Imperfections in Solids

what does Polycrystalline mean

metal has grains in all direction

• Uniform properties in all directions

• Uniform grain distribution

• Uniform texture

define Anisotropic

properties of metal vary with direction

• Some directions are stronger than others

• There is a preferential orientation for strength

  • If all grains are elongated in one direction = that direction is stronger

e.g. BCC iron

define Isotropic

Grains are randomly oriented

• All directions are equally strong

• No orientation preference for strength

compare Single crystal vs Polycrystals

single = are anisotropic

polycrystals = can be anisotropic or isotropic

steps in metal solidification

1. Nucleation

   1. Formation of stable nuclei

   2. Atoms go around and look for budies

   3. When critical mass is reached

      1. either Homogenous nucleation or Heterogenous nucleation

2. Growth of nuclei

   1. Formation of grain structure

   2. When stable nuclei cool and grow

   3. Grains are blocked by grain boundaries of other grains so their growth size is limited by it

what is Homogenous nucleation

Most simple

1. Metal provides atoms

2. Atoms join together to form nuclei

3. When critical size is reached = nuclei form into crystals

   1. Below critical size = embryo

   2. If it can't reach critical size, nucleus gets dissolved

4. As crystals cool, they grow and form grains

what is Heterogenous nucleation

Nucleation in a liquid on the surface of a structural material

-> called nucleating agent

-> used mainly in industry

1. Slow atoms join together to form nucleus

2. Nucleating agent reduces critical size needed to form crystals

   1. When critical size is reached = crystal forms

   2. Nucleating agent means that less cooling is required to form grains

define Equiaxed grains

• roughly the same size in all directions

  • Same property in all directions

  • Want fine, uniform grains in steel structures

define Columnar grains

• elongated grains

  • Grains grow towards heat

  • Stronger in one direction

what are the Types of imperfections

• Point defects

  • Vacancies

  • Interstitial atoms

  • Substitutional atoms

• Linear defects

  • Dislocations

• Planar defects

  • Grain boundaries

Point defects: vacancies

Vacant atomic site in atom

-> i.e. Missing atom

• Distortion in plane makes a vacancy

• More common than other point defects since it requires less energy to make

Point defects: Self-Interstitial atoms

Extra atoms positioned in atomic sites

-> i.e. Extra atom

• Less common since it requires energy to insert an atom

Point defects: Substitutional

Impurity and host have similar atomic properties

• Follow Hume-Rothery rule:

  • Similar atomic radius

    • ∆r = <15%

  • Similar electronegativity

  • Similar valence electron number

  • Same crystal structure

    • E.g. bcc + bcc

• Atoms of impurity fill vacancy of host = increase atomic density = stronger material

  • Fill in missing atoms

• E.g. Copper in nickel

Point defects: Interstitial

Impurity has a smaller atomic size than host

• Low concentration of impurity = uniform distribution in A

  • Small atoms fill interstitial sites -> small spaces in between atom

  • Property of alloy is still similar to host

Second Phase Materials

• what are they

• how do they form

High concentration of impurity greater than differential solubility % = forms 2nd phase particle

• Excess of impurity in host

• Forms a different metal with different chemical composition and crystal structure

Calculating equilibrium concentration

The stable number of atomic flaws that minimizes the material's total free energy at a specific temperature

• Varies with temperature

• Is unitless

What is differential solubility

Determines the percentage of impurity that can be dissolved in the host

• E.g. Cu in Ni -> 100% solubility

  • Only 1 phase material

  • Can have around 50% Cu and 50% Ni

• E.g. Cu in AL -> 19.6%

  • >20% Cu = won't penetrate crystallographic plane and fill vacancies

  • Creates two phased material

• Smaller differential solubility for interstitial than substitutional atoms

  • Interstices are more cramped

  • Too many interstitial atoms = causes crystal structure to bulge

  • Interstitial atoms apply too much force on other atoms

  • Causes distortion in material

Calculating differential solubility

• weight %

• atom %

Average atomic weight of an alloy

Ca = % of material A

Cb = % of material b

Average density of an alloy

How to calculate whether an alloy is simple, FCC, BCC or HCP structure

1. write equation for average density

2. write equation for average atomic weight

3. use theoretical density equation and rearrange for no. of atoms

   1. avg density = (no. atoms x avg atomic weight) ÷ (avogadros number x volume of cell)

4. If no. of atoms =

   1. 1 → simple

   2. 2→ BCC

   3. 4 → FCC

   4. 6 →HCP

What are linear defects

One dimensional defects where atoms are misaligned

• Slip between crystal planes when dislocations move, causing plastic deformation

  • Before load = no dislocation

  • After load = dislocation

    • Force causes bonds across the slipping plane to break and be remade

    • Since load causes the grains to shift direction

• Useful since they slow down deformations in structure

• Generally we have both types at the same time

types of linear defects

Edge dislocation

Screw dislocation

what is an edge dislocation

• Extra half plane of atoms inserted into a crystal structure

  • i.e. Another plane penetrates the lattice and stops half way

• Burger's vector is perpendicular to dislocation line

What is a screw dislocation

• Spiral planar ramp due to shear deformation

  • Torsion (twist) in a plane due to load

• Burger's vector is parallel to dislocation line

What structures do dislocations happen more often in

Prefer close-packed plans and directions

• BCC = less dislocation prone since lower APF

• FCC and HCP = more dislocation prone due to higher APF

What are planar defects

Grain boundaries → Region between crystals

• Normally rough

• Has a different alignment

• Disordered

• Low density

  • Where crystals interact

  • High mobility, diffusivity and chemical reactivity

Types of grain boundaries

Twin boundary

Stacking faults

What are twin boundaries

Atom is between a grain boundary and is shared between crystals

• Can use electron diffraction to find grain orientation

• Colour represents direction of grain

• One colour = uniform orientation + undeformed

• Shading in a grain = deformation

○ Smaller grains are more stable

○ Larger grains often undergo deformation

What is a stacking fault

A plane is missing

Stacking fault vs edge dislocation in a microscope

-> stacking fault can be seen in more easily

-> edge dislocation needs an electron microscope

Types of microscopy techniques + uses

• optical microscope

  • grain boundaries

  • grain size

• scanning electron microscope (SEM)

  • Grain boundaries + orientation

  • Twin boundaries -> backscattered electron diffraction

• transmission electron microscope (TEM)

  • Stacking faults

  • Dislocations

• X-ray diffraction

  • Crystal structure