附件2
论文中英文摘要
作者姓名：陆海鸣
作者简介：陆海鸣，男，1980年02月出生，2001年09月师从于吉林大学蒋青教授，于2006年12月获博士学位。
中文摘要
界面是材料物理和化学性质发生突变的二维空间区域，材料的许多重要的物理和化学过程首先发生在界面。影响材料性能的界面现象，本质上是由于材料内部分子和界面分子不同的能量状态所产生的。界面原子失配且可能存在的空洞等缺陷，使得界面上原子之间结合键的键长与晶粒内的键长有所不同。由于界面原子之间的交互作用与内部原子之间的不同，从而产生了过剩Gibbs自由能——界面能，其通常被定义为塑性变形形成单位面积新界面所需的可逆功，其数值等于单位面积内界面原子总Gibbs自由能与内部原子Gibbs自由能之差。近几年来，纳米科学和纳米技术是材料科学与工程学科中迅猛发展的领域之一。随着材料尺寸减小到纳米尺度，界面/体积比增大，界面对材料性能的影响变得显著。
然而，我们对界面区域的认识和理解就理论和实际概念的发展和应用而言远落后于许多其它科学领域。在十九世纪晚期和二十世纪初期，热力学在界面交互作用的理论研究上迈出了一大步。由于计算机性价比的迅速提高，近几年来现代计算和分析技术使得对界面的独特本质以及界面交互作用的理解更加完善。然而，由于界面及其相关现象的复杂本性，完全令人满意的理论模型发展很慢，尤其是对界面能尺寸效应的了解还很少。而且在与界面有关的领域中还存在很多争议。另外，在现代科学中，由于计算机模拟技术的出现，经典热力学对界面现象的解释或多或少的被忽略了。但是许多关于界面理论和实验争议的出现也并不一定是一件坏事，它也可以成为继续基础和实践研究的动力。但是对那些需要运用基础研究成果的开拓者来说，这些争议所引起的不确定性有时会使解决实际界面问题的尝试复杂化。 尽管计算材料科学发展迅速，从经典热力学理论出发，建立处理以上界面现象的理论模型仍然非常重要。热力学理论发展了二百多年，已经被广泛地接受，而且热力学已经被拓展来处理只有几百个分子的纳米晶体。因此可以在102~1023个分子范围大小来讨论界面的能量变化。而计算机模拟通常讨论的是100~102个分子的行为，其尺寸跨度比热力学所能处理的尺 寸跨度要小得多，而且其结果仍然存在许多不确定性。因此采用热力学方法研究界面现象，特别是界面现象的尺寸效应，不仅没有过时，而且在纳米科学与技术发展的今天，更具有现实意义。
最近，通过修改经典的断键规则，我们建立了一个简单的、无任何可调参数的、可描述元素晶体低指数晶面固气界面能的热力学模型，并进而将之拓展来描述液体金属和半导体温度依赖的液气界面能及其自扩散系数。与此同时，结合已有的纳米晶体结合能尺度效应模型，我们也建立了描述固气界面能和液气界面能尺寸依赖性的模型。此外，根据Gibbs-Thomson 方程以及均匀形核理论，建立了模拟块体材料固液界面能的模型。具体内容如下所示：
1.通过修改经典的断键规则，建立了与表面原子配位数有关的、可计算元素晶体不同低
指数晶面固气界面能的热力学模型。模型对52种元素晶体（包括面心立方、体心立方、密排六方、简单立方和金刚石结构）固气界面能的预测与实验以及第一原理的结果符合的很好。
空中鼠标进而根据已有的纳米晶体结合能尺度效应模型建立了纳米晶体固气界面能的尺寸依赖性模型。根据该模型，固气界面能随着尺寸的减小而降低，然而不同晶面之间的固气界面能之比却没有尺度效应，仍然等于块体材料时的比值。通过和Na、Mg、Al、Cu、Au和Be纳米晶体固气界面能的实验以及其他理论结果的对比验证了该模型的正确性。
应用集成2.考虑到固体与液体在熔点时的结构和能量差远比固体与气体或者液体与气体之间的
结构和能量差小的多的事实，根据2.1节中建立的元素晶体固气界面能模型建立了描
(T)及其温度系数γ'lv(T)的热力学模型。
述液态金属和半导体温度依赖的液气界面能γ
lv
模型对50种液态金属和半导体γ
(T)和γ'lv(T)函数的预测与相应的实验和其他理论结
lv
果有着良好的一致性。根据该模型，在一定的温度范围内（包括T< T m和T≥T m），γlv(T)和γ'
(T)都正比于T，只不过前者随着T的增加而减小而后者则是随着T的增加而增加。
本田crm250lv
(T)模型、Stokes-Einstein方程以及Egry提出的关于黏度和γlv(T)之间的结合上述γ
lv
关系式，建立了描述液态金属和半导体介于熔点和沸点之间的温度依赖的自扩散系数D(T)的半经验表达式。此式对Li、Na、Rb、Cs、Au、Ag、Cu、Ni和Ge的D(T)函数的预测与实验以及其他方法获得的结果具有良好的一致性。根据该模型，自扩散系数随着温度的升高而增加，且在较大的温度范围内（包括T< T m和T≥T m），D(T) ∝T3/2。
考虑到熔点时固气界面能与液气界面能之间的密切关系，拓展2.2节中建立的尺寸依赖的固气界面能模型，建立了描述液气界面能以及δ的尺度效应的热力学模型。模型
(r)函数的预测与Tolman公式以及计算机模拟的结果对液态金属Na和Al以及水滴γ
lv
都一致，这表明Tolman公式也可以适用于尺寸非常小的液滴。在纳米尺寸范围时，
与γ
sv
(r)函数一样，γlv(r)值也是随着尺寸的减小而下降；但δ(r)值却是随着液滴尺寸的减小而增加，而且δ(r)在整个尺寸范围内都是正值。
3.基于Gibbs-Thomson方程以及均匀形核理论，并结合改进的吉布斯自由能差函数g m(T)
和温度依赖的熔化焓函数∆H m(T)，建立了模拟块体材料固液界面能γsl(∞)的模型。通过和实验数据以及其他理论结果的对比发现：模型对62种金属和38种有机晶体的γsl(∞)值的预测和实验及其他理论结果具有良好的一致性。
结合已有的尺寸依赖的固液界面能γ
sl
(r)模型发现，Turnbull通过过冷实验和经典形
核理论得到的固液界面能值γ
CNT 与γ
sl
(r n,T n)而不是γsl(∞)非常吻合，这引起了对经典形
核理论的重新审视。尽管在经典形核理论中g m(T)函数过于简单而γsl的尺寸依赖性又被忽略，但是本
模型和经典形核理论对于T n和γsl(r n,T n)的预测都非常吻合，这可能是由于g m(T)和γsl(r)函数之间的相互补偿所引起的。另外也发现，γsl(r,T)和∆H m/V s之间的线性关系在任何过冷度下总是成立。
关键词：纳米晶体；界面能；尺寸和温度效应
Size-dependent interface energy
Lu Haiming
ABSTRACT
Surfaces or interfaces are the two-dimensional regions where physical and chemical properties
of materials change enormously. Many important physical and chemical processes of materials
firstly happen at the surfaces. The interface phenomena, which affect the materials behaviors, are in
nature produced by different energetic states of molecules on the interface in comparison with those
within the materials. The atomic mismatch between interfaces and flaws possibly extended result in
the differences of bond lengths between interface atoms and interior ones. Since the molecular
interactions on the interfaces differ from those on the interior of phases, the excess specific Gibbs
free energy or interface energy for molecules of unit interface area exists. Note that interface energy
is defined as the reversible work per unit area to form a new solid surface and equals the difference
between the total Gibbs free energy of interface molecules and that within the phases per unit area.
Nanoscience and nanotechnology are one of the rapidly developed fields in materials science and
engineering in recent years. As size of materials drops to nanometer size range, interface/volume
ratio increases and thus interface effect on materials properties becomes evident.
However, our understanding of the nature of the interfacial region has historically lagged behind those in many other scientific areas in terms of the development and implementation of both theoretical and practical concepts. Great strides were made in the theoretical understanding of interactions at interfaces in the late nineteenth and early twentieth centuries by thermodynamics. Modern computational and analytical techniques made available in the last few years have led to significant advances toward a more complete understanding of the unique nature of interfaces and t
he interactions that result from their unique nature due to the rapid increase of computation ability/price ratio of computers. Nevertheless, because of the unusual and sometimes complex character of interfaces and associated phenomena, the development of fully satisfying theoretical models has been slow. Especially, it is rare to understand the size dependence of interface energy. Moreover, there exists a great deal of controversy in many areas related to interfaces. Also, the classic thermodynamics has more or less neglected to interpret the interface phenomena in modern science due to the appearance of computer simulation technique. Note that many present controversies in theories and experiments in interface phenomena are not bad, since it represents the fuel for continued fundamental and practical research. However, for the practitioner who needs to apply the fruits of fundamental research, such uncertainty can sometimes complicate attempts to solve practical interfacial problems.
In spite of an increasing body of excellent computational materials science, the classic thermodynamics remain importance to model the above phenomena. This is because that, on one hand, the thermodynamics theory has been developed more than two hundreds of years and the theory has been widely accepted since the history of science demonstrate a belief in the universal nature of thermodynamics; on the other size, the thermodynamics can be extended to sizes of nanoc
rystals having several hundreds of molecules. Thus, the thermodynamics can be employed to discuss the changes of interface energy with 102~1023molecules while the computer simulations often deal with the behaviors of 100~102 molecules. Not only the size span studied in the computer simulations is much smaller than that in the thermodynamics, but also the computer simulations remain many uncertainties in this size range. As results, it is not outdated and even practical with the development of nanoscience and nanotechnology to study the interface phenomena in the light of the thermodynamics, especially for the size dependences of interface phenomena.
Recently, we have established a simple thermodynamical formula without adjustable parameters to determine the surface energy of low-index surfaces of elemental crystals through modifying the classic broken-bond rule. Further, the above model is extended to describe the
temperature-dependent surface tension and self-diffusion coefficient of liquid metals and semiconductors. At the same time, we have also developed size-dependent surface energy and surface tension models by combining previous model for the size-dependent cohesive energy. Moreover, in terms of Gibbs-Thomson equation and the classic nucleation theory, the model to estimate the bulk solid-liquid interface energy has also been established. The detailed contents are listed as follows:
1.Through modifying the classic broken-bond rule, we have established a thermodynamical
model to estimate the surface energy of different low-index surfaces of elemental crystals noted that surface energy is related to the coordination number of surface atoms. The model predictions for 52 elemental crystals, including face-centered cubic, body-centered cubic, hexagonal close-packing, simple cubic and dimond structures, are in good agreements with experimental results and the first-principles calculations.
甜蜜的来世Further, we have also established a model for the size-dependent surface energy of nanocrystals based on a previous formula for the size-dependent cohesive energy. In terms of this model, the surface energy falls as the size of crystals decreases to several nanometers, while the surface energy ratio between different facets is size-independent and equals the corresponding bulk ratio. Through comparing with experimental and other theoretical results for the surface energies of Na, Mg, Al, Cu, Au, and Be nanocrysta, the validity of our model is confirmed.
2.In the light of the model for surface energy of elemental crystals established in section 2.1盐酸纳洛酮
and the consideration of the fact that the structural and energetic differences between solid and liquid are very small in comparison with those between solid and gas or between liquid and gas, tem
perature-dependent surface tension γlv(T) and its temperature coefficient γ'lv(T) for liquid metals and semiconductors are thermodynamically determined. The model predictions for 50 liquid metals and semiconductors correspond well to the available experimental and other theoretical results. It is found based on this model that γlv(T m) ∝
钋210
H v/V s2/3, both γlv(T) and γ'lv(T) functions are proportional to T over a certain temperature
range, including T < T m and T≥T m. However, γlv(T) decreases while γ'lv(T) increases when T increases.
Combining the above expression for γlv(T), Stokes-Einstein equation, and the relation between the viscosity and γlv(T) proposed by Egry, the temperature-dependent self-diffusion coefficient D(T) in liquid metals and semiconductors between the melting
