EGN 3365 Lecture Notes - Lecture 8: Atomic Packing Factor, Diffraction Grating, Metal
12 Jun 2018
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Unit cell: smallest repetitive volume which contains the complete lattice pattern of a crystal.
Linear Density: # of atoms/ unit length of direction vector
Miller Indices: Reciprocals of the (three) axial intercepts for a plane, cleared of fractions & common multiples. All parallel planes have same Miller
indices.
An alloy is a blend of a host metal and one or more other elements which are added to change the properties of the host metal.
In a substitutional alloy the atoms of one metal replace atom in the crystal lattice. Crystal structure may stay the same or change
Interstitial alloys are formed when hetero atoms occupy interstitial octahedral
and tetrahedral holes of the host metal lattice.
usually a small nonmetal atom
Single crystals: vary with direction (anisotropic)
Polycrystals: May/may not vary with direction (isotropic)
Polymorphism: Two or more distinct crystal structures for the same material
(allotropy/polymorphism)
Atoms may assemble into crystalline or amorphous structures.
Common metallic crystal structures are FCC, BCC, and HCP. Coordination number
and atomic packing factor are the same for both FCC and HCP crystal structures.
We can predict the density of a material, provided we know the atomic weight,
atomic radius, and crystal geometry (e.g., FCC, BCC, HCP). The max concentration of C in iron ~ 2%
Crystallographic points, directions and planes are specified in terms of indexing schemes.
Crystallographic directions and planes are related to atomic linear densities and planar densities.
Materials can be single crystals or polycrystalline. Material properties generally vary with single crystal orientation (i.e., they are anisotropic), but
are generally non-directional (i.e., they are isotropic) in polycrystals
with randomly oriented grains.
Some materials can have more than one crystal structure. This is referred to as polymorphism (or allotropy).
X-Ray Diff- Diffraction gratings must have spacings comparable to the wavelength of diffracted radiation. Spacing is the distance between parallel
of atoms.
Bragg and his father W.H. Bragg discovered that diffraction could be treated as reflection from evenly spaced planes if monochromatic x-radiation
was used: Bagg’s La: lada = 2d si(theta) A polycrystalline sample should contain
thousands of crystallites.
Therefore, all possible diffraction
peaks should be observed.
powder pattern- peak positions
→ diesio of the eleetay
cell
peak Itesity → otet of the
elementary cell
peak oadeig → stai/ystallite size
salig fato→ uatitatie phase amount Atoms may assemble into crystalline or amorphous structures.
Common metallic crystal structures are FCC, BCC, and HCP. Coordination number and atomic packing factor are the same for both FCC and HCP
crystal structures. We can predict the density of a material, provided we know the atomic weight, atomic radius, and crystal geometry (e.g., FCC,
BCC, HCP). Crystallographic points, directions and planes are specified in terms of indexing schemes. Crystallographic directions and planes are
related to atomic linear densities and planar densities. Materials can be single crystals or polycrystalline. Material properties generally vary with
single crystal orientation (i.e., they are anisotropic), but are generally non-directional (i.e., they are isotropic) in polycrystals
with randomly oriented grains. Some materials can have more than one crystal structure. This is referred to as polymorphism (or allotropy).
Solidification- result of casting of molten material. Crystals grow until they meet each other. NO perfect crystals. Many material properties are
improved by the presence of imperfections and deliberately modified (alloying and doping). All real solids are impure. The simplest of the point
defect is a vacancy, or vacant lattice site. All crystalline solids contain vacancies. Principles of thermodynamics is used explain the necessity of the
existence of vacancies in crystalline solids. The presence of vacancies increases (randomness) of the crystal. At oo tepeatue, pue sile is
highly corrosion resistant, but also very soft. The addition of copper improves the strength and maintains good corrosion behavior. Solid solution is
a homogenous throughout. Vacancies exist in ceramics for both cations/anions. Interstitials are not normally observed for anions because anions
are large relative to the interstitial sites.
Atomic Size Ratios and the Location of Atoms in Unit Cells
Packing
Type of Hole
Radius Ratio
hcp or fcc
tetrahedral
0.22 - 0.41
hcp or fcc
octahedral
0.41 - 0.73
Simple Cubic
cubic
0.73 - 1.00
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Document Summary
Unit cell: smallest repetitive volume which contains the complete lattice pattern of a crystal. Linear density: # of atoms/ unit length of direction vector. Miller indices: reciprocals of the (three) axial intercepts for a plane, cleared of fractions & common multiples. An alloy is a blend of a host metal and one or more other elements which are added to change the properties of the host metal. In a substitutional alloy the atoms of one metal replace atom in the crystal lattice. Crystal structure may stay the same or change. Atomic size ratios and the location of atoms in unit cells. Interstitial alloys are formed when hetero atoms occupy interstitial octahedral and tetrahedral holes of the host metal lattice. usually a small nonmetal atom. Polymorphism: two or more distinct crystal structures for the same material (allotropy/polymorphism) Atoms may assemble into crystalline or amorphous structures.
