19th Ave New York, NY 95822, USA

# 物理代写|固体物理代写solid physics代考|The reciprocal lattice

my-assignmentexpert™ 固体物理solid physics作业代写，免费提交作业要求， 满意后付款，成绩80\%以下全额退款，安全省心无顾虑。专业硕 博写手团队，所有订单可靠准时，保证 100% 原创。my-assignmentexpert™， 最高质量的固体物理solid physics作业代写，服务覆盖北美、欧洲、澳洲等 国家。 在代写价格方面，考虑到同学们的经济条件，在保障代写质量的前提下，我们为客户提供最合理的价格。 由于统计Statistics作业种类很多，同时其中的大部分作业在字数上都没有具体要求，因此固体物理solid physics作业代写的价格不固定。通常在经济学专家查看完作业要求之后会给出报价。作业难度和截止日期对价格也有很大的影响。

my-assignmentexpert™ 为您的留学生涯保驾护航 在物理physics作业代写方面已经树立了自己的口碑, 保证靠谱, 高质且原创的物理physics代写服务。我们的专家在固体物理solid physics代写方面经验极为丰富，各种固体物理solid physics相关的作业也就用不着 说。

## 物理代写|固体物理代写solid physics代考|Fundamentals of x-ray diffraction by a lattice

The construction of crystal structures according to the formal rules developed in the previous section finds full experimental evidence by means of x-ray crystallography [10-12], where an electromagnetic radiation with a typical wavelength in the range 0.01-10nm is made incident on and then diffracted by a solid state crystalline sample.

The experimental situation is qualitatively summarised in figure 2.14: an incoming x-ray beam is collimated on a crystalline sample and the corresponding diffracted beam is collected by a detector as a distribution of light points, separated by regions of low brightness. They correspond, respectively, to the positions of maximum and minimum intensity of the diffracted beam; this picture is known as diffractogram. Assuming that the sample consists of a discrete distribution of atomic scattering centres and analysing by the laws of optics [13] all the angles formed between the direction of the incident and diffracted beams (as well as their intensities), it is possible to reconstruct the space distribution of the centres. In other words, from the distribution of the light points on the diffractogram it is eventually possible to specify the atomic architecture of the investigated sample.

## 物理代写|固体物理代写solid physics代考|Von Laue scattering conditions

We now perform a detailed analysis of the scattering events occurring in x-ray diffraction. Let $\mathbf{k}{\text {in }}$ be the wavevector of the incoming monochromatic plane wave with amplitude $$\mathcal{A}{\text {in }}(\mathbf{r}, t)=\mathcal{A}{0} \exp \left[i\left(\mathbf{k}{\text {in }} \cdot \mathbf{r}-\omega t\right)\right],$$
where $\omega$ is its angular frequency, while $\mathbf{r}$ and $t$ indicate the position in space and time, respectively. Our goal is to predict the amplitude $\mathcal{A}_{\text {out }}$ of the scattered waves. To this aim we adopt a model originally developed by M von Laue and based on two simplifying assumptions: (i) the incoming beam is weak enough that its interaction with the sample does not affect the underlying crystal structure and (ii) the scattering events are elastic, that is, x-rays do not lose energy by diffusion (i.e. their intensity is unaffected by scattering).

## 物理代写|固体物理代写SOLID PHYSICS代考|Reciprocal lattice vectors

The reciprocal lattice is formally described by the same concepts developed in section 2 for the direct one. More specifically, its points are given by

$$\mathbf{G}=m_{1} \mathbf{b}{1}+m{2} \mathbf{b}{2}+m{3} \mathbf{b}{3},$$ where $\left{\mathbf{b}{1}, \mathbf{b}{2}, \mathbf{b}{3}\right}$ are named reciprocal translation vectors and $m_{1}, m_{2}, m_{3}=$ $\pm 1, \pm 2, \pm 3, \ldots$. The maximum scattering vectors $\mathbf{K}$ entering equation (2.10) lie on this reciprocal lattice and, therefore, they must fulfil equation (2.12); accordingly, by setting $\mathbf{K}=\mathbf{G}$, after some little algebra we obtain that the Laue conditions are satisfied if
$$\mathbf{b}{1}=2 \pi \frac{\mathbf{a}{2} \times \mathbf{a}{3}}{\mathbf{a}{1} \cdot \mathbf{a}{2} \times \mathbf{a}{3}} \quad \mathbf{b}{2}=2 \pi \frac{\mathbf{a}{3} \times \mathbf{a}{1}}{\mathbf{a}{1} \cdot \mathbf{a}{2} \times \mathbf{a}{3}} \quad \mathbf{b}{3}=2 \pi \frac{\mathbf{a}{1} \times \mathbf{a}{2}}{\mathbf{a}{1} \cdot \mathbf{a}{2} \times \mathbf{a}{3}} .$$

## 物理代写|固体物理代写SOLID PHYSICS代考|RECIPROCAL LATTICE VECTORS

$$\mathbf{G}=m_{1} \mathbf{b}{1}+m{2} \mathbf{b}{2}+m{3} \mathbf{b}{3},$$ where $\left{\mathbf{b}{1}, \mathbf{b}{2}, \mathbf{b}{3}\right}$ are named reciprocal translation vectors and $m_{1}, m_{2}, m_{3}=$ $\pm 1, \pm 2, \pm 3, \ldots$. The maximum scattering vectors $\mathbf{K}$ entering equation (2.10) lie on this reciprocal lattice and, therefore, they must fulfil equation (2.12); accordingly, by setting $\mathbf{K}=\mathbf{G}$, after some little algebra we obtain that the Laue conditions are satisfied if
$$\mathbf{b}{1}=2 \pi \frac{\mathbf{a}{2} \times \mathbf{a}{3}}{\mathbf{a}{1} \cdot \mathbf{a}{2} \times \mathbf{a}{3}} \quad \mathbf{b}{2}=2 \pi \frac{\mathbf{a}{3} \times \mathbf{a}{1}}{\mathbf{a}{1} \cdot \mathbf{a}{2} \times \mathbf{a}{3}} \quad \mathbf{b}{3}=2 \pi \frac{\mathbf{a}{1} \times \mathbf{a}{2}}{\mathbf{a}{1} \cdot \mathbf{a}{2} \times \mathbf{a}{3}} .$$

## 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。