Lecture Notes - Chapter 4-Lecture 1.pptx

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

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4Point DefectsLocalized disruption in a regular crystalline arrangement on or between lattice sites.

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5Point DefectsVacancies : missing atoms (vacant atomic sites)

Vacancydistortion of planesVacancies can be formed during crystallization.

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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

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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).

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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

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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%)

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15Solid SolutionsComposition Conversion:

Atom percent to weight percent

weight percent to atom percent

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16Solid SolutionsDensity and atomic weight of binary alloys:

Average Density

Average Atomic Weight:

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17Solid Solutions

Acu=63.55 g/molAAl=26.97 g/mol

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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