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)

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

Imaging Grain Boundaries external surface grains in the solid if smooth, difficult to observe surface tension  smooth is not thermodynamically preferred thermal anneal or thermal ‘etch’ to equilibrate grain 1 grain 2   SS  SV  SS = 2  SV cos(   /2) balance of forces

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)

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

Volume Defects and Mechanics A secondary (different) material: “phase” –in metals: secondary phases tend to pin dislocations Pores –in ceramics: tend to be source of failure  = F/A  =  L/L ceramic metal Mechanical Behavior yy  frac Y Y Y – from chemical bonds  y – due to dislocation glide  y (obs) <<  y (theo)  frac – due to volume defects  frac (obs) <<  frac (theo) F F L x “graceful” failure “catastrophic” failure

Evaluate  frac (theoretical) F = dE/dR attractive repulsive F R R0R0 E R (interatomic distance) E0E0 R0R0 bond energy curve bond force curve  = F/A approximate  as sinusoidal  x  R 0 ~ a 0 linear region: fracture plane F F ??? /2 x = 0 simultaneous failure

Evaluate  frac (theoretical) 1.  ~ a o  2. Obtain  by equating mechanical energy (work) of creating two surfaces to their surface energy a0a0 /2 x = 0  x surface energy / area of fracture = 2  Griffith’s equation If some plastic deformation occurs:  eff =  surf +  plastic

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

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

Fracture Behavior In failure: custom: failure: K, K C 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 fracture toughness stress intensity factor critical stress intensity indep. of geometry depends on crack length depends on geometry To strengthen ceramics, pay attention to cracks

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

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

molten potassium salt 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  tension compression  tension compression NaO*SiO 2 K Na once crack penetrates compressive region, material shatters explosively

Strengthening of Ceramics Transformation toughening Cool ZrO 2 : cubic  tetragonal  monoclinic Modify with CaO: cubic  tetragonal  monoclinic + cubic Rapid cooling: tetragonal  monoclinic is slow obtain tetragonal + cubic cubic tetragonal crack catalyzes tetragonal  monoclinic transition increase in volume upon transition  V places compressive stress on crack (closes it)

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