MAE 381 EXAM 1

Describe Metals

• Crystal Structre

• Free electrons

• Good Conductor

• Stiff, Ductile/Resistant to Fracture

Describe Ceramics

• Ionic + Covalent bonding

• Strong and Stiff

• Susceptible to Fracture

• High melting point, low conductivity

• Ex: Al2O3 (aluminum oxide), SiO2 (Silicone dioxide/sand)

Describe Polymers

• Chain like structure

• Low density/soft

• Low melting points

• Low conductvity

• Ex: PVC (Polyvinyl chloride), plastics, rubber

Describe Composites

• Mixture of two or all of the polymers, ceramics, metals

• Ex: Fiberglass

What are different types of advanced materials?

1. Semiconductors - Used in electronics

2. Biomaterials - to be implanted in the human body

3. Smart materials - Can sense and respond to environmental changes

4. Nanomaterials - behavior dominated by quantum mechanical effects and surface phenomena

What formula to use to calculate # of atoms in volume

(Volume/ volume per cell) x (Atoms/Cell)

How to calculate # of atoms on surface

(Atoms/m²)(m² surface area)

What are the two allotropes of carbon?

Graphite and Diamond

Describe the properties of Graphite

• Hexagonal structure

• density = 2.26g/cm³

• Hybridization = sp²

• Soft (think of pencil lead), conductor, opaque

• Strong covalent bonds

Describe the qualities of Diamond

• FCC Crystal Structure

• density = 3.5g/cm³

• Hybridization = sp³

• Hard

• electric insulator

• thermal conductor

• transparent

• high melting point

What are the three primary bonding types?

Ionic, Covalent, Metallic

What is the secondary bonding type?

Van der Waals bonding

What is the relationship between attractive force and radial distance?

F approaches zero as r/R = 1

What is the net force on two atoms?

F_net = F_attractive + F_repulsive

What is the net energy between two atoms?

E_net = E_attractive + E_repulsive

What is E_o, the bonding energy?

Energy required to move two atoms to an infinite separation

What is ionic bonding?

Electron transfer between metals and nonmetals (valence electrons given to atoms in need)

What is the result of ionic bonding?

Attractive bonding forces are Coulombic, where opposite electrical charges attract.

What is the formula for attractive energy?

E_attract = -A / r
A is given in the formula sheet

r is the distance between the center of the two charges

What is the formula for repulsive energy?

E_R = B/(r^n)

B and n depend on the ionic system

What is the net energy formula?

E_n = -A/r + B/r^n

What kind direction is ionic bonding?

Non directional - Magnitude of bond is equal in all directions

What neighbors must each ion have for the structure to be stable?

Each cation must be next to an anion, vice versa

What is a coordination number?

The number of atoms / neighbors an atom is touching/has.

How to determine stability with r/R ratio?

if r/R < the minimum, then it is unstable

if r/R > the minimum, it is stable

Why is the highest CN closest to the calculated chosen?

Lower energy - if it was higher energy, more instability + disorder.

What charge must solids be to pack ions into a solid?

Positive charge = Negative charge ; must be neutrally charged

What is the CN of cesium chloride (CsCl)

8

What is the CN of Zinc Sulfide (ZnS)

4

What is the predominant bonding type in ceramics?

Ionic bonding

Describe covalent bonding

The sharing of electrons, with similar electronegativity needed

Is covalent bonding directional?

Yes

What is bond hybridization?

The mixing of two or more atomic orbitals in order to increase atom stability. Directional.

How dimensional is the sp² hybridization

2-Dimensional

How dimensional is the sp³ hybridization

3-Dimensional

Describe Metallic bonding

• Valence electrons delocalized/detached

• “electron cloud”

• Non-directional

What determines the strength of a metallic bond?

• # of delocalized electrons

• charge of the cation (metal)

• Size of the cation

• More valence electrons = more strong, higher charge = more strong

What creates stronger metallic bonding?

Greater electrostatic interaction - the ability for atoms to attract to e/o

What is a property of a good electrical conductor in a metal?

Delocalized electrons move easily in an electric field

What is the relationship between ductility and atomic properties?

Non directional, so positive cores can be moved anywhere without breakage

Is Van der Waals bonding stronger or weaker than Primary bonding?

Weaker

What is van der waals bonding the result of?

Dipoles: the separation of positive and negative portions of an atom/molecule
ex: saran wrap clinging to bowl

What are the three types of dipole bonds?

1. Permanent dipole bonds

2. Polar molecule induced dipole bonds

3. fluctuating induced dipole bonds

Describe permanent dipole bonds (keesom interactions)

Coulombic attraction between polar molecules

ex: acetone has weak permanent dipole bonds bc it evaporates when exposed to air quickly. water has strong bc it takes longer to evaporate

Describe polar molecule induced dipole bonds (debye force)

Dipole can induce another dipole in electrically symmetric atom or molecule

Ex: fish need oxygen, but oxygen is mixed into water bc its bonds are weak and cannot resist the warping force of the water

Describe Fluctuating induced dipole (London dispersion forces)

Creation of small dipoles from distortion of electrical symmetry.

Everything is weakly bonded in small quantities, but as quantities increase the weak bonds increase and is able to become a substance

Describe percentage of ionic character?

larger difference between electronegativities = more ionic

Formula for force of attraction is what

F_A = A/r²

(add the two radii)

What is the coefficient of thermal expansion?

How much a material expands/contracts with temp change

What is the relationship between bond strength and thermal expansion?

Weak bonding = higher thermal expansion coeff, vice versa

What is electrical resistivity?

Atoms vibrating about their equilibrium position

Higher temp = more vibration, vice versa

Electrical resistivity formula?

rho = RA/L

What is a crystal structure composed of?

a Lattice and a basis

What is a lattice?

3D array of regularly spaced points in space

What is a basis?

Atoms/materials attached to the lattice points

A crystal is composed of what?

Repeating unit cells!

Difference between primitive and non-primitive unit cells

Primitive: Single lattice

Non-Primitive: More than one lattice point (more common)

What are the top 3 most important crystal structures?

1. Cubic (SC, BCC, FCC)

2. Hexagonal (HCP)

3. Tetragonal (BCT)

Simple cubic is what?

Primitive Cubic (P-Cubic)

Face centered cubic is what?

FCC

Body centered cubic is what?

Innenzentriert Cubic (I-Cubic)

Describe the Simple Cubic Structure

• Lattice: P-Cubic

• Basis: 1 atom

• CN = 6

• Lattice constant (a) = 2xR

• Atoms per unit cell = 1

• V_unit cell: a³

• APF_sc: 0.523

• Ex: polonium

What is the atomic packing factor (APF)?

APF = Volume of Atoms / Volume of Unit cell
Fraction of the volume occupied by atoms

Describe Body-Centered Cubic

• Lattice: I-Cubic

• Basis: 1 atom

• CN = 8

• Lattice constant (a) = 4R/ sqrt(3)

• Atoms/Unit cell = 8×1/8 + 1 = 2 a/uc

• APF = 0.68

Describe Face-Centered Cubic

• Lattice: F-Cubic

• Basis: 1 atom

• CN = 12

• Lattice constant (a) = 4R/sqrt(2)

• Atoms/Unit Cell = 8corners(1/8) + 6faces(0.5) = 4

• APF = 0.74

• Stacking Sequence: ABCABC

Describe Hexagonal Close Packed (HCP)

• APF = 0.74

• CN = 12

• Lattice parameters: a, c

• Stacking Sequence: ABAB

• Atoms/Unit Cell: 3 + 2(1/2) +12 (1/6) = 6

• 3 lattice points/Unit Cell

• Basis: 2 atoms (Top and bottom)

What is the density formula

rho = (atoms/unit cell)(Atomic weight) / (volume of unit cell)(Avogadros number)

volume of unit cell = lattice constant (a) cubed

What is polymorphism?

Ability of a solid material to take forms in multiple crystal structures

Single element case: allotropy

Ex: Carbon (graphite and diamond), Iron at room temp vs high temp

What is the general type of ceramic crystal structures?

AX-Type

A = Cation (+)

X = Anion (-)

What is the structure of rock salt? (Ceramic crystal example)

Lattice: F-cubic

Basis: 1 Na, 1 Cl

What is the structure of cesium chloride? (Ceramic crystal example)

Lattice: P-Cubic

Basis: Cs + Cl

What is the structure of zinc blende? (Ceramic crystal example)

Lattice: F-Cubic

Basis: 1 Zn, 1 S

Describe the A_m X_p type (ceramic crystal structure)

Ratio is no longer 1 element : 1 element

Lattice: F-Cubic

Basis (ex): 2 F + 1 Ca

What is the notation for crystallographic points/planes"?

[ q r s ] (like x y z)

put points in parentheses, integers in brackets (always use integers)

What is a “Family of directions”

Non parallel directions can be crystallo… equal, spacing of atoms the same

cubic family : < 1 0 0 >

In cubic crystals, directions w the same indices are equal dont matter sign or order

What is the problem solving process for finding crystallographic planes?

1. Intercepts w/ axes a, b, c

2. Reciprocals of the intercepts

3. Reduce to integers

4. Put in parentheses

What is a family of planes?

Planes that are crystallographically equal (same atomic packing)

Ex: ( 1 1 1 ) family, FCC closed packed planes

How do you convert [ u v w ] to [ u v t w ]

u = 1/3 (2U-V)

v = 1/3 (2V-U)

t = -(u+v)

w = w

How do you represent miller-bravais indices on a hexagonal plane

[ a1 a2 a3 z ]

making plane is same as the other process but in the a(n) directions