Transcript Chapter 4
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
Atomic Composition Bonding X’tal Structure 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
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Chapter 4-
Point Defects – 0 dim.
- localized disruption in regularity of the lattice - on and between lattice sites Vacancy Substitutional
3 Types: 1. Substitutional Impurity
- occupies normal lattice site - dopant ☺ , e.g., P in Si - contaminant Li + in NaCl
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 Interstitial 6
Chapter 4-
POINT DEFECTS
• Vacancies : -vacant atomic/lattice sites in a structure.
Vacancy distortion of planes • Self-Interstitials : -"extra" atoms positioned between atomic sites.
distortion of planes self interstitial Chapter 4- 3
Population of vacancies in a crystal
• In a crystal containing N atomic sites, the number n
d
of vacant sites:
n d = 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!
No. of defects Activation energy No. of potential defect sites.
N D N
exp
Q D k T Temperature Boltzmann's constant (1.38 x 10-23 J/atom K) (8.62 x 10-5 eV/atom K) Each lattice site is a potential vacancy site Chapter 4 4
ESTIMATING VACANCY CONC.
• Find the equil. # of vacancies in 1m of Cu at 1000C.
• Given: N D N
For 1m3, N = exp
x
k Q T D
0.9eV/atom = 2.7 1273K
·
10 -4 NA ACu 8.62 x 10-5 eV/atom-K x 1m3 = 8.0 x 1028 sites • Answer: Chapter 4 6
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 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.
Reprinted with permission from 5.75
m
m by 5.75
m
Nature (K.F. McCarty, 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 m.) 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-
10 min BREAK
Chapter 4-
Point Defects: Vacancies & Interstitials
Schematic representation of a variety of point defects: (1) vacancy; (2) self-interstitial; E i > E v (3) interstitial impurity; , so ?
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 brasses with varying properties of copper and zinc ; the proportions of zinc and copper can be varied to create a range
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:
precipitates
while solute atoms are being added, new compounds / structures may form beyond solubility limit, or solute forms local 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
solvent should be crystallize in the same structure - solute and •
Electronegativities
encouraged - solute and solvent should have comparable electronegativites, otherwise new inter-metallic phases are • 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 (e.g., Cu in alloy Ni ) Interstitial (e.g., C in alloy 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.
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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
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microstructures of annealed brass
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 crystals growing grain structure liquid • Crystals grow until they meet each other
Callister & Rethwisch 8e.
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Chapter 4-
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Polycrystalline Material
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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 7e.
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 ~ 8cm Adapted from Fig. 4.7, Callister 6e.
grain boundaries heat flow Adapted from Fig. 4.10, Callister 6e. (Fig. 4.10 is from Metals Handbook, Vol. 9, 9th edition, Metallography and Microstructures, Am. Society for Metals, Metals Park, OH, 1985.) Chapter 4- 15
Optical Microscopy
• Useful up to 2000X magnification.
• Polishing removes surface features (e.g., scratches) • Etching changes reflectance, depending on crystal orientation.
Adapted from Fig. 4.13(b) and (c),
Callister 7e.
(Fig. 4.13(c) is courtesy of J.E. Burke, General Electric Co.
crystallographic planes 0.75mm
Micrograph of brass (a Cu-Zn alloy)
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 - 1,000,000X) • 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 – 3dim
• Voids – coalesced vacancies • Cracks • Pits • Grooves • Inclusions • Precipitates SEM of CVD GaN 35
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 atomic arrangement order name
regular
ordered
long-range crystalline “crystal”
disordered
random* short-range amorphous “glass” 36
Chapter 4-
Single Crystal Disorder Polycrystalline Grain boundaries Amorphous Grains 37
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-
Quiz 3
G v A B C, D E Vacancy, Dislocation, Substitutional impurity atom, Self interstitial atom, Interstitial impurity atom, Precipitate of impurity atoms 39
Chapter 4-