WK13 - Intro to Material Physics

Question 1

What is the nature of Ionic, Covalent, Hydrogen and Metallic Bonding?

Answer 1

Ionic Bonding
• lattice structure that consists of a regular arrangement of oppositely-charged ions held together by strong electrostatic forces (typically metal-nonmetal)
• transfer of electrons
• can conduct when molten/aqueous (not when solid) and high melting points

Covalent Bonding
• pair of electrons are shared between two atoms (typically nonmetals)

Hydrogen bonding
• interaction involving hydrogen atoms located between a pair of other atoms having a high affinity for electrons
• weaker than ionic or covalent but stronger than van der Waals forces
•molecules are bound together by weaker intermolecular forces, hence simple molecules have low boiling points

Metallic Bonding
• positive metal ions held together by a sea of negative delocalised electrons from the outer shells of the metal atoms.
• metals are very malleable as the layers of atoms can slide over one another, also great conductors

Question 2

Crystalline vs amorphous structures

Answer 2

Crystalline Materials
• atoms arranged in periodically repeating arrays which are termed crystal or lattice structures
• metals have simple crystal structures (FCC, BCC, HCP)
• two main types: single and polycrystalline
Amorphous (Non-crystalline)
• atoms arranged in an irregular manner, without any short or long range order in atomic arrangements
• plastics, glass etc

Question 3

What is the main difference between random packing and ordered packing structures?

Answer 3

Energy
• dense, ordered packing structures are typically packed closer together (smaller r) and sit at a lower bond energy, hence are more stable

Question 4

What is the coordination number and Atomic Packing Factor (APF)? How to calculate?

Answer 4

Coordination Number = number of nearest neighbour or touching atoms

APF = (volume of atoms in unit cell)/(volume of unit cell)
*assume hard spheres for atoms

Question 5

What is the APF for simple Cubic? How many atoms are in the unit cell? Coordination number?

Answer 5

= 8 x 1/8 = 1 atom/unit cell

APF = (1 x 4/3pi(R)^3)/a^3 = 0.52
Where R = 0.5a

Coordination = 6

Question 6

How many atoms are in BCC? What is the APF? Coordination?

Answer 6

= 1 (Center) + 8 (corners)*1/8 = 2 atoms

APF = (2 x 4/3piR^3)/a^3 = 0.68
R = SQRT(3)*a/4

Coordination = 8

Question 7

FCC - Number of atoms, coordination, APF?

Answer 7

= 6(face)1/2 + 8(corners)1/8 = 4 atoms

APF = 0.74 where R = SQRT(2)*a/2

Coordination = 12

Question 8

What is the APF and what is it telling you?

Answer 8

APF is a dimensionless quantity that indicates how closely atoms are packed in a unit cell.

Tells you what percent of an object is made of atoms vs empty space

Question 9

What is the FCC and HPC stacking sequence?

Answer 9

FCC - ABCABCABC…

HPC - ABABAB…

Question 10

What is the theoretical density of a unit cell, rho

Answer 10

Density = rho = (Mass of atoms in Unit cell)/(Total volume of unit cell)

= (nA/N_A)/V_c = nA/Vc*NA

n = number of atoms per unit cell
A = atomic weight (of element)
Vc = Volume of unit cell = a^3 (for cubic)
NA = Avogadros number = 6.022x10^23

Question 11

What is a point Coordinate?

Answer 11

A lattice position in a unit cell

Determined as fractional multiples of a,b and c unit cell edge lengths

Question 12

What are Miller Indices?

Answer 12

Miller indices = h k l where these are the reciprocals of the intercepts of the plane on the unit cell.
e.g. a surface has intercepts of a/2, a and infinity. The reciprocal Miller indices are then 2 1 0

Question 13

How do u calculate the spacing, d, between adjacent (hkl) lattice planes?

Answer 13

d(hkl) = a/SQRT(h^2 + k^2 + l^2)

Where a is the size of the unit cell

*only true of crystals where the primitive lattice vectors are orthogonal

Question 14

How does XRD use Bragg’s Law to analyse materials?

Answer 14

The inter-planar spacing, d, of a crystal is used for characterisation and identification purposes

Angle incoming must be v similar to diffracted angle hence, only elastic interactions (those conserving energy) contribute to the diffracted signal used in XRD.
•in elastic scattering (Compton scattering an fluorescence) are also picked up by the detectors and account for the background signal

Question 15

What are the two main types of defects?

Answer 15

Point defects - vacancies, interstitials and substitutional atoms

Large scale - dislocations, grain boundaries, twins and surfaces.

Question 16

How to calculate the number of vacancies?

Answer 16

Nv = Nsexp(-Qv/KbT)

Nv = number of vacancies
Ns = number of regular lattice sites
Qv = Energy needed to form a vacant lattice site
Kb = boltzmann’s constant
T = Temperature

Question 17

What is an Interstitial vacancy? What are the two types?

Answer 17

Vacancy - Atom has lefter its site and has to go somewhere
• it can move to the surface
• atom can stay in the crystal but not at a lattice point (interstitial)

Self-interstitial - Atom same as others
Interstitial impurity - misplaced atom different from atoms in lattice

Question 18

What are substitutional impurities?

Answer 18

Impurity atoms can substitute into the lattice, taking the lattice site of one of the atoms from the original material.

There is a size limit to an impurity atom compared to the lattice atoms for it to be incorporated substitutionally

Question 19

What are the two main types of dislocations?

Answer 19

Edge dislocations - a termination of a plane of atoms in the middle of the crystal and can be interpreted as an additional half-plane of atoms in between two planes. (2D only)

Screw dislocations - shifted out of the plane of the material (3D)

Most dislocations are a combination of the two

Question 20

What are grains, grain boundaries? Single vs polycrystalline

Answer 20

Grains - different regions of the same crystal structure at different orientations

Single crystal/monocrystalline - A material with a single grain

Polycrystalline - A material with lots of grains

Grain boundaries - interface between two regions of different crystalline order or orientation

High angle grain boundaries are where vacancies etc are more likely to form and are more vulnerable to chemical attack, stress etc

Question 21

Describe phases, phase boundaries, precipitates vs inclusions

Answer 21

Phase - a region of material that has a defined crystal structure and composition

A material with 2+ phases is known as multiphase
• dominant phase is called the matrix phase, whilst others are called phase precipitates or inclusions.
•• precipitates - coherency to the matrix
•• inclusions - a rejection of elements not happy in the matrix phase

Phase boundary is not a grain boundary
• a material can be multiphase but still a single crystal

Question 22

What is the Lennard-Jones potential?

Answer 22

V = 4e[(x/r)^12 - (x/r)^6]
V = potential energy
e = depth of the potential well
x = position of zero potential
r = distance between the particles

Describes the potential energy of the interaction between two non-bonding atoms or molecules based in their distance of separation

Question 23

Why is it useful to model atoms connected via springs?

Answer 23

These ‘springs’ follow the Lennard Jones potential

Useful for understanding the transfer of vibrational/thermal energy through longitudinal waves — called phonons

Question 24

Difference between high stiffness and high strength?

Answer 24

High stiffness - has a high youngs modulas, requires high loads to elasticity deform it
- slope of stress strain curve in elastic region

High strength - which requires high loads to plastically deform it
- yield strength is maximum stress before plastic deformation occurs

Question 25

What is an isotropic material, how does it connect shear, elastic moduli and Poisson’s ratio?

Answer 25

Isotropic - behaviour is the same in all directions

E = 2G(1 + v)
G = shear modulas
E = Young’s modulas
v = Poisson’s ratio

Question 26

Define: (1) Limit of proportionality
(2) Yield strength/stess

Answer 26

(1) the point at which linear behaviour ends between stress and strain (elastic up to past* this point)

(2) the point at which the material ceases to behave classically and begins to deform in a manner that cannot be recovered (plastic deformation)
• linear before this point but plastic after
• I.e won’t return to its original shape

Question 27

Define a ductile and brittle material

Answer 27

Ductile - sustains significant plastic deformation prior to fracture
• most metals

Brittle - no significant plastic deformation prior to fracture
• glass, ceramics

Question 28

Sketch the stress-strain graph for ductile steel

Answer 28

See internet

Question 29

Provide characteristics of brittle and ductile materials

Answer 29

Brittle - have high yield strength but they don’t elongate much and then suddenly fail

Ductile - elastic up to a certain yield strength then deform plastically and elongate in a non-linear fashion.

** polymers and metals are both ductile but their plastic behaviours differ wildly

Question 30

What is the difference between strength and stiffness?

Answer 30

Strength - resistance to failure by permanent deformation
• requires high loads to permanently deform or break

Stiff - a measure of resistance to deform elastically
• high stiffness material requires high loads to elasticity deform it

A material can have high stiffness but low strength

Question 31

Define the following
(1) stiffness (Young’s Modulas | Shear Modulas | Bulk Modulas)
(2) Yield Strength
(3) Ultimate Tensile Strength (UTS)
(4) Ductility

Answer 31

(1) how much elastic deformation a material experiences under stress

(2) how much stress a material can experience before plastic deformation occurs

(3) maximum stress a ductile material can experience before it weakens to failure

(4) how much a material can plastically deform before failure

Question 32

What is elongation to failure?

Answer 32

Amount of strain it can experience before failure in tensile testing

*measure of the ductility of materials

Question 33

(1) What is the relationship between strength and density?
(2) How does this relationship differ to stiffness-density?

Answer 33

(1) Typically a linear relationship

(2) broadly similar, however range of stiffness for metals much shorter
Range of densities for ceramics much wider

Question 34

Define Hardness

(2) standard scale?

Answer 34

“Resistance to localised plastic deformation”

Relative value and results can vary with the type of tests

mohs hardness - sapphire and diamond are rated 9/10 and 10/10 respectively for hardness

Question 35

(1) Define Toughness

(2) How to calculate

(3) Brittle vs ductile toughness?

Answer 35

(1) “Energy absorbed during fracture of a material”

(2) Area under the entire stress-strain curve

(3) Ductile materials that experience more strain before failure are typically rougher than brittle materials

Question 36

On a subatomic level, how would you describe elastic and plastic deformation?

Answer 36

Elastic - stretching of atomic bonds (reversible)

Plastic - motion of dislocations (irreversible)

Question 37

What do the <abc> notation indicate in crystallographic directions. Provide an example (abc notation for vectors)</abc>

Answer 37

For some crystal structures, several non parallel directions with different indices are crystallographically equivalent
- the spacing of atoms along each direction is the same

In cubic crystals, all the following directions are equivalent
- [100], [010], [001] and their anti equals
Equivalent directions may be grouped together into a ‘family’ which is enclosed in an <100>

Furthermore, directions in cubic crystals having the same indices without regard for order or sign - [123] & [213] - are equivalent.

Question 38

What is the notation for crystallographic planes?

Answer 38

Miller indices - (hkl)

xyz —> abc where the max point of edge axis in the unit cell is equal to abc respectively. Hence half way across the x-axis would equal a/2.

The points of interception are noted - A B C

(hkl) = (a/A b/B c/C) where infinity represents the plane never intercepting with the axis.

Question 39

Sketch (001) (110) & (111) planes

Answer 39

See internet

Question 40

What is the coordination number, atoms/unit cell and APF for a HCP crystal structure?

Answer 40

Coordination number = 12

atoms per unit cell = 6

APF = 0.74 (same as FCC)

Examples - cadmium, magnesium, titanium, zinc