【作者】 齐卫宏；

【导师】 汪明朴； 徐根应；

【作者基本信息】 中南大学 ， 材料物理与化学， 2004， 博士

【摘要】 本研究旨在建立起全面描述金属纳米微粒热力学性能的尺寸效应和形状效应的理论模型，研究涉及以下内容： (1) 提出了一个新的无量纲的参数——“形状因子”来描述纳米微粒形状差异对于基本性能的影响，给出了形状因子明确的定义、计算方法；推导出了微粒尺寸、形状因子、微粒总原子数、表面原子数以及比表面积等纳米微粒基本表征量之间的定量关系式。 (2) 提出了一个新的纳米微粒晶体形成模型，即纳米微粒可以看作是从块状晶体中取出的一个纳米尺度的粒子，按能量最低原理自发达到热力学平衡而形成。基于这个模型，推导出了纳米微粒晶格参数的计算公式，公式的计算结果和实验值符合得很好。 (3) 从结合能的基本概念出发，提出了固体的结合能在数值上等于组成固体的所有原子在自由态时的表面能减去固体的表面能的表述，进一步建立了描述纳米微粒结合能的表面能模型。通过考虑固体表面原子有大量的悬空键，而且表面原子有弛豫这一实验事实，建立了纳米微粒结合能的键模型。两种模型计算结果与Mo和W纳米微粒实验结果一致，但键模型的计算结果与实验值符合得更好。同时，还证明了文献中的液滴模型是本研究提出的表面能模型的一个特例。 (4) 根据熔解温度与结合能的关系，推导出了一个计算自由表面纳米微粒熔解温度的公式；对于镶嵌在高熔点基体中并与基体形成共格界面的纳米微粒，通过考虑基体原子对于纳米微粒表面原子成键的影响，推导出了计算非自由表面纳米微粒熔解温度的公式，并预测了这种非自由表面纳米微粒的过热现象。进一步推导出了预测自由表面纳米微粒和镶嵌在高熔点基体中并与基体形成共格界面的非自由表面纳米微粒的熔解熵和熔解焓的计算公式。 (5) 通过考虑相图计算公式中的基本参数——熔解温度和熔解焓的尺寸效应和形状效应，研究了完全互溶的二元纳米微粒系统的相图。对Cr—Mo二元系统的研究表明，纳米微粒的相图的固相线和液相线要比相应块体材料的固相线和液相线低，但固、液相线变化的幅度基本相同，这和文献中只考虑纳米微粒熔解温度的尺寸效应得到的相图不同。 (6)基于纳米微粒结合能的键模型，再根据结合能和空位形成能的关系，推导出了计算自由表面纳米微粒空位形成能和空位浓度的计算公式。研究表明，纳米微粒的空位形成能和空位浓度是纳米微粒尺寸和形状因子的函数，微粒尺寸是影响空位形成能和空位浓度变化的主要因素。若不考虑微粒形状对于空位形成能的影响，最终计算的空位形成能的误差可达10%。 (7)基于纳米微粒键模型的基本思路，推导出了计算自由表面纳米线和纳米薄膜的结合能、熔解温度、熔解嫡、熔解焙、空位形成能以及空位浓度的计算公式。研究表明，在不考虑表面原子弛豫的情况下，相同尺寸的球形纳米微粒、纳米线和纳米薄膜的结合能(熔解温度、空位形成能)变化量之比为3:2:1，相应的熔解嫡在一级近似下也有这个比值关系。更多还原

【Abstract】 The present work aims at developing a general model to account for size effects and shape effects of the thermodynamic properties of metallic nanoparticles. The main contents are listed in the following:(1) A new dimensionless parameter, i.e. shape factor, is proposed to account for the particle shape difference of nanoparticles, where its definition and calculation method are also shown. Furthermore, the relational expressions between particle size, shape factor, number of total atoms, number of surface atoms and specific surface area have also been derived.(2) A new lattice model of nanoparticle is proposed, where a nanoparticle is moved out from the bulk crystal and form in thermodynamic equilibrium. Based on this model, the expression for the size and shape dependent lattice parameter of nanoparticles has been derived, and the corresponding computational results are consistent with the experimental ones.(3) Based on the basic concept of cohesive energy, we have proposed that the cohesive energy of a solid equals the difference between the total surface energy of all isolated atoms of the solid and the surface energy of the solid, which leads to the surface energy model; By considering the large number of dangling bonds of the surface atoms and surface relaxation of nanoparticles, the bond model has been established. Both calculation results are consistent with the experimental values of the cohesive energy of Mo and W nanoparticles, and the results of bond model are more close to the experimental values. Furthermore, it is proved that the liquid drop model in literature is a special case of surface energy model.(4) A formula has been derived to account for the melting temperature of free surface nanoparticles based on the relationship between the cohesive energy and the melting temperature of solids. By considering the matrix effect on the bonds of the surface atoms , an expression is developed to describe the melting temperature of the nanopaticles embedded in a matrix with high melting temperature and formingcoherent interface with matrix, where the superheating of these nanoparticles has been explained. Furthermore, we have obtained the relations accounting for the size and shape dependent melting entropy and melting enthalpy of nanoparticles with free and non-free surface.(5) By considering size effects and shape effects on the melting temperature and the melting enthalpy of nanoparticles, the phase diagram of nanoparticles of binary systems is calculated, and the calculation results show that the solidus and the liquidus of phase diagram of nanopaticles are lower than that of the corresponding the bulk systems, but the amplitude of variation are similar. The present results are different from that reported in literatures, where the size effect on the melting temperature is only considered.(6) Based on the bond energy model of nanoparticles and the relationship between cohesive energy and vacancy formation energy, the expressions for the vacancy formation energy and the vacancy density of nanoparticles have been derived. It is shown that both the vacancy formation energy and the vacancy density of nanoparticles depend on the particle size and shape factor, and the particle size is the major factor affecting these two properties. If one neglects the particle shape effect on the vacancy formation energy, the error in the final results may reach 10%.(7) Based on the method of bond model, the expressions for the size dependent cohesive energy .melting temperature , melting entropy , melting enthalpy, vacancy formation energy and vacancy density of nanowires and nanofilms have been established. It is found that the ratio for the cohesive energy of spherical nanoparticle, nanowire and nanofilm in the same size is 3:2:1 when their surface relaxation is neglected, and their melting temperature, vacancy formation energy and melting entropy (in the first approximation) follow the same ratio.更多还原