Introductory Solid State Physics with MATLAB Applications

Javier E. Hasbun, Trinanjan Datta

• Publisher: CRC Press
• Year: 2019
• ISBN:
  9781466512375
• Edition: 1
• Topic: Scienze fisiche
• Subtopic: Chimica

Solid state physics, the study and prediction of the fundamental physical properties of materials, forms the backbone of modern materials science and has many technological applications. The unique feature of this text is the MATLAB®-based computational approach with several numerical techniques and simulation methods included. This is highly effective in addressing the need for visualization and a direct hands-on approach in learning the theoretical concepts of solid state physics. The code is freely available to all textbook users.

Additional Features:

• Uses the pedagogical tools of computational physics that have become important in enhancing physics teaching of advanced subjects such as solid state physics
• Adds visualization and simulation to the subject in a way that enables students to participate actively in a hand-on approach
• Covers the basic concepts of solid state physics and provides students with a deeper understanding of the subject matter
• Provides unique example exercises throughout the text
• Obtains mathematical analytical solutions
• Carries out illustrations of important formulae results using programming scripts that students can run on their own and reproduce graphs and/or simulations
• Helps students visualize solid state processes and apply certain numerical techniques using MATLAB®, making the process of learning solid state physics much more effective
• Reinforces the examples discussed within the chapters through the use of end-of-chapter exercises
• Includes simple analytical and numerical examples to more challenging ones, as well as computational problems with the opportunity to run codes, create new ones, or modify existing ones to solve problems or reproduce certain results

1

Introduction

Contents

1.1What Is Solid State Physics

1.2Crystal Structure Basics

1.2.1The Lattice and the Basis

1.2.2The Lattice Translation Vector

1.2.3Primitive Translation Vectors

1.2.4More on the Basis and the Crystal Structure

1.2.5Primitive Cell

1.2.6The Wigner-Seitz Cell

1.3Basic Lattice Types

1.3.1Crystal to Cartesian Coordinates

1.4Properties of the Cubics

1.4.1The Simple Cubic

1.4.2The Body-Centered Cubic

1.4.3The Face-Centered Cubic

1.5Indexing of Crystal Planes (Miller Indices)

1.6Examples of Crystal Structures

1.6.1Sodium Chloride (Salt)

1.6.2Cesium Chloride

1.6.3Close-Packed: Hexagonal and Cubic

1.6.4Diamond

1.6.5Zinc-Sulfide or Zinc-Blende

1.7Atomic Surface Microscopes

1.8Element Properties Table

1.9Chapter 1 Exercises

1.1 What Is Solid State Physics?

Solid state physics is mainly concerned with the study of crystals. Crystals are considered to be systems of atoms arranged in particular and infinitely repeatable patterns. The arrangement of the atoms can be in one, two, or three dimensions as conceptually shown in Figure 1.1.1 for finite size examples. It is the overall periodicity of the atomic arrangement that enables the understanding of crystals. The interaction of the atomic electrons with the ions in a crystal is of primary interest. Whereas Figure 1.1.1(c) is a three-dimensional example of a few atoms in a simple cubic system (eg., polonium), a quantum wire is a system that closely resembles a one-dimensional system of atoms (Ref. [1]), and a hexagonal lattice of atoms, or graphene sheet, is an example of a two-dimensional crystal (Ref. [2]). Images of both the quantum wire and a graphene sheet are shown in Figure 1.1.2.

Figure 1.1.1: Examples of crystals in (a) one, (b) two, and (c) three dimensions. Here the black dots represent atoms.

Figure 1.1.2: (a) A transmission electron microscope (TEM) image of a quantum wire (adapted from Ref. [1], reprinted with permission), (b) a scanning transmission electron microscope (STEM) image of a finite layer of graphene (adapted from Ref. [2]), and (c) a drawing of a finite size graphene lattice with the filled circles representing the atoms.

As the understanding of crystal structures grew, physicists could later extend learned techniques and begin to recognize the importance of amorphous systems, such as glass and liquids. In such systems, however, the best one can hope for is the presence of short range order, as shown for diamond in Figure 1.1.3, rather than the long range order that characterizes crystals. In Figure 1.1.3(a) the carbon atoms are placed...