MIME 260 Quiz 2 (lectures 2 + 3)

Bonding Force

Bonding Force

F(attractive) - F(repulsive) at r

Potential energy(-Bonding energy)

PE = PE(attractive) + PE(repulsive) = -BE

How to find r0

r0 where slope of PE = 0, so differentiate PE

how to find BE

plug r0 into PE equation and multiple result by -1

How to find Fmax

Max is where slope of F = 0, so differentiate F, Fmax negative bc force to break bond

dF/dr at r0

resistance to deformation

thermal expansion coefficient

1/T(r-r0)/r0, where r = average separation

crystalline materials

atoms pack in periodic 3D arrays, metals, ceramics, some polymers

noncrystalline(amorphous) materials

atoms have no periodic packing, occurs for long chain polymers

crystal structure

ordered arrangements of atoms, ions, or molecules in a crystal structure

crystal structure =

lattice + basis

Lattice

a regularly spaced array of points

Space lattice parameters

6: 3 side lengths, 3 angles

Unit Cell

smallest portion of crystal lattice that shows 3D pattern of entire crystal

7 crystal systems

cubic, tetragonal, hexagonal, rhombohedral, orthorhombic, monoclinic, triclinic

cubic

a=b=c, angles = 90

tetragonal

a=b=!c, angles = 90

orthorhombic

no sides same, angles = 90

monoclinic

no sides same, A=B=90, C=!90

Rhombohedral

a=b=c, A=B=90, C=!90

Hexagonal

a=b=!c, A=B=90, C=120

Triclinic

no sides same, no angles same

Bravais lattices(14)

Simple(P), Body-centered(I), Base-centered(C), Face-centered(F)

Crystal Structures in Metallic Materials

Metallic materials densely packed bc metallic bonding not directional, atomic radii are same or close, electron cloud shield cores from each other

3 common structures in Metals

Face-centered cubic, Body-centered cubic, hexagonal close packed

Body-centered cubic (BCC)

2 atoms/unit cell, r = sqrt(3)a0/4, CN = 8, APF = .68

Face-centered Cubic (FCC)

4 atoms/unit cell, r = sqrt(2)a0/4, CN = 12, APF = .74

Hexagonal Close packed (HCP)

6 atoms/unit cell, c = 4sqrt(6)r/3, 2r=a, CN = 12, APF = .74

coordination number

number of nearest neighbors of each atom

atomic packing factor =

volume of atoms in unit cell/total unit cell volume

what do CN and APF tell us about a crystal?

bonding density and packing efficiency

estimation of material density =

atomic mass*(atoms/cell)/volume of unit cell

allotropy

possibility of the existence of two or more different crystal structures for a substance

polymorphism

ability of a solid material to exist in more than one form or crystal structure

ideal ratio c/a for hcp

1.633