Solid State Physics (1) Phys3710 Lecture 1

1. Solid State Physics (1) Phys3710 Lecture 1 Department of Physics Dr Mazen Alshaaer Second semester 2013/2014 Ref.: Prof. Charles W. Myles, Department of Physics, Texas Tech University

2. Primary Textbook Introduction to Solid State Physics, by Charles Kittel, 8th Edition. 1. Elementary Solid State Physics: Principles & Applications, M. Ali Omar 2. Solid State Physics, by Neil W. Ashcroft & N. David Mermin. Course Objective • To expose students to the rich, broad, varied field of SOLID STATE PHYSICS • Solid State Physics is about many different kinds of solids.We'll discuss the microscopic physics of mostly,CRYSTALLINEsolids, including metals, insulators, & semiconductors.

3. Chapter 1: Crystal Structure

4. The (Common) Phases of Matter This doesn’t include Plasmas, but these are the “common” phases!! “Condensed Matter”includes both of these.We’ll focus onSolids!

5. Gases • Gaseshave atoms or molecules that do not bond to one another in a range of pressure, temperature & volume. • These molecules haven’t any particular order & move freely within a container.

6. Similarto gases, Liquids have no atomic/molecular order & they assume the shape of their containers. Applying low levels of thermal energy can easily break the existing weak bonds. Liquids & Liquid Crystals • Liquid Crystalshave mobilemolecules, but a type of long rangeorder can exist; the molecules havea permanent dipole. Applying anelectric field rotates the dipole & establishes order within thecollection of molecules. 6

7. Solids • Solidsconsist of atoms or moleculesundergoing thermal motionabout their equilibrium positions, which are at fixed pointsin space. • Solidscan be crystalline, polycrystalline, or amorphous. • Solids(at a given temperature, pressure, volume)have stronger interatomic bondsthan liquids. • So,Solidsrequire more energy to break the interatomic bondsthan liquids.

8. Crystal Structure Topics 1.Periodic Arrays of Atoms 2.Fundamental Types of Lattices 3.Index System for Crystal Planes 4.Simple Crystal Structures 5.Direct Imaging of Crystal Structure 6.Non-ideal Crystal Structures 7.Crystal Structure Data

9. Objectives At the end of this Chapter, you should: 1. Be able toidentify a unit cellin a symmetrical pattern. 2.Know that (in 3 dimensions) there are 7Possible unit cell shapes. 3.Be able to define cubic, tetragonal, orthorhombic & hexagonal unit cell shapes

10. Periodic Arrays of Atoms Experimental Evidence of periodic structures. (See Kittel, Fig. 1.) The external appearance of crystals gives some clues to this. Fig. 1 shows that when a crystal is cleaved, we can see that it is built up of identical “building blocks”. Further, the early crystallographers noted that the index numbers that define plane orientations are exact integers. Cleaving a Crystal

11. Elementary Crystallography

12. The Three General Types of Solids Single Crystal Polycrystalline Amorphous Each type is characterized by the size of the orderedregion within the material. An ordered region is a spatial volume in which atoms or molecules have a regular geometric arrangement or periodicity.

13. Crystalline Solids • A Crystalline Solid is the solid form of a substance in which the atoms or moleculesare arranged in a definite, repeating pattern in three dimensions. • Single Crystals, ideally have a high degree of order, or regular geometric periodicity, throughout the entire volume of the material.

14. A Single Crystalhas an atomic structure that repeats periodically across its whole volume. Even at infinite length scales, each atom is related to every other equivalent atom in the structure by translational symmetry. Single Crystals SinglePyrite Crystal Amorphous Solid

15. Polycrystalline Solids • A Polycrystalline Solidis made up of an aggregate of many small single crystals(crystallites or grains). Polycrystalline materialshave a high degree of order over many atomic or moleculardimensions.These ordered regions, or single crystal regions, vary in size & orientationwith respect to one another.These regions are called grains(or domains)& are separated from one another by grain boundaries. • The atomic ordercan vary from one domain to the next.The grains are usually 100 nm - 100 microns in diameter. Polycrystals with grains that are < 10 nm in diameter are called nanocrystallites. Polycrystalline Pyrite Grain

16. Amorphous Solids • Amorphous (Non-crystalline) Solids are composed of randomly orientated atoms, ions, or molecules that do not form defined patterns or lattice structures.Amorphous materialshave order only within a few atomic or molecular dimensions. They do not have any long-range order, but they have varying degrees of short-range order.Examples of amorphous materialinclude amorphous silicon, plastics, & glasses.

17. Departures From the “Perfect Crystal” • A “Perfect Crystal”is an idealization that does not exist in nature. In some ways, even a crystalsurfaceis animperfection, because the periodicity is interrupted there. • Each atom undergoes thermal vibrations around their equilibrium positions for temperatures T > 0K. These can also be viewed as “imperfections”. • Also, Real Crystals always have foreign atoms (impurities), missing atoms (vacancies), & atoms in between lattice sites (interstitials) where they should not be. Each of these spoils the perfect crystal structure.

18. Crystallography Crystallography ≡The branch of science that deals with the geometric descriptionof crystals & their internal arrangements. It is the science of crystals & the math used to describe them. It is aVERY OLD fieldwhich pre-dates Solid State Physicsby about a century! So (unfortunately, in some ways) much of the terminology (& theory notation) of Solid State Physics originated in crystallography. The purpose of Ch. 1 of Kittel’s book is mainly to introduce this terminology to you.

19. Solid State Physics Started in the early 20th Century when the fact that Crystals Can Diffract X-rays was discovered. • This was around the same time that the new theory of Quantum Mechanics was being accepted & applied to various problems. Some of the early problems it was applied to were the explanation of observed X-ray diffraction patterns for various crystals & (later) the behavior of electrons in a crystalline solid.

20. Crystallography A Basic Knowledge of Elementary Crystallography is Essential for Solid State Physicists!!! • A crystal’s symmetry has a profound influence on many of its properties. • A crystal structure should be specified completely, concisely & unambiguously. • Structures are classified into different types according to the symmetries they possess. • In this course, we only consider solids with “simple” structures.

21. Crystal Lattice Crystallography focuses on the geometric properties of crystals. So, we imagine each atom replaced by a mathematicalpoint at the equilibrium position of that atom. ACrystal Lattice(or a Crystal) ≡ An idealized description of the geometry of a crystalline material. ACrystal ≡A 3-dimensional periodic array of atoms. Usually, we’ll only consideridealcrystals.“Ideal”means one with no defects, as already mentioned. That is, no missing atoms, no atoms off of the lattice sites where we expect them to be, no impurities,…Clearly, such an ideal crystalnever occurs in nature. Yet, 85-90% of experimental observations on crystalline materials is accounted for by considering only ideal crystals! Crystal Lattice & Structure of Platinum Platinum Platinum Surface (Scanning Tunneling Microscope)

22. Mathematically A Lattice is Defined as an Infinite Array of Points in Space in which each point has identical surroundings to all others. The points are arranged exactly in a periodic manner. y B C D E α b O x a A Crystal Lattice 2 Dimensional Example   22

23. Ideal Crystal ≡ An infinite periodic repetition of identical structural units in space. • The simplest structural unit we can imagine is a Single Atom.This corresponds to a solid made up of only one kind of atom ≡ An Elemental Solid. • However, this structural unit could also be a group of several atoms or even molecules. The simplest structural unit for a given solid is called theBASIS

24. The structure of anIdeal Crystalcan be described in terms of a mathematical construction called aLattice. A Lattice ≡ • A 3-dimensional periodic array of points in space. For a particular solid, the smallest structural unit, which when repeated for every point in the lattice is called the Basis. • The Crystal Structure is defined once both the lattice & the basis are specified. That is Crystal Structure ≡Lattice + Basis

25. Crystalline Periodicity • In a crystalline material, the equilibrium positions of all the atoms form a crystal Crystal Structure ≡ Lattice + Basis For example, see Fig. 2. Lattice  Basis  Crystal Structure

26. Crystalline Periodicity Crystal Structure ≡ Lattice + Basis For another example, see the figure. Crystal Structure  Lattice  Basis 

27. Crystalline Periodicity Basis   Crystal Structure ≡ Lattice + Basis Another example. Crystal Structure   Lattice 

28. A Two-Dimensional Bravais Lattice with Different Choices for the Basis

29. 2 Dimensional Lattice y y B C D B C D E α b F G b x O x O a A a A Lattice with atoms at corners of regular hexagons E H 29

30. The atoms do not necessarily lie at lattice points!! Crystal Structure = Lattice + Basis Basis  30