Lecture 6
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4 types of defects, what do defects influence ?
point defects line defects 2D defects 3D defects (bulk). Defects have a big impact on the properties of the material
4 types of 0D defects, what do they lead to ? consequence ?
1) vacancy : missing atom 2) interstitial : not on lattice point 3) large substitution : foreign material 4) small substitution : foreign material Lattice planes are deformed -> stiffness of material increases
vacancies : what kind of defect, formula at thermal equilibrium, entropy ?
thermal defects : number depends on T (higher T = more vacancies). c_v = exp(-deltaU / R*T). more vacancies = higher entropy
what does the concentration of vacancies influence ?
• Thermally activated processes such as diffusion • segregation • plastic deformation
0D defects in ionic crystals : stoichiometric lattices and non-stoichiometric lattices
1) stoichiometric (all of same concentration) - schottky : vacancies on lattice sites - anti-schottky : vacancies on interstitials - frenkel : metal vacancies and interstitials - anti-frenkel : non-metal vacancies and interstitals - anti-structural disorder : metal on non-metal sires and non-metal on metal sites 2) non-stoichiometric : electrons are redistributed resulting in conductivity -> changes diffusion, deformation, optical properties, …
dislocations : what can generate them, two types, what characterizes them ?
• crystal formation, stress / T gradients, stresses at higher dimensional effects • edge and screw • burgers vector b : magnitude and direction of lattice distorsion resulting from a dislocation
edge dislocation : what is it, burgers vector
Additional half lattice plane. Vector is perpendicular to dislocation line.
screw disloc : vector ?
vector is parallel to dislocation line (step height)
vector when combined disloc ?
the vector is neither parallel nor perpendicular to disloc line -> bent
how can a disloc move ? in what direction ? exception ?
Under application of force / stress. Gliding only happens in planes, determined by direction of burgers vector. Only exception is screw disloc : can change the glide plane (cross-gliding)
climbing of dislocations
Dislocations move by absorbing or emitting vacancies. When a dislocation absorbs vacancies, it moves upwards, away from the obstacle, and then re-emits vacancies to continue its motion. strongly dependent on T
dislocation jogs
happens when two dislocations interact (jogs of two screw dislocs are an edge disloc -> hindrance of future movement)
stress and strain in dislocation networks, how can disloc vanish ?
Compressive and tensile stresses -> defect clustering. Edge disloc can vanish if they are opposite type
energy to build a screw disloc ? why do they not exist in thermodynamic equilibrium ?
E = Gb^2/4pi * ln(r1/r0) G = shear modulus (big value) r0 = radius of disloc nucleus (3 A) r1 = half mean distance of disloc in solid state (1 micron) They don’t exist because they are non energetically favorable (in equilibrium, the crystal wants to be at minimal energy state)
burgers vectors in simple lattices
fcc : b = a/2<110> bcc: b = a/2<111> or a<100> hcp: b = a<11-20> or b = c<0001>
2D lattice defects : what, how can they be formed
Stacking faults : created during crystal formation or formed out of dislocations
what is a partial disloc ?
A partial dislocation has a Burgers vector that is shorter than a unit lattice translation vector for the crystal structure.
3D defects, angle ?
Grain boundaries with slightly misoriented grains (mosaic). alpha = a/d when a = interatomic distance, d = distance between edge dislocs
order of increased defect densities
single crystal < polycrystalline < nanocrystalline < amorphous