Reading: Chapter 4 Core Problems: 2, 16, 17, 19, 24
Self-help Problems: 1, 3, 24, 28
Objectives of Chapter 4
Introduce the three basic types of imperfections: point defects, line defects (or dislocations), and surface defects. Explore the nature and effects of different types of defects.
Figure 4.1 Point defects: (a) vacancy, (b) interstitial atom, (c) smallsubstitutional atom, (d) large substitutional atom, (e) Frenkel defect, (f) Schottky defect. All of these defects disrupt the perfect arrangement of the surrounding atoms.
(c) 2003 Brooks/Cole Publishing / Thomson Learning
1. Point Defects
Point defects - Imperfections, such as vacancies, that are located typically at one sites in the crystal. Vacancy - An atom or an ion missing from its regularcrystallographic site. Interstitial defect - A point defect produced when an atom is placed into the crystal at a site that is normally not a lattice point. Substitutional defect - A point defect produced when an atom is removed from a regular lattice point and replaced with a different atom, usually of a different size.
Equilibrium Concentration: Point Defects
• Equilibrium concentration varieswith temperature! No. of defects No. of atoms Activation energy
⎛ −Q ⎞ Nv v = exp ⎜ ⎜ ⎝ kT ⎠ N
Qv is the energy required for the formation of a vacancy Q ↑ → NV↓ T ↑ → NV ↑
Vacancies are introduced into metals and alloys during solidification at high temperature. Vacancies play an important role in determining the rate at which atoms or ions can move around, or diffuse ina solid material, especially in pure metals.
Example 4.1 The Effect of Temperature on Vacancy Concentrations
Calculate the concentration of vacancies in copper at room temperature (25oC). What temperature will be needed to heat treat copper such that the concentration of vacancies produced will be 1000 times more than the equilibrium concentration of vacancies at room temperature? Assume that20,000 cal are required to produce a mole of vacancies in copper. Example 4.1 SOLUTION The lattice parameter of FCC copper is 0.36151 nm. The basis is 1, therefore, the number of copper atoms, or lattice points, per cm3 is:
4 atoms/cell n = = 8.47 × 10 22 copper atoms/cm3 −8 3 (3.6151 × 10 cm)
Example 4.1 SOLUTION (Continued) At room temperature, T = 25 + 273 = 298 K:
⎛ − Qν ⎞ nν = nexp⎜ ⎟ ⎝ RT ⎠ cal ⎛ ⎞ − 20,000 ⎜ ⎟ ⎛ 22 atoms ⎞ mol ⎟ = ⎜ 8.47 × 10 ⎟ . exp⎜ 3 cal cm ⎠ ⎝ ⎜ 1.987 × 298K ⎟ ⎜ ⎟ mol − K ⎝ ⎠ = 1.815 × 108 vacancies/cm 3
We could do this by heating the copper to a temperature at which this number of vacancies forms:
⎛ − Qν ⎞ nν = 1.815 × 10 = n exp⎜ ⎟ T=375 K ⎝ RT ⎠ = (8.47 × 1022 ) exp( −20,000 /(1.987 × T )), T = 102o C
Extended defects - Defects thatinvolve several atoms/ions and thus occur over a finite volume of the crystalline material (e.g., dislocations, stacking faults, etc.).
Screw dislocation: spiral planar ramp resulting from shear deformation b || to dislocation line
Burgers Vector: Magnitude and direction of lattice distortion
The perfect crystal (a) is cut and sheared one atom spacing, (b) and (c). Theline along which shearing occurs is a screw dislocation. A Burgers vector b is required to close a loop of equal atom spacings around the screw dislocation.
Edge dislocation: extra half-plane of atoms inserted in a crystal structure b ⊥ to dislocation line
The perfect crystal in (a) is cut and an extra plane of atoms is inserted (b). The bottom edge of the extra plane is an edge dislocation(c). A Burgers vector b is required to close a loop of equal atom spacings around the edge dislocation.
A mixed dislocation. The screw dislocation at the front face of the crystal gradually changes to an edge dislocation at the side of the crystal.
Schematic of slip line, slip plane, and slip (Burgers) vector for (a) an edge dislocation and (b) for a screw dislocation.
The motion of...