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Imperfections In Solids
Engineering 45 Imperfections In Solids Bruce Mayer, PE Licensed Electrical & Mechanical Engineer
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Learning Goals Learn The Forms of Defects in Solids
Use metals as Prototypical Example How the number and type of defects Can be varied and controlled How defects affect material properties Determine if “Defects” or “Flaws” are Desirable UNdesirable
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Classes of Imperfections
POINT Defects Atomic Vacancies Interstitial Atoms Substitutional Atoms LINE Defects (Plane Edge) Dislocations Area Defects Grain Boundaries Usually 3-D HRTEM image of SrTiO3 Grain Boundary * ULTRAMICROSCOPY, vol 86 (2001) pp
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Point Defects Vacancy MISSING atom at Lattice Site
distortion of planes self- interstitial distortion of planes Self-Interstitial “Extra” Atom “Squeezed” into the Lattice Structure
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Point Defect Concentration
Equilibrium Defect Concentration Varies With Temperature; e.g., for Vacancies: No. of defects Activation energy æ - ö N Q v ç v ÷ = exp ç ÷ No. of potential è ø N k T defect sites. Temperature Boltzmann's constant k = 1.38x10-23 J/at-K 8.62x10-5 eV/at-K N Every Lattice Site is a Potential Vacancy
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Measure Activation Energy
Recall The Defect Density Eqn Take the ln of Eqn This of the form This form of a Negative Exponential is called an Arrhenius Relation Svante Arrhenius: , Chem Nobel 1903
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Measure Activation Energy cont
Meausure ND/N vs T By ENGR25 method of Function Discovery N v slope N v ln - Q /k v exponential dependence! T 1/ T RePlot in Linear Form y = mx + b Find the Activation Energy from the Slope
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Vacancy Concentration Exmpl
In Defect Density Rln QD Can Take Two forms Qv Vacancies Qi Interstitials Consider a Qv Case Copper at 1000 C Qv = 0.9 eV/at ACu = 63.5 g/mol = 8400 kg/cu-m Find the Vacancy Density First Find N in units of atoms per cu-m
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Vacancy Concentration cont
Since Units Chk: Now apply the Arrhenius ºC 275 ppm Vacancy Rate At 180C (Pizza Oven) The Vacancy Rate 98 pptr
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Observing Equil Vacancy Conc
Low energy electron microscope view of a (110) surface of NiAl. 575μm X 575μm Image 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. I sland grows/shrinks to maintain equil. vancancy conc. in the bulk.
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Point Impurities in Solids
Two outcomes if impurity (B) added to host (A) Solid solution of B in A (i.e., random dist. of point defects) Substitutional alloy (e.g., Cu in Ni) Interstitial alloy (e.g., C in Fe) OR Solid solution of B in A plus particles of a NEW PHASE (usually for a larger amount of B) Second phase particle different composition (chem formula) often different structure e.g.; BCC in FCC
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W. Hume – Rothery Rule The Hume–Rothery rule Outlines the Conditions for substitutional solid soln Δr (atomic radius) < 15% Proximity in periodic table i.e., similar electronegativities Same crystal structure for pure metals Valency All else being equal, a metal will have a greater tendency to dissolve a metal of higher valency than one of lower valency
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Imperfections in Solids
Application of Hume–Rothery rules Solid Solutions 1. Would you predict more Al or Ag to dissolve in Zn? 2. More Zn or Al in Cu? Element Atomic Crystal Electro- Valence Radius Structure nega- (nm) tivity Cu FCC C H O Ag FCC Al FCC Co HCP Cr BCC Fe BCC Ni FCC Pd FCC Zn HCP
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Apply Hume – Rothery Rule
Would you predict more Al or Ag to dissolve in Zn? Δr → Al (close) Xtal → Toss Up ElectronNeg → Al Valence → Al Element Atomic Crystal Electro- Valence Radius Structure nega- (nm) tivity Cu FCC C H O Ag FCC Al FCC Co HCP Cr BCC Fe BCC Ni FCC Pd FCC Zn HCP More Zn or Al in Cu? Δr → Zn (by far) Xtal → Al ElectronNeg → Zn Valence → Al
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Composition/Concentration
Composition Amount of impurity/solute (B) and host/solvent (A) in the SYSTEM. Two Forms Weight-% Atom/Mol % Where mJ = mass of constituent “J” Where nmJ = mols of constituent “J” Convert Between Forms Using AJ
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Linear Defects → Dislocations
Edge dislocation: extra half-plane of atoms linear defect moves in response to shear stress and results in bulk atomic movement (Ch 7,8) cause of slip between crystal planes when they move
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Movement of Edge Dislocations
Dislocations Move Thru the Crystal in Response to Shear Force Results in Net atomic Movement or DEFORMATION
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Motion of Edge Dislocation
Dislocation motion requires the successive bumping of a half plane of atoms (from left to right here). Bonds across the slipping planes are broken and remade in succession
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Carpet Movement Analogy
Moving a Large Carpet All At Once Requires MUCH Force (e.g.; a ForkLift Truck) Using a DISLOCATION Greatly Facilitates the Move Dislocation
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Carpet Dislocation Continue to Slide Dislocation with little effort to the End of the Crystal Note Net Movement at Far End Dislocation
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Dislocations First PREDICTED as defects in crystals since theoretical strength calculations (due to multibond breaking) were far too high as compared to experiments later invention of the Transmission Electron Microscope (TEM) PROVED their Existence deformed steel (40,000X) Ti alloy (51,500X) * move through crystal lattice permanent deformation * CREATED during deformation * can act as obstacles, if too many → Work Harding
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Interfacial Defects 2D, Sheet-like Defects are Termed as Interfacial
Some Macro-Scale Examples Solid Surfaces (Edges) Bonds of Surface Atoms are NOT Satisfied Source of “Surface Energy” in Units of J/sq-m Stacking Faults – When atom-Plane Stacking Pattern is Not as Expected Phase Boundaries – InterFace Between Different Xtal Structures
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Interface Def. → Grain Boundaries
are Boundaries BETWEEN crystals Produced by the solidification process, for example Have a Change In Crystal Orientation across them IMPEDE dislocation motion Generally Weaker that the Native Xtal Typically Reduce Material Strength thru Grain-Boundary Tearing Crack Along GB
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Area Defects: Grain Boundaries
Schematic Representation Note GB Angles Metal Ingot: GB’s Follow Solidification Path ~ 8cm
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Optical Microscopy Since Most Solid Materials are Opaque, MicroScope Uses REFLECTED Light These METALLOGRAHPIC MScopes do NOT have a CONDENSOR Lens
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Optical MicroScopy cont
The Resolution, Z The Magnification, M Where Light Wavelength 550 nm For “White” Light (Green Ctr) NA Numerical Aperture for the OBJECTIVE Lens 0.9 for a Very High Quality Lens Typical Values Z 375 nm Objects Smaller than This Cannot be observed Objects Closer Together than This Cannot Be Separated Mtrue 200
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Optical MicroScopy cont.2
Sample Preparation grind and polish surface until flat and shiny sometimes use chemical etch use light microscope different orientations → different contrast take photos, do analysis e.g. Grain Sizing
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Optical MicroScopy cont.3
Grain Boundaries are imperfections, with high surface energy are more susceptible to etching; may be revealed as dark lines due to the change of direction in a polycrystal ASTM E-112 Grain Size Number, n microscope polished surface surface groove grain boundary Where N grain/inch2 Fe-Cr alloy
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Electron Microscopy For much greater resolution, use a BEAM OF ELECTRONS rather that light radiation Transmission Electron Microscopy (TEM): VERY high magnifications contrast from different diffraction conditions very thin samples needed for transmission Scanning Electron Microscopy (SEM): surface scanned, TV-like depth of field possible
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Atomic Force MicroScopy
AFM is Also called Scanning Probe Microscopy (SPM) tiny probe with a tinier tip rasters across the surface topographical map on atomic scale Polymer
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SEM Photo Scaling MEMS Hinge ► Find Rectangle Length Lactual
2.91 in-photo This is an SEM photograph of a MEMS microscopic hinge. The hinge is connected to the edge of a mirror, which can be seen in the right part of the micrograph. The flexible springs in the hinge allow the mirror to tilt and pivot. The mirror is connected to two vertical lifters (outside the field of view of this photograph). This hinge, combined with the lifting action of the two vertical lifters, allow the mirror to be pointed in a variety of directions. The mirror is used in optical switching systems. 3.02 in-photo
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SEM Photo Scaling Use “ChainLink” Cancellation of Units (c.f. ENGR10)
Thus the Rectangular Connecting Bracket is about 48µm in Length
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Olympus DUV Metallurgical Mscope
Deep Ultraviolet Microscope U-UVF248
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