Chapter 5:

1. Chapter 5: Imperfections: Interfacial and Volumetric Defects

2. Grains Orientation Grains in a metal or ceramic; the cube depicted in each grain indicates the crystallographic orientation of the grain in a schematic fashion.

3. Grains of Tantalum and TiC Micrographs showing polycrystalline (a) tantalum and (b) TiC.

4. Mean Linear Intercept Low-angle grain-boundary observed by high-resolution transmission electron microscopy. Positions of individual dislocations are marked by Burgers circuits. (Courtesy of R. Gronsky)

5. Tilt and Twist Boundaries Low-angle tilt boundary.

6. Low-angle twist boundary

7. Grain-Boundary Energy with Misorientation Variation of grain-boundary energy γ gb with misorientation θ. (Adapted with permission from A. G. Guy, Introduction to Materials Science (New York: McGraw-Hill, 1972), p. 212.)

8. Coincidence Boundary Coincidence lattice made by every seventh atom in the two grains, misoriented 22◦ by a rotation around the <111> axis. (Adapted from M. L. Kronberg and H. F. Wilson, Trans. AIME, 85 (1949), 501.)

10. Interface between alumina and NiAl2O4 Interface between alumina and NiAl2O4 (spinel). (a) High-resolution TEM. (b) Representation of individual atomic positions. (Courtesy of C. B. Carter.)

11. Grain Size vs. Volume Fraction of Intercrystal Regions The effect of grain size on calculated volume fractions of intercrystal regions and triple junctions, assuming a grain boundary thickness of 1 nm. (Adapted from B. Palumbo, S. J. Thorpe, and K. T. Aust, Scripta Met., 24 (1990) 1347.)

12. Ledge Formation in Grain Boundary Models of ledge formation in a grain boundary. (Reprinted with permission from L. E. Murr, Interfacial Phenomena in Metals and Alloys (Reading, MA: Addison Wesley, 1975), p. 255.)

13. Grain Boundary Ledges Grain boundary ledges observed by TEM. (Courtesy of L. E. Murr.)

14. Tilt Boundary Image and atomic position model of an approximately 32◦ [110] tilt boundary in gold; note the arrangement of polygons, which represents the boundary. (From W. Krakow and D. A. Smith, J. Mater. Res. 22 (1986) 54.)

16. Twinning in FCC metals Schematic of twinning in FCC metals.

17. Deformation Twins Deformation twins in (a) iron-silicon (Courtesy of O. V¨ohringer) and (b) stainless steel.

18. Deformation Twins in Silicon Nitride Deformation twins in silicon nitride observed by TEM. (a) Bright field. (b) Dark field. (c) Electron diffraction pattern showing spots from two twin variants, A and B. (Courtesy of K. S. Vecchio.)

19. Stress-Strain Curve Due to Twinning Serrated stress–strain curve due to twinning in a Cd single crystal. (Adapted with permission from W. Boas and E. Schmid, Z. Phys., 54 (1929) 16.)

20. Twinning in HCP Metals Twinning in HCP metals with c/a ratio more than or Dislocation motion at less √3.

21. Twinning Due to Dislocation Motion Effect of temperature on the stress required for twinning and slip (at low and high strain rates). (Courtesy of G. Thomas.)

22. Mechanical Effects (a) Stress–strain curves for copper (which deforms by slip) and 70% Cu–30% Zn brass (which deforms by slip and twinning). (b) Work-hardening slope dσ/dε as a function of plastic strain; a plateau occurs for brass at the onset of twinning. (After S. Asgari, E. El-Danaf, S. R. Kalidindi, and R. D. Doherty, Met. and Mater. Trans., 28A (1997) 1781.)

23. Effect of Temperature and Stacking-Fault Energy on Twinning Stresses Effect of temperature on twinning stress fore a number of metals. (From M. A. Meyers, O. Voehringer, and V. A. Lubarda, Acta Mater., 49 (2001) 4025.) Effect of stacking-fault energy on the twinning stress for several copper alloys. (From M. A. Meyers, O. Voehringer, and V. A. Lubarda, Acta Mater., 49 (2001) 4025.)

24. Temperature-Strain Rate Plots Temperature–strain rate plots with slip and twinning domains; (a) effect of grain size in titanium; (b) effect of stacking-fault energy in copper–zinc alloys. (From M. A. Meyers, O. Voehringer, and V. A. Lubarda, Acta Mater., 49 (2001) 4025.)

25. Grain-Size Strengthening Hall–Petch plot for a number of metals and alloys. Y. S. indicates yield strength.

27. Hall-Petch Plot σy= σ0 + kD−1/2 σy - is the yield stress σ0 - is a frictional stress required to move dislocations k - is the H--P slope D is the grain size Hall–Petch plot for iron and low-carbon steel extending from monocrystal to nanocrystal; notice the change in slope. (After T. R. Smith, R. W. Armstrong, P. M. Hazzledine, R. A. Masumura, and C. S. Pande, Matls. Res. Soc. Symp. Proc., 362 (1995) 31.)

28. Frank-Read Source Frank–Read source operating in center of grain and producing two pileups at grain 1 boundaries; the Frank–Read source in grain 2 is activated by stress concentration.

29. Dislocation Activity at Grain Boundaries in Stainless Steel Dislocation activity at grain boundaries in AISI 304 stainless steel (˙ε = 10−3 s−1). (a) Typical dislocation profiles after a strain of 0.15%. (b) Same after a strain of 1.5%. (Courtesy of L. E. Murr.)

30. Meyers-Ashworth Theory Sequence of stages in (a) polycrystalline deformation, starting with (b) localized plastic flow in the grain-boundary regions (microyielding), forming (c) a work-hardened grain-boundary layer that effectively reinforces the microstructure.

31. Deformation Twins Deformation twins in shock-loaded nickel (45 GPa peak pressure; 2 μs pulse duration). Plane of foil (100); twinning planes (111) making 90◦. (Courtesy of L. E. Murr.) Strength of wire-drawn and recovered Fe–0.003% C as a function of transverse linear-intercept cell size. Recovery temperatures (in ◦C) as indicated. (Adapted with permission from H. J. Rack and M. Cohen, in Frontiers in Materials Science: Distinguished Lectures, L. E. Murr, ed. (New York: M. Dekker, 1976), p. 365.)

32. Nanocrystalline Materials Gleiter representation of atomic structure of a nanocrystalline material; white circles indicate grain-boundary regions. (Courtesy of H. Gleiter.)

33. Hall-Petch Relationships Stress–strain curves for conventional (D = 50 μm) and nanocrystalline (D = 25 μm) copper. (Adapted from G. W. Nieman, J. R. Weertman, and R. W. Siegel, Nanostructured Materials, 1 (1992) 185.) Hall–Petch relationship for nanocrystalline copper. (After G. W. Nieman, J. R. Weertman, and R. W. Siegel, Nanostructured Matls., 1 (1992) 185)

34. Classical Hall-Petch Classical Hall–Petch slope compared with Meyers–Ashworth equation and computations assuming a grain-boundary region and grain interior with different work-hardening curves. As grain size is decreased, grain-boundary region gradually dominates the deformation process. (From H.-H. Fu, D. J. Benson, and M. A. Meyers, Acta Mater., 49 (2001) 2567.)

35. Voids in Titanium Carbide Voids (dark spots marked by arrows) in titanium carbide. The intergranular phase (light) is nickel, which was added to increase the toughness of the TiC.

36. Voids (a) Transmission electron micrograph illustrating faceted grain-interior voids within alumina and (b) voids in titanium carbide; dislocations are pinned by voids.