Chapter 4

1. Chapter 4 Imperfections in Solids Dr. Mohammad Abuhaiba, PE

2. Why Study Imperfections in Solids? • Properties of materials are affected by the presence of imperfections • Crystalline defect:a lattice irregularity having one or more of its dimensions in the order of an atomic diameter • Classification of imperfections is made according to geometry or dimensionality of the defect. • 3 basic types of imperfections: • Point defects (PD) • Line defects (dislocations) • Surface defects, SD Dr. Mohammad Abuhaiba, PE

3. Point Defects (PD) • Localized disruptions in otherwise perfect atomic or ionic arrangement in a crystal structure. • These imperfections may be introduced by movement of atoms or ions when they gain energy: • by heating • during processing • by introduction of impurities • doping • Impurities: elements or compounds that is present from raw materials or processing. • Dopants: elements or compound that is deliberately added, in known concentrations, at specific location in the microstructure, with an intended beneficial effect on properties or processing. Dr. Mohammad Abuhaiba, PE

4. Point Defects (PD)4.2 Vacancies and self-interstitials • Produced when an atom or an ion is missing from its normal site in the crystal structure (Figure 1). • Are introduced into metals & alloys during solidification at high temperatures. Dr. Mohammad Abuhaiba, PE

5. Point Defects (PD)4.2 Vacancies and self-interstitials Point Defects: • Vacancy • Interstitial • small substititionalatom • large substititionalatom • Frenkel defect • Schottkydefect Dr. Mohammad Abuhaiba, PE

6. Point Defects (PD)4.2 Vacancies and self-interstitials • Concentration of vacancies increases exponentially with T: • Nv = total no. of vacancies per cm3 • N = no. of atoms per cm3 • Qv = energy required for the formation of a vacancy • k = Gas constant = 1.38×10-23J/atom.K = 8.62×10-5 eV/atom.K • T = absolute temp in K Dr. Mohammad Abuhaiba, PE

7. Point Defects (PD)4.2 Vacancies and self-interstitials • For most metals, the fraction Nv/N just below the melting point is on the order of 10-4 • A self-interstitial: an atom from the crystal that is crowded into an interstitial site, a small void space that under ordinary circumstances is not occupied Dr. Mohammad Abuhaiba, PE

8. Example 4.1: Number-of-Vacancies Computation at a Specified Temperature Calculate the equilibrium number of vacancies per cubic meter for copper at 1000 °C. The energy for vacancy formation is 0.9 eV/atom; the atomic weight and density (at 1000 ° C) for copper are 63.5 g/mol and 8.4 g/cm3, respectively. Dr. Mohammad Abuhaiba, PE

9. 4.3 Impurities in Solids • The addition of impurity atoms to a metal will result in the formation of a solid solution and/or a new 2nd phase depending on: • Kinds of impurity • Their concentrations • Temperature • Solvent (host): element or compound that is present in the greatest amount • Solute: element or compound present in a minor concentration Dr. Mohammad Abuhaiba, PE

10. 4.3 Impurities in SolidsSolid Solutions • A solid solution forms as: • the solute atoms are added to the host material, • the crystal structure is maintained and • no new structures are formed. • A solid solution is also compositionally homogenous, the impurity atoms are randomly and uniformly dispersed within the solid. Dr. Mohammad Abuhaiba, PE

11. 4.3 Impurities in SolidsSubstitutional Defects • Introduced when one atom or ion is replaced by a different type of atom or ion. • Can be introduced either as an impurity or as a deliberate addition. • No. of defects is relatively independent of T. • Examples: dopants such as P or B into Si. • If we add Cu to Ni, Cu atoms will occupy crystallographic sites where Ni atoms would normally be present. Dr. Mohammad Abuhaiba, PE

12. 4.3 Impurities in SolidsSubstitutional Defects Rules for Substitutional solid solution: • Atomic size factor: difference in atomic radii between the two atom types is less than 15%. Otherwise, the solute atoms will create substantial lattice distorsions and a new phase will form. • Same Crystal structure for both solvent and solute • Electronegativity: the more electropositive one element and the more electronegative the other, the greater is the likelihood that they will form an intermetallic compound instead of a substituional solid solution • Valences: a metal will have more of a tendency to dissolve another metal of higher valence than one of a lower valence Dr. Mohammad Abuhaiba, PE

13. 4.3 Impurities in SolidsInterstitialDefects • Formed when an extra atom or ion is inserted into the crystal structure at a normally unoccupied position. • C atoms occupy interstitial sites in Fe crystal structure, introducing a stress in the localized region of the crystal in their vicinity. • If there are DLs in the crystals trying to move around these types of defects, they face a resistance to their motion, making it difficult to create permanent deformation in metals & alloys. • This is one important way of increasing strength of metallic materials. • No. of interstitial atoms or ions in structure remain nearly constant with T. Dr. Mohammad Abuhaiba, PE

14. 4.4 Specification of composition • Weight % basis • Atom % basis Dr. Mohammad Abuhaiba, PE

15. 4.4 Specification of composition • Composition Conversions: Eq. 4.6and 4.7 • Concentration in terms of mass of one component per unit volume of material: Eq4.9 • Average density and average atomic weight: Eq4.10and 4.11 Dr. Mohammad Abuhaiba, PE

16. Example 4.2Derivation of Composition-Conversion Equation Derive Equation 4.6a. Dr. Mohammad Abuhaiba, PE

17. Example 4.3Composition Conversion—From Weight Percent to Atom Percent Determine the composition, in atom percent, of an alloy that consists of 97 wt% aluminum and 3 wt% copper. Dr. Mohammad Abuhaiba, PE

18. 4.5 Dislocations - Linear Defects • DLs are line imperfections in an otherwise perfect crystal. • 3 types of DLs: • screw • Edge • mixed • DLs are useful in increasing strength of metals & alloys. Dr. Mohammad Abuhaiba, PE

19. 4.5 Dislocations - Linear DefectsEdge DL (EDL) • Slicing partway through a perfect crystal, spreading the crystal apart, & partly filling the cut with an extra plane of atoms. • The bottom edge of this inserted plane represents the EDL. • BV is perpendicular to the EDL. Dr. Mohammad Abuhaiba, PE

20. 4.5 Dislocations - Linear DefectsScrew DLs (SDL) • Cut partway through a perfect crystal and then skew the crystal one atom spacing. Dr. Mohammad Abuhaiba, PE

21. 4.5 Dislocations - Linear DefectsScrew DLs (SDL) • Following a crystallographic plane one rev around axis on which crystal was skewed, starting at a point x & traveling equal atom spacing in each direction, we finish one atom spacing below our starting point (y). • The vector required to complete the loop & return us to our starting point is the Burgers vector (BV) b. • The axis, around which we trace this path, is the screw DL. • BV is parallel to the SDL. Dr. Mohammad Abuhaiba, PE

22. 4.5 Dislocations - Linear DefectsMixed DLs Dr. Mohammad Abuhaiba, PE

23. 4.5 Dislocations - Linear Defects • When a shear force acting in direction of BV is applied to a crystal containing a DL, DL can move by breaking bonds between atoms in one plane. • The cut plane is shifted slightly to establish bonds with the original partial plane of atoms. • This shift causes DL to move one atom spacing to the side. Dr. Mohammad Abuhaiba, PE

24. 4.5 Dislocations - Linear Defects • If this process continues, DL moves through crystal until a step is produced on the exterior of crystal; the crystal has then been deformed. • Speed with which DLs move in materials is close to or greater than speed of sound. Dr. Mohammad Abuhaiba, PE

25. 4.5 Dislocations - Linear Defects Figure 4.6 A transmission electron micrograph of a titanium alloy in which the dark lines are dislocations. 51,450. (Courtesy of M. R. Plichta, Michigan Technological University.) Dr. Mohammad Abuhaiba, PE

26. 4.6 Interfacial DefectsExternal Surfaces • Along the external surface, • crystal structure terminates • Surface atoms are not bonded to maximum number of nearest neighbors, and are therefore in a higher energy state than atoms at interior positions. • bonds of these surface atoms that are not satisfied give rise to a surface energy • To reduce this energy, materials tend to minimize total surface area. • For example, liquids assume a shape having a minimum area - droplets become spherical. Dr. Mohammad Abuhaiba, PE

27. 4.6 Interfacial DefectsSurface defects (SD) • SDs are the boundaries, or planes, that separate a material into regions, each region having the same crystal structure but different orientations. • Grains and grain boundaries. Dr. Mohammad Abuhaiba, PE

28. 4.6 Interfacial DefectsSurface defects (SD) • By reducing the grain size, • we increase the no. of grains, and hence increase amount of grain boundary area. • Any DL moves only a short distance before encountering a GB and being stopped, and strength of metallic material is increased. Dr. Mohammad Abuhaiba, PE

29. 4.6 Interfacial DefectsSmall Angle Grain Boundaries (SAGB) • an array of DLs that produces a small mis-orientation between the adjoining crystals (F4.19). • Because energy of surface is less than that of a regular GB, SAGBs are not effective in blocking slip. • SAGB formed by EDL are called tilt boundaries, and those caused by SDL are called twist boundaries. Dr. Mohammad Abuhaiba, PE

30. 4.6 Interfacial DefectsPhase Boundaries • Phase boundaries exist in multiphase materials (Section 9.3), wherein a different phase exists on each side of the boundary. • Each of the constituent phases has its own distinctive physical and/or chemical characteristics. • Phase boundaries play an important role in determining the mechanical characteristics of some multiphase metal alloys. Dr. Mohammad Abuhaiba, PE

31. 4.6 Interfacial DefectsTwin Boundaries (TB) • a plane across which there is a special mirror image mis-orientation of the crystal structure (F4.9). • Twins can be produced when a shear force, acting along the twin boundary, causes the atoms to shift out of position. • Twinning occurs during deformation or HT of certain metals. • TB interferes with the slip process and increase the strength of metal. Dr. Mohammad Abuhaiba, PE

32. 4.6 Interfacial DefectsStacking Faults • occur in FCC metals, • represent an error in stacking sequence of CPP. • Normally a stacking sequence of ABCABCABC is produced in a perfect FCC crystal. • Suppose the following sequence is produced: ABC ABABC ABC • This small region, which has HCP stacking sequence instead of FCC stacking sequence, represents a stacking fault. • Stacking faults interfere with the slip process. Dr. Mohammad Abuhaiba, PE

33. 4.7 Bulk or Volume Defects • Includes: • Pores • Cracks • foreign inclusions • other phases • normally introduced during processing and fabrication steps. Dr. Mohammad Abuhaiba, PE

34. 4.8 Atomic Vibrations • Every atom in a solid material is vibrating very rapidly about its lattice position • within the crystal. • In a sense, these atomic vibrations may be thought of as imperfections • or defects. • At any instant of time not all atoms vibrate at the same frequency and amplitude, nor with the same energy. • At a given temperature there will exist a distribution of energies for the constituent atoms about an average energy. • Over time the vibrational energy of any specific atom will also vary in a random manner. Dr. Mohammad Abuhaiba, PE

35. 4.8 Atomic Vibrations • With rising temperature, this average energy increases • Temperature of a solid is really just a measure of the average vibrational activity of atoms and molecules. • At room temperature, a typical vibrational frequency is on the order of 1013vibrations / second, whereas the amplitude is a few thousandths of a nanometer. • Many properties and processes in solids are manifestations of this vibrational atomic motion. • For example, melting occurs when the vibrations are vigorous enough to rupture large numbers of atomic bonds. Dr. Mohammad Abuhaiba, PE

36. 4.10 Microscopic TechniquesMicroscopic Examination • Grain size and shape are only two features of what is termed microstructure. • Applications of microstructural examination: • Understand the relation between properties and structure • Predict properties of materials once these relationships have been established. • Design alloys with new property combinations • Monitor and control results of heat treatment • Study the mode of mechanical fracture Dr. Mohammad Abuhaiba, PE

37. 4.10 Microscopic TechniquesMicroscopic Techniques • Optical microscopy • Electron microscope • Transmission Electron microscope • Scanning Electron microscope • Scanning probe microscopy Dr. Mohammad Abuhaiba, PE

38. 4.10 Microscopic TechniquesOptical microscopy • Used in a reflecting mode • Contrasts in the image produced result from differences in reflectivity of the various regions of the microstructure • Specimen surface must be ground and polished to a smooth and mirrorlike finish • Microstructure is revealed using chemical etching • Chemical reactivity of grains of some single phase materials depends on crystalographicorientation Dr. Mohammad Abuhaiba, PE

39. 4.10 Microscopic TechniquesOptical microscopy • In a polycrystalline specimen, etching char vary from grain to grain • F4-13 • Small grooves form along grain boundaries as a result of etching. • Since atoms along GB regions are more chemically active, they dissolve at a greater rate than those within the grains. • GBs reflect light at an angle different from that of grains themselves (F4-14) • 2000X Dr. Mohammad Abuhaiba, PE

40. 4.10 Microscopic TechniquesElectron Microscopy • An image is formed using beams of electrons • A high velocity electron will become wave like with a wave length that is inversely proportional to its velocity • The electron beam is focused and the image formed with magnetic lenses Dr. Mohammad Abuhaiba, PE

41. 4.10 Microscopic TechniquesTransmission Electron microscope (TEM) • Image seen with TEM is formed by an electron beam that passes through specimen • Transmitted beam is projected onto a fluorescent screen or a photographic film • 1000,000X Dr. Mohammad Abuhaiba, PE

42. 4.10 Microscopic TechniquesScanningElectron microscope (SEM) • Surface of specimen to be examined is scanned with a beam of electrons and the reflected beam of electrons is collected then displayed at the same scanning rate on a cathode ray tube. • The surface may or may not be polished and etched but it must be electrically conductive • Very thin metallic surface coating must be applied to non-conductive materials • Up to 50,000X Dr. Mohammad Abuhaiba, PE

43. 4.10 Microscopic TechniquesScanning Probe Microscopy (SPM) • Neither light nor electrons is used to form image • Microscope generate a topographical map on an atomic scale • 109X • 3-D magnified images • Variety of environments • SPM employ a tiny probe with a very sharp tip that it brought into close proximity of specimen surface Dr. Mohammad Abuhaiba, PE

44. 4.10 Microscopic TechniquesScanning Probe Microscopy (SPM) • Probe is raster scanned across the plane of the surface • During scanning, probe experiences deflections perpendicular to this plane in response to electronic or other interactions between the probe and the specimen surface • The in surface plane and out of plane motions of the probe are controlled by piezoelectric ceramic components. Dr. Mohammad Abuhaiba, PE

45. 4.11 Grain Size Determination • Intercept method • ASTM method • Standard comparison charts • Each is assigned a number ranging from 1 to 10 (grain size number) at 100X • N =2n-1 • n =grain size number • N = average number of grains per square inch at 100X Dr. Mohammad Abuhaiba, PE

46. Example Problem 4.4Computations of ASTM Grain Size Number and Number of Grains per Unit Area • Determine the ASTM grain size number of a metal specimen if 45 grains per square inch are measured at a magnification of 100. • For this same specimen, how many grains per square inch will there be at a magnification of 85? Dr. Mohammad Abuhaiba, PE

47. Howe Work Assignment • 1,4, 6, 11, 16, 21, 25, 27, 32, 35 • Due Monday 10/10/2011 Dr. Mohammad Abuhaiba, PE