Why are we interested IMPERFECTIONS IN SOLIDS Crystals

Why are we interested IMPERFECTIONS IN SOLIDS ? “Crystals are like people, it is the defects in them which tend to make them interesting!” - Colin Humphreys. Crystals in nature are never perfect, they have defects ! Chapter 4 - 1

Imperfections in Solids Is it enough to know bonding and structure of materials to estimate their macro properties ? BONDING + STRUCTURE + DEFECTS PROPERTIES Color/Price of Precious Stones Mechanical Properties of Metals Properties of Semiconductors Corrosion of Metals Defects do have a significant impact on the properties of materials Chapter 4 -

Imperfections in Solids Bonding X’tal Structure Thermo-Mechanical Processing Atomic Composition Microstructure: Materials properties Addition and manipulation of defects Chapter 4 -

Perfection… In terms of: 1. Chemical composition – pure 2. Atomic arrangement – defect free • • • Both are critical in determining the performance of material. But, real engineering materials are not perfect. Properties can be altered through defect engineering. 4 Chapter 4 -

Classification of Defects The defects are classified on the basis of dimensionality: • • 0 -dimensional: point defects 1 -dimensional: line defects 2 -dimensional: interfacial defects 3 -dimensional: bulk defects 5 Chapter 4 -

Point Defects – 0 dim. - localized disruption in regularity of the lattice - on and between lattice sites 3 Types: 1. Substitutional Impurity - occupies normal lattice site - dopant ☺, e. g. , P in Si - contaminant Li+ in Na. Cl 2. Interstitial Impurity - occupies position between lattice sites - alloying element ☺, e. g. , C in Fe - contaminant, H in Fe 3. Vacancy - unoccupied lattice site - formed at time of crystallization Vacancy Substitutional Interstitial 6 Chapter 4 -

• Vacancies: POINT DEFECTS -vacant atomic/lattice sites in a structure. • Self-Interstitials: -"extra" atoms positioned between atomic sites. Chapter 4 - 3

Population of vacancies in a crystal • In a crystal containing N atomic sites, the number nd of vacant sites: nd = the number of defects (in equilibrium at T) N = the total number of atomic sites per mole ΔHd = the energy necessary to form the defect T = the absolute temperature (K) k = the Boltzmann constant A = proportionality constant 8 Chapter 4 -

EQUIL. CONCENTRATION: POINT DEFECTS • Equilibrium concentration varies with temperature! Chapter 4 - 4

ESTIMATING VACANCY CONC. • Find the equil. # of vacancies in 1 m 3 of Cu at 1000 C. • Given: • Answer: Chapter 4 -

Point Defects: Vacancies & Interstitials • Most common defects in crystalline solids are point defects. • At high temperatures, atoms frequently and randomly change their positions leaving behind empty lattice sites. • In general, diffusion (mass transport by atomic motion) - can only occur because of vacancies. Chapter 4 -

OBSERVING EQUIL. VACANCY CONC. • Low energy electron microscope view of a (110) surface of Ni. Al. • 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. Mc. Carty, 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 mm by 5. 75 mm. ) Copyright (2001) Macmillan Publishers, Ltd. Question: Where do vacancies go ? Chapter 4 - 7

Point Defects in Ionic Crystals Maintain global charge neutrality 1. Schottky Imperfection formation of equivalent (not necessarily equal) numbers of cationic and anionic vacancies 2. Frenkel Imperfection formation of an ion vacancy and an ion interstitial 13 Chapter 4 -

Point Defects: Vacancies & Interstitials Schematic representation of a variety of point defects: (1) vacancy; (2) self-interstitial; Ei > Ev , so ? (3) interstitial impurity; less distortion caused (4, 5) substitutional impurities The arrows represent the local stresses introduced by the point defects. Chapter 4 -

Impurities / Solid Solutions • Impurities are atoms which are different from the host/matrix • All solids in nature contain some level of impurity – Very pure metals 99. 9999% – For Cu how much does that make ? ~ 1 impurity per 100 atoms • Impurities may be introduced intentionally or unintentionally. – Examples: carbon added in small amounts to iron makes steel, which is stronger than pure iron. Boron is added to silicon change its electrical properties. Pt and Cu are added to Gold to make it stronger, also! • Alloys - deliberate mixtures of metals – Example: sterling silver is 92. 5% silver – 7. 5% copper alloy. Stronger than pure silver. Chapter 4 -

Brass: Brass (pirinç) is an alloy of copper and zinc; the proportions of zinc and copper can be varied to create a range of brasses with varying properties Chapter 4 -

Bronze is a metal alloy consisting primarily of copper, usually with tin (kalay, Sn) as the main additive. It is hard and brittle, and it was particularly significant in antiquity. Chapter 4 -

Solid Solutions Solid solutions are made of a host (the solvent or matrix) which dissolves the minor component (solute). The ability to dissolve is called solubility. • Solvent: in an alloy, the element or compound present in greater amount • Solute: in an alloy, the element or compound present in lesser amount Solid Solution: • homogeneous • maintain crystal structure • contain randomly dispersed impurities (substitutional or interstitial) Second Phase: while solute atoms are being added, new compounds / structures may form beyond solubility limit, or solute forms local precipitates Nature of the impurities, their concentration, reactivity, temperature and pressure, etc decides the formation of solid solution or a second phase. Chapter 4 -

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 Chapter 4 -

Factors affecting Solid Solubility • Atomic size factor - atoms need to “fit” => solute and solvent atomic radii should be within ~ 15% • Crystal structures - solute and solvent should be crystallize in the same structure • Electronegativities - solute and solvent should have comparable electronegativites, otherwise new inter-metallic phases are encouraged • Valency - generally more solute goes into solution when it has higher valency than solvent Chapter 4 -

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) OR Substitutional alloy (e. g. , Cu in Ni) Interstitial alloy (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 4 - 8

Line Defects - Dislocations • Dislocations are linear defects: the interatomic bonds are significantly distorted only in the immediate vicinity of the dislocation line. This area is called the dislocation core. • Dislocations also create small elastic deformations of the lattice at large distances. 22 Chapter 4 -

DISLOCATIONS • Material permanently deforms as dislocation moves through the crystal. • Bonds break and reform, but only along the dislocation line at any point in time, not along the whole plane at once. • Dislocation line separates slipped and unslipped material. Chapter 4 -

LINE DEFECTS Dislocations: • are line defects, • cause slip between crystal plane when they move, • produce permanent (plastic) deformation. Schematic of a Zinc Crystal (HCP): • before deformation • after tensile elongation slip steps Chapter 4 - 11

Dislocations and Materials Strength Easily form dislocations and allow mobility; Not limited with coordination numbers Remember Covalent Bond ! How many bonds to break ? Finding an equivalent site ? Very large Burgers vector size; Finding an equivalent site and overcoming repulsive forces ! Chapter 4 -

Surface- Planar Defects • Grain Boundaries SEM (Scanning electron microscope) image (showing grains and grain boundaries) Photomicrographs of typical 26 Chapter 4 microstructures of

Imperfections in Solids • 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 nuclei liquid crystals growing grain structure Adapted from Fig. 4. 14(b), Callister & • Crystals grow until they meet each other 27 Chapter 4 - 27

Polycrystalline Material 28 Chapter 4 -

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 7 e. Chapter 4 -

AREA DEFECTS: GRAIN BOUNDARIES Grain boundaries: • • are boundaries between crystals. are produced by the solidification process, for example. have a change in crystal orientation across them. impede dislocation motion. Metal Ingot Schematic Adapted from Fig. 4. 7, Callister 6 e. ~ 8 cm Adapted from Fig. 4. 10, Callister 6 e. (Fig. 4. 10 is from Metals Handbook, Vol. 9, 9 th edition, Metallography and Microstructures, Am. Society for Metals, Metals Park, OH, 1985. ) Chapter 4 - 15

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. 4. 13(b) and (c), Callister 7 e. (Fig. 4. 13(c) is courtesy of J. E. Burke, General Electric Co. Micrograph of brass (a Cu-Zn alloy) 0. 75 mm Chapter 4 -

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. Chapter 4 -

Scanning Tunneling Microscopy (STM) • Atoms can be arranged and imaged! Photos produced from the work of C. P. Lutz, Zeppenfeld, and D. M. Eigler. Reprinted with permission from International Business Machines Corporation, copyright 1995. Carbon monoxide molecules arranged on a platinum (111) surface. Iron atoms arranged on a copper (111) surface. These Kanji characters represent the word “atom”. Chapter 4 -

Bulk – Volume Defects – 3 dim • • • Voids – coalesced vacancies Cracks Pits Grooves Inclusions Precipitates SEM of CVD Ga. N 34 Chapter 4 -

Summary - Atomic Arrangement SOLID: Smth. which is dimensionally stable, i. e. , has a volume of its own classifications of solids by atomic arrangement ordered disordered atomic arrangement regular random* order long-range short-range name crystalline amorphous “crystal” “glass” 35 Chapter 4 -

Disorder Single Crystal Polycrystalline Amorphous Grain boundaries Grains 36 Chapter 4 -

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 4 -

G Quiz v A B C, D E Vacancy, Dislocation, Substitutional impurity atom, Self interstitial atom, Interstitial impurity atom, Precipitate of impurity atoms 38 Chapter 4 -