Imperfections  lecture 2
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Dr sama eldek

Dr sama eldek
professor of physics
faculty of Science -Cairo university

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Imperfections  lecture 2 Imperfections lecture 2 Presentation Transcript

  • Imperfections in Solid Materials R. Lindeke ENGR 2110
  • In our pervious Lecture when discussing Crystals we ASSUMED PERFECT ORDER In real materials we find: Crystalline Defects or lattice irregularity Most real materials have one or more “errors in perfection” 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
  • ISSUES TO ADDRESS... • What are the solidification mechanisms? • What types of defects arise in solids? • Can the number and type of defects be varied and controlled? • How do defects affect material properties? • Are defects always undesirable?
  • Imperfections in Solids • Solidification- result of casting of molten material – 2 steps • Nuclei form • Nuclei grow to form crystals – grain structure • Start with a molten material – all liquid nuclei liquid crystals growing grain structure Adapted from Fig.4.14 (b), Callister 7e. • Crystals grow until they meet each other
  • Polycrystalline Materials Grain Boundaries • regions between crystals • transition from lattice of one region to that of the other • ‘slightly’ disordered • low density in grain boundaries – high mobility – high diffusivity – high chemical reactivity Adapted from Fig. 4.7, Callister 7e.
  • Solidification Grains can be - equiaxed (roughly same size in all directions) - columnar (elongated grains) ~ 8 cm heat flow Columnar in area with less undercooling Shell of equiaxed grains due to rapid cooling (greater ∆T) near wall Adapted from Fig. 4.12, Callister 7e. Grain Refiner - added to make smaller, more uniform, equiaxed grains.
  • Point Defects • Vacancies: -vacant atomic sites in a structure. Vacancy distortion of planes • Self-Interstitials: -"extra" atoms positioned between atomic sites. distortion of planes selfinterstitial
  • SELF-INTERSTITIAL: very rare occurrence • This defect occurs when an atom from the crystal occupies the small void space (interstitial site) that under ordinary circumstances is not occupied. • In metals, a self-interstitial introduces relatively (very!) large distortions in the surrounding lattice.
  • POINT • The simplest of theDEFECTS a vacancy, or vacant lattice site. point defect is • 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: Total no. of atomic sites Energy required to form vacancy Equilibrium no. of vacancies Nv= N exp(-Qv/kT) T = absolute temperature in °Kelvin k = gas or Boltzmann’s constant
  • Measuring Activation Energy  −Q Nv v  = exp   kT N • We can get Qv from an experiment. • Measure this... • Replot it... Nv ln N exponential dependence! T defect concentration Nv N     note: N= N A ρ El AEl slope -Qv /k 1/T
  • Example Problem 4.1 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/cm 3, respectively. Solution. Use equation 4.1. Find the value of N, number of atomic sites per cubic meter for copper, from its atomic weight Acu, its density, and Avogadro’s number NA. N A ρ (6.023 x10 23 atoms / mol )(8.4 g / cm 3 )(106 cm 3 / m 3 ) N= = ACu 63.5 g / mol = 8.0x10 28 atoms / m 3 Thus, the number of vacancies at 1000 C (1273K ) ie equal to
  • Continuing:  Qv  N v = N exp −   kT    (0.9eV  = (8.0x10 atoms / m ) exp  (8.62 x10 −5 eV / K )(1273K )    28 3 = 2.2x10 25 vacancies/m 3 And Note: for MOST MATERIALS just below Tm  Nv/N = 10-4 Here: 0.0022/8 = .000275 = 2.75*10-4
  • 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) OR Substitutional 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 new phase (usually for a larger amount of B) Second phase particle --different composition --often different structure.
  • Imperfections in Solids Conditions for substitutional solid solution (S.S.) • Hume – Rothery rules – 1. ∆r (atomic radius) < 15% – 2. Proximity in periodic table • i.e., similar electronegativities – 3. Same crystal structure for pure metals – 4. Valency equality • All else being equal, a metal 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 ElectroRadius Structure (nm) 1. Would you predict more Al or Ag to dissolve in Zn? More Al because size is closer and val. Is higher – but not too much – FCC in HCP 2. More Zn or Al in Cu? Surely Zn since size is closer thus causing lower distortion (4% vs 12%) Cu C H O Ag Al Co Cr Fe Ni Pd Zn 0.1278 0.071 0.046 0.060 0.1445 0.1431 0.1253 0.1249 0.1241 0.1246 0.1376 0.1332 Valence negativity FCC 1.9 +2 FCC FCC HCP BCC BCC FCC FCC HCP 1.9 1.5 1.8 1.6 1.8 1.8 2.2 1.6 +1 +3 +2 +3 +2 +2 +2 +2 Table on p. 106, Callister 7e.
  • Imperfections in Solids • Specification of composition – weight percent m1 C1 = x 100 m1 + m2 m1 = mass of component 1 – atom percent n m1 C = x 100 n m1 + n m 2 ' 1 nm1 = number of moles of component 1
  • Wt. % and At. % -- An example Typically we work with a basis of 100g or 1000g given: by weight -- 60% Cu, 40% Ni alloy 600 g nCu = = 9.44m 63.55 g / m 400 g nNi = = 6.82m 58.69 g / m 9.44 ' CCu = ≈ .581 or 58.1% 9.44 + 6.82 6.82 ' CNi = ≈ .419 or 41.9% 9.44 + 6.82
  • Converting Between: (Wt% and At%) C1 ∗ A2 C = × 100 C1 ∗ A2 + C2 ∗ A1 ' 1 C2 ∗ A1 C = ×100 C1 ∗ A2 + C2 ∗ A1 ' 2 C ∗ A1 C1 = ' × 100 ' C1 ∗ A1 + C2 ∗ A2 Converts from wt % to At% (Ai is atomic weight) ' 1 ' C2 ∗ A2 C2 = ' ×100 ' C1 ∗ A1 + C2 ∗ A2 Converts from at % to wt% (Ai is atomic weight)
  • Determining Mass of a Species per Volume   C 1 C1" =   C1 + C2 ρ ρ  1 2   C " 2 C2 =   C1 + C2 ρ ρ  1 2  ÷ ÷× 103 ÷ ÷   ÷ ÷×103 ÷ ÷  ∀ ρi is density of pure element in g/cc • Computed this way, gives “concentration” of speciesi in kg/m3 of the bulk mixture (alloy)
  • Line Defects Are called Dislocations: And: • slip between crystal planes result when dislocations move, • this motion produces permanent (plastic) deformation. Schematic of Zinc (HCP): • before deformation • after tensile elongation Adapted from Fig. 7.8, Callister 7e. slip steps which are the physical evidence of large numbers of dislocations slipping along the close packed plane {0001}
  • Linear Defects (Dislocations) – Are one-dimensional defects around which atoms are misaligned • 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 resulting from shear deformation – b is || (parallel) to dislocation line Burger’s vector, b: is a measure of lattice distortion and is measured as a distance along the close packed directions in the lattice
  • Edge Dislocation Edge Dislocation Fig. 4.3, Callister 7e.
  • Motion of Edge Dislocation • Dislocation motion requires the successive bumping of a half plane of atoms (from left to right here). • Bonds across the slipping planes are broken and remade in succession. Atomic view of edge dislocation motion from left to right as a crystal is sheared. http://www.wiley.com/college/callister/CL_EWSTU01031_S/vmse/dislocation (Courtesy P.M. Anderson)
  • Screw Dislocations Dislocation line Burgers vector b b (b) (a) Adapted from Fig. 4.4, Callister 7e.
  • Edge, Screw, and Mixed Dislocations Mixed Edge Adapted from Fig. 4.5, Callister 7e. Screw
  • Imperfections in Solids Dislocations are visible in (T) electron micrographs Adapted from Fig. 4.6, Callister 7e.
  • Dislocations & Crystal Structures • Structure: close-packed planes & directions are preferred. close-packed plane (bottom) view onto two close-packed planes. close-packed directions close-packed plane (top) • Comparison among crystal structures: FCC: many close-packed planes/directions; HCP: only one plane, 3 directions; BCC: none “super-close” many “near close” • Specimens that were tensile tested. Mg (HCP) tensile direction Al (FCC)
  • Planar Defects in Solids • One case is a twin boundary (plane) – Essentially a reflection of atom positions across the twinning plane. Adapted from Fig. 4.9, Callister 7e. • Stacking faults – For FCC metals an error in ABCABC packing sequence – Ex: ABCABABC
  • MICROSCOPIC EXAMINATION Applications • To 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
  • MACROSCOPIC EXAMINATION: The shape and average size or diameter of the grains for a polycrystalline specimen are large enough to observe with the unaided eye.
  • Optical Microscopy • Useful up to ∼2000X magnification (?). • Polishing removes surface features (e.g., scratches) • Etching changes reflectance, depending on crystal orientation since different Xtal planes have different reactivity. crystallographic planes Adapted from Fig. 4.13(b) and (c), Callister 7e. (Fig. 4.13(c) is courtesy of J.E. Burke, General Electric Co. Micrograph of brass (a Cu-Zn alloy) 0.75mm
  • Optical Microscopy Grain boundaries... • are planer imperfections, • are more susceptible to etching, • may be revealed as dark lines, • relate change in crystal orientation across boundary. polished surface (a) surface groove grain boundary ASTM grain size number N = 2n-1 number of grains/in2 at 100x magnification Fe-Cr alloy (b) Adapted from Fig. 4.14(a) and (b), Callister 7e. (Fig. 4.14(b) is courtesy of L.C. Smith and C. Brady, the National Bureau of Standards, Washington, DC [now the National Institute of Standards and Technology, Gaithersburg, MD].)
  • GRAIN 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 processing Linear Intercept method • Straight lines are drawn through several photomicrographs that show the grain structure. • The grains intersected by each line segment are counted • The 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.
  • 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 (@100x) 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 MAGNIFICATION
  • Determining Grain Size, using a micrograph taken at 300x • We count 14 grains in a 1 in2 area on the image • The report ASTM grain size we need N at 100x not 300x • We need a conversion method! 2  M  n −1 NM  ÷ =2  100  M is mag. of image N M is measured grain count at M now solve for n: log( N M ) + 2 ( log ( M ) − log ( 100 ) ) = ( n − 1) log ( 2 ) ∴ n= n= log ( N m ) + 2 log ( M ) − 4 +1 log ( 2 ) log ( 14 ) + 2 log ( 300 ) − 4 + 1 = 7.98 ≅ 8 0.301
  • For this same material, how many Grains would I expect /in2 at 100x? N =2 n −1 8 −1 =2 ≅ 128 grains/in 2 Now, how many grain would I expect at 50x? 2 2  100   100  NM = 2 ∗  ÷ = 128*  ÷  M   50  2 2 N M = 128* 2 = 512 grains/in 8 −1
  • At 100x Number of Grains/in2 600 500 400 300 200 100 0 0 2 4 6 Grain Size number (n) 8 10 12
  • Electron Microscopes  beam of electrons of shorter wave-length (0.003nm) (when accelerated across large voltage drop) Image formed with Magnetic lenses High resolutions and magnification (up to 50,000x SEM); (TEM up to 1,000,000x)
  • Scanning Tunneling Microscopy (STM) • Uses a moveable Probe of very small diameter to move over a surface • 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”.
  • Summary • Point, Line, and Area defects exist in solids. • The number and type of defects can be varied and controlled – T controls vacancy conc. – amount of plastic deformation controls # of dislocations – Weight of charge 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 desirable or not. – Inclusions can be intention for alloy development