Defects

Summary of Lattice Defects

Defect	Type	Improved Materials Properties	Adversely affected Materials Properties
Point Defect	Vacancy f(T)	- Diffusivity - Color Centers - Ionic Conductivity	- Electron mobility - Carrier Lifetime
	Substitutional	- Conductivity (dopant) - Strength (hardness) - Characteristic T (like TM)	- Conductivity (impurities) - Ductility - Characteristic T
	Interstitial	- Strength - Characteristic T - Electrical Properties	- Ductility - Characteristic T - Electrical Properties
Line Defect	Dislocation	- Ductility (Malleability) - Strength (at high density)	- Strength - Yield Stress - Optical Properties - Lasing Action
Planar Defect	Grain Boundaries	- Strength - Electrical Properties - Magnetic Properties	- Creep - Electrical Properties - Magnetic Properties

Energetics of 2D Superficial Defects

Surface Corrosion

Inside a material, metal atoms are surrounded by other atoms. This makes them low-energy since they are bound everywhere. However, on the surface of the material, atoms are not bound everywhere and are therefore in a thermodynamically unstable state, making them more reactive.

This allows for the surface of metals to be prone to corrosion (reaction with outside elements) on the surface.

$$E_{\text{Free Energy Surface}}>E_{\text{Internal}}$$

Stacking Faults

In FCC crystals, we can have stacking faults: a layer is missing and therefore resembles an HCP structure for a small segment. This makes the materials with more of these faults to be more resistant to plastic deformation.

We define “Stacking Fault Energy” as the energy per unit area required to create a stacking fault. When this is high (such as in aluminium), it is common to see slipping occur as the material gets deformed.

Metal	${\gamma }_{\text{SFE}}$​ ($mJ{m}^{-2}$)
Aluminium	166
Zinc	140
Copper	78
Magnesium	125
Silver	22
91Cu:9Si (Silicon Brass)	5
Gold	45
Zirconium	240
Nickel	128
304 Stainless steel	21
Cobalt (FCC)	15
70Cu:30Zn (Brass)	20

$E_{\text{SF}}$ decreases as we add impurities (solute atoms) to an alloy.

Twinning

When stacking fault energy is low, such as in brass, stainless steel (also common in HCP metals such as titanium and magnesium), we tend to get Mechanical Twinning: a planar defect where small fractions of the crystal volume which rotate to form a mirror image (a twin) of the original lattice.

Twinning

Mechanical twinning is a plastic deformation mechanism in crystalline materials where a shear stress causes a portion of the lattice to reorient into a mirror image of the surrounding matrix. It occurs as a rapid, stress-mediated process often at low temperatures or high strain rates, particularly in HCP metals and low-stacking fault energy FCC alloys, typically forming thin, lens-shaped regions.

Warning

Twinning involves only small sections of the lattice. These small sections will reverse the direction with respect to the rest of the structure.

Twinning is promoted by:

• Low temperatures
• High strain rates
  • Explosions, impacts, or ballistic hits (slip is too slow to accommodate rapid deformation)
• Large grain size
  • Small grains resist twinning.
• Low SFE

A use for this

The presence of “twins” in a material which has failed can hint at the reason for its failure. For example, in a plane crash in the 90s, an investigation showed that parts of the steel of the plane’s frame had signs of twinning, which told them that the plane was likely hit by an explosive rocket. (Explosion = high $\frac{d\epsilon }{dt}$)

Deformation Mechanism Map

The following diagram shows how different stress rates and temperatures affect the way the material plastically deforms.

Feature	Slip	Twinning
Volume Involved	Involves all volume of the crystal	Takes part into a small fraction of the crystal volume, the amount of deformation is small
Surface Effect	Slip leaves a series of steps (lines) at the free surface after deformation	Twinning leaves a small but defined twin after deformation
Lattice Orientation	The lattice direction does not change	The lattice direction changes
Atomic Movement	All atoms on one side of the slip plane move equal distances	Atoms move distances proportional to their distance from the twinning plane corresponding to a fraction of the interatomic distance

Grain Boundaries

1. We can’t always see grain boundaries. We need to use some sort of etching to actually see them.
2. Grain boundaries are high-energy and usually have free interstitial sites.
3. Because of these interstitial sites, impurities tend to clump up on grain boundaries

We have two different types of grain boundaries depending on the difference in orientation between the two grains $\theta$:

• Low Angle Grain Boundaries (LAGB)
  • $\theta <15°$
  • Since the misalignment is not significant, the energy of the GB is relatively low and closer to the energy within the grain
  • The structure is adjusted by inserting an occasional “extra half-plane” of atoms to “bridge the gap”
  • Mathematically, this acts just like a vertical stack of edge dislocations
    • The energy is the sum of energies of those dislocations
    • Higher angle $⟹$ More dislocations needed $⟹$ Higher energy (linear-ish behaviour)
• High Angle Grain Boundaries (HAGB)
  • $\theta >15°$
  • Beyond around 15°, the misalignment is huge
  • In these GBs, grain boundaries have a layer of disordered (quasi-amorphous) structure as the material transitions from one orientation to another
  • At this point, energy is maximized and increasing energy beyond $\sim 15°$ will not increase it much further.
    • Here, energy is constant and at its maximum

An example for Copper

Consequences of grain boundaries:

• They are sources and sinks for dislocations
• They contribute to mechanical strengthening and change the sliding system
• They act as sinks for impurities dissolved in the alloy
• They contribute to the formation of second phases
  • Primary nucleation sites for the growth of second phases
• They are material portions with no crystallinity (amorphous)

Micro-Yielding

When a polycrystalline material is stretched, local tensile stresses will be stronger around grain boundaries. This means GBs will yield before the overall material has started yielding. This phenomenon is called micro-yielding.

The dislocation forests created via this micro-yielding are responsible for strengthening the overall structure by applying a stress which counters the external one, leading to an overall lower stress.

GB Ledges and Gb’s Dislocation Source

When dislocations hit grain boundaries, they tend to get stuck and can’t proceed further. This way, the GB acts as a ledge or a sink for dislocations.

However, after many dislocations pile up, or if stress is high enough, the energy will be too high and the GB will act as a powerful dislocation source, emitting dislocations. This is somewhat similar to Frank-Read Dislocation Sources, but in this case, the obstacle is a GB.

Grains

ASTM defines a value that describes grain density.

$$N=2^{n-1}⟹n={\log }_{2}N+1$$

Where:

• $N$ is the number of grains per square inch
• $n$ is the grain size number

Frank-Read Dislocation Sources

$$\tau =\frac{Gb}{L}$$

• $\tau$: Critical shear stress, or the stress required such that dislocations “replicate” as shown above
• $G$: Shear Modulus (How stiff is it to shear?)
• $b$: Burgers Vector (magnitude of the lattice distortion)
• $L$: The length of the source (distance between the two pinning points shown as $A,B$ above)

$Sr$-Modified $AlSi$ Casting

Normally, silicon is very brittle, while aluminium is quite soft. A pure $AlSi$ alloy therefore has quite poor mechanical properties. We can therefore add a small amount of $Sr$ or $Na$ into the alloy before casting to create very fine structures, strengthening the material.

As shown, the addition of a tiny amount of $Sr$ can completely change the structure of the material, turning it from a weak material with large and sharp precipitates, to very fine eutectic colonies.