Chapter 4 – 1 ISSUES TO ADDRESS IN THIS CHAPTER Linear defects Interfacial/planar defects Volume defects CHAPTER 4 (+12): IMPERFECTIONS IN SOLIDS Point defects There is no such a thing as a perfect crystal! Are defects good for properties Why do we study materials imperfections Chapter 4 – 2 Callister study guide 4.4: No need to study composition conversions 4.5 – 4.7: Study all parts 4.8: Not covered CHAPTER 4: IMPERFECTIONS IN SOLIDS 4.1 – 4.3: Study all parts 4.9 – 4.10: Covered in week 13 4.11: Not covered 12.15: Study all part Chapter 4 – 3 Types of Imperfections Vacancy atoms Interstitial atoms Substitutional atoms Point defectsZero-dimensional defects DislocationsLinear defectsOne-dimensional defects Grain Boundaries Twin Boundaries Stacking Faults Interfacial/planar defects Two-dimensional defects Three-dimensional defects Volume defects Impurity inclusions Pores Cracks Defects are places where the periodic array of atoms stop. We will learn in Chapter 7 that: Dislocations are the most important defects for mechanical properties including yield strength, tensile strength, and ductility. Other defects affect the mechanical properties through their interactions with dislocations that affect dislocation behaviours. Chapter 4 – 4 Vacancies: -vacant atomic sites in a structure. Self-Interstitials: -“extra” atoms positioned between atomic sites. Point Defects Vacancy distortion of planes self- interstitial distortion of planes Lattice distortion increases system energy Chapter 4 – 5 Boltzmann’s constant (1.38 x 10 -23 J/atom-K) (8.62 x 10-5 eV/atom-K) Nv N= exp -Qv kT No. of defects No. of total Atomic sites Activation energy Temperature (Kelvins= oC + 273) Equilibrium concentration varies with temperature! Equilibrium Concentration of Point Defects __Nv N ~ 10-4 at T just below melting High temperature and low activation energy → high density of point defects. Q for vacancies < Q for self- interstitials → more vacancies than self-interstitial atoms. Chapter 4 - 6 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. Observing Equilibrium Vacancy Concentration Island grows/shrinks to maintain equil. vancancy conc. in the bulk. Chapter 4 - 7 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. Point Defects in Alloys Solvent Solute Chapter 4 - 8 xx x x x x x x x xx x x Interstitial positions in FCC structure Tetrahedral Octahedral xx x x x x x x x xx x x In an FCC unit cell (the messages below are very important for crystal structures of ceramics): 4 atoms – 8 (corners) x 1/8 + 6 (face centers) x 8 tetrahedral interstitial positions – each corner forms a tetrahedrons with 3 face-centers. 4 octahedral interstitial positions – 1 (center) + 12 (edge centers) x 1/4 Chapter 4 - 9 Concentration Specification of composition – weight percent 100x 21 1 1 mm m C + = m1 = mass of component 1 100x 21 1' 1 mm m nn n C + = nm1 = number of moles of component 1 – atom percent For industry as industry does not count the numbers of atoms. Mainly for research wt.% at.% Chapter 4 - 10 Frenkel Defect --a cation is out of place. Schottky Defect --a paired set of cation and anion vacancies. Equilibrium concentration of defects kT/QDe~ - Point Defects in Ceramic Structures Schottky Defect: Frenkel Defect 2 12 Charge neutrality requirement for point defects Chapter 4 - 11 Impurities must also satisfy charge balance = Electroneutrality Ex: NaCl Substitutional cation impurity Impuritie
s (Point Defects in Ceramics) Na+ Cl- initial geometry Ca2+ impurity resulting geometry Ca2+ Na+ Na+ Ca2+ cation vacancy Substitutional anion impurity initial geometry O2- impurity O2- Cl- anion vacancy Cl- resulting geometry 12 Chapter 4 – 12 are line defects, slip between crystal planes result when dislocations move, produce permanent (plastic) deformation. Dislocations: Schematic of a Plastic Deformation Process: before deformation after tensile elongation slip steps Line Defects Chapter 4 – 13 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 Chapter 4 – 14 Imperfections in Solids Edge Dislocation Burgers circuit – clockwise, counterclockwise b I line_ Chapter 4 – 15 Imperfections in Solids Screw Dislocation Burgers vector b Dislocation line b (a) (b) Screw Dislocation b // line Chapter 4 – 16 Edge, Screw, and Mixed Dislocations Edge Screw Mixed A dislocation line has only one Burgers vector but its type can vary from one portion to another depending on the curvature of the local dislocation line and the orientation relationship between the dislocation line and its Burgers vector. Chapter 4 – 17 Dislocations seen in TEM Dislocations are visible in electron micrographs 8 steps down 8 steps right 8 steps up 8 steps left Edge-on Edge-on Inclined Inclined Chapter 4 – 18 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 Chapter 4 – 19 Close-packed planes/directions A B C A A A B B B C C Chapter 4 – 20 Dislocations in Ceramics Ex: GaN Copied from APL 72 (1998)2680 12 In ceramic with a Perovskite structure Copied from Nature Comm. 13 (2022) 335 The structure of a dislocation core in ceramics is much more complicated than that in metals. Chapter 4 – 21 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 Chapter 4 – 22 TEM images of twins and a stacking fault in FCC Twins Stacking Fault Twin: ABCABCABCBACBACBA Twin plane SF: ABCABCBCABC or ABCABACABCABC “A” is removed “A” is inserted Chapter 4 – 23 Twins and Stacking Faults FCCWhat is the relationship between twins and SFs What if SFs appear periodically ABCABCABCABCABCABCABC Chapter 4 – 24 Other interfacial defects External surfaces Grain boundaries Anti-phase domain boundaries Phase boundaries … Chapter 4 – 25 Volume defects (impurity precipitates) Chapter 4 – 26 Volume defects (impurity precipitates) 1.5mm Chapter 4 – 27 Point, Line, plane and Volume 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.) Summary Chapter 4 – 28 Point defects including vacancy, interstitial atoms and substitutional atoms; solid solution, solute and solvent; (equilibrium) concentration of point defects (4.3, 4.5) and its relationships with temperature and activation energy; edge, screw, and mixed dislocations; Burgers vectors; relationship between dislocations and crystal structures; twins and stacking faults and their relationship; volume defects. Concepts and equations to be remembered