## 物理代写|固体物理代写Solid-state physics代考|KYA322

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|Classification of solids

Symmetry has been largely used in the previous sections to rigorously classify crystalline solids. Other criteria can in fact be followed, based on physical properties of any kind. For instance, by looking at the mechanical response under load we can discriminate between elastic or plastic materials, as well as classify their fracture, failure, and yield behaviours; similarly, by investigating the interaction between electromagnetic waves and solids, we can separate them according to their optical properties. However, the most fruitful classification scheme based on a physical property is likely based on the configuration assumed by the crystalline valence electrons. This approach relies on the frozen-core approximation presented in section 1.3.2; since at this stage we have not yet developed any knowledge about the electronic structure of a solid state system, we will proceed at a more qualitative (but nevertheless useful in the next chapters ${ }^{18}$ ) level than allowed by symmetry classification.

The first step consists in making a difference between metals and insulators. While the most rigorous definition is only provided by the quantum band theory (see chapter 8), for the present discussion it is sufficient to rely just on phenomenological inputs: metals are good electrical conductors, while insulators are not. Whenever subjected to the action of an external electric field, metals are crossed by a current of charge carriers. This evidence is qualitatively attributed to the fact that valence electrons form a conduction gas of nearly-free charged particles: under the action of an external electric field, the conduction gas is accelerated, giving rise to current phenomena. On the other hand, in an insulator the density of such a gas is so small, that the resulting current density is comparatively negligible. From these considerations we draw a qualitative picture: in a metal system, ions sitting at lattice positions are embedded into a ‘glue’ of valence electrons which form an almost uniform charge distribution.

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

A final question still remains to be answered: how much work $E_{\text {cohesive }}$ is needed to assemble a set of atoms into a crystalline solid? This quantity is defined as the difference in energy between a configuration where atoms lie at infinite distance and a configuration where they form a bound crystal. Let us name $E_{T}^{\text {free atoms }}$ the total energy of $N$ free atoms (possibly of different chemical species) and $E_{T}^{\text {crystal }}$ the energy of their crystalline configuration, then we calculate the cohesive energy per atom as
$$e_{\text {cohesive }}=\frac{1}{N}\left[E_{T}^{\text {free atoms }}-E_{T}^{\text {crystal }}\right],$$
while of course $E_{\text {cohesive }}=N e_{\text {cohesive }}$.
The most fundamental approach for calculating the cohesive energy is quantum mechanical [21], as formally shown in equation (1.13) (since $E_{\text {cohesive }}$ does depend on the ground-state energy of the solid). This is the only way to proceed for metals and covalent crystals where valence electrons are totally or partially delocalised. On the other hand, for molecular and ionic crystal it is possible to follow a much simpler, although phenomenological, approach $[10,11,15]$ where a number of simplifications are assumed, in that: atoms are treated classically (we place them at rest exactly in positions corresponding to crystalline lattice sites with no quantum zero-point energy effects included; the valence electron charge distribution is treated by classical electrostatics); the calculation is performed by imposing an arbitrary value of the lattice constant(s); and the temperature is set to zero (no free energy contributions are accounted for). By imposing that the derivative of the cohcsive energy with respect to the lattice constant(s) is zero, we obtain their equilibrium values: those ones at which the real crystal is found in stable equilibrium at zero pressure.
In moleculur crystals binding is due to the balance between interatomic attractive dipolar interactions (long-ranged and weak) and Pauli repulsion between electron clouds (occurring at short distance and very strong).

# 固体物理代写

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

$$e_{\text {cohesive }}=\frac{1}{N}\left[E_{T}^{\text {free atoms }}-E_{T}^{\text {crystal }}\right],$$

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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。