介于计算的系统平均收缩量与内核平均收缩量之间。
采用分子动力学方法计算了颗粒直径介于2– 9 nm (颗粒包含原子数从537–28475)的BCC结构难熔金属V纳米颗粒的熔化行为。发现受表面效应的影响,V纳米颗粒的熔化温度比常规晶体V低,并且随颗粒尺寸的减小而减小,计算的结果与热力学液滴模型的预测值符合得很好。对于V纳米颗粒的熔化过程,可以描述为两个阶段:首先是表层的逐步预熔,预熔层的厚度大约为2–3个晶格常数;其后就是整个颗粒的瞬间完全熔化。纳米颗粒熔化时的熔化焓与颗粒粒径的倒数间存在近似线性反比的关系。颗粒在低温时的扩散主要局限于表层原子的扩散,由于随颗粒尺寸的减小,表面原子占有数增加,所以小尺寸颗粒的扩散系数大。利用原子径向均方振动幅度(RMSVA)研究了颗粒表层原子的热振动,表层原子的非谐效应明显增强。纳米液滴的凝固结晶模拟表明,相对于同尺寸纳米颗粒的熔化温度而言,纳米液滴凝固时所需的有效过冷度随液滴尺寸的减小而降低。液滴凝固时在其表面处形核。受颗粒内部密堆积结构和表面效应的影响,FCC结构金属的小尺寸液滴凝固后得到了二十面体结构。
从计算原子的Voronoi胞体积出发,研究了纳米晶体Ag的热膨胀性能。受无序晶界结构的影响,相对于晶粒内部原子,晶界原子表现出一定的过剩体积。纳米晶体的热膨胀与完整晶体基本接近。纳米晶体中晶粒的热膨胀比完整晶体略高,而晶界的热膨胀比完整晶体低。晶粒与晶界的相互作用致使纳米晶体的热膨胀与平均晶粒尺寸基本无关。
利用分子动力学方法计算了纳米晶体Ni的原子振动性能。结果表明,随温度的升高,纳米晶体表现出与常规晶体类似的声子软化现象,并且其软化效应主要由晶粒相原子的振动所引起。从300 K到900 K的温度范围内,晶界相的偏振动态密度基本上与温度无关。在简谐近似条件下计算了纳米晶体的基本热力学量,发现同常规晶体相比,纳米晶体的比热和振动熵升高,振动自由能降低。如果将纳米晶体看作是由晶粒相和晶界相构成的一种复合材料,纳米晶体的振动热力学量可以从对应两相的热力学量线性叠加得到。由于纳米晶体中界面增强的非谐效应,纳米晶体的德拜温度比常规晶体低,并且随平均晶粒尺寸的减小而减小。
采用纳米晶体的Voronoi元胞构建法,通过外推纳米晶体的平均晶粒尺寸至无限小值,得到了非晶相结构。利用分子动力学方法模拟了纳米晶体Ag (平均晶粒尺寸介于1.31– 12.12 nm)的熔化行为。结果表明纳米晶体中连续的熔化过程起始于晶界。随着纳米晶体的熔化,表征液态结构的三种典型键对(1551)、(1431)和(1541)迅速增加。纳米晶体的熔化温度比常规晶体低,纳米晶体的熔化温度随晶体平均晶粒尺寸的变化表现为两个特征区域。对于纳米晶体Ag,当平均晶粒尺寸大于约4 nm时,熔化温度随晶粒尺寸的减小而减小;随着平均晶粒尺寸的进一步减小,纳米晶体Ag的熔化温度基本上不再随晶粒尺寸而变化。这是因为支配纳米晶体熔化温度的主导相由晶粒部分转变为晶界部分。由于晶体和非晶体之间的本质结构差异,导致非晶体Ag的固液转变温度明显比纳米晶体的熔化温度低。
对比研究了常规过冷液体凝固结晶和纳米晶体熔化过程中的微观结构演变。过冷态液体凝固结晶时的过程表现为三个特征阶段:形核、核的快速长大和缓慢的结构弛豫过程。根据经典形核理论,液体凝固时的均匀形核需要达到一定的过冷度,研究了过冷度对凝固结晶过程和结晶后材料织构的影响。运用Johnson-Mehl-Avrami (JMA)方程讨论了液体结晶到固体的转变动力学。
利用分子动力学方法结合分析型EAM模型,研究了纳米晶体Ag的等温晶粒生长行为,分析讨论了退火温度和晶粒尺寸对纳米晶体晶粒生长行为的影响。同常规多晶体材料的晶粒生长一样,高退火温度和小晶粒尺寸增强了纳米晶体的晶粒生长。纳米晶体Ag的等温晶粒生长曲线大致可以描述为两个阶段:指数生长和线性弛豫阶段。在纳米晶体的晶粒生长过程中,除了晶界迁移机制外,还存在颗粒的旋转机制。另外,晶体生长过程中形成的位错或层错在纳米晶体的生长过程中起到了一个类似中介的作用。
通过构建一个简单的热力学模型,结合分析型EAM理论,计算了Au和Pt的自由纳米颗粒形成AuPt合金纳米颗粒的形成焓。讨论了在纳米尺度下表面效应对常规不互溶金属的合金纳米颗粒的合金化能力和相稳定性的影响。结果表明,合金纳米颗粒的形成焓除表现出与常规体合金类似的随合金组分变化的规律外,还表现出显著的尺寸相关性,并且存在尺寸效应和组分效应间的竞争。对比常规不互溶合金的正形成焓,合金纳米颗粒在小尺寸和稀固溶组分的条件下具有负的形成焓,这表明在纳米尺度下,不互溶体系的合金化能力和相稳定性增强。另外,表面偏聚作用导致不互溶体系的合金纳米颗粒在比较大的尺寸范围表现出负形成焓。分子动力学模拟表明,成分和结构均匀的AuPt合金纳米颗粒在升温时趋向于形成核壳结构。
研究了FeAl合金纳米颗粒熔化及其纳米液滴的冷却凝固过程。同单元素的金属纳米颗粒类似,颗粒表层存在明显的预熔现象。合金纳米颗粒的熔化温度随颗粒尺寸的减小而减小,与热力学模型预测的纳米颗粒的熔化温度随颗粒尺寸的变化规律一致。合金纳米液滴的冷却凝固表明,液滴的合金组分对其冷却凝固性能有着重要的影响。对于Fe、Al成分比(Fe : Al)接近3 : 1的纳米液滴,凝固后得到类似于无序固溶体结构的晶态纳米颗粒,结晶过程中于液滴的表层形核;而对于成分比接近1 : 1的液滴,在比较低的冷却速率下仍然得到了非晶态结构。
本文所使用的分析型嵌入原子方法通过拟合体原子的性质得到,但无需调整任何参数即能预测纳米结构的热力学性质,并且得到与实验相符合的结果,说明该理论简便可行、具有普适性和系统性。为系统建立普适的原子尺度材料设计理论奠定了基础。
In the present thesis, with the analytic embedded atom method (EAM), thethermodynamic properties, such as melting behavior, thermal expansion, atomicthermal vibration and atomic self-diffusion of typical nanostructured metals andalloys are studied systematically. Some of the results have a good agreement withexperimental data and theoretical predictions.
According to the theory that a stable system has a minimum energy, themean lattice contraction of nanoparticles have been calculated with a static method.It is found that the lattice contraction ratio decreases linearly with the reciprocalof particle size. The size and temperature effects on lattice distortion of Ag andPt nanoparticles have been investigated in terms of atomic mean bond length us-ing molecular dynamics simulations. The average values of lattice contractionover the whole system are larger than that of the experimental data, and the av-erage value of lattice contraction in the inner core has a better agreement withthe experiment results. This phenomenon is mainly resulted by inhomogeneouslattice distortion. The surface distortion and the size effect on the inner core dis-tortion are remarkable. As the grain size increases to a certain degree, the inho-mogeneous surface lattice distortion is mainly localized to the outer shell with athickness of 2-3 lattice parameters.
Molecular dynamics has been performed to study the melting evolution,atomic diffusion and vibrational behavior of BCC metal vanadium nanoparticleswith number of atoms ranging from 537 to 28475 (diameters around 2-9 nm). Theresults reveal that the melting temperature of nanoparticle is in inverse propor-tion to the reciprocal of nanoparticle size linearly, and in good agreement with theprediction of thermodynamic liquid-drop model. For the vanadium nanoparticle,the melting process can be described as two stages, firstly the stepwise premelt-ing on the surface layer with a thickness of 2-3 perfect lattice constant, and thenthe abrupt overall melting of the whole cluster. The heat of fusion of nanoparticleis also in linearly inverse proportion to the reciprocal of nanoparticle size. Thediffusion is mainly localized to the surface layer at low temperature and increasewith the reduction of nanoparticle size at the same temperature. The radial meansquare vibration amplitude (RMSVA) is developed to study the anharmonic effect on surface shells. The simulation of solidification of nanodroplets indicates thatthe effective supercooled degree decreases with the reduction of droplet size. Thenucleation in the process of solidification occurs on the surface layer of droplet.Affected by close packed structure and surface effect, the small droplets of FCCmetals exhibit structural characteristic of icosahedron after solidification.
The thermal expansion of nanocrystalline Ag is investigated by calculatingatomic Voronoi volume. Affected by grain boundary structure, the atoms ongrain boundary exhibit excess volume against atoms in the interior of grain. Thethermal expansion of grains in nanocrystal is slightly higher than that of a perfectlattice, while the thermal expansion of grain boundaries in nanocrystal is lowerthan that of a perfect lattice. The thermal expansion of nanocrystals is almostindependent on mean grain size.
The molecular dynamics simulations have been performed to study the vi-brational properties of nanocrystalline nickels. The obtained results reveal thatthe similar phonon softening as in the perfect lattice mainly focuses on grainsin nanocrystalline materials, and the partial vibrational density of states of grainboundary phase is almost insensitive to temperature from 300 K to 900 K, espe-cially within the range of low frequency. The nanocrystalline materials have ahigher specific heat and vibrational entropy, and lower vibrational free energyrelative to the conventional crystals. Supposing the nanocrystalline material canbe treated as a composite constituted by grain and grain boundary (GB) phases,the vibrational thermodynamic properties can be well determined from the pro-portion of GBs and the corresponding thermodynamic properties of grain andGB phases. The Debye temperature of nanocrystalline materials is quantitativelylower than that of the conventional crystals and decreases with the reduction ofmean grain size.
In the atomic scale, the melting behaviors of nanocrystalline Ag with themean grain size ranging from 1.21 to 12.12 nm have been investigated with themolecular dynamics simulations, and a method to determine the melting temper-atures of the infinite polycrystalline nanostructured materials are presented. It isfound that the melting in the nanostructured polycrystals starts from their grainboundaries, and the relative numbers of the three typical bonded-pairs, (1551),(1431) and (1541) existing in the liquid phase increase rapidly with the evolve-ment of melting. The grain size variation of melting temperature exhibits twocharacteristic regions. As mean grain size above about 4 nm for Ag, the melt- ing temperatures decrease with decreasing grain size, and it can be estimatedfrom the size dependent melting temperature of the corresponding nanoparti-cles. However, with grain size further shrinking, the melting temperatures almostkeep a constant. This is because the dominant factor on the melting temperatureof nanocrystal shifts from grain phase to grain boundary. By extrapolating themean grain size of nanocrystal to an infinitesimal value, an amorphous phasehas been obtained from the Voronoi construction. As a result of fundamentaldifference in structure, the amorphous phase has a much lower solid-to-liquidtransformation temperature than that of nanocrystal.
Molecular dynamics simulations have been performed to obtain the atomic-scale details of crystallization from supercooled liquid. The radial distributionfunction and common neighbor analysis provide a visible scenario of structuralevolution in the process of phase transition. The crystallization from supercooledliquid is characterized by three characteristic stages: nucleation, rapid growth ofnucleus and slow structural relaxation. The homogeneous nucleation occurs at alarger supercooling temperature, which has an important effect on the process ofcrystallization and the subsequent crystalline texture. The kinetics of transitionfrom liquid to solid is well described by Johnson-Mehl-Avrami equation.
Isothermal grain growth behaviors, including the effect of temperature andmean grain size, of nanocrystalline Ag are investigated using the molecular dy-namics simulations. The small grain size and high temperature accelerate thegrain growth, it is the same as the conventional polycrystalline materials. Thegrain growth processes of nanocrystalline Ag are well characterized by an expo-nent growth curve, followed by a linear relaxation stage. Beside grain boundarymigration and grain rotation mechanisms, the dislocations (or stacking faults)sever as the intermediate role in the grain growth process.
The surface and size effects on the alloying ability and phase stability of im-miscible alloy nanoparticles have been studied with calculating the heats of for-mation of Au-Pt alloy nanoparticles from the single element nanoparticles of theirconstituents (Au and Pt) with a simple thermodynamic model and an analyticembedded atom method. The results indicated that, besides the similar composi-tional dependence of heat of formation as in bulk alloys, the heat of formation ofalloy nanoparticles exhibits notable size-dependence, and there exists a competi-tion between size effect and compositional effect on the heat of formation of im-miscible system. Contrary to the positive heat of formation for bulk-immiscible alloys, a negative heat of formation may be obtained for the alloy nanoparticleswith a small size or dilute solute component, which implies a promotion of thealloying ability and phase stability of immiscible system on a nanoscale. Thesurface segregation results in an extension of the size range of particles with anegative heat of formation. The molecular dynamics simulations have indicatedthat the structurally and compositionally homogeneous AuPt nanoparticles tendto form a core-shell structure with temperature increasing. The melting tempera-ture of FeAl alloy nanoparticles decreases linearly with the reciprocal of particlesize. In the solidification of alloy nanodroplets, the alloy component has an im-portant effect on the process of solidification and final structure.
Only by fitting the bulk properties of metals, the analytic EAM can predictthermodynamical properties of nanostructured materials without any parameterabout nanostructure. This work is helpful to establish the theory of materials de-sign in the atomic scale systematically.
本文首先简要地介绍了纳米结构的一些基本概念和当前有关纳米材料结构和热力学性能的研究进展,及用到的理论与方法,包括分析型嵌入原子模型,分子动力学方法和结构分析技术等,然后说明了运动上述理论和技术计算热力学性能的基本方法。
利用静态计算方法,从能量的角度计算了Ag、Pt纳米颗粒的晶格常数。计算的结果与热力学的预测值符合得很好。在高比表面率的作用下,纳米颗粒的平均晶格常数随颗粒尺寸的降低而减小,晶格收缩率与颗粒粒径的倒数间存在近似线性关系。采用分子动力学弛豫技术,从平均原子键长的角度研究了纳米颗粒的非均匀晶格畸变。发现纳米颗粒的表层晶格收缩量明显比内核区域大,并且表层区表现出明显的非均匀晶格收缩。当颗粒尺寸大到一定值时,非均匀的表层晶格收缩主要集中于表层2– 3个晶格常数的厚度。受非均匀晶格畸变的影响,实验上测量的颗粒晶格收缩量介于计算的系统平均收缩量与内核平均收缩量之间。
采用分子动力学方法计算了颗粒直径介于2– 9 nm (颗粒包含原子数从537–28475)的BCC结构难熔金属V纳米颗粒的熔化行为。发现受表面效应的影响,V纳米颗粒的熔化温度比常规晶体V低,并且随颗粒尺寸的减小而减小,计算的结果与热力学液滴模型的预测值符合得很好。对于V纳米颗粒的熔化过程,可以描述为两个阶段:首先是表层的逐步预熔,预熔层的厚度大约为2–3个晶格常数;其后就是整个颗粒的瞬间完全熔化。纳米颗粒熔化时的熔化焓与颗粒粒径的倒数间存在近似线性反比的关系。颗粒在低温时的扩散主要局限于表层原子的扩散,由于随颗粒尺寸的减小,表面原子占有数增加,所以小尺寸颗粒的扩散系数大。利用原子径向均方振动幅度(RMSVA)研究了颗粒表层原子的热振动,表层原子的非谐效应明显增强。纳米液滴的凝固结晶模拟表明,相对于同尺寸纳米颗粒的熔化温度而言,纳米液滴凝固时所需的有效过冷度随液滴尺寸的减小而降低。液滴凝固时在其表面处形核。受颗粒内部密堆积结构和表面效应的影响,FCC结构金属的小尺寸液滴凝固后得到了二十面体结构。
从计算原子的Voronoi胞体积出发,研究了纳米晶体Ag的热膨胀性能。受无序晶界结构的影响,相对于晶粒内部原子,晶界原子表现出一定的过剩体积。纳米晶体的热膨胀与完整晶体基本接近。纳米晶体中晶粒的热膨胀比完整晶体略高,而晶界的热膨胀比完整晶体低。晶粒与晶界的相互作用致使纳米晶体的热膨胀与平均晶粒尺寸基本无关。
利用分子动力学方法计算了纳米晶体Ni的原子振动性能。结果表明,随温度的升高,纳米晶体表现出与常规晶体类似的声子软化现象,并且其软化效应主要由晶粒相原子的振动所引起。从300 K到900 K的温度范围内,晶界相的偏振动态密度基本上与温度无关。在简谐近似条件下计算了纳米晶体的基本热力学量,发现同常规晶体相比,纳米晶体的比热和振动熵升高,振动自由能降低。如果将纳米晶体看作是由晶粒相和晶界相构成的一种复合材料,纳米晶体的振动热力学量可以从对应两相的热力学量线性叠加得到。由于纳米晶体中界面增强的非谐效应,纳米晶体的德拜温度比常规晶体低,并且随平均晶粒尺寸的减小而减小。
采用纳米晶体的Voronoi元胞构建法,通过外推纳米晶体的平均晶粒尺寸至无限小值,得到了非晶相结构。利用分子动力学方法模拟了纳米晶体Ag (平均晶粒尺寸介于1.31– 12.12 nm)的熔化行为。结果表明纳米晶体中连续的熔化过程起始于晶界。随着纳米晶体的熔化,表征液态结构的三种典型键对(1551)、(1431)和(1541)迅速增加。纳米晶体的熔化温度比常规晶体低,纳米晶体的熔化温度随晶体平均晶粒尺寸的变化表现为两个特征区域。对于纳米晶体Ag,当平均晶粒尺寸大于约4 nm时,熔化温度随晶粒尺寸的减小而减小;随着平均晶粒尺寸的进一步减小,纳米晶体Ag的熔化温度基本上不再随晶粒尺寸而变化。这是因为支配纳米晶体熔化温度的主导相由晶粒部分转变为晶界部分。由于晶体和非晶体之间的本质结构差异,导致非晶体Ag的固液转变温度明显比纳米晶体的熔化温度低。
对比研究了常规过冷液体凝固结晶和纳米晶体熔化过程中的微观结构演变。过冷态液体凝固结晶时的过程表现为三个特征阶段:形核、核的快速长大和缓慢的结构弛豫过程。根据经典形核理论,液体凝固时的均匀形核需要达到一定的过冷度,研究了过冷度对凝固结晶过程和结晶后材料织构的影响。运用Johnson-Mehl-Avrami (JMA)方程讨论了液体结晶到固体的转变动力学。
利用分子动力学方法结合分析型EAM模型,研究了纳米晶体Ag的等温晶粒生长行为,分析讨论了退火温度和晶粒尺寸对纳米晶体晶粒生长行为的影响。同常规多晶体材料的晶粒生长一样,高退火温度和小晶粒尺寸增强了纳米晶体的晶粒生长。纳米晶体Ag的等温晶粒生长曲线大致可以描述为两个阶段:指数生长和线性弛豫阶段。在纳米晶体的晶粒生长过程中,除了晶界迁移机制外,还存在颗粒的旋转机制。另外,晶体生长过程中形成的位错或层错在纳米晶体的生长过程中起到了一个类似中介的作用。
通过构建一个简单的热力学模型,结合分析型EAM理论,计算了Au和Pt的自由纳米颗粒形成AuPt合金纳米颗粒的形成焓。讨论了在纳米尺度下表面效应对常规不互溶金属的合金纳米颗粒的合金化能力和相稳定性的影响。结果表明,合金纳米颗粒的形成焓除表现出与常规体合金类似的随合金组分变化的规律外,还表现出显著的尺寸相关性,并且存在尺寸效应和组分效应间的竞争。对比常规不互溶合金的正形成焓,合金纳米颗粒在小尺寸和稀固溶组分的条件下具有负的形成焓,这表明在纳米尺度下,不互溶体系的合金化能力和相稳定性增强。另外,表面偏聚作用导致不互溶体系的合金纳米颗粒在比较大的尺寸范围表现出负形成焓。分子动力学模拟表明,成分和结构均匀的AuPt合金纳米颗粒在升温时趋向于形成核壳结构。
研究了FeAl合金纳米颗粒熔化及其纳米液滴的冷却凝固过程。同单元素的金属纳米颗粒类似,颗粒表层存在明显的预熔现象。合金纳米颗粒的熔化温度随颗粒尺寸的减小而减小,与热力学模型预测的纳米颗粒的熔化温度随颗粒尺寸的变化规律一致。合金纳米液滴的冷却凝固表明,液滴的合金组分对其冷却凝固性能有着重要的影响。对于Fe、Al成分比(Fe : Al)接近3 : 1的纳米液滴,凝固后得到类似于无序固溶体结构的晶态纳米颗粒,结晶过程中于液滴的表层形核;而对于成分比接近1 : 1的液滴,在比较低的冷却速率下仍然得到了非晶态结构。
本文所使用的分析型嵌入原子方法通过拟合体原子的性质得到,但无需调整任何参数即能预测纳米结构的热力学性质,并且得到与实验相符合的结果,说明该理论简便可行、具有普适性和系统性。为系统建立普适的原子尺度材料设计理论奠定了基础。
In the present thesis, with the analytic embedded atom method (EAM), thethermodynamic properties, such as melting behavior, thermal expansion, atomicthermal vibration and atomic self-diffusion of typical nanostructured metals andalloys are studied systematically. Some of the results have a good agreement withexperimental data and theoretical predictions.
According to the theory that a stable system has a minimum energy, themean lattice contraction of nanoparticles have been calculated with a static method.It is found that the lattice contraction ratio decreases linearly with the reciprocalof particle size. The size and temperature effects on lattice distortion of Ag andPt nanoparticles have been investigated in terms of atomic mean bond length us-ing molecular dynamics simulations. The average values of lattice contractionover the whole system are larger than that of the experimental data, and the av-erage value of lattice contraction in the inner core has a better agreement withthe experiment results. This phenomenon is mainly resulted by inhomogeneouslattice distortion. The surface distortion and the size effect on the inner core dis-tortion are remarkable. As the grain size increases to a certain degree, the inho-mogeneous surface lattice distortion is mainly localized to the outer shell with athickness of 2-3 lattice parameters.
Molecular dynamics has been performed to study the melting evolution,atomic diffusion and vibrational behavior of BCC metal vanadium nanoparticleswith number of atoms ranging from 537 to 28475 (diameters around 2-9 nm). Theresults reveal that the melting temperature of nanoparticle is in inverse propor-tion to the reciprocal of nanoparticle size linearly, and in good agreement with theprediction of thermodynamic liquid-drop model. For the vanadium nanoparticle,the melting process can be described as two stages, firstly the stepwise premelt-ing on the surface layer with a thickness of 2-3 perfect lattice constant, and thenthe abrupt overall melting of the whole cluster. The heat of fusion of nanoparticleis also in linearly inverse proportion to the reciprocal of nanoparticle size. Thediffusion is mainly localized to the surface layer at low temperature and increasewith the reduction of nanoparticle size at the same temperature. The radial meansquare vibration amplitude (RMSVA) is developed to study the anharmonic effect on surface shells. The simulation of solidification of nanodroplets indicates thatthe effective supercooled degree decreases with the reduction of droplet size. Thenucleation in the process of solidification occurs on the surface layer of droplet.Affected by close packed structure and surface effect, the small droplets of FCCmetals exhibit structural characteristic of icosahedron after solidification.
The thermal expansion of nanocrystalline Ag is investigated by calculatingatomic Voronoi volume. Affected by grain boundary structure, the atoms ongrain boundary exhibit excess volume against atoms in the interior of grain. Thethermal expansion of grains in nanocrystal is slightly higher than that of a perfectlattice, while the thermal expansion of grain boundaries in nanocrystal is lowerthan that of a perfect lattice. The thermal expansion of nanocrystals is almostindependent on mean grain size.
The molecular dynamics simulations have been performed to study the vi-brational properties of nanocrystalline nickels. The obtained results reveal thatthe similar phonon softening as in the perfect lattice mainly focuses on grainsin nanocrystalline materials, and the partial vibrational density of states of grainboundary phase is almost insensitive to temperature from 300 K to 900 K, espe-cially within the range of low frequency. The nanocrystalline materials have ahigher specific heat and vibrational entropy, and lower vibrational free energyrelative to the conventional crystals. Supposing the nanocrystalline material canbe treated as a composite constituted by grain and grain boundary (GB) phases,the vibrational thermodynamic properties can be well determined from the pro-portion of GBs and the corresponding thermodynamic properties of grain andGB phases. The Debye temperature of nanocrystalline materials is quantitativelylower than that of the conventional crystals and decreases with the reduction ofmean grain size.
In the atomic scale, the melting behaviors of nanocrystalline Ag with themean grain size ranging from 1.21 to 12.12 nm have been investigated with themolecular dynamics simulations, and a method to determine the melting temper-atures of the infinite polycrystalline nanostructured materials are presented. It isfound that the melting in the nanostructured polycrystals starts from their grainboundaries, and the relative numbers of the three typical bonded-pairs, (1551),(1431) and (1541) existing in the liquid phase increase rapidly with the evolve-ment of melting. The grain size variation of melting temperature exhibits twocharacteristic regions. As mean grain size above about 4 nm for Ag, the melt- ing temperatures decrease with decreasing grain size, and it can be estimatedfrom the size dependent melting temperature of the corresponding nanoparti-cles. However, with grain size further shrinking, the melting temperatures almostkeep a constant. This is because the dominant factor on the melting temperatureof nanocrystal shifts from grain phase to grain boundary. By extrapolating themean grain size of nanocrystal to an infinitesimal value, an amorphous phasehas been obtained from the Voronoi construction. As a result of fundamentaldifference in structure, the amorphous phase has a much lower solid-to-liquidtransformation temperature than that of nanocrystal.
Molecular dynamics simulations have been performed to obtain the atomic-scale details of crystallization from supercooled liquid. The radial distributionfunction and common neighbor analysis provide a visible scenario of structuralevolution in the process of phase transition. The crystallization from supercooledliquid is characterized by three characteristic stages: nucleation, rapid growth ofnucleus and slow structural relaxation. The homogeneous nucleation occurs at alarger supercooling temperature, which has an important effect on the process ofcrystallization and the subsequent crystalline texture. The kinetics of transitionfrom liquid to solid is well described by Johnson-Mehl-Avrami equation.
Isothermal grain growth behaviors, including the effect of temperature andmean grain size, of nanocrystalline Ag are investigated using the molecular dy-namics simulations. The small grain size and high temperature accelerate thegrain growth, it is the same as the conventional polycrystalline materials. Thegrain growth processes of nanocrystalline Ag are well characterized by an expo-nent growth curve, followed by a linear relaxation stage. Beside grain boundarymigration and grain rotation mechanisms, the dislocations (or stacking faults)sever as the intermediate role in the grain growth process.
The surface and size effects on the alloying ability and phase stability of im-miscible alloy nanoparticles have been studied with calculating the heats of for-mation of Au-Pt alloy nanoparticles from the single element nanoparticles of theirconstituents (Au and Pt) with a simple thermodynamic model and an analyticembedded atom method. The results indicated that, besides the similar composi-tional dependence of heat of formation as in bulk alloys, the heat of formation ofalloy nanoparticles exhibits notable size-dependence, and there exists a competi-tion between size effect and compositional effect on the heat of formation of im-miscible system. Contrary to the positive heat of formation for bulk-immiscible alloys, a negative heat of formation may be obtained for the alloy nanoparticleswith a small size or dilute solute component, which implies a promotion of thealloying ability and phase stability of immiscible system on a nanoscale. Thesurface segregation results in an extension of the size range of particles with anegative heat of formation. The molecular dynamics simulations have indicatedthat the structurally and compositionally homogeneous AuPt nanoparticles tendto form a core-shell structure with temperature increasing. The melting tempera-ture of FeAl alloy nanoparticles decreases linearly with the reciprocal of particlesize. In the solidification of alloy nanodroplets, the alloy component has an im-portant effect on the process of solidification and final structure.
Only by fitting the bulk properties of metals, the analytic EAM can predictthermodynamical properties of nanostructured materials without any parameterabout nanostructure. This work is helpful to establish the theory of materials de-sign in the atomic scale systematically.
引文
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