## 物理代写|固体物理代写Solid-state physics代考|PHYSICS7544

2022年7月27日

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## 物理代写|固体物理代写Solid-state physics代考|Point defects

Lattice imperfections involving just a single atom are named point defects: their pictorial representation is reported in figure 2.17. They are more specifically referred to as native or non-native: the former ones correspond to the vacancy and selfinterstitial case, previously introduced; the latter ones, instead, are generated whenever an atom is added of a chemical species not found in the pristine crystal. Of course, in lattices with a basis various kinds of vacancies and self-interstitials in fact exist. Furthermore, in two-atom compound crystals we can also find the anti-site defect, corresponding to a position exchange between two unalike nearest neighbouring atoms. Sometimes point defects gather to form small defect aggregates. The most common aggregates are defect clusters (where, for instance, a number of vacancies or self-interstitials precipitate, thus forming, respectively, a small void or an inclusion in the host crystal) and Frenkel pairs (where a bound pair of a vacancy and a selfinterstitial is formed). Finally, an atom can replace a regular crystalline atom, belonging to a different chemical species: this configuration is known as a substitutional impurity.

An important feature missing so far in our discussion is that the underlying lattice is deformed by the presence of defects. We can say that this is per se another kind of defect which, in this case, is described in terms of an induced lattice strain field: interatomic distances are varied with respect to the ideal case and the bond network is accordingly distorted. In figure $2.18$ we provide a rendering of this concept in the simple case of a two-dimensional square lattice which offers the possibility of a very intuitive graphics.

## 物理代写|固体物理代写Solid-state physics代考|Extended defects

Lattice defects involving multi-atomic configurations are called extended defects and represent lattice errors. The two most significant cases we limit our attention to are dislocations and grain boundaries.

Dislocations are line defects: a crystal lattice is ‘dislocated’ with respect to a line defined by an appropriate vector $\mathbf{L}{\mathrm{d}}$. The concept is illustrated in figure $2.20$ (top) for the two different cases of edge dislocation and screw dislocation. Dislocations are described crystallographically by a set of two vectors: the first one is $\mathbf{L}{\mathrm{d}}$, while the second vector (indicated with the symbol $\mathbf{B}{\mathrm{d}}$ ) is called Burgers vector and it is graphically represented in figure $2.20$ (bottom) in the case of an edge dislocation. Basically, $\mathbf{B}{\mathrm{d}}$ represents the difference in path when the dislocation core is shortcircuited in the defective lattice or when the same path is followed in the perfect lattice ${ }^{16}$. By means of the pair $\left{\mathbf{L}{\mathrm{d}}, \mathbf{B}{\mathrm{d}}\right}$ we can distinguish the two kinds of extended line defects in that $\mathbf{L}{\mathrm{d}}$ and $\mathbf{B}{\mathrm{d}}$ are normal or parallel in edge or screw dislocations, respectively.

Dislocations play a fundamental role in plasticity ${ }^{17}$. Qualitatively, a plastic deformation is due to the generation-migration-accumulation sequence of a dislocation forest. Another situation where dislocations are found is at the interface between two lattice-mismatched crystals. In this case, in an attempt to accommodate the unalike interatomic spacings on the planes parallel to the interface, the two crystals deform (by stretching or by compression provided that the lattice constant is smaller or larger, respectively) and thus they store elastic energy. When the lattice mismatch is sizeable, the accumulated elastic energy can be sufficient to be converted into formation work of dislocations, whose generation allows recovery of the pristine lattice spacings far away from the dislocation core.

# 固体物理代写

## 有限元方法代写

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## MATLAB代写

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。