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Lecture_9 - NE 125: Lecture 9 NE Chapter 4 Crystal Defects...

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Unformatted text preview: NE 125: Lecture 9 NE Chapter 4 Crystal Defects II Instructor: William K. O’Keefe, P.Eng. wkokeefe@engmail.uwaterloo.ca “Office Hours”: Mondays 1:30 to 2:20 RCH 106 Teaching Assistant (TA): Hua (Leanne) Wei h6wei@engmail.uwaterloo.ca Reminder: Mid term exam Tuesday February 12 (2 weeks and 4 days from now) Chapters 1, 2, 3, 4 and 6 of textbook; possibly part of Ch 8 Week 3 Reading: Shackelford 6th Ed, Chapter 4 Assignment 3 (handout) problem set due: 28 January 2007 NE 125: Introduction to Materials Science and Engineering Introduction Chapter Four: Crystal Defects Classification of Crystal Defects Point defects: Point vacancies, self interstitials, impurities (substitutional and interstitial) impurities Linear Defects: - Edge dislocation - Screw dislocation - Mixed dislocations Planar Defects and Interfacial Defects Planar Bulk or Volume Defects - grain boundaries: twin boundaries, tilt boundary, twist boundary, small angle and high angle boundaries grain - surface coordinative unsaturation - porosity, microcracks, foreign inclusions, porosity, - induced or introduced during materials processing induced NE 125: Introduction to Materials Science and Engineering Introduction Review: Point Defects Vacancies and Self Interstitials Vacancy Self-Interstitial Self interstitials introduce large distortions in lattice; much less common than vacancy Non-stoichiometric compounds: Eg. Fe1-xO, where x ~ 0.05 NE 125: Introduction to Materials Science and Engineering Introduction Review: Crystal Defects Imperfections and Entropy ∆ G = ∆ H – T∆ S (G = Gibbs energy, H = enthalpy, S = entropy, T =temperature) In nature, thermodynamic driving forces direct systems towards minimizing Gibbs free energy and increase entropy Crystal solids are characterized by order and periodicy Introduction of imperfections and defects increases entropy All crystal solids contain vacancies. The equilibrium number of vacancies (Nv) can be calculated: Qv N v= N exp − kT N = total number of atomic sites Qv = activation energy for creation of vacancy k = Boltzman’s constant 1.38 x 10-23 J/atom*K T = absolute temperature NE 125: Introduction to Materials Science and Engineering Introduction Review: Crystal Defects Frenkel and Schottky Defects Frenkel defect Frenkel defects are most often encountered in open structures such as wurtzite and sphalerite (low coordination numbers) Schottky defect Schottky defect (eg. ceramics): vacancy in both anion and cation site such that the net charge on structure remains unchanged Often encountered in metals which can assume more than one oxidation state (transition metals) Frenkel defect: Atom or ion is displaced into an interstitial site NE 125: Introduction to Materials Science and Engineering Introduction Chapter Four: Crystal Defects Some more terminology Anisotropic / Anisotropy: When the physical properties of single crystals depend on the crystallographic direction When Eg. Index of refraction of light, electrical conductivity, thermal conductivity, modulus of elasticity Eg. may be different in [111] and [100] directions may Isotropic / Isotropy When measured properties are independent of crystallographic direction Texture Texture Most polycrystalline materials have crystals oriented randomly and behave isotropically However, some polycrystalline materials have crystals oriented in preferential directions and are However, said to have texture. The material property has averaged value texture NE 125: Introduction to Materials Science and Engineering Introduction Chapter Four: Crystal Defects Anisotropy and Anisotropic Materials [1] R.W. Hertzberg, Deformation and Fracture Mechanics of Engineering Materials, 3rd Ed., Wiley and Sons (1989) NE 125: Introduction to Materials Science and Engineering Introduction Chapter Four: Crystal Defects Grain Boundaries High angle grain boundary Low angle grain boundary A grain boundary is the region a few atomic diameters wide separating grains (single crystals) with distinct grain crystallographic orientations orientations Small (or low) angle grain boundary: a few degrees High angle grain boundary: larger angle of misalignment Despite discontinuity, cohesive forces along boundary are present, maintaining strength of materials (Grain boundary energy at interfacial region); energy is larger for high angle misalignment NE 125: Introduction to Materials Science and Engineering Introduction Chapter Four: Crystal Defects Grain Boundaries The surface energy at the boundary is greater for smaller grain size The (Larger surface area to volume ratio) (Larger Surface energy provides cohesive forces in polycrystalline materials. Reducing the Surface grain size can increase mechanical strength. Thermodynamic driving force for grain growth (minimize surface energy) Thermodynamic Discontinuities in polycrystalline materials may decrease thermal and electrical Discontinuities conductivity conductivity NE 125: Introduction to Materials Science and Engineering Introduction Chapter Four: Crystal Defects Grain Boundaries Tilt Boundary A low angle grain boundary resulting from the low alignment of edge dislocations separated by a distance D distance D=b/θ (θ in radians) Two adjacent grains tilted relative to each other by a few degrees θ [1] From Shackelford, Introduction to Materials Science for Engineers, 6th Edition; Used by permission NE 125: Introduction to Materials Science and Engineering Introduction Chapter Four: Crystal Defects Grain Boundaries Twin Boundary Atoms on one side of the boundary are in mirror Atoms positions with respect to atoms on the other side of the boundary side Twin boundary Twist Boundary Is formed when the angle of misorientation is Is parallel to the boundary. Can be represented by an array of screw dislocations an NE 125: Introduction to Materials Science and Engineering Introduction Chapter Four: Crystal Defects Grain Size Determination ASTM Grain Size Number (n) Grain structure is observed at 100 X magnification N = avg. number of grains per sq. inch @ 100 X avg. n = ASTM grain number N =2 n −1 ln ( N ) ⇔ n = 1+ ln( 2 ) Illustration from Shackelford “Introduction to Materials Science for Engineers”, 6th Ed; Used by permission NE 125: Introduction to Materials Science and Engineering Introduction Chapter Four: Crystal Defects Sample Problems Sample < blackboard > blackboard ...
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