ENT 219 BIOMATERIALS IMPERFECTION DEFECTS IN SOLIDS Chapter

ENT 219 BIOMATERIALS IMPERFECTION / DEFECTS IN SOLIDS Chapter 5 - 1

Defects in Solids • Idealized solid does not exist • All contain large number of various defects or imperfections. • Classification of crystalline imperfections is frequently made according to geometry or dimensionality of the defect. • Many of the important properties of materials are due to the presence of imperfections. • Affecting the behavior of materials – examples, alloy is much harder and stronger than pure metals • Crystalline defect is mean a lattice irregularity Chapter 5 - 2

Types of Imperfections • Vacancy atoms • Interstitial atoms • Substitutional atoms • Dislocations • Grain Boundaries Point defects Due to deviation around a point or an atom in a crystal Line defects Due to deviation in the entire row of lattice points Area defects Chapter 5 - 3

• Vacancies: Point Defects in Metals -vacant atomic sites in a structure. Vacancy distortion of planes • Self-Interstitials: -"extra" atoms positioned between atomic sites. distortion of planes selfinterstitial Chapter 5 - 4

Point Defects in Metal The equilibrium number of vacancies, Nv • Equilibrium concentration varies with temperature! No. of defects No. of potential defect sites Activation energy formation of vacancy æ Q Nv v = exp çç è k. T N ö ÷÷ ø Temperature Boltzmann's constant -23 (1. 38 x 10 J/atom-K) -5 (8. 62 x 10 e. V/atom-K) Each lattice site is a potential vacancy site Chapter 5 - 5

Measuring Activation Energy • We can get Qv from an experiment. æ Q Nv v ç ç exp = è k. T N • Measure this. . . • Replot it. . . Nv ln N exponential dependence! T defect concentration Nv N ö ÷÷ ø slope -Qv /k 1/T Chapter 5 - 9

Estimating Vacancy Concentration • Find the equil. # of vacancies in 1 m 3 of Cu at 1000 C. • Given: r = 8. 4 g/cm 3 A Cu = 63. 5 g/mol Qv = 0. 9 e. V/atom NA = 6. 02 x 1023 atoms/mol 0. 9 e. V/atom æ Q ö Nv = v ÷÷ -4 exp çç è k. T ø = 2. 7 x 10 N For 1 m 3 , N = r x NA A Cu 1273 K 8. 62 x 10 -5 e. V/atom-K x 1 m 3 = 8. 0 x 1028 sites • Answer: Nv = (2. 7 x 10 -4)(8. 0 x 1028) sites = 2. 2 x 1025 vacancies Chapter 5 - 10

Question Calculate the energy for vacancy formation in silver, given the equilibrium number of vacancies at 800 degrees Celsius is 3. 56 x 1023 m-3. The atomic weight and density for silver are respectively 107. 9 g/mol and 9. 5 g/cm 3. Chapter 5 - 11

Point Defects in Ceramics (i) • Vacancies -- vacancies exist in ceramics for both cations and anions • Interstitials -- interstitials exist for cations -- interstitials are not normally observed for anions because anions are large relative to the interstitial sites Cation Interstitial Cation Vacancy Anion Vacancy Adapted from Fig. 5. 2, Callister & Rethwisch 3 e. (Fig. 5. 2 is 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. ) Chapter 5 - 12

Point Defects in Ceramics (ii) • Frenkel Defect -- a cation vacancy-cation interstitial pair. • Shottky Defect -- a paired set of cation and anion vacancies. Shottky Defect: Frenkel Defect Adapted from Fig. 5. 3, Callister & Rethwisch 3 e. (Fig. 5. 3 is 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. ) • Equilibrium concentration of defects Chapter 5 - 13

Impurities in Metals • A pure metal consisting of only one type of atom just isn’t possible • Impurity or foreign atoms will always be present • Some will exist as crystalline point defects. • Most familiar metals are not highly pure but exist as alloys. • Alloying in metals: to improve mechanical strength and corrosion resistance • Example: Sterling silver is 92. 5% silver – 7. 5% copper alloy Chapter 5 - 14

Impurities in Metals (i) 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. Chapter 5 - 15

Imperfections in Metals (ii) Conditions for substitutional solid solution (S. S. ) • W. Hume – Rothery rule – 1. Difference, r in atomic radius between the 2 atom types is < 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 Chapter 5 - 16

Imperfections in Metals (iii) Application of Hume–Rothery rules – Solid Solutions Element 1. Would you predict more Al or Ag to dissolve in Zn? 2. More Zn or Al in Cu? Cu C H O Ag Al Co Cr Fe Ni Pd Zn Atomic Crystal Radius Structure (nm) 0. 1278 0. 071 0. 046 0. 060 0. 1445 0. 1431 0. 1253 0. 1249 0. 1241 0. 1246 0. 1376 0. 1332 Electronegativity Valence FCC 1. 9 +2 FCC HCP BCC FCC HCP 1. 9 1. 5 1. 8 1. 6 1. 8 2. 2 1. 6 +1 +3 +2 +2 Table on p. 159, Callister & Rethwisch 3 e. Chapter 5 - 17

Imperfections in Metals (ii) • Interstitial solid solution – Impurity atom fills the void or interstices among the host atom – The atomic diameter of an interstitial impurity must be substantially smaller than the host atoms. – Example: Carbon forms an interstitial solid solution when added to iron: the max concentration is 2%. • The atomic radius of the carbon is much less than that of iron: 0. 071 nm vs. 0. 124 nm. Chapter 5 - 18

Impurities in Ceramics • Electroneutrality (charge balance) must be maintained when impurities are present Cl • Ex: Na. Cl Na + • Substitutional cation impurity cation vacancy Ca 2+ Na + without impurity Ca 2+ impurity • Substitutional anion impurity O 2 - without impurity Cl Cl O 2 - impurity Ca 2+ with impurity anion vacancy with impurity Chapter 5 - 19

Point Defects in Polymers • Defects due in part to chain packing errors and impurities such as chain ends and side chains Adapted from Fig. 5. 7, Callister & Rethwisch 3 e. Chapter 5 - 20

Specification of Composition • It is often necessary to express the composition of an alloy in terms of its constituent element – weight percent m 1 = mass of component 1 – atom percent nm 1 = number of moles of component 1 Chapter 5 - 21

Line Defects Dislocations: • are line defects, • slip between crystal planes result when dislocations move, • produce permanent (plastic) deformation. Schematic of Zinc (HCP): • before deformation • after tensile elongation slip steps Chapter 5 - 22

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 perpendicular ( ) to dislocation line • Screw dislocation: – spiral planar ramp resulting from shear deformation – b parallel ( ) to dislocation line Burger’s vector, b: measure of lattice distortion Chapter 5 - 23

Imperfections in Solids Edge Dislocation Fig. 5. 8, Callister & Rethwisch 3 e. Chapter 5 - 24

Imperfections in Solids Screw Dislocation line Burgers vector b b (b) (a) Adapted from Fig. 5. 9, Callister & Rethwisch 3 e. Chapter 5 - 25

Edge, Screw, and Mixed Dislocations Mixed Edge Adapted from Fig. 5. 10, Callister & Rethwisch 3 e. Screw Chapter 5 - 26

Imperfections in Solids Dislocations are visible in electron micrographs Fig. 5. 11, Callister & Rethwisch 3 e. Chapter 5 - 27

Dislocations & Crystal Structures • Structure: close-packed planes & directions are preferred. view onto two close-packed planes. close-packed plane (bottom) 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 • Specimens that were tensile tested. Mg (HCP) tensile direction Al (FCC) Chapter 5 - 28

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. Chapter 5 - 29

Optical Microscopy • Useful up to 2000 X magnification. • Polishing removes surface features (e. g. , scratches) • Etching changes reflectance, depending on crystal orientation. crystallographic planes Adapted from Fig. 5. 18(b) and (c), Callister & Rethwisch 3 e. (Fig. 5. 18(c) is courtesy of J. E. Burke, General Electric Co. ) Micrograph of brass (a Cu-Zn alloy) 0. 75 mm Chapter 5 - 30

Optical Microscopy Grain boundaries. . . • are imperfections, • are more susceptible to etching, • may be revealed as dark lines, • change in crystal orientation across boundary. polished surface (a) surface groove grain boundary ASTM grain size number N = 2 n-1 2 number of grains/in at 100 x magnification Fe-Cr alloy Adapted from Fig. 5. 19(a) and (b), Callister & Rethwisch 3 e. (Fig. 5. 19(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]. ) (b) Chapter 5 - 31

Electron 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 X) • Atomic resolution possible • Electron beam focused by magnetic lenses. • Example: Transmission Electron Microscopy (TEM) & Scanning Electron Microscopy (SEM). Chapter 5 - 32

Scanning electron microscopy (SEM) • Most recent and extremely useful investigative tool. scanning an images with a high-energy beam of electron in a raster scan pattern. • A wide range of magnifications is possible, from about 10 times (about equivalent to that of a powerful handlens) to more than 500, 000 times. • Also very great depth of field. Chapter 5 - 33

SEM image of the corrosion layer on the surface of an ancient glass fragment SEM image of normal circulating human blood Chapter 5 - 34

Chapter 5 - 35

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. ) Chapter 5 - 36