4-IMPERFECTIONS-CHPT 4-MIAE 221-2023

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Concordia University *

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Material Science

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Oct 30, 2023

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1 IMPERFECTIONS IN SOLIDS Chapter 4 MIAE 221 – Materials Science

Notes# 4A - MIAE 221 (adapted from Callister) 2 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? CHP 4: IMPERFECTIONS IN SOLIDS

Notes# 4A - MIAE 221 (adapted from Callister) 3 • Solidification - result of casting of molten material – 2 steps • Nuclei of solid phase start to form • Nuclei grow to form crystals – when crystal boundaries meet form grain structure • Start with a molten material – all liquid Imperfections in Solids nuclei crystals growing grain structure liquid

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4 Imperfections in Solids There is no such thing as a perfect crystal. Crystalline imperfections (or defects) are always present. • Many of the properties of materials are sensitive to the presence of imperfections. • Crystalline defect refers to a lattice irregularity with dimensions on the order of an atomic diameter. • What kinds of crystalline imperfections exist in solids? Notes# 4A - MIAE 221 (adapted from Callister)

Notes# 4A - MIAE 221 (adapted from Callister) 5 • Vacancy atoms • Interstitial atoms • Substitutional atoms Point defects Types of Imperfections • Dislocations Line defects • Grain Boundaries Area (interfacial) defects

Notes# 4A - MIAE 221 (adapted from Callister) 6 • Vacancies :-vacant atomic sites in a structure. • Self-Interstitials : -"extra" atoms positioned between atomic sites. Very rare as big distortion. Point Defects Vacancy distortion of planes self- interstitial distortion of planes

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Notes# 4A - MIAE 221 (adapted from Callister) 7 VACANCY Vacancy - Missing atom from lattice site . Sometimes produced during solidification, sometimes by physical factors, (heating, neutrons, working) but present in all crystals (increases the randomness- entropy-of the crystal). Usually low in number but reaches 1 vacancy per 10,000 atoms as temperature rises to melting point. Vacancy on silicon surface

Notes# 4A - MIAE 221 (adapted from Callister) 8 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 vacancies No. of potential defect sites. Activation energy Temperature Each lattice site is a potential vacancy site • Equilibrium concentration varies with temperature ! Equilibrium Concentration of Point Defects (depending on units)

Notes# 4A - MIAE 221 (adapted from Callister) 9 We can get Q from an experiment; taking natural logs of both sides…. • Measure N D as a function of T. Then: 1/ T N N D ln 1 - Q D /k slope MEASURING ACTIVATION ENERGY , Q D T k Q N N D D 1 ln − =       T N N D 1 versus ln Plot       N v N = exp - Q v k T

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