ISSUES TO ADDRESS... What types of defects arise in solids? Can the number and type of defects be varied and controlled?

Transcription

1 CHAPTER 4: IMPERFECTIONS IN SOLIDS ISSUES TO ADDRESS... What types of defects arise in solids? Can the number and type of defects be varied and controlled? How do defects affect material properties? Are defects undesirable?

2 TYPES OF IMPERFECTIONS Vacancy atoms Interstitial atoms Substitutional atoms Dislocations Grain Boundaries Point defects Line defects Area defects

3 POINT DEFECTS Vacancies: -vacant atomic sites in a structure. distortion of planes Vacancy Self-Interstitials: -"extra" atoms positioned between atomic sites. distortion of planes selfinterstitial

4 EQUIL. CONCENTRATION: POINT DEFECTS Equilibrium concentration varies with temperature! No. of defects No. of potential defect sites. Each lattice site is a potential vacancy site N D N = exp Q D kt Activation energy Temperature Boltzmann's constant (1.38 x J/atom K) (8.62 x 10-5 ev/atom K)

5 MEASURING ACTIVATION ENERGY We can get Q from an experiment. Measure this... N D = Q exp D N kt Replot it... ND N exponential dependence! ND ln N 1 slope -QD/k T defect concentration 1/T

6 ESTIMATING VACANCY CONC. Find the equil. # of vacancies in 1 m 3 of Cu at 1000 C. ρ = 8.4 g/cm 3 ACu = 63.5g/mol QV = 0.9eV/atom NA = 6.02 x atoms/mole For 1m 3, N = ρ x Answer: 0.9eV/atom N D N = exp Q D = kt K 8.62 x 10-5 ev/atom-k NA x 1m 3 = 8.0 x sites ACu ND = x sites = 2.2x vacancies

7 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 alloy (e.g., Cu in Ni) Interstitial alloy (e.g., C in 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.

8 Weight Percentage Alloy Composition Binary Ternary, Quaternary, (2 components) (3, 4, components) m1 m j C1 = 100 C j = 100 m1 + m2 m Atomic or Mole Percentage ' nm1 C1 = 100 ' nmj C j = 100 nm1 + nm2 n ' 1 m n m 1 = A 1 i i i mi C ' 1 C1 A2 = C A + C 1 ' ' 1 1 ' 2 2 A C A C1= C A + C A Conversion formulas

9 Dislocations Dislocations Line defects Most important class of defects for ductile crystalline materials (metals!) Burgers vector b Basic lattice deformation Edge Dislocations b perpendicular to the dislocation line Schematic atomic structure of an edge dislocation

10 Schematic perspective view Screw Dislocations View of plane ABCD Screw dislocation line Burgers vector b Basic lattice deformation Screw Dislocations b parallel to the dislocation line

11 Mixed Dislocations Schematic perspective view Schematic of dislocation line Edge Mixed View of plane ABCD Screw

12 Images of Dislocations Surface GaN Sapphire ~1 µm Dislocations in Ti alloy Dislocations in GaN

13 Interfacial Defects Two-dimensional defects also referred to as planar defects Free surfaces Surfaces are defects typical energies J/cm 2 Grain Boundaries Borders between crystals with different orientation High angle grain boundary Large misorientation Low-angle grain boundary Small misorientation Consists of walls of dislocations

14 Low Angle Grain Boundaries Edge dislocations Example of a tilt boundary Grain 1 Grain 2 Low angle boundaries d θ b/d θ = Grain-Grain misorientation b = Burgers vector d = dislocation spacing Grain Boundary

15 Observation of Microstructures Optical Microscopy (referred to as metallography, ceramography, ) 1 mm = 1000 µm Optical micrograph of brass Resolution of optical microscopy λ light 500 nm

16 Observation of Microstructures Optical Microscope Transmission Electron Microscope FEI Tecnai F kv FE TEM/STEM (UCSB) TEM/STEM Resolution ~ 1 Å

17 Observation of Microstructures Scanning Electron Microscope Typical SEM Image SEM Resolution ~ 10 Å

18 Observation of Microstructures Scanning Probe Microscopy (SPM) Common modes Scanning Tunneling Microscopy (STM) Atomic Force Microscopy (AFM) SPM Resolution: ~ 1 Å AFM Image: GaN

19 CHAPTER 6: MECHANICAL PROPERTIES ISSUES TO ADDRESS... Stress and strain: What are they and why are they used instead of load and deformation? Elastic behavior: When loads are small, how much deformation occurs? What materials deform least? Plastic behavior: At what point do dislocations cause permanent deformation? What materials are most resistant to permanent deformation? Toughness and ductility: What are they and how do we measure them?

20 ELASTIC DEFORMATION 1. Initial 2. Small load 3. Unload bonds stretch δ F Elastic means reversible! F Linearelastic δ return to initial Non-Linearelastic

21 PLASTIC DEFORMATION (METALS) 1. Initial 2. Small load 3. Unload bonds stretch planes & planes still shear sheared δelastic + plastic δplastic F F Plastic means permanent! linear elastic δplastic linear elastic δ

22 ENGINEERING STRESS Tensile stress, σ: Shear stress, τ: Ft Ft F Area, A Area, A Fs Ft σ= F t A o original area before loading τ= F s A o Stress has units: N/m 2 or lb/in 2 Fs F Ft

23 COMMON STATES OF STRESS Simple tension: cable F F Ao = cross sectional Area (when unloaded) σ = F A o σ σ Simple shear: drive shaft A c M 2R M Fs A o τ = F s A Ski lift (photo courtesy P.M. Anderson) o τ Note: τ = M/AcR here.

24 OTHER COMMON STRESS STATES (1) Simple compression: A o Canyon Bridge, Los Alamos, NM (photo courtesy P.M. Anderson) Balanced Rock, Arches National Park (photo courtesy P.M. Anderson) σ = F A o Note: compressive structure member (σ < 0 here).

25 OTHER COMMON STRESS STATES (2) Bi-axial tension: Hydrostatic compression: Pressurized tank (photo courtesy P.M. Anderson) σθ > 0 Fish under water (photo courtesy P.M. Anderson) σz > 0 σ < 0 h

26 Tensile strain: Shear strain: θ/2 ENGINEERING STRAIN δ/2 Lateral strain: ε= δ L o ε L = δ L δ L /2 w o δ/2 δ L /2 L o w o π/2 π/2 - θ γ = tan θ θ/2 Strain is always dimensionless.

27 STRESS-STRAIN TESTING Typical tensile specimen Typical tensile test machine load cell Adapted from Fig. 6.2, Callister 6e. extensometer specimen moving cross head gauge length = (portion of sample with reduced cross section) Other types of tests: --compression: brittle materials (e.g., concrete) --torsion: cylindrical tubes, shafts. Adapted from Fig. 6.3, Callister 6e. (Fig. 6.3 is taken from H.W. Hayden, W.G. Moffatt, and J. Wulff, The Structure and Properties of Materials, Vol. III, Mechanical Behavior, p. 2, John Wiley and Sons, New York, 1965.)

28 LINEAR ELASTIC PROPERTIES Modulus of Elasticity, E: (also known as Young's modulus) Hooke's Law: σ = E ε Poisson's ratio, ν: ν = ε ε L L ε ε metals: ν ~ 0.33 ceramics: ~0.25 polymers: ~0.40 Units: E: [GPa] or [psi] ν: dimensionless σ -ν 1 E 1 Linearelastic ε F F simple tension test

29 OTHER ELASTIC PROPERTIES Elastic Shear modulus, G: τ = G γ Elastic Bulk modulus, K: P= -K V Vo τ P -K 1 1 G γ V Vo Special relations for isotropic materials: E E G = K = 2(1+ν) 3(1 2ν) P M P M simple torsion test P pressure test: Init. vol =V o. Vol chg. = V 11

30 YOUNG S MODULI: COMPARISON E(GPa) 10 9 Pa Metals Alloys Tungsten Molybdenum Steel, Ni Tantalum Platinum Cu alloys Zinc, Ti Silver, Gold Aluminum Magnesium, Tin Graphite Ceramics Semicond Diamond Si carbide Al oxide Si nitride <111> Si crystal <100> Glass-soda Concrete Graphite Polymers Polyester PET PS PC Composites /fibers Carbon fibers only CFRE( fibers)* Aramid fibers only AFRE( fibers)* Glass fibers only GFRE( fibers)* GFRE* CFRE* GFRE( fibers)* CFRE( fibers)* AFRE( fibers)* Epoxy only Eceramics > Emetals >> Epolymers Based on data in Table B2, Callister 6e. Composite data based on reinforced epoxy with 60 vol% of aligned carbon (CFRE), aramid (AFRE), or glass (GFRE) fibers PP HDPE PTFE Wood( grain) 0.2 LDPE