近代价键理论 - 图文(5)

(2) 格子分类成平面格子（无数并置的平行四边形）和空间格子（无数并置的平行六

面体）。

3．晶胞（Unit cells）

(1) 在晶格中，含有晶体结构，具有代表性的最小单元，称为单元晶胞，简称晶胞。 (2) 在晶胞中的各结点上的内容必须相同。例如：铝是面心立方结构，其晶胞中的六

个面心和八个顶点都是铝原子（或铝离子），而NaCl晶体也是面心立方结构，则

六个面心和八个顶点都必须是Na+离子，或都必须是Cl离子。

??? (3) 晶胞参数 晶胞参数：a、b、c、α、β、γ 根据不同的晶胞参数，

－

cβaγαb Cubic a = b = c，α = β = γ = 90?，即晶胞参数为a

Tetragonal a = b ≠ c，α = β = γ = 90?，即晶胞参数为a、c

Orthorhombic a ≠ b ≠ c，α = β = γ = 90?，即晶胞参数为a、b、c Trigonal a = b = c，α = β = γ ≠ 90?，即晶胞参数为a、b、c、α Hexagonal a = b ≠ c，α = β = 90?，γ = 120?，即晶胞参数为a、c

Monoclinic a ≠ b ≠ c，α = β = 90?，γ ≠ 90?，即晶胞参数为a、b、c、γ

Triclinic a ≠ b ≠ c，α ≠ β ≠ γ ≠ 90?，即晶胞参数为a、b、c、α、β、γ

(4) 分数坐标 用来表示晶胞中质点的位置

例如： 简单立方 立方体心 立方面心

(0, 0, 0), (0, 0, 0) (0, 0, 0), (

111111111,,) (,,0), (,0,), (0,,) 222222222Fig. 8.11 The coordinates of atoms in the unit cell

在分数坐标中，绝对不能出现1，因为1即0。这说明晶胞是可以前后、左右、上下平移的。等价点只需要一个坐标来表示即可，上述三个晶胞中所含的质点分别为1、2、4，所以分数坐标分别为1组、2组和4组。

(5) 晶面指数 晶面在三维空间坐标上的截距的倒数（h、k、l）来表示晶体中的晶

面，称为晶面指数，如立方晶系中(100),(110),(111)面分别为

(100) (110) (111)

lkoh

Fig. 8.12 Selected planes and their Miller indices for cubic system

用X-ray的衍射可以测量晶体中的面间距，2d·sinθ = n·λ。 d－晶体的面间距，θ－衍射角，n－衍射级数，λ－X-ray的波长。 对于立方晶系，面间距（d）晶胞参数(a)之间的关系式：

dh,k,l?a/h2?k2?l2

137

Fig. 8.13 Constructive interference of X-ray scattered by atoms in lattice planes. Two beams of X-rays, scattered

by atoms in two suceessive layers of a simple cubic crystal, are shown.

4．根据晶体中质点内容的不同，晶体可分类成：金属晶体（metallic crystals）、离子晶

体(ionic crystals)、原子晶体(atomic crystals)、分子晶体(molecular crystals)、混合晶体(mixture crystals)

二、金属键与金属晶体（Metallic Bond and Metallic Crystals）

1．金属键理论（Metallic bond）

Important information on the nature of the chemical bonds in metals can be obtained from the two specific features distinguishing them from covalent and ionic compounds. Metals differ from all other substances, first, in their high electrical and thermal conductivity and, second, in being crystalline substances in ordinary conditions (except mercury) with high coordination numbers (see, for example, Fig.

Fig 8.14 Arrangement of atoms 8.14).

in a lithium crystal It follows from the first property that at least some of the

electrons can move throughout a piece of metal. On the other hand, it follows from the crystal structure of metals that their atoms are not linked to each other by localized two-electron bonds since the number of valence electrons in an atom is not sufficient to form such bonds with all its neighbours. Lithium, for example, crystallizes in a cubic or regular body-centred lattice and each of its atoms has eight close neighbours within the crystal. (1) 改性的共价键理论

The simplest metallic bonding model is the electron-sea (or electron-gas) model. In

this model, the valence electrons are free to move through the bulk metal structure

(hence the term electron sea) and even leave the metal, thereby producing positive ions. It is valence electrons, then, that convey electric current, and it is the motion of the valence electrons that transfers heat through a metal. However, this model is more qualitative than quantitative.

(2) 能带理论（band theory）（以分子轨道理论为基础）

Molecular orbital theory provides a more comprehensive model of metallic bonding.

This extension of molecular orbital theory is sometimes called band theory, which we will illustrate by looking at the orbitals of sodium.

(a) 能带理论的基本要点

(i) 按照分子轨道理论，把整个金属晶体看作一个大分子，把金属中能级相同

的原子轨道线性组合（原子轨道重叠）起来，成为整个金属晶体共有的若干分子轨道，合称为能带(energy band)，即金属晶体中的n个原子中的每一种能量相等的原子轨道重叠所形成的n个分子轨道，称为一个能带；

138

Fig. 8.15 Bands of molecular orbitals in a metal crystal.

Fig. 8.16 The partially filled band of “molecular

orbitals” in a metal. (Left) The highest filled level is referred to as the Fermi level. (Right) The electrons are freer to move in the now partially filled levels, this property accounts for the electrical conductivity of metals.

Fig. 8.17 Band theory applied to semiconductors

and insulators. In contrast to metals, the band of filled levels (the valence band) is separated from the band of empty levels (the conduction band) by a band gap. The band gap can range from just a few kJ·mol?1 to 500 kJ·mol?1 or more.

(ii) 按照分子轨道法，金属晶体中的多原子形成多原子离域键，n个原子轨道

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