Presentation on theme: "A (0001) plane for an HCP unit cell is show below."— Presentation transcript:
1A (0001) plane for an HCP unit cell is show below. Each of the 6 perimeter atoms in this plane is shared with three other unit cells, whereas the center atom is shared with no other unit cells; this gives rise to three equivalent atoms belonging to this plane.In terms of the atomic radius R, the area of each of the 6 equilateral triangles that have been drawn is , or the total area of the plane shown is .. And the planar density for this (0001) plane is equal toor the total area of the plane shown is(b) the atomic radius for titanium is nm. Therefore, the planar density for the (0001) plane is
3Point Defects Self-interstitial: atom crowded in ‘holes’ Vacancy: a vacant lattice siteIt is not possible to create a crystal free of vacancies.About 1 out of 10,000 sites are vacant near melting.Self-interstitials are much less likely in metals, e.g.,as it is hard to get big atom into small hole - there islarge distortions in lattice required that costs energy.Thermodynamics (temperature and counting) provides an expression forVacancy Concentration:Qv=vacancy formation energykB= 1.38 x 10–23 J/atom-K = 8.62 x 10–5 eV/atom-KDefects ALWAYS cost energy!
4Imperfections in Solids Conditions for substitutional solid solution (S.S.)W. Hume – Rothery rule1. r (atomic radius) < 15%2. Proximity in periodic tablei.e., similar electronegativities3. Same crystal structure for pure metals4. ValencyAll else being equal, a metal will have a greater tendency to dissolve a metal of higher valency than one of lower valency
5Imperfections in Solids Application of Hume–Rothery rules – Solid SolutionsWould you predict more Al or Ag to dissolve in Zn?More Al because size is closer7.43 % vs 8.48 % – FCC in HCPand val. Is higher – but not tooMuch!2. More Zn or Alin Cu?Surely Zn since size is closerthus causing lower distortion(4% vs 12%)Element Atomic Crystal Electro- Valence Radius Structure nega- (nm) tivityCu FCC C H O Ag FCC Al FCC Co HCP Cr BCC Fe BCC Ni FCC Pd FCC Zn HCPTable on p. 106, Callister 7e.
6Imperfections in Solids Linear Defects (Dislocations)Are one-dimensional defects around which atoms are misalignedEdge dislocation:extra half-plane of atoms inserted in a crystal structureb to dislocation lineScrew dislocation:spiral planar ramp resulting from shear deformationb to dislocation lineBurger’s vector, b: measure of lattice distortion and is measured as a distance along the close packed directions in the lattice
8Burgers Vector.The magnitude and the direction of the displacement are defined by a vector, called the Burgers Vector.(a), starting from the point P, we go up by 4 steps, then move towards right by 5 steps, move down by 4 steps and finally move towards left by 5 steps to reach the starting point P. Now the Burgers circuit gets closed.When the same operation is performed on the defect crystal (b) we end up at Q instead of the starting point!So, we have to move an extra step to return to P, in order to close the Burgers circuit.BV= = b
9Motion of Edge Dislocation • Dislocation motion requires the successive bumpingof a half plane of atoms (from left to right here).• Bonds across the slipping planes are broken andremade in succession.Atomic view of edgedislocation motion fromleft to right as a crystalis sheared.(Courtesy P.M. Anderson)
10Edge Dislocations Exiting Crystal Form Steps Burger’sVector = bShear stressThe caterpillar or rug-moving analogy
11Screw dislocation. The spiral stacking of crystal planes leads to the Burgers vector being parallel to the dislocation line.
12Imperfections in Solids Screw DislocationScrew DislocationbDislocationlineBurgers vector b(b)(a)Adapted from Fig. 4.4, Callister 7e.
13Edge, Screw, and Mixed Dislocations Adapted from Fig. 4.5, Callister 7e.
16Imperfections in Solids Dislocations are visible in electron micrographsAdapted from Fig. 4.6, Callister 7e.
17Dislocations & Crystal Structures • Structure: close-packedplanes & directionsare preferred.view onto twoclose-packedplanes.close-packed directionsclose-packed plane (bottom)close-packed plane (top)• Comparison among crystal structures:FCC: many close-packed planes/directions;HCP: only one plane, 3 directions;BCC: none• Specimens thatwere tensiletested.Mg (HCP)tensile directionAl (FCC)
18Planar Defects: Surfaces All defects cost energy (energy is higher than perfect crystal)Surfaces, grain, interphase and twin boundaries, stacking faultsPlanar Defect Energy is Energy per Unit Area (J/m2 or erg/cm2)Surfaces: missing or fewer number of optimal or preferred bonds.surface
19SURFACE IMPERFECTIONS Surface imperfections arise from a change in the stacking of atomic planes on or across a boundary.The change may be one of the orientations or of the stacking sequence of atomic planes.In geometric concept, surface imperfections are two- dimensional. They are of two types external and internal surface imperfections.
20EXTERNAL SURFACE IMPERFECTIONS They are the imperfections represented by a boundary. At the boundary the atomic bonds are terminated.The atoms on the surface cannot be compared with the atoms within the crystal. The reason is that the surface atoms have neighbors on one side only. Where as the atoms inside the crystal have neighbors on either sides. This is shown in figure. Since these surface atoms are not surrounded by others, they possess higher energy than that of internal atoms.For most metals, the energy of the surface atoms is of the order of 1J/m2.
21AREA DEFECTS: GRAIN BOUNDARIES • are boundaries between crystals.• are produced by the solidification process, for example.• have a change in crystal orientation across them.• impede dislocation motion.Metal Ingot~ 8cmgrainboundariesAdapted from Fig. 4.10, Callister 6e. (Fig is from Metals Handbook, Vol. 9, 9th edition, Metallography and Microstructures, Am. Society for Metals, Metals Park, OH, 1985.)15Adapted from Fig. 4.7, Callister 6e.
22Planar Defects in Solids One case is a twin boundary (plane)Essentially a reflection of atom positions across the twin plane.Stacking faultsFor FCC metals an error in ABCABC packing sequenceEx: ABCABABCAdapted from Fig. 4.9, Callister 7e.
23STACKING FAULTSWhenever the stacking of atomic planes is not in a proper sequence throughout the crystal, the fault caused is known as stacking fault.For example, the stacking sequence in an ideal FCC crystal may be described as A-B-C-A-B-C- A-B-C-……. But the stacking fault may change the sequence to A-B-C-A-B-A-B-A-B-C. The region in which the stacking fault occurs (A-B-A-B) forms a thin region and it becomes HCP.This thin region is a surface imperfection and is called a stacking fault.
24Microscopic Examination Crystallites (grains) and grain boundaries. Vary considerably in size. Can be quite largeex: Large single crystal of quartz or diamond or Siex: Aluminum light post or garbage can - see the individual grainsCrystallites (grains) can be quite small (mm or less) – necessary to observe with a microscope.
25MACROSCOPIC EXAMINATION: The shape and average size or diameter of the grains for a polycrystalline specimen are largeenough to observe with the unaided eye.
26MICROSCOPIC EXAMINATION ApplicationsTo Examine the structural elements and defects that influence the properties of materials.Ensure that the associations between the properties and structure (and defects) are properly understood.Predict the properties of materials once these relationships have been established.Structural elements exist in ‘macroscopic’ and ‘microscopic’ dimensions
27Optical Microscopy Polarized light metallographic scopes often use polarized light to increase contrastAlso used for transparent samples such as polymers
28Optical Microscopy • Useful up to 2000X magnification. • Polishing removes surface features (e.g., scratches)• Etching changes reflectance, depending on crystal orientation.0.75mmcrystallographic planesAdapted from Fig. 4.13(b) and (c), Callister 7e. (Fig. 4.13(c) is courtesyof J.E. Burke, General Electric Co.Micrograph ofbrass (a Cu-Zn alloy)
29Optical Microscopy Grain boundaries... Fe-Cr alloy grain boundarysurface groovepolished surface(a)• are imperfections,• are more susceptibleto etching,• may be revealed asdark lines,• change in crystalorientation acrossboundary.Adapted from Fig. 4.14(a) and (b), Callister 7e.(Fig. 4.14(b) is courtesyof L.C. Smith and C. Brady, the National Bureau of Standards, Washington, DC [now the National Institute of Standards and Technology, Gaithersburg, MD].)
30GRAIN SIZE DETERMINATION The grain size is often determined when the properties of a polycrystalline material are under consideration. The grain size has a significant impact of strength and response to further processingLinear Intercept methodStraight lines are drawn through several photomicrographs that show the grain structure.The grains intersected by each line segment are countedThe line length is then divided by an average number of grains intersected.The average grain diameter is found by dividing this result by the linear magnification of the photomicrographs.
31N = 2 n-1 ASTM (American Society for testing and Materials) ASTM has prepared several standard comparison charts, all having different average grain sizes. To each is assigned a number from 1 to 10, which is termed the grain size number; the larger this number, the smaller the grains.VISUAL CHARTS each with a numberQuick and easy – used for steelN = 2 n-1No. of grains/square inchGrain size no.
32High resolutions and magnification (50,000x SEM); (TEM 1,000,000x)
34Scanning Tunneling Microscopy (STM) • Atoms can be arranged and imaged!Photos produced from the work of C.P. Lutz, Zeppenfeld, and D.M. Eigler. Reprinted with permission from International Business Machines Corporation, copyright 1995.Carbon monoxide molecules arranged on a platinum (111) surface.Iron atoms arranged on a copper (111) surface. These Kanji characters represent the word “atom”.
35Summary • Point, Line, and Area defects exist in solids. • The number and type of defects can be variedand controlled (e.g., T controls vacancy conc.)• Defects affect material properties (e.g., grainboundaries control crystal slip).• Defects may be desirable or undesirable(e.g., dislocations may be good or bad, dependingon whether plastic deformation is desirable or not.)