Chapter 3 Outline Flashcards
What type of solids are most solids (structure-wise)?
crystalline
What is short-range order?
local arrangement of nearest-neighbor atoms around a central atom
What is long-range order?
orders over distances much greater than the bond length
What range order who amorphous solids show? (in 3D)
- Short-range order in 3D, but no long-range order
What range order who crystalline solids show? (in 3D)
- show both short-range order and long-range order in 3D
Are most metals amorphous or crystalline?
crystalline?
What structure do ceramics and polymers have (crystalline, amorphous, etc.)?
either crystalline, amorphous or a combination
How many lattice types does each crystal belong to?
one and only one
Lattice definition
A 3D array of lattice points, each of which has identical surroundings (mathematically latencies can extend to infinity)
What are lattice points?
vertices of a unit cell
What are lattice parameters?
lengths of the unit cell edges
What is a unit cell?
- the smallest representation of a material. - - In crystals, it is the smallest patterned collection of atoms or ions that repeat in space
What determines what class a lattice type belongs to?
the lengths and angles within a unit cell
Cubic Lattice axial lengths and angles
Axial Lengths: a=b=c
Angles: ⍺=β=γ=90
Cubic bravais lattice
SC, BCC, FCC
Tetragonal axial lengths and angles
Axial lengths: a=b≠c
Angles: ⍺=β=γ=90
Tetragonal bravais lattice
SC, BCC
Cubic Lattice symbol
P, I, F
Lattice symbols meanings
P = primitive
I = body-centered
F = face centered
R = rhombohedral
Tetahredral lattice symbol
P, I
Orthorhombic axial lengths and angles
Axial Lengths: a≠b≠c
Angles: ⍺=β=γ=90
Orthrombic bravais lattice
SC, BCC, FCC, Base
Orthrombic lattice symbol
P,I,C,F
Rhombohedral axial lengths and angles
Axial lengths: a=b=c
Angles: ⍺=β=γ≠90
Rhombohedral bravais lattice
SC
Rhombohedral lattice symbol
R
Hexagonal axial lengths and angles
Axial lengths: a=b≠c
Angles:⍺=β=90, (γ=120)
Hexagonal bravais lattice
SC
Hexagonal lattice symbol
P
Monoclinic axial lengths and angles
Axial lengths: a≠b≠c
Angles: ⍺=γ=90 (β≠90)
Monoclinic bravais lattice
SC, Base
Monoclinic lattice symbol
P,C
Triclinic Axial lengths and angles
Axial lengths: a≠b≠c
Angles: ⍺≠β≠γ
Triclinic bravais lattice
SC
Triclinic lattice symbol
P
Simple cubic lattice description
atoms located in each corner
How many bravais lattices are there?
- 14
- categorized P,I,F,(A,B,C),R
Simple cubic lattice description
atoms located in each corner
Body-centered cubic lattice description
atoms at each corner plus one in the center of the 6 faces
Face-centered cubic lattice description
atoms at each corner in the center of each of the 6 faces
Base-centered lattice description
rectangular with atoms at each corner and one in the center of the top and bottom faces
Simple hexagonal lattice description
8 faces
hexagonal close-packed lattice description
- a variation of SH
- Ideally has 6 atoms per cell
How are directions, planes, and families of planes represented by vectors?
Directions: [] brackets; negative numbers represented by bar over the number
planes: () brackets
families of planes: {} brackets
How to calculate planes?
- intercept position on axis
- reciprocal of intercept
- Reduce all fractions by multiplying all values until they are all whole numbers
How can angles between two directions be determined?
by taking the vector dot product
A*B= |A||B|cos ⍬
Atomic packing factor equation
volume of atoms in the unit cell / volume of the unit cell = (# atoms in cell) *( volume of an atom)/ volume of the unit cell
What are intersticies?
the largest holes between the atoms in a lattice
Where are interstices in FCC Latticies? How many sites per cell?
- at the center of the unit cell and center of each edge
- 4 sites per unit cell
Where are the interstices in BCC lattices? How many sites per cell?
- at the center of each face and the center of each edge
- 6 sites per unit cell
How do waves undergo constructive interference/ diffraction?
- 2 waves of equal amplitude and are in phase collide
- the amplitude of the composite wave is 2x that of the components, causing diffraction
What is destructive wave interference?
when the composite wave is equal to zero at all points
Bragg’s Law equation? What does it describe?
2dsin⍬=nλ
- when the x-ray is incident onto a crystal surface, its angle of incidence, θ, will reflect back with a same angle of scattering, θ
What is linear density?
the number of atoms centered along a direction within one unit cell/ length of the line contained within one unit cell
What is planar density?
the number of atoms centered on a plane one cell/ are of the plan contained within one unit cell
CHAtomic packing factor definition
volume of atoms in the unit cell per unit volume
