CHAPTER 4: IMPERFECTIONS IN SOLIDS

1. CHAPTER 4:IMPERFECTIONS IN SOLIDS • Deviations from perfect structure • Not always adverse, and many times deliberately introduced • Can be classified according to dimensionality: • Point Defects (affect one or two atom positions) – “zero” dimension • Linear Defects (a.k.a. dislocations) – 1-D • Interfacial or boundary defects – 2-D • Volume Defects – 3-D

2. POINT DEFECTS A. Vacancies: -vacant lattice sites. -formed during solidification or as a result of atomic vibrations. Equilibrium number of vacancies: • Total number of atomic sites (per unit volume) • Energy of activation (energy needed to form one vacancy) [J/atom] • Boltzmann’s constant [J/atom-K] • Absolute temperature Typical value just below melting temp:

3. ESTIMATING VACANCY CONC. 3 • Find the equil. # of vacancies in 1m of Cu at 1000C. • Given: • Answer:

4. Point Defects B. Self-interstitial: -"extra" atom crowded between atomic site (interstitial site). -produces large distortions – not highly probable.

5. C. Impurities Two outcomes if impurity (B) is added to host (A): 1. Solid solution of B in A (i.e., random dist. of point defects) OR Substitutional alloy (e.g., Cu in Ni) Interstitial alloy (e.g., C in Fe) 2. Solid solution of B in A plus particles of a new phase (usually for a larger amount of B) Second phase particle --different composition --often different structure.

6. Impurities • Solid Solutions: • Solute – minority atoms • Solvent – majority atoms • Crystal structure of solvent is maintained – solute atoms are randomly distributed. • Types of Solid solutions: • Substitutional – impurity atoms replace host atoms • Atomic radii difference is < ±15% • Complete Solubility: • Relative atomic radii • Same crystal structure • Electronegativities • Valence • Ex. Cu & Ni (both FCC, RCu=0.128 nm, RNi=0.125 nm; Electroneg: 1.9 & 1.8) • b) Interstitial – impurity atoms fill interstitial spaces • Small impurity atom • Ex: Carbon in iron, RC=0.071, RFe=0.124 nm.

7. COMPOSITION Definition: Amount of impurity (B) and host (A) in the system. Two Ways of describing relative amounts: • Weight % • Atom % (also called mole%)

8. • Conversion between wt % and at% in an alloy:

10. Other Composition Equations: • Mass of component 1 per unit volume of solution (kg/m3): • Average Density and Average Atomic Weight

11. LINE DEFECTS Dislocations: • one-dimensional defects around which atoms are misaligned. • Edge Dislocation – • - plane of atoms terminates w/in the crystal • - Dislocation line – defined along the edge of extra half-plane. • - above: compressed, below: pulled apart

12. 2) Screw dislocation – • Formed by a shear stress • Upper front region is shifted to the right relative • Also linear wrt dislocation line.

13. 3) Mixed dislocation - combination Burger’s vector -magnitude and direction of lattice distortion Edge: Burger’s vector perpendicular to dislocation line Screw: parallel Mixed: neither parallel nor perpendicular

14. INTERFACIAL DEFECTS a. External surface • surface atoms not bonded to max number of nearest neighbors are at a higher energy state surface energy b. Grain boundaries • separate regions of different crystallographic orientations. • grain boundary energy – atoms along the grain boundary are not bonded to maximum number of neighbors. Effect of grain size Effect of angle of misalignment

15. Interfacial Defects c. Others • twin boundary. • stacking faults • phase boundaries Volume Defects Pores, cracks foreign inclusions

16. OPTICAL MICROSCOPY • to study microstructure (grain size and shapes). • specimen is polished and etched • usually analyzed as a photomicrograph

17. Grain Size Intercept Method: • Draw straight lines of same length and random orientation, • Count number of grains intersected by each line. • Line length ÷ # grains [m/grain]; average, then ÷ magnification ASTM Grain Size Number

18. 1. A one-dimensional imperfection wherein the plane of atoms terminates within the crystal is called a(n) • Dislocation. • Vacancy. • Edge dislocation. • Screw dislocation.

19. 2) Which of the following will increase the equilibrium number of vacancy for a given crystal? • Higher temperature • Higher activation energy for vacancy. • Higher atomic weight. • None of the above.

20. 3) Which of the following will form an interstitial solid solution with Iron? • Nitrogen • Nickel • Copper • Aluminum.

21. 4) Which of the following conditions need to be satisfied for a substitutional solid solution of incomplete solubility? • Radius difference of less than 15% • Same crystal structure • Same valence • Similar electronegativies. • All of the above.

22. 5) It is known that a certain solid solution has a composition 50wt% A – 50wt% B, and that the atomic weight of A is higher than that of B. Which of the following is true regarding the Atom% of the solid? • 50 at% A • Higher than 50 at% A • Lower than 50 at% A • None of the above.

23. 6) Which of the following interfacial defects has the least amount of surface energy per unit volume? • Small grains with large angles of misalignment. • Large grains with small angles of misalignment. • Small grains with small angles of misalignment. • Large grains with large angles of misalignment.

24. 7) For an FCC crystal, along which direction is the linear density the smallest? • [100] • [110] • [111]