Chapter 4: Crystal Structure Flashcards
Structure of materials
Arrangement of atoms in a material to minimize bond energy.
Short ranged order (SRO)
Regular and predictable arrangement of atoms over a short distance. Based on the coordination number of atoms.
Short ranged order (SRO) examples
amorphous materials (wax, glass, liquids)
Long ranged order (LRO)
Regular and predictable arrangement of atoms over infinitely great distances.
Long ranged order (LRO) examples
Crystalline solids, tempered chocolate
Crystalline materials
3D structures where the material is arranged regularly. (SRO & LRO)
Amorphous materials
Solids that are non-crystalline
Metallic structures
Crystalline
Ceramic structures
Crystalline and/or amorphous
Polymer structures
Amorphous and/or partially crystalline
Semiconductor structures
Crystalline
Composite structures
Crystalline and amorphous
Unit cell
Smallest indivisible group of atoms of a substance that has the overall symmetry of a crystal. A group of unit cells is a LRO crystal structure.
Mass density
Representation of the amount of mass (or the number of particles) of a substance.
Mass density formula
p = (nM)/(VNa)
Lattice parameters
Edge length of a unit cell
Lattice
3D network of points
Crystal basis
Repeating unit centered on lattice points
Bravis lattice
Array of discrete points with an arrangement and orientation that look exactly the same from any of the discrete points. Each point has the same surroundings
Atomic packing factor
APF = (Volume of atoms in unit cell) / (Volume of unit cell)
Simple cubic (SC) structure
Quarter atoms at each corner, 2 atoms in the unit cell. CN = 6, a = 2r, APF = 0.52
Linear packing factor
LPF = (length of vector covered by atom) / (length of vector)
Face centered cubic (FCC) structure
Quarter atoms in each corner, half atoms on each face, 4 atoms in the unit cell. CN = 12, a = 2sqrt(2)r, APF = 0.74. Close packed bravis lattice with sequence ABCABC
Planar packing factor
PPF = (area covered by atoms) / (area of atom)
Body centered cubic (BCC) structure
Quarter atoms in each corner, 1 atom in the center, 3 atoms in the unit cell. CN = 8, a = 4/sqrt(3)r, APF = 0.68. Bravis lattice.
Hexagonal close packed (HCP) structure
7 close packed atoms on alternating layers with 3 atoms in the hollows, 6 atoms in the unit cell. CN = 12, a = 2r, APF = 0.74. Close packed with sequence ABAB
Packing sequence and ductility
The closer packed atoms are, the more ductile the material. FCC is more ductile than HCP since slip is possible in every direction.
Miller indices
Way to describe points, lines, planes in 3D space using h, k, l. Negative numbers are written with bars above them.
Directions
Written without commas inside square brackets. Families use pointed brackets.
Points
Written with commas and no brackets. Range from 0 to 1.
Planes
Written without commas inside brackets. Families use curly brackets and rely on spacing
Crystal defects
Control diffusion and plasticity. Eliminated to reduce total energy.
Point defects
Crystal disturbances at a single point.
Vacancies
Empty lattice sites that occur spontaneously.
Vacancy ratio
Nv/Nt = e^(-Q/RT)
Solute atoms
Atoms dissolved into the crystal lattice to remove vacancies, forms a solid solution.
Substitutional solute atoms
Atoms replace the solute on the lattice site due to being a similar size/electronegativity.
EX: nickel in gold
Interstitial solute atoms
Small atoms go in between lattice atoms.
EX: Carbon in steel
Atomic vibrations
Atoms vibrate about their lattice positions at 10^13Hz and release the extra energy responsible for thermal activation.
Line defects/dislocations
Atom planes are distorted so that half planes end inside the crystal. Motion produces slip and plastic deformation.
Interfacial defects
Phase and orientation changes between grain boundaries
Volume defects
Void formation at grain boundaries
Bregg’s law
Describes the interaction of x-rays and crystal lattices.
Bregg’s law formula
nλ = 2d(hkl)sinθ
Interplanar spacing formula
d(hkl) = a/sqrt(h^2+k^2+l^2)
X-Ray diffraction
Used to determine crystal structure. Crystalline structures have many diffraction angles while amorphous ones have few.