Engineering Materials - Chapter 4 Imperfection Part 2 PDF

Engineering Materials Chapter 4 Crysta l Defects and Noncrystalline Structure- Im perfection Dr. Pitak Vararittichai  In our pervious Lecture when discussing Crystals we ASSUMED...

Engineering Materials Chapter 4 Crysta l Defects and Noncrystalline Structure- Im perfection Dr. Pitak Vararittichai  In our pervious Lecture when discussing Crystals we ASSUMED PERFECT ORDER In real materials, we fi nd: Crystalline Defects or lattice irregularity M ost real materials ha ve one or more "errors in perfec tion" with dimensions on the order of an atomic diameter to many lattice sites Defects can be classification: 1. according to geometry (point, line or plane) 2. dimensions of the defect Forming a liquid solution of water and alcohol. Mixing occurs on the molecular scale. Water A lcohol - 0 -=- Liq uid so lution We can define this m ixture/so lution on a weight or "atomic" basis Mixing on the molecula r scale A similar discussion can apply to " m ixtures" of metals - called alloys Crystallization or Solidification Crystallization or Solidification Crystallization or Solidification Crystallization or Solidification Crystallization or Solidification Grain Formation Nucleation Grain Formation  Point Defects - in the solid state are more predicta ble Vacancies : -vacant atomic sites in a structure. Vacancy distortion of planes Self-Intersti t ials: -"extra " atoms positioned between atomic sites. self interstitial distortion of p lanes  POINT DEFECT S The simplest of the point defect is a vacancy, or vacant lattice site. All crystalline solids contain vacancies. Principles of thermodynamics is used explain the necessity of the existence of vacancies in crystalline solids. The presence of vacancies increases the entropy (randomness) of the crystal. The equilibrium number of vacancies for a given quantity of material depends on and increases with temperature as follows: (an Arrhenius model) Tot no. of atomic sites Energy required toform vacancy Equilibritun no. of vaccancies / N v= N e (-Qv /kT) T =absolute temperatu re in °Kelvin k = gas or Roltzn,ann's constant  Point Defects in Alloys Two outcomes if impurity (B) added to host (A): Solid solution of B in A (i.e., random dist. of point defects) Solid solution of B in A plus particles of a new phase (usually for a larger amount of B) Second phase particle --different composition --often different structure. Solid solution of nickel in copper shown along a {100} plane. This is a substitutiona l solid solution with nickel atoms substituting for copper atoms on FCC atom sites.  Imperfections in Solids Conditions for substitutiona l solid solution (S.S.) Hume - Rothery rules - 1. Δr (atomic radius) < 15% - 2. Proximity in periodic ta ble i.e., similar electronegativities - 3. Same crystal structure for pure meta ls - 4. Valency equa lity All else being equal, a meta l will have a greater tendency to dissolve a metal of higher valency than one of lower valency (it provides more electrons to the "cloud"}  Imperfections in Solids Application of Hume-Rothery rules - Solid Solutions Element Atomic Crystal Electro- Valence Radius Structure nega- 1. Would you predict (nm} tivity more Al or Ag Cu 0.1278 FCC 1.9 +2 c 0.071 t o dissolve in Zn? H 0.046 More Al because size is closer and val. Is 0 0.060 higher - but not too much because of Ag 0.1445 FCC 1.9 +1 structural differences - FCC in HCP Al 0.1431 FCC 1.5 +3 2. More Zn or Al Co 0.1253 HCP 1.8 +2 Cr 0.1249 BCC 1.6 +3 in Cu? Fe 0.1241 BCC 1.8 +2 Ni 0.1246 FCC 1.8 +2 Surely Zn since size is closer th us causing Pd 0.1376 FCC 2.2 +2 lower distortion (4% vs 12%) Zn 0.1332 HCP 1.6 +2 Table on p. 105, Callister le.  Imperfections in Solids Specif ication of composit ion - weight percent m 1 = mass of component 1 m 2 = mass of component 2 - atom percent c = n m1 x 100 nm 1 + n m2 nm1 = number of moles of component 1 nm2 = number of moles of component 2  Wt. % and At. % -- An example Typically we work with a basis weight (l 0 0 g or 1 kg) or moles given: alloy by weight -- 60% Cu, 40% Ni 600g = 9.44m ncu = 63.55g I m nNi = 400g = 6.82m 58.69g I m. Ccu = 9.44 = 0.581 or 58.1% 9.44 + 6.82. 6.82 C Ni i = = 0.419 or 41.9% 9.44 + 6.82 Converting Between: (Wt% and At%) Interstitial solid solution applies to carbon in a -iron. The carbon atom is small enough to fit with some strain in the interstice (or opening) among adjacent Fe atoms in this important steel structure. But the intersti tial solubility is quite low since the size misrratch of the site to t he radi us of a carbon atom is only abou t 1/4 Random, substitution solid solution can occur in Ionic Crystal line mater ials as well. Here of NiO in M gO. The 0 2 - arrangement is unaffected. The substi tution occurs among Ni 2+ and Mg 2+ ions. A substi tution solid solution of Al20 3 in M gO is not as simple as the case of NiO in MgO. The requirement of charge neutrali ty in the overall compound per mi ts only two Al3+ ions to f ill every three M g2+ vacant sites, leaving oneMg 2+ vacancy.  Iron oxide, Fe1_x0 with x = 0.05, is an example of a nonstoichiometric compound. Similar to the case of Figure 4.6, both Fe2+ and Fe3+ ions occupy the cation sites, with one Fe2 + vacancy occurr ing for every two Fe3 + ions present. o Vacancy  Defects in Ceramic Structures Frenkel Defect --a cation is out of place. Shottky Defect --a paired set of cation and anion vacancies. Shottky... : - Defect: from W.G. Moffatt, G.W. Pearsall, and J. Wulff, The Structure and Properties of Materials , Vol. 1, Structure, John Wiley and Sons, Inc., p. 78. =e - QD / kT Equilibrium concentration of defects  Defects in Ceramic Structures Frenkel Defect --a cation is out of place. Shottky Defect --a paired set of cation and anion vacancies. slip steps which are the physical evidence of large numbers of dislocations slipping along the close packed plane Linear Defects (Dislocations) - Are one-dimensional defects around which atoms are m isa ligned Edge dislocation : - extra half-plane of atoms inserted in a crystal structure - b (the berger's vector) is (perpendicular) to dislocation line Screw dislocation: spiral planar ramp result i ng from shear deformation b is II (parallel) to dislocation line Burge r 's vector, b: is a measure of lattice distortion and is measured as a d ista nce a long t he close packed d irections in the lattice  Edge Dislocat io n Burgers vector b Edge dislocation line Fig. 4.3. Callister l e. Definition of the Burgers vecto r b, relative to an edge dislocation. (a) In the perfect crystal, an mx n atomic step loop closes at the startin g point. (b) In the region of a dislocation, the same loop does not close, and the closure vector (b) represents the ma gnitude of the (a) structural defect. For the edge dislocation, the Burgers vector is perpendicular to the dislocation line. (b) Screw dislocation. The spiral stacking of crystal planes leads to the Burgers vector being parallel to the dislocation line. Dislocation line " " ' Burgers vector, b Mixed dislocation. This dislocation has both edge and screw character with a single Burgers vector consistent with the pur e edge and pure screw regions. D islocation line - r - -....L t_ _ ,,,,..,. Burgers vector fo r the aluminum oxide str ucture. The large repeat distance in this relatively complex str ucture causes the Burgers vector to be broken up into two (f or 0 2- ; or four (for Al 3 +) partial dislocations, each representing a smaller slip step. This complexity is associated with the brittleness of ceramics compared with metals. (From W D. Kingery, H. K. Bowen, and D. R. Uhlmann, Introduction to Ceramics, 2nd ed., John Wiley & Sons, Inc., New York, 1976.}  Imperfections in Solids Dislocations are visible in (T) electron m icrographs Ada pte d from Fig. 4.6, Callister l e.  Dislocations & Crystal Structures Structure: close-packed view onto two close-packed planes & directions planes. are preferred. close-packed plane (bottom) * close-packed directions close-packed plane (top) Comparison among crysta l structures: FCC: many close-packed p lanes/directions; HCP: only one plane, 3 d irections; BCC: none "super-close" many "near close" Specimens that M g (HCP) were tensile Tensile direction tested. Al (FCC)  Planar Defects in Solids One case is a twin boundary (plane) - Essentially a reflection of atom positions across the twi nning plane. Twin plane (bounda ry) Adapted from Fig. 4.9, Callister 7e. Stacking faults For FCC metals an error in ABCABC packing sequence - Ex: ABCABABC Simple view of the surface of a crystalline material. A more detailed model of the elaborate ledgelike str ucture o f the surface of a crystalline mater ial. Each cube represents a single atom. [From J. P. Hir th and G. M. Pound, J. Chem. Phys. 26, 1216 {1957).] Typical optical microg raph of a grain struct ure, l 00 x. The material is a low-carbon steel. The grain bound aries have been lightly etched with a chemical solution so that they reflect light differentl y from the po lished grains, thereby giving a distinctive contrast. {From Metals Handbook, 8th ed., Vol. 7: Atlas of Microstructures of Industrial Alloys, American Nita1 lOOX Society for Metals, Metals Park, OH, 19 72.} Simple grain-boundary str ucture. This is termed a tilt boundar y because it is for med when two adjacent crystalline grains are tilted relative to each other by a fe w degrees (Ɵ). The resulting structure is equivalent to isolated edge dislocations separated by the distance b/ Ɵ, where b is the leng th of the Burgers vector, b. {From W. T. Read, Dislocations in Crysta ls,. M cGraw-Hill Book Company, New York, 1953. Reprinted with per mission of the McGraw-Hill Book Company.) The ledge Growth leads to structu res with Grain Boundrics The shape and average size or diameter of the grains for some polycrystalline specimens are large enough to observe with the unaided eye. (Macrosocipic examination) -l. 10 H igh-pu rily F H, lllf>. polycrystl'llline lead ingot in wh ich the individual grains may be discerned. 0.7 X. (Re produced with permission from Mewls Handbook. Vol. 9, 9th edition. A1ewlfvgrap/Jy and M i crostr // Cl /l res, American Society for Me tals, Jvlc tals Park , 0 11, 1985.) Specimen f or the calculation of the grain-size number G is defined at a magnification of lOOx. This mater ial is a low -carbon steel similar to that show n in Figure 4.18. (From M e t a ls Handbook., 8th ed.., Vol. 7: Atlas of Microstructures of Industrial Alloys., Amer ican Society for Metals., Metals Park., OH., 1972.) Nital l OOX  Optica l Microscopy Useful up to - 2000X magnification (?). Polishing removes surface features (e.g., scratches) Etching changes reflecta nce, depending on crysta l orientation since different Xta l planes have different reactivity. Microscope Courtesy of J.E. Burke, General Electric Co. Micrograph of brass (a Cu-Zn alloy) + - 0.75mm - - +  Optica l Microscopy Since Grain boundaries... are planer imperfections, are more susceptible to etching, may be revealed as polished surface dark lines, relate change in crysta l surface groove orientation across grain boundary boundary. (courtesy of L.C. Smith and C. Brady, t he National Bureau of ASTM grain Standa rds, Washin gton, DC [no w t he National Instit ute of size number Standards and Technology, Gaithersburg, M D ].) N =2 n-1 numbe r of grains/in2 at lOOx (b) magnificat ion  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 (@ l OOx) each with a number Quick and easy - used for steel Grain size no. No. of grains/square inch N = 2 n-1 NOTE: The ASTM grain size is related (or relates) a grain area AT 100x M AGNIFICATION Two-dimensional schematics give a compar ison of (a) a crystalline oxide and (b) a non-cr ystalline oxide. The non crystalline material retains shor t-range order (the tr iangular ly coordinated buildin g block), but loses long -range order (crystallinity ). This illustration was also used to def ine glass in Chapter 1 {Figure 1.8). (a) (b) Bernal model of an amorphous metal structure. The irregular stacking of atoms is represented as a connected set of polyhedra. Each polyhedron is produced by drawing lines between the centers of adjacent atoms. Such polyhedra are irregular in shape and the stacking is not repetitive. A chemical impur ity such as Na+ is a glass modi fier, break ing up the random networ k and leaving nonbr idging oxygen ions. [From B. E. Warren, J. Am. Ceram. Soc. 24, 256 {194 1}.J Schematic illustration of medium-range order ing in a C a 0 -Si0 2 glass. Edge shar ing Ca0 6 octahedr a have been identified by neutron-diff raction exper iments. [From P. H. Gaskell et al.J Nature 350J 675 {1991}.]  Summary Poin t, Line, Surface and Volumetric defects exist in solids. The number and type of defects can be varied and controlled - T controls vacancy cone. - amount of plastic deformation controls # of dislocations - Weight of cha rge materials determine concentration of substitutional or interstitial point 'defects' Defects affect material properties (e.g., grain boundaries control crystal slip). Defects may be desirable or undesirable - e.g., dislocations may be good or bad, depending on whether plastic deformation is desira ble or not. - Inclusions can be intention for alloy development