Presentation on theme: "CHAPTER 4: IMPERFECTIONS IN SOLIDS"— Presentation transcript:
1 CHAPTER 4: IMPERFECTIONS IN SOLIDS ISSUES TO ADDRESS...• What are the solidification mechanisms?• What types of defects arise in solids?• Can the number and type of defects be variedand controlled?• How do defects affect material properties?• Are defects undesirable?
2 Imperfections in Solids Solidification-result of casting of molten material( metals and alloys)the size and shape of the structure depends on thecooling rate2 stepsNuclei formNuclei grow to form crystals – grain structureStart with a molten material – all liquidnucleicrystals growinggrain structureliquidCrystals grow until they meet each other
3 Polycrystalline Materials Grain Boundariesregions between crystalstransition from lattice of one region to that of the otherslightly disorderedlow density in grain boundarieshigh mobilityhigh diffusivityhigh chemical reactivity
4 SolidificationGrains can be - equiaxed (roughly same size in all directions)- columnar (elongated grains)~ 8 cmheatflowShell of equiaxed grains due to rapid cooling (greater T) near wallColumnar in area with less undercoolingGrain Refiner - added to make smaller, more uniform, equiaxed grains.
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.
6 Types of Imperfections Point defects• Vacancy atoms• Interstitial atoms• Impurities defects ( for solid solution)Line defects ( dislocation)Edge dislocationScrew dislocationmixed dislocation
7 Planar defects (interfacial defects) external surfaces, grain boundaries,twin boundaries,stacking faultanti phase boundariesBulk defects ( volume defects)Voids are small regions where there are noatoms, and can be thought of as clusters ofvacancies.Impurities can cluster together to form smallregions of a different phase. These are oftencalled precipitates.
8 Point Defects Vacancy self- interstitial • Vacancies: -vacant atomic sites in a structure.Vacancydistortionof planes• Self-Interstitials:-"extra" atoms positioned between atomic sites.self-interstitialdistortionof planes
9 Impurities defects: Substitutional or interstitial - Substitutional : impurity atoms type A substitutional atomstype B in structure- Interstitial : atoms type A fill the voids or interstices amongthe atoms type Bsubstitinterstitial
10 Equilibrium Concentration: Point Defects • Equilibrium concentration varies with temperature!Equil.No. of defectsActivation energyæ-öNQvçv÷=expç÷èøTotal No. of atomic sitesNkTTemperatureBoltzmann's constant-23(1.38 x 10J/atom-K)-5(8.62x10eV/atom-K)
11 Measuring Activation Energy ç÷Nv=exp-QkTæèöø• We can get Qv froman experiment.• Measure this...NvTexponentialdependence!defect concentration• Replot it...1/TNvln-Q/kslope
12 Estimating Vacancy Concentration • Find the equil. # of vacancies in 1 m3 of Cu at 1000C.• Given:3r= 8.4 g/cmA= 63.5 g/molCuQ= 0.9 eV/atomN= 6.02 x 1023atoms/molAv8.62 x 10-5eV/atom-K0.9 eV/atom1273Kç÷Nv=exp-QkTæèöø= 2.7 x 10-4For 1 m3, N =NACurx1 m3= 8.0 x 1028 sites• Answer:Nv=(2.7 x 10-4)(8.0 x 1028) sites = 2.2 x 1025 vacancies
13 Observing Equilibrium Vacancy Conc. • Low energy electronmicroscope view ofa (110) surface of NiAl.• Increasing T causessurface island ofatoms to grow.• Why? The equil. vacancyconc. increases via atommotion from the crystalto the surface, wherethey join the island.Island grows/shrinks to maintainequil. vancancy conc. in the bulk.
14 Point Defects in solid solution SOLID SOLUTIONS: A solid solution forms when, as the solute atoms are added to the solvent atoms,the crystal structure is maintained, and no new structures are formed.Solvent (host atoms):represents the element or compound that is present in the greatestSolute: is used to denote an element or compound present in a minor concentration. It is dissolved in the solvent.
15 There are several features of the solute and solvent atoms that determine the degree to which the former dissolvesin the latter; these are as follows(for perfect solid solution)Atomic size factor: Δr less than 15% for solute and solventCrystal structure: must be the same for bothElectro-negativity: the more e.negativ.one element and the more e.positiv. Another for good solid solutionValences: Other factors being equal, a metal will have more of a tendency to dissolve another metal of higher valency than one of a lower valency.
16 Point Defects in solid solution Two outcomes if impurity (B) added to host (A):• Solid solution of B in A (i.e., random dist. of point defects)ORSubstitutional solid soln.(e.g., Cu in Ni)Interstitial solid soln.(e.g., C in Fe)• Solid solution of B in A plus particles of a newphase (usually for a larger amount of B)Second phase particle--different composition--often different structure.
17 Imperfections in Solids Conditions for substitutional solid solution (S.S.)W. Hume – Rothery rule1. ( atomic size factor) r (atomic radius) < 15%2. Proximity in periodic tablei.e., similar electronegativities3. Same crystal structure for pure metals of bothatoms type4. Valencyex. of substitu. solid solution copper and nickel
18 Ex. of substitu. solid solution copper and nickel r = .125 nmboth have FCC crystal structureelectronegat. = 1.9valences +2 for bothEx. Of interstit. Solid solution is carbon added to ironr of C << r of ironthe maximum concent. Of C in iron is less than 10%
19 Imperfections in Solids Application of Hume–Rothery rules – Solid Solutions1. Would you predict more Al or Ag to dissolve in Zn?2. More Zn or Alin Cu?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 HCP
20 Imperfections in Solids Specification of composition( or concentrationof alloy in terms of its constituent elements)weight percentm1 = mass of component 1nm1 = number of moles of component 1atom percent
21 problemWhat is the composition , in atom percent of an alloy that contains 33 g copper and 47 g zinc?Solution: first becomes necessary to compute the number of moles of both Cu and Zn, Thus, the number of moles of Cu is justLikewise, for Zn
23 problem2What is the composition, in atom percent, of an alloy that consists of 5.5 wt% Pb and 94.5 wt% Sn(tin)?Solution:
24 Line Defects Dislocations: Schematic of Zinc (HCP): slip steps • are line defects,• slip between crystal planes result when dislocations move,• produce permanent (plastic) deformation.Schematic of Zinc (HCP):• before deformation• after tensile elongationslip steps
25 Imperfections 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
26 Imperfections in Solids Edge DislocationFig. 4.3, Callister 7e.
27 Motion 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.
28 Imperfections in Solids Screw DislocationScrew DislocationbDislocationlineBurgers vector b(b)(a)
33 Planar (interfacial)Defects in Solids External surfaces one of most obvious boundaries, along which the crystal structure terminates. Surface atoms are not bonded to the maximum number of nearest neighbors, and are therefore in a higher energy state than the atoms at interior positionsGrain boundaries occur where the crystallographic direction of the lattice abruptly changes. This usually occurs when two crystals begin growing separately and then meet.
34 Planar Defects in Solids twin boundary (plane)Essentially a reflection of atom positions across the twin plane.there is a specific mirror lattice symmetry; that is, atoms on one side of the boundary are located in mirror-image positions of the atoms on the other side. The region of material between these boundaries is appropriately termed a twin
35 Stacking faults: occur in a number of crystal structures, but the common example is in close-packed structures. Face centered cubic (FCC) structures differ from hexagonal close packed (HCP) structures only in stacking orderFor FCC metals an error in ABCABC packing sequenceEx: ABCABABCAnti phase boundaries: occur in ordered alloys: in this case, the crystallographic direction remains the same, each side of the boundary has an opposite phase: For example if the ordering is usually ABABABAB, an anti phase boundary takes the form of ABABBABA
36 problem For each of the following stacking sequences found in FCC metals, cite the type of planar defect that exists:…..A B C A B C B A C B A……A B C A B C B C A B C
37 Solution:The interfacial defect that exists for this stacking sequence is a twin boundary, which occurs at the indicated positionThe stacking sequence on one side of this position is mirrored on the other sideb) The interfacial defect that exists within this FCC stacking sequence is a stacking fault, which occurs between the two lines.Within this region, the stacking sequence is HCP.
38 Bulk(volume) defectsThese include pores, cracks, foreign inclusions, and other phases. They are normally introduced during processing and fabrication stepsVoids are small regions where there are no atoms, and can be thought of as clusters of vacancies.Impurities can cluster together to form small regions of a different phase. These are often called precipitates.
39 Microscopic Examination Crystallites (grains) and grain boundaries. Vary considerably in size. Can be quite largeex: Large single crystal of diamondex: Aluminum light garbage can see the individual grainsCrystallites (grains) can be quite small (mm or less) – necessary to observe with a microscope.
40 Microscopic Examination Several important applications of micro-structural examinations are as follows:To ensure that the association between the properties and structure ( and defects ) are properly understoodTo predict the properties of materials once these relationship have been establishedTo design the alloys with new property combinationsTo determine whether or not a material has been correctly heat treatedTo ascertain the mode of mechanical fracture
41 Optical Microscopy • Useful up to 2000X magnification. • Polishing removes surface features (e.g., scratches)• Etching changes reflectance, depending on crystalorientation.0.75mmthe chemical reactivity of the grains of some single-phase materials depends on crystallographic orientationcrystallographic planesMicrograph ofbrass (a Cu-Zn alloy)
42 Optical Microscopy Grain boundaries... Fe-Cr alloy • are imperfections,• are more susceptibleto etching,• may be revealed asdark lines,• change in crystalorientation acrossboundary.Fe-Cr alloy(b)grain boundarysurface groovepolished surface(a)
43 Optical Microscopy Polarized light metallographic scopes often use polarized light to increase contrastAlso used for transparent samples such as polymers
44 Microscopy Optical resolution ca. 10-7 m = 0.1 m = 100 nm For higher resolution need higher frequencyX-Rays? Difficult to focus.Electronswavelengths ca. 3 pm (0.003 nm)(Magnification - 1,000,000X)Atomic resolution possibleElectron beam focused by magnetic lenses.Optical microscopy good to ca. wavelength of lightHigher frequenciesX-rays – good idea but difficult to focusElectrons - wavelength proportional to velocity with high voltage (high acceleration) get wavelengths ca. 3pm (0.003nm) (x1,000,000)
45 Scanning Tunneling Microscopy (STM) • Atoms can be arranged and imaged!Carbon monoxide molecules arranged on a platinum (111) surface.Iron atoms arranged on a copper (111) surface. These Kanji characters represent the word “atom”.
46 Summary • 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.)