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# 化学代写|无机化学代考Inorganic Chemistry代写|SCCHM1003 The description of the structures of solids

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## 化学代写|无机化学代考Inorganic Chemistry代写|The description of the structures of solids

The arrangement of atoms or ions in simple solid structures can often be represented by different arrangements of hard spheres. The spheres used to describe metallic solids represent neutral atoms because each cation can still be considered as surrounded by its full complement of electrons. The spheres used to describe ionic solids represent the cations and anions because there has been a substantial transfer of electrons from one type of atom to the other.

## 化学代写|无机化学代考Inorganic Chemistry代写|Unit cells and the description of crystal structures

A crystal of an element or compound can be regarded as constructed from regularly repeating structural elements, which may be atoms, molecules, or ions. The ‘crystal lattice’ is the geometric pattern formed by the points that represent the positions of these repeating structural elements.
(a) Lattices and unit cells
Key points: The lattice defines a network of identical points that has the translational symmetry of a structure. A unit cell is a subdivision of a crystal that when stacked together following translations reproduces the crystal.

A lattice is a three-dimensional, infinite array of points, the lattice points, each of which is surrounded in an identical way by neighbouring points. The lattice defines the repeating nature of the crystal. The crystal structure itself is obtained by associating one or more identical structural units, such as atoms, ions, or molecules, with each lattice point. In many cases the structural unit may be centred on the lattice point, but that is not necessary.
A unit cell of a three-dimensional crystal is an imaginary parallel-sided region (a ‘parallelepiped’) from which the entire crystal can be built up by purely translational displacements; ${ }^{1}$ unit cells so generated fit perfectly together with no space excluded. Unit cells may be chosen in a variety of ways but it is generally preferable to choose the smallest cell that exhibits the greatest symmetry. Thus, in the two-dimensional pattern in Fig. 3.1, a variety of unit cells (a parallelogram in two dimensions) may be chosen, each of which repeats the contents of the box under translational displacements. Two possible choices of repeating unit are shown, but (b) would be preferred to (a) because it is smaller. The relationship between the lattice parameters in three dimensions as a result of the symmetry of the structure gives rise to the seven crystal systems (Table $3.1$ and Fig. 3.2). All ordered structures adopted by compounds belong to one of these crystal systems; most of those described in this chapter, which deals with simple compositions and stoichiometries, belong to the higher symmetry cubic and hexagonal systems. The angles $(\alpha, \beta, \gamma)$ and lengths $(a, b, c)$ used to define the size and shape of a unit cell, relative to an origin, are the unit cell parameters (the ‘lattice parameters’); the angle between $a$ and $b$ is denoted $\gamma$, that between $b$ and $c$ is $\alpha$, and that between $a$ and $c$ is $\beta$; a triclinic unit cell is illustrated in Fig. 3.2.

## 化学代写|无机化学代考Inorganic Chemistry代写|Unit cells and the description of crystal structures

(a) 晶格和晶胞

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MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。