Material Science Chapter 4

CHAPTER 4: Defects in Solids ISSUES TO ADDRESS... • 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 undesirable? • What are the solidification mechanisms?

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 Imperfections in Solids Adapted from Fig.4.14 (b), Callister 7e. Crystals grow until they meet each other nuclei crystals growing grain structure liquid

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) Columnar in area with less undercooling Shell of equiaxed grains due to rapid cooling (greater  T ) near wall Grain Refiner - added to make smaller, more uniform, equiaxed grains. heat flow Adapted from Fig. 4.12, Callister 7e. ~ 8 cm

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.

Types of Imperfections • Vacancy atoms • Interstitial atoms • Substitutional atoms Point defects • Dislocations Line defects • Grain Boundaries Area defects

Point Defects • Vacancies : -vacant atomic sites in a structure. • Self-Interstitials : -"extra" atoms positioned between atomic sites. Vacancy distortion of planes self- interstitial distortion of planes

Equilibrium Concentration: Point Defects Boltzmann's constant (1.38 x 10 -23 J/atom-K) (8.62 x 10 -5 eV/atom-K)   N v N  exp  Q v k T       No. of defects No. of potential defect sites. Activation energy Temperature Each lattice site is a potential vacancy site • Equilibrium concentration varies with temperature!

Measuring Activation Energy • We can get Q v from an experiment.   N v N = exp  Q v k T       • Measure this... N v N T exponential dependence! defect concentration • Replot it... 1/ T N N v ln - Q v / k slope

Estimating Vacancy Concentration • Find the equil. # of vacancies in 1 m 3 of Cu at 1000  C. • Given: A Cu = 63.5 g/mol  = 8.4 g / cm 3 Q v = 0.9 eV/atom N A = 6.02 x 10 23 atoms/mol For 1 m 3 , N = N A A Cu  x x 1 m 3 = 8.0 x 10 28 sites 8.62 x 10 -5 eV/atom-K 0.9 eV/atom 1273K   N v N  exp  Q v k T       = 2.7 x 10 -4 • Answer: N v = (2.7 x 10 -4 )(8.0 x 10 28 ) sites = 2.2 x 10 25 vacancies

Observing Equilibrium Vacancy Conc. • Low energy electron microscope view of a (110) surface of NiAl. • Increasing T causes surface island of atoms to grow. • Why? The equil. vacancy conc. increases via atom motion from the crystal to the surface, where they join the island. Reprinted with permission from Nature (K.F. McCarty, J.A. Nobel, and N.C. Bartelt, "Vacancies in Solids and the Stability of Surface Morphology", Nature, Vol. 412, pp. 622-625 (2001). Image is 5.75  m by 5.75  m.) Copyright (2001) Macmillan Publishers, Ltd. I sland grows/shrinks to maintain equil. vancancy conc. in the bulk.

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) OR Substitutional solid soln. (e.g., Cu in Ni ) Interstitial solid soln. (e.g., C in Fe ) Second phase particle --different composition --often different structure.

Imperfections in Solids Conditions for substitutional solid solution (S.S.) W. Hume – Rothery rule 1.  r (atomic radius) < 15% 2. Proximity in periodic table i.e., similar electronegativities 3. Same crystal structure for pure metals 4. Valency All else being equal, a metal will have a greater tendency to dissolve a metal of higher valency than one of lower valency

Imperfections in Solids Application of Hume–Rothery rules – Solid Solutions 1. Would you predict more Al or Ag to dissolve in Zn? 2. More Zn or Al in Cu? Table on p. 106, Callister 7e. Element Atomic Crystal Electro- Valence Radius Structure nega- (nm) tivity Cu 0.1278 FCC 1.9 +2 C 0.071 H 0.046 O 0.060 Ag 0.1445 FCC 1.9 +1 Al 0.1431 FCC 1.5 +3 Co 0.1253 HCP 1.8 +2 Cr 0.1249 BCC 1.6 +3 Fe 0.1241 BCC 1.8 +2 Ni 0.1246 FCC 1.8 +2 Pd 0.1376 FCC 2.2 +2 Zn 0.1332 HCP 1.6 +2

Imperfections in Solids Specification of composition weight percent m 1 = mass of component 1 n m1 = number of moles of component 1 atom percent

Line Defects • are line defects, • slip between crystal planes result when dislocations move, • produce permanent (plastic) deformation. Dislocations : Schematic of Zinc (HCP): • before deformation • after tensile elongation slip steps Adapted from Fig. 7.8, Callister 7e.

Imperfections in Solids 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  to dislocation line Screw dislocation: spiral planar ramp resulting from shear deformation b  to dislocation line Burger’s vector, b : measure of lattice distortion

Imperfections in Solids 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. (Courtesy P.M. Anderson)

Imperfections in Solids Screw Dislocation Adapted from Fig. 4.4, Callister 7e. Burgers vector b Dislocation line b (a) (b) Screw Dislocation

Edge, Screw, and Mixed Dislocations Adapted from Fig. 4.5, Callister 7e. Edge Screw Mixed

Imperfections in Solids Dislocations are visible in electron micrographs Adapted from Fig. 4.6, Callister 7e.

Dislocations & Crystal Structures • Structure: close-packed planes & directions are preferred. view onto two close-packed planes. close-packed plane (bottom) close-packed plane (top) close-packed directions • Comparison among crystal structures: FCC: many close-packed planes/directions; HCP: only one plane, 3 directions; BCC: none • Specimens that were tensile tested. Mg (HCP) Al (FCC) tensile direction

Planar Defects in Solids One case is a twin boundary (plane) Essentially a reflection of atom positions across the twin plane . Stacking faults For FCC metals an error in ABCABC packing sequence Ex: ABCABABC Adapted from Fig. 4.9, Callister 7e.

Microscopic Examination Crystallites (grains) and grain boundaries. Vary considerably in size. Can be quite large ex: Large single crystal of quartz or diamond or Si ex: Aluminum light post or garbage can - see the individual grains Crystallites (grains) can be quite small (mm or less) – necessary to observe with a microscope.

Optical Microscopy • Useful up to 2000X magnification. • Polishing removes surface features (e.g., scratches) • Etching changes reflectance, depending on crystal orientation. Micrograph of brass (a Cu-Zn alloy) Adapted from Fig. 4.13(b) and (c), Callister 7e. (Fig. 4.13(c) is courtesy of J.E. Burke, General Electric Co. crystallographic planes 0.75mm

Optical Microscopy Grain boundaries... • are imperfections, • are more susceptible to etching, • may be revealed as dark lines, • change in crystal orientation across boundary. 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].) ASTM grain size number N = 2 n -1 number of grains/in 2 at 100x magnification Fe-Cr alloy (b) grain boundary surface groove polished surface (a)

Optical Microscopy Polarized light metallographic scopes often use polarized light to increase contrast Also used for transparent samples such as polymers

Microscopy Optical resolution ca. 10 -7 m = 0.1  m = 100 nm For higher resolution need higher frequency X-Rays? Difficult to focus. Electrons wavelengths ca. 3 pm (0.003 nm) (Magnification - 1,000,000X) Atomic resolution possible Electron beam focused by magnetic lenses.

Scanning Tunneling Microscopy (STM) • Atoms can be arranged and imaged! Carbon monoxide molecules arranged on a platinum (111) surface. Photos produced from the work of C.P. Lutz, Zeppenfeld, and D.M. Eigler. Reprinted with permission from International Business Machines Corporation, copyright 1995. 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 (e.g., T controls vacancy conc.) • 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.)

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Material Science Chapter 4

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