Chapter 4 Review

Question 1

What is a Point Defect?

Answer 1

A point defect is a localized disruption in the lattice pattern

Point defects are not necessarily “bad” or “good.”
Point defects always exist in crystal structures.
Material strength is greatly affected by the presence of point defects.

Question 2

What kinds of Point defects exist?

Answer 2

Vacancy: (an atom is missing from a lattice site)
Interstitial: (an atom at an interstitial site disrupts the pattern)
Substitutional: (an atom of a different SIZE occupies a lattice site)

Frenkel Defect: (2 interstitial atoms share a lattice site)
Schottky defect: (an ionic pair is missing to preserve a stochiometric ratio)

Question 3

What equation describes the number of vacencies in a material?

Answer 3

n_v = n * e^( -Q / R * T )

n_v = n * e^( -Q / R * T ) is referred to as an Arrhenius relation

n_v - # of vacancies per cm3
n - # of atoms per cm3
Qv – Activation energy (energy required to produce one mole of vacancies J/mol)
R – gas constant
T – temperature (K)

Question 4

What are dislocations?

Answer 4

Dislocations are LINE DEFECTS and represent an interruption in the lattice pattern

Question 5

What types of dislocations exist?

Answer 5

1. Screw dislocations: lattice is displaced in parallel to the line defect.
2. Edge dislocations: lattice is displaced perpendicular to the line defect.
3. Mixed dislocation: combination of a edge and screw dislocation.

Question 6

What is dislocation motion?

Answer 6

Dislocation motion is Plastic deformation.
Permanent shift of lattice position of an atom, or line of atoms
Driven by shear stress acting on the slip system

Question 7

What are Slip, Slip plane, Slip Direction, and Slip system?

Answer 7

Slip – another word for “dislocation motion” or “plastic flow”
Slip plane – the plane in which the dislocation line moves
Slip direction – the direction in which the dislocation moves
Slip system – the combination of a slip plane and a slip direction.

Question 8

How does the metallic bond promote slipping?

Answer 8

Since the electrons are not tied to individual atoms, but are shared amongst all the atoms via the electron cloud, the atoms are able to slide around easier than if they were covalently bonded.

Floating in the sea (metalic) vs tied down by an anchor (covalent)

Question 9

What is activation energy?

Answer 9

Threshold energy amount to break free of bonds

Question 10

What is Peierls-Nabarro stress?
(Also known as critical resolved shear stress by non-nerds)

Answer 10

The magnitude of shear stress required to get a dislocation to move.

Given by: t = c * e^( - k * d / b)

d: interplanar spacing
b: magnitude of Burger’s vector
c: related to shear modulus
k: related to Poisson’s ratio

AS INTERPLANAR SPACING INCREASES, REQUIRED STRESS DECREASES (EASIER FOR DISLOCATION TO MOVE IF SLIP PLANES ARE MORE WIDELY SPREAD OUT)

Question 11

How do dislocations tend to move?
And why do they tend to move as such?

Answer 11

Dislocations tend to move across closed packed planes in close (or closest) packed directions.

This is to conserve energy. Going up then down then up requires more energy than coasting along straghter. Think climbing mountain in Maine.

Question 12

What is the Burger’s vector?

Answer 12

Mr. Tensor’s son who runs the burger joint dowtown

It’s the magnitude/direction of walking along dislocation in a ‘square’ and seeing how much and in what direction you need to add to complete the square.

Question 13

What’s the big deal about dislocations in metals?

Answer 13

1. Dislocations provide a mechanism for plastic deformation in metals.
   * By shifting one line of atoms at a time, instead of a whole plane of atoms, a lower load is required to initiate slip.
   * The metallic bond allows a line of atoms to easily adapt to a new lattice position after a dislocation passes by.
2. Dislocations provide ductility to metals.
   * Again, the metallic bond allows shifting of the lattice and thus the material does not break
3. Interfering with dislocation motion allows us to control a material’s strength and ductility.
4. Dislocation Density represents the length of dislocations (line defects) per unit volume. Typically, this is on the order of 106 cm/cm3 for “unworked” materials.

Question 14

What is Schmid’s Law?

Answer 14

Basically calculates the actual (resolved) shear stress on any slip system due to externally provided stress. If this resolved shear stress exceeds critical resolved shear stress (CRSS) then slip will occur.

Maximum resolved shear stress occurs when both angles are 45 degrees

Question 15

What does Schmids Law, the tendancy of dislocations to occur along close packed planes/directions, and the different amount of closed packed planes/directions in FCC, BCC, and HCP imply?

Answer 15

Closed Packed Structures have lower critical resolved stress than Body Centered Cubic, but BBC’s have lots of slip systems.

FCC’s have a reasonable maount of variously oriented slip systems

HCP have very few slip systems

Cross Slip:

Question 16

What is Cross Slip?

Answer 16

When a dislocation moving on one slip plane that encounters an obstacle (and is blocked from further movement) shifts to a second intersecting slip system, also properly oriented, and continues to move.

Question 17

What are surface defects?

Answer 17

Boundaries or planes that separate the material into different regions.

1. Grain Boundaries
2. Small angle grain boundaries , caused by an array
   of dislocations, are not as effective as impeding
   dislocation motion as are regular grain boundaries.
3. Stacking faults, disruptions in the stacking order (e.g. ABCABCABABC)

Higher energy surface imperfections impede dislocation motion
more than lower energy imperfections

Grain boundaries are the most important, and prevalent, type of surface defect; they seriously impede dislocation motion.

Thus, the more grain boundaries are present (i.e. the
smaller the grain size), the stronger the material.

Question 18

What equation relates yield strength and grain size?

Answer 18

The relationship between yield strength and grain size (all other variables held constant) is given by the Hall-Petch equation:

σy = σ0 + (Kd)^ (-1/2)

σy: Yield strength
σ0/K: material constants
d average diameter of grains.

GRAIN BOUNDARIES ‘STOP’ DISLOCATION MOTION

INCREASING NUMBER OF GRAIN BOUNDARIES (WHICH IS EQUIVALENT TO PRODUCING SMALLER GRAINS) WILL STRENGTHEN THE MATERIAL.

Question 19

What are the important takeaways from Defects?

Answer 19

Defects serve as impediments to dislocation motion. Thus,
when a dislocation encounters a defect, a higher resolved shear stress is required to keep the dislocation moving. This requires a higher applied load, and thus the material is stronger

Impeding dislocation motion is the essense of strengthening metals. Point defects disrupt the lattice structure by altering the interatomic distance. Point defects impede dislocation motion since dislocations need a higher resolved shear stress to pass through disruptions in the lattice. Line defects also hinder disloction motion, so increasing dislocation density hinders dislocation motion and strengthens the material (strain hardening)

Question 20

How are strength and ductility related in metals?

Answer 20

Typically, incresing strength decreases ductility.
Not always true, but generally right.
Always true for metals of same alloy