4. Crystal Defects

• only extend over a few atomic spacing

• Point defect occur at the latticepoints or their vicinities.

• Increase of electricalresistivity in metals.

• Increase of electricalconductivity in ionic crystals.

• Diffusion in solids.

• Change in mechanical properties.

• Elongation due to the defect andthermal lattice expansion.

• Vacancy

• INTERSTITIAL

• SUBSTITUTIONS

• COLOUR CENTRE

• In a Schottky defect an atom ismissing from one of the latticesites. It leaves a “vacancy”.

• A neighbouring atom diffusesinto the vacancy, so the vacancymay diffuse into the crystal.

• The surrounding atoms movearound and hence distort thecrystal structure.

  
  

• When an extra atom is forcedinto the lattice we speak of aninterstitial defect.

• The defects can occur afterion or neutron irradiation.

• Like in the case of a vacancythe surrounding will react witha distortion of the lattice.

• If this atom originally came froma lattice site, leaving a vacancy,it is a Frenkel defect.

• In a Substitutional defect aforeign atom replaces a hostatom on a lattice site.

• Again the surrounding distorts.

• Usually an atom substitutes at alattice site of similar atomic size.

• Substitutional defects can beused to strengthen materials.

A colour centre is a defect that causes a transparent crystalto absorb in the visible region of electromagnetic waves andhence becomes coloured.

• A stacking fault refers to aninterruption in the stackingsequence of a crystal structure.

• This may refer to a missing oradditional layer or atoms.

• It causes additional strain.

• Crystal twinning occurswhen two crystals share the same crystal lattice.

• Easily observed by optical microscopy.

• Most likely to occurin hcp crystals

• additional or missing plane ofatoms results in displacement.

• The material above the slipplane moves relative to thatbelow, producing strain.

• Dislocations run through theentire crystal and eitherterminate at the surface orform a closed loop.

• Often denoted by the symbol ⊥

• b vertical to displacment

• In a screw dislocationthe boundary of theslipped region lies parallelto the direction of slip.

• The atoms rearrangearound the dislocation inthe form of a helix.

• This also causesstrain in the material.

• b parallel to Dislocation

• A screw dislocation involves shearing oneportion of a perfect crystal with respect toanother portion on one side of a line (AB).

• Screw dislocation aid crystal growthbecause the newly arriving atom canattach to two or three atoms instead ofone atom and thereby form more bonds.

• describes the direction and amount of slip

• How to determine the burger vector:

  1. In a perfect crystal trace a closed loopusing multiple of atomic jumps.

  2. Repeat the same steps in a real crystal.

• The extra vector needed to close the loopis the Burgers vector

• For edge dislocations b is perpendicular to the dislocation line.

• For screw dislocations b is parallel to the dislocation line.

is the total length of dislocation line in a unitvolume

• Deformation of crystals occurs by multiplication of dislocations.

• If the source of a defect lies in the centre of the crystal rather than at the surface it is referred to as a Frank-Read-Source.

• Plastic deformation is produced by dislocation motion.

• The slip systems of the material depend on the type of lattice.

the slip planes are (111) and

the slip directions are <110>

the slip planes are (0001) and

the slip direction is <112_0>

slip planes are (110), (112) and (123) and

the slip direction the body diagonal <111>

• is the stress at whichthe atomic bonds break

• For glasses and ceramics:

• After elastic deformation materialsreturn to their original length (1).

• Further increase in stressresults in plastic deformationafter which the material doesnot return to its original length (2).

• When stress is reapplied there is anew short elastic region after whichplastic yielding occurs again (3).

• The material is hardened by the initialamount of plastic deformation

• In the first stage dislocation movefreely over large distances.

• Dislocation multiplication andinteraction lead to an increase instress for further deformation.

• At the end of stage 1 dislocationsstart to hinder each other.

• Since there is only one glide planein hcp crystals, the basal plane,a hcp crystal continues todeform until it fractures.

• Resistance to dislocation motionoccurs in stage 2 of work hardening.

• This occurs due to dislocationsrepelling each other or piling up.

• Vacancies and interstitial defectsoccur when dislocations cutthrough a forest of dislocations.

• The process of work hardeningcontinues at this stage

• At this stage the stress is highenough top avoid obstacles.

• When a screw dislocation movesfrom one slip plane to another itis referred to as cross slip.

• Cross slip can occur in FCC and BCC crystals which have several equivalent slip planes.

• The rate of work hardening decreases.

• The yield drop in a bcc crystals is notan intrinsic property but depends onthe testing procedure.

• Rapid dislocation multiplication leadsextension more quicklythan the tensile machine.

• Occurs due to impurity lockingin BCC crystals

• Precipitates can impedethe motion of dislocations.

• The precipitate acts as a pinning pointfor the dislocation.

• Hardening by precipitatesis referred to as Orowan hardening.

• Examples areAl hardened by Cu,and steel

• Metals are polycrystalline,they consist of small crystals called grains.

• Grain boundaries obstructthe motion of dislocations.

• Grain boundary strengtheningis also referred to as Hall–Petch strengthening

• The yield strength is proportionalto the Petch constant k anddepends on the grain size D.

• Some materials, such as glass,do not exhibit plastic deformation.

• These brittle materialscrack under stress.

• Cracks occur at inclusions,dislocations grain boundaries.

• Grain boundaries are obstaclesto fracture propagation.

• Therefore materials with smallcrystallites are stronger.

• Around room temperature theresistivity 𝜌 of a material increaseslinearly with temperature (T).

• The conductivity 𝜎 is proportional tothe mean free path 𝜏 betweencollisions.

• At moderate temperatures themean free path is limited bythermal vibrations of the lattice.

• At low T the mean free path isdetermined by defects and impurities

• Thermal energy causes thelattice of a crystal to vibrate.

• Only certain energy values areallowed; they are quantized.

• A phonon is a quantumof vibrational energy.

• This is analogous to a photonbeing the quantum of electro-magnetic radiation.

• It states that the resistivity ρ of a metal is composed of a temperature-dependent term that arises from the scattering of electrons by the lattice vibrations (phonons) and a temperature-independent term that arises from the scattering of electrons by defects.

• ρ(T) = ρ[Phononen](T) + ρ[Defekte]

• Scattering of electronsoccurs of phonons and impurities

• The temperaturedependence of resistivity:ρ[T] = AT

where 𝜌𝑝 is the increase in resistivity per point defect.