论文题目：复杂晶体化学键介电理论及其在材料科学中的应用
作者简介：高发明，男,1966年05月出生，2000年09月师从于燕山大学李东春教授，于2002年04月获博士学位。
摘
要
完全依靠理论来设计新型材料一直是材料科学家的梦想。从原理上讲，这完全可能，因为材料的组成原子和物理学的基本定律就决定了材料的性能。尽管第一性原理计算在只使用材料成分的情况下就可预测材料性能，但多数局限在与材料的电子行为和热力学性质相关的性能方面。目前，在第一性原理计算所提供的信息和材料宏观性能之间仍然存在一些鸿沟。因此，在材料宏观性能和微观电子结构之间架起一座桥梁是现代材料科学的重要主题。实践表明，一些半经验理论在材料设计中仍是行之有效的研究手段。
化学键理论是人们理解晶体结构与性能关系的一个根本性手段，在功能晶体性能的预测研究领域具有广阔的应用前景。特别是Phillips和Van Vechten提出的化学键介电理论已成功地应用于二元体系的材料设计。在新材料的研究中，多元体系已占主导地位。为此寻求适用于多元体系的理论方法势在必行。本论文的主要研究内容和获得的主要研究结果如下:
1. 3d过渡金属化合物化学键参数的计算方法
张思远教授通过引入键子式的概念提供了将复杂多键问题转化为二元化合物单键问题的途径。 在此基础上，本文鉴于大多数功能材料都含有d过渡元素，而d电子效应对化学成键有复杂的影响，在合理考虑3d电子特殊作用的基础上，给出了一种3d过渡金属化合物化学键的计算方法。从而使我们能够方便地处理和分析各种复杂晶体的化学键性质。
2．化学位移与化学环境因子
根据光谱、电子能谱和穆斯堡尔谱学中化学键对谱线影响的经验规律，进一步利用共价性和极化率定义了化学环境因子这一概念，并发现它能够有效地描述波谱学中化学位移的变化趋势，从而揭示了波谱化学位移的化学键实质。具体得出了57Fe、119Sn等核在不同氧化态时同质异能位移与化学环境因子的定量关系。这些定量关系式的获得, 使我们能够利用复杂晶体介电理论来计算各种复杂晶体中的同质异能位移, 一方面这种定量关系为穆斯堡尔谱解谱工作提供了依据, 反过来讲穆斯堡尔谱实验也可以验证复杂晶体化学键介电理论的正确性和有效性。
3．六角铁氧体的化学键性质
六角铁氧体是一类很有发展前途的垂直磁记录材料和微波吸收材料。本文利用化学沉淀法制备了M-、W-型六角铁氧体。利用差热分析、SEM、XRD、TEM、Mossbauer谱进行了表征和分析。利用复杂晶体化学键的介电理论研究了M-、W-和R-型六角铁氧体化学键的性质和Mossbauer谱同质异能位移，解决了六角铁氧体的多晶位Mossbauer谱的计算，计算结果与实验值相当一致，为深入研究复杂六角铁氧体的化学键性质提供了新的有效手段。
4．高温氧化物超导体的化学键性质
利用复杂晶体化学键的介电理论系统地研究了Y系、Bi系、Tl系和Hg系等高温氧化物超导体的化学键性质。发现在所有超导体化合物中CuO键均有较大的共价特征, 与文献中有效价和电子密度图的研究结果是一致的, 而且我们的定量结果使得成键图象更加清晰。利用化学环境因子的概念研究了119Sn掺在123、 214、Bi-2212、Bi-2223、Tl-1223、Hg-1223等超导体中的同质异能位移。计算结果与相应的实验值相当一致。说明我们得到的化学键参数的合理性。利用化学环境因子的概念研究了57Fe掺在123、214、Bi-2201、Bi-2212、Bi-2223、Tl-2212、Tl-2223、Tl-1223、Hg-1223等超导体中的同质异能位移。主要峰位计算结果与文献值相一致, 并对其他弱峰位的指派也作了详细讨论。基于高温超导体电声子相互作用机制，建立了高温超导体临界转变温度与共价性的关系。
5. 共价晶体硬度和化学键
超硬材料在现代科学和工程技术领域一直发挥着巨大作用。寻找硬度与金刚石相当或超过金刚石的新型超硬材料已经成为理论和实验研究的焦点问题。然而，硬度是一个复杂的宏观物理量，难以用第一性原理描述。在过去的二十多年里，材料工作者预测超硬材料不得不被简化为寻找具有高体弹性模量和剪切弹性模量的物质，那是因为体弹性模量和剪切弹性模量均可由第一性原理直接计算出来。这种方法明显有其局限性。事实上，材料的硬度是特别的、独立的物理量，它既不同于体弹性模量也不同于剪切弹性模量，它和这两量之间不存在一一对应关系。因而阐明硬度的本质是极其重要的。我们认为晶体的宏观性质与化学键有直接关系，因而从化学键的观点出发研究物质的硬度是合理的。
5.1 纯共价晶体的硬度
我们认为共价固体硬度是本征的并等于单位面积上所有键对压头的抵抗力之和。键对压头的抵抗力可以用能隙来表征，单位面积上的共价键数由价电子密度确定。基于这个假设，纯共价晶体的硬度可表示为：
H (GPa) = A Na Eg （1）
其中A为比例系数， Eg 为能隙，Na为单位面积上的共价键数。Na表示为：
（2）
式中，ni是i原子在晶胞中的个数，Zi是i原子的价电子数，V是晶胞体积，Ne是价电子密度。
5.2 极性共价晶体的硬度
公式（1）只适用于纯的共价晶体。对于极性共价晶体，化学键虽然仍以共价成分为主外，但是部分离子成键特性也必须考虑。离子键是由长程静电作用力造成的，它不影响硬度。最近的工作表明在极性共价晶体中滑移激活能正比于Phillips同极共价能隙Eh，同时指出Eh能够表征共价键的强度。因而我们在计算极性共价晶体硬度时，应该从总能隙Eg中扣除掉由离子成键贡献的异极能隙C，而只留下同极共价能隙Eh来表征极性共价晶体的硬度。另一方面，部分离子成键也会导致共价键电荷的损失，使极性共价晶体与纯共价晶体相比呈现一较小的单位面积共价键数（Na）*。为了考虑这种影响，我们在纯共价晶体单位面积共价键数Na的基础上作一修正，引入一指数修正因子e-afi（其中a是常数，fi是离子性），即极性共价晶体的单位面积共价键数（Na）* = Nae-afi。于是，极性共价晶体的硬度的指数回归方程为：
Hv (GPa) = A (Nae-afi)Eh = 14 (Na e-1.191fi) Eh （3）
公式(3)进一步可表达为：
（4）
其中d是键长。
5.3 多元晶体的硬度
大多数功能材料是多元晶体，因而发展复杂晶体硬度的计算方法具有重要意义。文献指出，多元晶体的硬度可表达为晶体中所有二元系统硬度的平均值。对多元晶体进行硬度试验时，强度较低的键有先断裂的趋势，因而我们认为多元晶体的硬度表示为所有二元键子式硬度的几何平均，即：
（5）
这些由μ类型键组成的二元晶体的硬度为：
（6）
其中
是在实际晶体中μ键的数目。
总之，利用我们得到的硬度公式成功地预测了典型的共价晶体包括新近合成的b-BC2N的硬度，对共价晶体的硬度给出了很好的物理解释，研究结果表明键密度、键长和离子性是极性共价固体硬度的三个决定因素。这一模型从本质上能够解决复杂多元体系的硬度问题。正如Physical Review Focus评论的那样：“所建立的硬度微观理论在新型超硬材料的设计中将是一个有用技术和有力工具”。
关键词：复杂晶体化学键理论，共价性，离子性，穆斯堡尔谱，六角铁氧体，超导体，硬度。
Abstract
It has always been a dream of materials scientists to design a novel material completely based on theory. In principle, this should be possible, because the constituent atoms and the basic laws of physics determine the properties of a material. First principles calculation plays an important role in predicting properties of a material only using composition, but its successes are concentrated on a fairly small selection of properties of a material, most of them electronic or thermodynamic. There is still a wide gap between the information that first principle calculation can produce and the macroscopic properties of materials. Therefore, building the connection between macroscopic properties and the microscopic electronic structure of a material is an important subject in modern materials science. In fact, some semi-empirical theories can still be the valid research methods.
Theory of chemical bonds is a fundamental method for us to understand the relationship between crystal structure and properties of a material, and can be widely applied in the research area of predicting the properties of a functional crystal. Especially the dielectric theory of chemical bond developed by Phillips and Van Vechten has been successfully applied in the design of binary compounds. Since the multicomponent compound systems are dominant in the novel materials, it is necessary to find a theory suitable for these systems. The main research works and results obtained are listed as following:
1. Calculation method of chemical bond parameters for 3d transition-metal compounds
Professor Siyuan Zhang has provided a method in which the issue of characterizing a complex compound with several bonding types can be transformed into one of characterizing a series of separated binary compound with single bonding by introducing bonding formula. On the basis of Zhang's chemical bond theory, considering most of the functional materials containing some transition-metal ions with d electrons which contribute to their bond characteristics, a calculation method of chemical bond parameters for 3d transition-metal compounds was presented by using a correction factor to consider the specific effects of 3d electrons on the bonding. This method makes us treat and analyze conveniently the bond characteristics in complex crystal.
2. Chemical shifts and chemical environmental factor
According to the empirical rules of influence of the chemical bond on spectrum, electron spectroscopy and Mossbauer spectroscopy, the chemical environmental factor was further defined with the covalency and polarizability of a bond. Since the factor can effectively describe the variation trends of the chemical shifts in the above spectra, the bond nature of the chemical shifts was revealed. The clear quantitative relations between the environmental factors and Mossbauer isomer shift of various ions such as 57Fe and 119Sn were obtained. we can predict the isomer shifts in all kinds of complex crystals by using this theory. On the one hand, these relations will be useful for us to analyze Mossbauer spectroscopy, and otherwise, the experiments in Mossbauer spectroscopy can verify validity of the chemical bond dielectric theory for the complex crystals.
3. Chemical bond properties of the complex hexagonal ferrites
Hexagonal ferrites are perdendicular magnetic recording and microwave-absorbing materials with potential applications. M- and W-type hexagonal ferrites were prepared by using chemical precipitation method, and characterized by DTA, SEM, XRD, TEM and Mossbauer spectroscopy. By using the chemical bond dielectric theory for complex crystals, we studied the properties of the chemical bonds and Mossbauer isomer shifts in the M-, W- and R-type hexagonal ferrites, and solved the issue in the calculation of Mossbauer spectra resulted from various crystallographic positions in hexagonal ferrites. The calculated results of Mossbauer isomer shifts are in agreement with their experimental values. This theory provides us a new and valid method further to study the bond properties of the complex hexagonal ferrites.
4. Chemical bond properties of superconductors
By using the chemical bond theory for complex crystal, the chemical bond properties of Y-, Bi-, Tl- and Hg-based superconductors were studied. The results show that the CuO bonds manifest more covalent character, which is in agreement with that from the effective valence and electronic charge-density figure in the literature. However, our quantitative calculations make images of the chemical bonding more clearly. Mossbauer isomer shifts of 119Sn-doped 123, 214, Bi-2212, Bi-2223, Tl-1223 and Hg-1223 superconductors were calculated by using the chemical environmental factor. We found a very good agreement between the theoretical and the corresponding experimental results. This illustrates the reasonableness of the calculated chemical bond parameters. In addition, Mossbauer isomer shifts of 57Fe-doped 123, 214, Bi-2201, Bi-2212, Bi-2223, Ti-2212, Tl-2223, Tl-1223 and Hg-1223 superconductors were also calculated by using the chemical environmental factor. The calculated results of main Doubles were agreed to the published values. The assignments of the other small Doubles were also discussed in detail. Based on the mechanism of electron-phonon interaction in high temperature superconductors, we constructed a relationship between the critical temperature and covalency of the superconductor.
5. Hardness of covalent crystals and chemical bonding
Superhard materials are of primary importance in modern science and technology. Intense theoretical and experimental interests have been focused on the possibility of finding new superhard materials comparable to or even surpassing covalent solid of diamond in hardness. However, hardness is a complex macroscopic physical property which can not be describe by the first-principles. In the last two decades, for materialists to search for superhard materials have to be simplified to search for materials with large bulk modulus or shear modulus, which can be evaluated directly by the first-principles. This method has obviously limitations because of no one-to-one correspondence between hardness and moduli. In fact, the hardness is special, and different from bulk modulus or shear modulus. Therefore, clarifying the nature of hardness is of utmost importance. We think that the macroscopic physical properties of crystals must have a direct relationship with their constituent chemical bonds. Therefore, for a given crystal, it is reasonable to investigate its origin of hardness by starting from the chemical bond viewpoint.
5.1 Hardness of covalent crystal
In our opinion, the hardness of covalent crystals is intrinsic and equivalent to the sum of resistance of each bond per unit area to indenter. This resistant force of bond can be characterized by energy gap, and the number of bond per unit area is determined by valence electron density. Based on this assumption, the hardness of covalent crystals should have a following form:
H (GPa) = A Na Eg (1)
where A is a proportional coefficient and Na is the covalent bond number per unit area. Na can be expressed as:
(2)
where ni is the number of i atom in the cell, Zi is the valence electron number of i atom, V is cell volume . Ne is the electron density.
5.2 Hardness of polar covalent crystal
Eq. (1) is only suitable for pure covalent crystals. For polar covalent crystals, besides covalent component, partial ionic component have to be considered. Ionic bonding results from long-range electrostatic force which is not directly related to hardness. Recent work also indicates that the activation energies of dislocation glide in polar covalent crystals are proportional to Phillips’ homopolar band gap Eh , which characterizes the strength of the covalent bond. Therefore, we can deduct the ionic contribution C from the factor Eg, leave only a homopolar component Eh for the hardness of polar covalent crystals. On the other hand, the partly ionic bonding results in the loss of covalent bond charge, further results in a smaller effective covalent bond number per unit area in comparison with that of Na for pure covalent crystals. Here we introduce a correction factor e-afi to describe this screening effect, i.e., use Nae-afi for polar covalent crystals instead of Na for pure covalent crystals in Eq. (1), where a is a constant, fi is ionicity of chemical bond. The exponential regression equation for the hardness of polar covalent crystals is obtained as follows:
Hv (GPa) = A (Nae-afi)Eh = 14 (Na e-1.191fi) (3)
Also Eq. (3) can be expressed as:
(4)
where d is the bond length.
5.3 Hardness of complex crystals
Since most of functional materials are multicomponent crystals, it is important to develop a calculation method for hardness of multicomponent crystals. The hardness of muticomponent crystals can be expressed as an average of hardness of all binary systems in the solid as indicated in literature. When there are differences in the strength among different types of bonds, the trend of breaking the bonds will start from a softer one. Therefore, the hardness Hv of complex crystals should be calculated by a geometric average of all binary bonds as follow:
(5)
where
is the hardness of binary compound composed by μ-type bond,
is the number of bond of type μ composing
the actual complex crystal.
In conclusion, our equations successfully predict the hardness for several typical covalent and polar covalent materials, including a recently-synthesized superhard material b-BC2N. This study gives a better physical understanding to hardness of a covalent solid. It tells us that bond density or electronic density, bond length and degree of covalent bonding are three determinative factors for the hardness of a polar covalent solid. This model could have substantial applications to complex multi-component solids where first-principles methods may be prohibitive. Just as comment in Physical Review Focus: "It appears to be a powerful and useful technique for predicting materials hardness".
Keywords: chemical bond theory of complex crystals, covalency, ionicity, Mossbauer spectroscopy, hexagonal ferrite, superconductor, hardness.
