Imperfections In Solids Engineering 45 Imperfections In Solids Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu

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

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 303-318

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

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

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: 1859-1927, Chem Nobel 1903

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

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 

Vacancy Concentration cont Since Units Chk: Now apply the Arrhenius Relation @1000 ºC  275 ppm Vacancy Rate At 180C (Pizza Oven) The Vacancy Rate  98 pptr

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.

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

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

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 0.1278 FCC 1.9 +2 C 0.071 H 0.046 O 0.060 Ag 0.1445 FCC 1.9 +1 Al 0.1431 FCC 1.5 +3 Co 0.1253 HCP 1.8 +2 Cr 0.1249 BCC 1.6 +3 Fe 0.1241 BCC 1.8 +2 Ni 0.1246 FCC 1.8 +2 Pd 0.1376 FCC 2.2 +2 Zn 0.1332 HCP 1.6 +2

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 0.1278 FCC 1.9 +2 C 0.071 H 0.046 O 0.060 Ag 0.1445 FCC 1.9 +1 Al 0.1431 FCC 1.5 +3 Co 0.1253 HCP 1.8 +2 Cr 0.1249 BCC 1.6 +3 Fe 0.1241 BCC 1.8 +2 Ni 0.1246 FCC 1.8 +2 Pd 0.1376 FCC 2.2 +2 Zn 0.1332 HCP 1.6 +2 More Zn or Al in Cu? Δr → Zn (by far) Xtal → Al ElectronNeg → Zn Valence → Al

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

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

Movement of Edge Dislocations Dislocations Move Thru the Crystal in Response to Shear Force Results in Net atomic Movement or DEFORMATION

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

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

Carpet Dislocation Continue to Slide Dislocation with little effort to the End of the Crystal Note Net Movement at Far End Dislocation

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

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

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

Area Defects: Grain Boundaries Schematic Representation Note GB Angles Metal Ingot: GB’s Follow Solidification Path ~ 8cm

Optical Microscopy Since Most Solid Materials are Opaque, MicroScope Uses REFLECTED Light These METALLOGRAHPIC MScopes do NOT have a CONDENSOR Lens

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

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

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

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

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

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

SEM Photo Scaling Use “ChainLink” Cancellation of Units (c.f. ENGR10) Thus the Rectangular Connecting Bracket is about 48µm in Length

Olympus DUV Metallurgical Mscope Deep Ultraviolet Microscope U-UVF248