1. Solid State Physics Yuanxu Wang School of Physics and Electronics Henan University wyxhenu@gmail.com 双语教学示范课程 1

2. Chapter 3 Crystal defect Crystal are like people. It is the defects that tend to make them interesting Colin Umphreys

3. Defects in Crystals  Real crystals are never perfect.  Always contain defects that affect their properties.  In many situations defects are desirable.  Four main types: point defects, line defects, grain boundary defects and volume defects.

4. Examples of defects  In diamonds, the number and type of defects determine the price.  Generation, accumulation and interaction of defects in different parts of a car determine the age.  Si crystals for IC fabrication should be defects free. Defects are specifically introduced.  Forging a metal introduces defects and increases the strength and elasticity of a tool.

5. Point Defects These defects arise when there are atoms missing or atoms are in irregular positions within a lattice. There are number of point defect types:  Lattice vacancies  Substitutional and interstitial impurities  Self impurities

6. Point defects 1. Vacancy 2. Self-interstitial 3. Interstitial impurity 4. Substitutional impurity 5. Substitutional impurity

7. Point Defects Vacancies: The No.1 of missing atoms (vacancies) increases with temperature. Atoms can frequently change their position leaving empty lattice site called vacancies. The number of vacancies N v increases exponentially with the absolute temperature T and is given by  Where N s = number of regular lattice sites K B = Boltzmann constant E v = energy needed to create a vacancy in a perfect crystal

8. The energy necessary for an atom to vacant site (and hence create a vacancy at its original site) is called the Activation Energy for vacancy motion E m. Interstitials: These are atoms squeezed in between regular lattice sites. If the interstitial atoms are of the same species as the lattice atoms, it is called “ Self –interstitial “. Creation of a self-interstitial requires more energy than that required for a vacancy creation. Frenkel Defects: Point defects in ionic crystals are charged as the ions themselves. To maintain charge neutrality several point defects can be created. A Frenkel defect is a pair of cation (positive ion) vacancy and a cation interstitial. Or it may be an anion vacancy and anion interstitial.

9. Schottky Defects: A Schottky defect is a pair of anion and cation vacancies. A perfect NaCl crystal 2 Frenkel defects Schottky defect

10. Question: Why metals can be plastically deformed and why the plastic deformation properties could be changed to a very large degree by forging without changing the chemical properties ? This phenomenon was explained by Taylor, Orowan and Olyani by using the concept of dislocations. Dislocations are thought of as extra lattice planes inserted in the crystal but not extending through all of the crystal but ending in the dislocation line. Motion of dislocations allows slip- Plastic Deformation – when interatomic bonds are fractured and reformed. Slip always occurs through dislocations motion.

11. Dislocations ( Line defects) :These defects produce lattice distortions centered about a line. A dislocation is the edge of an extra inserted fractional plane of atoms. Dislocations play a very important role in the deformation of crystals. Slip: Plastic deformation when interatomic bonds are fractured and reformed. Slip always occurs through dislocations motion. Slip plane: The plane in which a dislocation moves through a crystal

12. When a shear stress is applied, the dislocation moves, one atomic row after another, until one part of the crystal is displaced relative to the other. The motion of the dislocation causes the crystal to be permanently deformed.

13. On either side of the dislocation, the crystal lattice is perfect but in the vicinity of the dislocation the lattice is severely distorted. For a positive edge dislocation, the presence of the extra half plane causes the atoms above the slip plane to be in compression while those below are in tension.

14. Dislocations and slip Why dislocations allow slip at much lower stress than in a perfect crystal. If the top half of the crystal is slipping one plane at a time then only a small fraction of the bonds are broken at any given time and this would require much lower force. In the process of slipping one plane at a time a dislocation is created and propagates across the crystal. We do not have to break all the bonds simultaneously which would require much larger force. Motion of a dislocations: Moving a large carpet by creating a hump and then push it across.

15. Edge and Screw Dislocations Boundary between the slipped and unslipped regions lies perpendicular to the direction of slip. Edge Dislocation Screw Dislocation Boundary between the slipped and unslipped regions lies parallel to the direction of slip Edge dislocation

16. Dislocations Dislocation: A line defect which separates the slipped and unslipped regions of a crystal which is being deformed. Dislocation Density: N d is defined as the total length of dislocation line in unit volume. It is also equal to the number of dislocations which cut through a unit area which is randomly oriented in a crystal. The Burgers’ Vector: A dislocation cannot be described just in terms of its orientation since this can vary with position. The entire dislocation is characterized by a vector which represents the amount and direction of slip which is produced when that dislocation has passed right through the crystal in a certain direction. This vector is called the Burgers’ vector b.

17. The magnitude of b (called the strength of dislocation) is a repeat vector of the lattice. Burgers’ vector is constant throughout its length even though the orientation of the dislocation might change. This vector lies in the slip plane and is perpendicular to an edge dislocation and parallel to screw dislocation. To find the Burgers’ vector, we make a circuit from atom to atom counting the same number of atomic distances in all directions. If the circuit encloses a dislocation it will not close. The vector that closes the loop is the Burgers’ vector.

18. Burger’s Vector A dislocation is characterized by its Burgers vector: If you imagine going around the dislocation line, and exactly going back as many atoms in each direction as you have gone forward, you will not come back to the same atom where you have started. The Burgers vector points from start atom to the end atom of your journey. This "journey" is called Burgers circuit in dislocation theory.

19. The strength of Materials When a stress is applied to any material the general pattern : Initially there is a small amount elastic strain (<1%) If the stress is removed, the specimen returns to its original length. –Elastic behavior. As the stress is increased the specimen yields and this is followed by plastic deformation. The amount of plastic flow can be zero (brittle material) to more than 100%. When the

20. stress is removed the length decreases only slightly and if it is reapplied, there is first a new short elastic region and then plastic yielding starts again at the stress to which the specimen was previously loaded. The material is said to be hardened by the initial amount of plastic deformation. This is called Work Hardening. Stress

21. If the stress is relaxed to 0 at A and is then reapplied, there is a region of elastic deformation (dotted line) followed by yield at A. (Work Hardening). Construction materials are used under conditions of stress in which they must not yield. We would like to control the yield stress and find mechanism that can raise it highest possible value.

22. Brittle Fractures The deformation mechanisms give rise to plastic flow before ultimate failure of the sample. There are many materials such as glass and cast iron that exhibit brittle fracture without any plastic deformation. Brittle fractures are always associated with the existence or the formation of cracks. The cracks can be formed in many ways: during the production of glass or inclusion of graphite flakes in cast iron.

23. Grain Boundaries Found in Polycrystalline materials. Present paths for atoms to diffuse into the material and scatter light through transparent materials to make them opaque. the boundaries limit the lengths and motions of dislocations that can move. That means that smaller grains (more grain boundary surface area) strengthens materials. The size of grains can be controlled by the cooling rate. Rapid cooling (quenching) produces smaller grains. Large grains result in low strength materials.

24. Any defect in the regular lattice disrupts the motion of dislocations Motion of dislocations produces more dislocations which impede the motion of other dislocations and increases the strength of the material The size of the grains can be controlled by the cooling rate when the sample is produced from the melt. Rapid cooling (quenching) produces smaller grains whereas slower cooling results in larger gains. At room temperature, larger grains result in low strength, hardness and ductility.

25. Plastic deformation and Fracture  Elastic deformation: is reversible –involves bond stretching.  Plastic deformation; permanent- involves defects formation and movement  Strengthening: Impede the movement of dislocations- done by creating defects- point defects (alloying), dislocations (work hardening) and making smaller grains (fast cooling- quenching).