Chapter 4: Imperfections in the Atomic & Ionic Arrangements

Are defects useful?

Yes, because they can strengthen the material (strength, ductility, corrosion behaviour, conductivity)

How are defects created in the crystal lattice?

Through temperature, alloying, deformation, processing

Describe impurities

unwanted, present form raw materials or processing

Describe dopants/alloying elements

deliberately added, for beneficial effect on properties or processing

Why do we study imperfections?

• Controlling defects means controlling material behaviour

• Optimize performance

What are the 3 types of defects?

1. Point defects

2. Line defects

3. Surface defects

Describe point defects

• localized imperfection that disrupts the perfect crystal structure

• affects a region involving several atoms/ions

• dimensions of an atom

• single lattice point defects

• interstitial point defects

What are the types of point defects?

1. Vacancy (a)

2. Interstitial (b)

3. Substitutional (c) *note there is small and large

How are vacancies produced?

produced when an atom or an ion is missing from its normal site in the crustal structure

How is the concentration of a vacancy determined? What is the relationship in the formula?

As T increases, the exponent is less negative, so the fraction of vacancy increases (higher thermal energy introduces more motion)

What determines the activation energy for a material (Q_v)?

• bond strength

• crystal structure

• material type

• atomic packing

What are interstitial atoms?

atoms which are smaller than the host atom and fit into the interstitial sites

usually somewhat larger than the interstitial position and push the surrounding atoms out a bit creating a much larger volume of distorted lattice around it

What is a substitutional defect?

one atom/ion is replaced by a different type of atom/ion

ex. silicon is replaced with phosphorous or boron in the lattice

Which directions are easier or harder to deform?

find out answer**

Describe line defects

• dimensions of a row of atoms

• edge and screw dislocations → main example

• dislocations motion

• role of dislocations on deformation

Why are dislocations important?

Without dislocations, metals would be much harder to deform permanently

Describe surface defects

• dimensions of a plane of atoms

• grain boundaries (GBs)

What are grain boundaries?

• Regions where crystals with different orientations meet

• borders between grains where atoms are not properly spaced

What is the Frenkel defect?

vacancy-interstitial pair formed when an atom jumps from a normal position to an interstitial site (occurs in materials with ionic, metallic, covalent bonds)

What is the Schottky defect?

“stoichiometric” vacancy combinations in ionic materials (required to preserve charge neutrality)

Calculate the number of vacancies in copper at room temperature (25ºC). What will be
the temperature needed to produce 1000 times more than the equilibrium
concentration at room temperature? Assume 20 kCal / mole of vacancies is the energy
for formation, and Cu is FCC with 0.361 nm lattice parameter.

Answers: 1.85 × 10¹⁴ vacancies/m³ & 375K

What is an interstitial defect?

extra atom/ion inserted into the crystal at a normally unoccupied position

Does the number of interstitials vary with the temperature, in the same manner as vacancies?

Temperature does not create additional interstitial atoms in the same direct way that it creates vacancies.

Which iron lattice (BCC or FCC) is distorted to a larger extent by accepting interstitial carbon? *Note iron is a special case

radius of interstitial sites for BCC < the radius of interstitial sites for FCC < the radius of interstitial carbon

What structure do you think would accept more interstitial carbon?

FCC because it has larger interstitial sites

Will a defect atom occupy a substitutional or interstitial site?

Depends on:

• size and valence of guest atoms

• size and valence of host atoms that make up the lattice

• size of interstitial sites

Interstitial → usually when the guest atom is much smaller than host atom (ex. C for iron)

Substitutional → guest atom is similar size to host atom

• Atoms with similar bonding behaviour and valence are more likely to mix well

• Large difference in valence can make substitution harder (reduced solubility)

Describe solid solutions

when one type of atom (a solute) is dissolved into a crystal lattice of another element (a solvent), then a solid solution can be either substitutional or interstitial.

substitutional → solute atom replaces solvent lattice sites

interstitial → small atoms goes in the spaces between the atoms in the lattice

Layers of atoms tend to __________________ along certain crystallographic planes.

slide past each other

Plastic deformation in metals occurs…

mainly by shear

What happens when the shear stress is high enough?

Atomic planes slip relative to each other

What creates a shear components along an inclined plane?

Applied tensile force

Dislocation motion

• slip/glide

• atomic planes sliding past each other

What happens when dislocations align?

Dislocations will be annihilated

What are the three types of dislocations?

1. Edge

2. Screw

3. Mixed

How is an edge dislocation caused?

by an extra half-pane of atoms inside the crystal

How is a screw dislocation caused?

• by a spiral-like shear displacement of atomic planes

• when part of a crystal is sheared by about one atomic spacing relative to the other part

How is a mixed dislocation caused?

• combo of edge and screw

• most real dislocations are mixed because dislocation lines are usually curved, not perfectly straight

Burgers vector

• tells us the size and direction of the lattice mismatch caused by the extra half-plane of atoms

• shows the magnitude and direction of the permanent atomic displacement

• to determine the Burger’s vector direction you must trace the burger’s circuit clockwise around the dislocation

How to determine the Burgers vector?

1. start at top left of dislocation (x)

2. count equal # of steps in all directions (loop around 1 in clockwise direction)

3. when we arrive at the end point (y), the vector is drawn from start point to end point

What is the dislocation line?

the edge of the extra plane of atoms

For an edge dislocation, the Burgers vector is:

• perpendicular to the dislocation line

• parallel to the slip direction

• usually about one atomic spacing in magnitude

Label the diagram

Slip plane

The plane along which the dislocation moves

Slip direction

the direction in which atoms shift during slip

For a screw dislocation, the Burgers vector is:

• parallel to the dislocation line

• parallel to shear stress

In an edge dislocation, the dislocation line moves __________ to the Burger’s vector

parallel

In a screw dislocation, the dislocation line moves ______________ to the Burgers vector

perpendicular

How can we predict when/where plastic deformation will occur?

When materials experience…*unfinished

When might we want slip to occur?

Manufacturing

When might we not want slip to occur?

Service/loading

When is slip most likely to occur?

• along directions with high linear density

• between planes with high planar density and large interplanar spacing

High linear density & high planar density

Easy for bonds to be broken and reformed

Large interplanar spacing

Bonding not as strong

What do slips in metals explain?

They explain why strength is much less than the value predicted from the metallic bond

• provide ductility to metal

• can be controlled by interfering with movement of dislocations

Interstitial atoms

• strain field or lattice distortion around them

• reduce the strain if they are in the larger interstice at the bottom of the extra half plane

Substitutional atom

produce less strain if they associate themselves with a dislocation

What happens when a dislocation comes in contact with an interstitial atom?

Addition stress is required to move them forward ***need to double check

What is the end result of interstitial and substitutional atoms?

Both interstitial and substitutional will inhibit the mobility of dislocations, and result in an increase in strength

Elastic deformation

• reversible deformation

• bonds between atoms are stretched but not broken

• return to their equilibrium position when load is removed

Plastic deformation

• permanent deformation

• cause by dislocations moving through metal

• anything that impedes dislocation mobility strengthens the metal at the expense of ductility

Why are FCC materials so formable and ductile?

Both slip directions and planes are close packed

Why are BCC materials more brittle?

Even though they have 4x more slip systems than FCC, none of the planes are as closely-packed *direction are closely-packed

What is Peierls-Nabarro used for?

Calculate the amount of shear stress needed to overcome resistance (required to cause dislocation)

What is the Peierls-Nabarro equation?

τ = c exp [-kd/b]

τ = shear stress

d = interplanar slip plane spacing

c and k are material constants

• shear stress is lowest when b is smallest

• slip always occurs in the closest packed directions of crystals

Schmid’s Law equation

τ_r = σ cosλ cosϕ

What is Schmid’s Law?

Slip in a crystalline material begins when the resolved shear stress on a slip system reaches the critical resolved shear stress.

Critical Resolved Shear Stress

• shear stress required for slip to occur

• slip occurs when the applied stress produces a resolved shear stress

• if CRSS is high then a high applied stress is needed to cause deformation

What is τ_max?

τ_max = σ yield / 2

Grain

portion of the material within which the arrangement of the atoms is nearly identical

What happens at a material’s surface?

• The crystal ends abruptly resulting in improper coordination numbers and bonding

• Atoms on the surface are not in their equilibrium (low energy and configuration)

True or False: Compared to grain interiors, GBs are high energy regions,

True

What does a higher ASTM grain size number mean?

more grains in the same area, so the grains are smaller

What do smaller grains mean?

• more boundaries

• more shear stress required to continue deformation

• increase in strength and ductility

What is the Hall-Petch equation?

The effect of grain size on the yield strength of steel at room temperature

σ_y = σ_o + Kd^-1/2

σ_y : yield strength

σ_o : inherent strength of crystal lattice

K : Hall-Petch strengthening constant (locking parameter)

d : average grain diameter

Average linear intercept length equation

l = (total length of all test lines) / (total number of GBs intercepted)

How do material properties change in the Heat Affected Zone (HAZ)?

• recrystallization or annealing

• overaging (precipitation hardened materials

Low angle boundaries

An array of dislocations that produces a small misorientation (<15°) between the adjoining crystals

How is a tilt boundary formed?

by an array of edge dislocations

How is a twist boundary formed?

by an array of screw dislocations

True or False: Small grain boundaries have much higher energy than large angle grain boundaries

False

Twin boundary

• plane across which there is a special mirror image mis-orientation of the crystal structure, cause by shear force

• when exposed to shear the lattice can sometimes deform by forming a mirror lattice (a twin)

What does it mean when you see striped grains with straight edges?

Likely to be twins

Strain hardening

deforming a material to increase dislocation density and make it stronger

What does dislocation density mean?

stronger material

Grain-size strengthening

reduce grain size to increase strength

Precipitation strengthening

added atoms come together and form small particles inside the matrix

Do solid solutions form a separate particle/phase?

No

Are the particles in precipitation strengthening a different phase from the matrix?

Yes