Defects in Solids

1. Defects in Solids  • 0-D or point defects • vacancies, interstitials, etc. • control mass diffusion • 1-D or linear defects • dislocations • control deformation processes • 2-D or planar defects • grain boundaries, surfaces, interfaces, • heterophase boundaries • 3-D or volume defects • voids, secondary components (phases) 

2. Surface Tension as a Force surface tension, g energy / area L F x dx to increase liquid area, energy is required  we must do work on the system dwrev = Fdx = gdA A = 2Lx dA = 2Ldx Fdx = 2gLdx  F = 2gL Force of surface tension acts in a direction parallel to surface

3. Imaging Grain Boundaries external surface if smooth, difficult to observe grains in the solid surface tension  smooth is not thermodynamically preferred thermal anneal or thermal ‘etch’ to equilibrate balance of forces f gSV gSV grain 2 gSS grain 1 gSS = 2gSVcos(f/2)

4. Defects in Solids  • 0-D or point defects • vacancies, interstitials, etc. • control mass diffusion • 1-D or linear defects • dislocations • control deformation processes • 2-D or planar defects • grain boundaries, surfaces, interfaces, • heterophase boundaries • 3-D or volume defects • voids, secondary components (phases)  (mechanical properties – yield, metals)  (mechanical props – fracture, ceramics)

5. Volume Defects / Heterophase Boundaries • Composites • Two or more distinct types of materials, “phases” • Boundary between them is a heterophase interface • At grain boundaries • Second phase concentrated at triple contacts of host grain boundaries • Typical when liquid phase forms at high temperature A B liquid / amorphous interphase boundary grain 2 • Pores • 2nd phase is a void • increases scattering • thermal insulation • white, not transparent grain 1 f grain 3 Balance of forces gLS gLS gSS = 2gSLcos(f/2) gSS

6. Volume Defects and Mechanics F L • A secondary (different) material: “phase” • in metals: secondary phases tend to pin dislocations • Pores • in ceramics: tend to be source of failure F Mechanical Behavior Y – from chemical bonds sy – due to dislocation glide sy (obs) << sy (theo) sfrac – due to volume defects sfrac (obs) << sfrac (theo) ceramic sfrac x “catastrophic” failure Y s= F/A sy metal “graceful” failure Y e= DL/L

7. F Evaluate sfrac(theoretical) simultaneous failure bond energy curve fracture plane E R (interatomic distance) F R0 F = dE/dR E0 approximate s as sinusoidal  attractive F linear region: s = F/A  x R R0 l/2 repulsive R0 ~ a0 x = 0 bond force curve ???

8. Evaluate sfrac(theoretical) 1. l ~ ao  2. Obtain l by equating mechanical energy (work) of creating two surfaces to their surface energy s x a0 l/2 x = 0 surface energy / area of fracture = 2g If some plastic deformation occurs: geff = gsurf + gplastic Griffith’s equation

9. Evaluate sfrac(observed) Why?? Stress concentration at crack tips s = F/A can show: radius of curvature only this region of the material supports the load 2c take fracture to occur when: internal force lines ao atomically sharp crack tip in general: measured fracture stress is not an “inherent” material property

10. Evaluate sfrac(observed) Alternative derivation: again, consider energy balance = initial energy crack energy + surface energy - released strain energy 2c E(c) energy per unit thickness c* c take fracture to occur when: c > c* crack length as before: measured fracture stress is not an “inherent” material property

11. Fracture Behavior • In general: @ failure: custom: not @ failure: K, KC units: pressure(length)½ in practice, need to specify geometry of the experiment shear vs. tension, etc.  geometric constant characterization: put in a crack of known length and defined geometry depends on geometry depends on crack length indep. of geometry fracture toughness critical stress intensity stress intensity factor To strengthen ceramics, pay attention to cracks

12. KI Stress Intensity Factors Chiang, Bernie, and Kingery, “Physical Ceramics: Principles for Ceramic Science & Engineering” Wiley 1997

13. Crack-Loading Modes Courtney, “Mechanical Behavior of Materials,” McGraw-Hill 2000

14. tension s compression tension NaO*SiO2 molten potassium salt s compression Strengthening of Ceramics • Process to eliminate cracks (internal) • Polish to eliminate surface cracks • Blunt crack tip • Anneal (heat treat) to eliminate randomly distributed internal stresses • Quench (a silicate glass) to induce compressive stress on surface • Ion exchange to induce surface compressive stress once crack penetrates compressive region, material shatters explosively Na K

15. cubic tetragonal Strengthening of Ceramics • Transformation toughening • Cool ZrO2: cubic  tetragonal  monoclinic • Modify with CaO: cubic  tetragonal  monoclinic + cubic • Rapid cooling: tetragonal  monoclinic is slow obtain tetragonal + cubic crack catalyzes tetragonal  monoclinic transition increase in volume upon transition DV places compressive stress on crack (closes it)

16. Mechanical Properties • Elastic properties • depend on chemical bonding, not so sensitive to slight variations in composition, processing • Yield stress (metals) • can be manipulated by processing • fairly reproducible • Fracture stress (ceramics) • an almost meaningless property • depends on details of crack/pore distribution • achieving reproducibility is a major effort