1. IMPERFECTIONS IN SOLIDS Week 3 1

2. 2 Solidification - result of casting of molten material –2 steps Nuclei form Nuclei grow to form crystals – grain structure Start with a molten material – all liquid Imperfections in Solids Crystals grow until they meet each other nuclei crystals growing grain structure liquid

3. 3 Polycrystalline Materials Grain Boundaries regions between crystals transition from lattice of one region to that of the other slightly disordered low density in grain boundaries –high mobility –high diffusivity –high chemical reactivity

4. 4 Solidification Columnar in area with less undercooling Shell of equiaxed grains due to rapid cooling (greater  T) near wall Grain Refiner - added to make smaller, more uniform, equiaxed grains. heat flow Grains can be- equiaxed (roughly same size in all directions) - columnar (elongated grains) ~ 8 cm

5. 5 Imperfections in Solids There is no such thing as a perfect crystal. What are these imperfections? Why are they important? Many of the important properties of materials are due to the presence of imperfections. Crystalline defect -> a lattice irregularity having one or more of its dimensions on the order of an atomic diameter

6. 6 Vacancy atoms Interstitial atoms Substitutional atoms Point defects Types of Imperfections Dislocations Line defects Grain Boundaries Area defects

7. 7 Vacancies: -vacant atomic sites in a structure. Self-Interstitials: -"extra" atoms positioned between atomic sites. Point Defects Vacancy distortion of planes self- interstitial distortion of planes

8. 8 Boltzmann's constant (1.38 x 10 -23 J/atom-K) (8.62 x 10 -5 eV/atom-K)  N v N  exp  Q v kT       No. of defects No. of potential defect sites. Activation energy Temperature Each lattice site is a potential vacancy site Equilibrium concentration varies with temperature! Equilibrium Concentration: Point Defects

9. 9 We can get Q v from an experiment.  N v N = exp  Q v kT       Measuring Activation Energy Measure this... N v N T exponential dependence! defect concentration Replot it... 1/T N N v ln - Q v /k/k slope

10. EXAMPLE PROBLEM 4.1 Calculate the equilibrium number of vacancies per cubic meter for copper at 1000C. The energy for vacancy formation is 0.9 eV/atom; the atomic weight and density (at 1000C) for copper are 63.5g/mol and 8.4g/cm 3, respectively 10

11. 11 Find the equil. # of vacancies in 1m 3 of Cu at 1000  C. Given: A Cu = 63.5 g/mol  = 8.4 g/cm 3 Q v = 0.9 eV/atom N A = 6.02 x 10 23 atoms/mol Estimating Vacancy Concentration For 1 m 3, N = N A A Cu  x x1 m 3 = 8.0 x 10 28 sites 8.62 x 10 -5 eV/atom-K 0.9 eV/atom 1273K  N v N  exp  Q v kT       = 2.7 x 10 -4 Answer: N v =(2.7 x 10 -4 )(8.0 x 10 28 ) sites = 2.2 x 10 25 vacancies  =N.A cu /V.N A

12. 12 Low energy electron microscope view of a (110) surface of NiAl. Increasing T causes surface island of atoms to grow. Why? The equil. vacancy conc. increases via atom motion from the crystal to the surface, where they join the island. Observing Equilibrium Vacancy Concentration. Island grows/shrinks to maintain equil. vancancy conc. in the bulk.

13. IMPURITIES IN SOLIDS Impurity or foreign atoms will always be present, and some will exist as crystalline point defects Alloys -> impurity atoms have been added intentionally to impart specific characteristics to the material Alloying with copper significantly enhances the mechanical strength without depreciating the corrosion resistance appreciably The addition of impurity atoms to a metal will result in the formation of a solid solution 13

14. 14 Two outcomes if impurity (B) added to host (A): Solid solution of B in A (i.e., random distribution of point defects) Solid solution of B in A plus particles of a new phase (usually for a larger amount of B) OR Substitutional solid soln. (e.g., Cu in Ni) Interstitial solid soln. (e.g., C in Fe) Second phase particle --different composition --often different structure. Point Defects in Alloys

15. 15 Imperfections in Solids Conditions for substitutional solid solution (S.S.) W. Hume – Rothery rule –1.  r (atomic radius) < 15% –2. Proximity in periodic table i.e., similar electronegativities –3. Same crystal structure for pure metals –4. Valency All else being equal, a metal will have a greater tendency to dissolve a metal of higher valency than one of lower valency

16. Substitutional Solid Solution – Cu-Ni The atomic radii for copper and nickel are 0.128 and 0.125nm, respectively Both have the FCC crystal structure Their electronegativities are 1.9 and 1.8 Valencies for Cu and Ni are +2 16

17. 17 Imperfections in Solids Application of Hume–Rothery rules – Solid Solutions 1. Would you predict more Al or Ag to dissolve in Zn? 2. More Zn or Al in Cu? ElementAtomicCrystalElectro-Valence Radius Structure nega- (nm) tivity Cu0.1278FCC1.9+2 C0.071 H0.046 O0.060 Ag0.1445FCC1.9+1 Al0.1431FCC1.5+3 Co0.1253HCP1.8+2 Cr0.1249BCC1.6+3 Fe0.1241BCC1.8+2 Ni0.1246FCC1.8+2 Pd0.1376FCC2.2+2 Zn0.1332HCP1.6+2

18. Conditions for Interstitial Impurity The atomic diameter of an interstitial impurity must be substantially smaller than that of the host atoms The maximum allowable concentration of interstitial impurity atoms is low Even very small impurity atoms are ordinarily larger than the interstitial sites, and as a consequence they introduce some lattice strains on the adjacent host atoms Different crystal structures can fill interstitials 18

19. 19 Specification of Composition –weight percent m 1 = mass of component 1 n m1 = number of moles of component 1 – atom percent

20. 20 are line defects, slip between crystal planes result when dislocations move, produce permanent (plastic) deformation. Dislocations: Schematic of Zinc (HCP): before deformation after tensile elongation slip steps Dislocations - Line Defects

21. 21 Imperfections in Solids Linear Defects (Dislocations) –Are one-dimensional defects around which atoms are misaligned Burgers vector ( b ) represents the magnitude and direction of the distortion of dislocation in a crystal lattice Dislocation Line -> A curve running along the center of a dislocation. Edge dislocation: –extra half-plane of atoms inserted in a crystal structure –b  to dislocation line Screw dislocation: –spiral planar ramp resulting from shear deformation –b  to dislocation line

22. 22 Imperfections in Solids Edge Dislocation

23. 23 Dislocation motion requires the successive bumping of a half plane of atoms (from left to right here). Bonds across the slipping planes are broken and remade in succession. Atomic view of edge dislocation motion from left to right as a crystal is sheared. Motion of Edge Dislocation

24. 24 Imperfections in Solids Screw Dislocation Burgers vector b Dislocation line b (a) (b) Screw Dislocation

25. 25 Edge, Screw, and Mixed Dislocations Edge Screw Mixed

26. 26 Imperfections in Solids Dislocations are visible in electron micrographs 51,450 magnified

27. 27 Planar Defects in Solids One case is a twin boundary (plane) –Essentially a reflection of atom positions across the twin plane. A twin boundary is a special type of grain boundary across which there is a specific mirror lattice symmetry Annealing twins are typically found in metals that have the FCC crystal structure, while mechanical twins are observed in BCC and HCP metals

28. Planar Defects in Solids Stack Fault are found in FCC metals when there is an interruption in the ABCABCABC... stacking sequence of close-packed planes Phase boundaries exist in multiphase materials across which there is a sudden change in physical and/or chemical characteristics 28

29. Bulk or Volume Defects Other defects exist in all solid materials that are much larger than those discussed These include pores, cracks, foreign inclusions, and other phases They are normally introduced during processing and fabrication steps. 29

30. Numerical Problems Problems 4.1 to 4.5 and 4.7 to 4.25 30