Lecture Notes - Chapter 4-Lecture 1.pptx
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Chapter 4: Imperfections in Solids
Chapter 4: Imperfections in Solids
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Chapter 4 -2TOPICSChapter 4: Imperfections in Solids Imperfections in SolidsPoint DefectsInterstitialVacanciesSolid solutionsLine DefectsEdge DislocationScrew DislocationPlanar Defects MicroscopyElectron MicroscopyOptical MicroscopyScanning Probe Microscopy
Chapter 4 -2
Good Imperfections:
Dopants (ex: P in Si increases its conductivity)Alloying element (ex: Mg in Al increases its strength)
3Imperfections in SolidsThere is no such thing as a perfect crystal. There area always imperfections.
Bad Imperfections: Contaminants (ex: H in Fe)
Dopant: an element that is inserted into a substance to alter its electrical or optical properties
Chapter 4 -3
4Point DefectsLocalized disruption in a regular crystalline arrangement on or between lattice sites.
Chapter 4 -4
5Point DefectsVacancies : missing atoms (vacant atomic sites)
Vacancydistortion of planesVacancies can be formed during crystallization.
Chapter 4 -5
6Solidification- result of casting of molten material2 stepsNuclei form Nuclei grow to form crystals grain structureStart with a molten material all liquidWhat causes Imperfections in Solids?Crystals grow until they meet each other
grain structure
crystals growing
nucleiliquid
Chapter 4 -6
7The number of vacancies that we can expect to find in a given material at a certain temperatures:Equilibrium Concentration:Point DefectsBoltzmann's constant
NvN=expQvkTNo. of defects per unit volumeTotal number ofatomic sites perunit volumeEnergy required for the formation of one vacancyAbsolute Temperature
Chapter 4 -7Bonding energy and thermal energy competing.
8Question:Compare the fraction of atoms sites that are vacant in copper at room temperature (23C) and at its melting temperature (1085C).The energy for vacancy formation is 0.9 eV/atomEquilibrium Concentration:Point Defects
Chapter 4 -8Bonding energy and thermal energy competing.
9Question:Compare the number of vacancies in copper at room temperature (23C) and at its melting temperature (1085C). The energy for vacancy formation is 0.9 eV/atom. The atomic weight and density for copper are 63.5 g/mol and 8.4 g/cm respectively.Equilibrium Concentration:Point Defects
Chapter 4 -9Bonding energy and thermal energy competing.
10 Self-Interstitials:-"extra" atoms positioned between atomic sites.Point Defects
self-interstitialdistortion of planesSelf-interstitials are not very probable in metals:Self-interstitials introduce large distortions in the surrounding lattice because of high atomic packing factor (the atoms are much larger than the interstitial position).
Chapter 4 -10
Point DefectsSolid Solution: form when the solute atoms are added to the host material.The crystal structure is maintained.The composition is homogeneous.
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Substitutional: impurity atoms replace the host atoms(e.g., Cu in Ni)
Interstitial:impurity atoms fill the voids(e.g., C in Fe)
Chapter 4 -12Substitutional Solid Solutions: Factors that determine the degree to which a solute is dissolved in a solvent:Hume Rothery rules2. Proximity in periodic tablesimilar electronegativitiesAtomic Size: Difference in atomic radii < 15%Crystal Structuresmust be the same4. ValencesIf other factors are being equal, a metal will have a greater tendency to dissolve a metal of higher valency than to dissolve one of a lower valency.Example: Bronze(Copper and Nickel)CuNiAtomic radius (nm).128.125Crystal StructureFCCFCCElectronegativity1.91.8Valences12
Chapter 4 -12
13Application of HumeRothery rules1. Which of these elements would you expect to form a substitutional solid solution having complete solubility with nickel?
2. Which of these elements would you expect to form a substitutional solid solution of incomplete solubility with nickel?2. Which of these elements would you expect to form a an interstitial solid solution with nickel?
Chapter 4 -13
14Solid SolutionsHow to express the composition of an alloy in terms of its composing elements:
m1 = mass of component 1m2 = mass of component 2
weight percent (wt%)
nm1 = number of moles of component 1nm2 = number of moles of component 2 atom percent (at%)
Chapter 4 -14
15Solid SolutionsComposition Conversion:
Atom percent to weight percent
weight percent to atom percent
Chapter 4 -15
16Solid SolutionsDensity and atomic weight of binary alloys:
Average Density
Average Atomic Weight:
Chapter 4 -16
17Solid Solutions
Acu=63.55 g/molAAl=26.97 g/mol
Chapter 4 -17
18Solid SolutionsCalculate the unit cell edge length for an 80 wt% Ag20 wt% Pd alloy. the crystal structure for this alloy is FCC.
density of Pd: 12.02 g/cm3density of Ag: 10.49 g/cm3Atomic mass of Pd: 106.4 g/molAtomic mass of Ag: 107.87 g/mol
Chapter 4 -18
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