Lecture 5 - Order in Solids Flashcards
What is amorphous structure?
Non-dense, random packing of atoms/molecules within a solid.
What is crystalline structure?
Dense, regular packing of atoms/molecules within a solid.
Which is a lower energy structure and why: Crystalline or amorphous?
Crystaline structures are typically more stable/lower energy due to their dense, regular-packed structure.
What is a single crystal?
entire solid is one long crystal
What is a polycrystal?
Several crystals packed together in one solid
What is the best 2-dimension packing structure?
“Closed packed” structures (hexagonal) because it minimizes the amount of empty space within a crystal
What are properties of metallic crystals?
Densely packed crystals (extra), simplest structure
Why are metallic crystals so densely packed?
- Typically only one element present (all atomic radii are equal)
- Metallic bonding is non-directional
- small intramolecular or atomic distance lowers bond energy
- Electron cloud shields positive cores from repulsive forces
What is a unit cell?
smallest repetitive volume which
contains the complete pattern of a crystal.
What is the coordination number (CN)?
Number of neighbouring particles that come in direct contact with one given particle in a hard sphere model.
For the simple cubic structure: CN, atoms/unit cell, a/R relationship?
CN: 6
atoms/unit cell = 1
a = 2R
What is the formula for the atomic packing factor?
APF = (# of atoms/unit cell)(volume of atom with R in terms of a)/(volume of unit cell which is a^3)
For the body centred cubic structure: CN, atoms/unit cell, a/R relationship?
CN: 8
atoms/unit cell = 2
a = 4R/sqrt(3)
For the face centred cubic structure: CN, atoms/unit cell, a/R relationship?
CN: 12
atoms/unit cell: 4
a = 2Rsqrt(2) –> a^2+a^2=(4R)^2
For the hexagonal close packed structure: CN, atoms/unit cell?
CN: 12
atoms/unit cell: 6
Why do compounds have more complex crystal structures?
Differences in atomic radii yields more possible structures.
How are compound structures typically described?
describing the lattice of one particle type and describing how the voids in this structure are filled by other types of particles.
ex: CsCl: simple cubic atom cell with central voids occupied by the other atom.
What are the two types of voids within FCC structures of compounds?
- Octahedral (CN = 6)
- Tetrahedral (CN = 4)
How many types of each void appear in FCC structure per unit cell?
Octahedral = 4 voids
Tetrahedral = 8 voids
What is the “Rock Salt” structure?
FCC structure with all octahedral voids occupied by the other atom.
ex: LiF, NaF, KCl… all ionic salts
What is the “Zincblende” structure?
FCC structure with half of the tetrahedral voids occupied by the other atom.
ex: diamonds (except voids are filled with other carbons)
What is the theoretical density formula?
density = (atoms/unit cell)(atomic weight)/(volume of unit cell)(Avogadros number)
What is polymorphism?
When metals or non-metals can have different types of crystal structures depending on pressure/temperature conditions.
What is allotropy?
When elemental solids have different types of crystal structures depending on pressure/temperature conditions
What is a crystal system?
The overall geometry of the unit cell.
What is a crystal lattice?
The actual position of the atoms within the geometry of the unit cell.
What is Bragg’s law? (definition ish)
The law explains the relationship between an x-ray light shooting into and its reflection off from crystal surface.
When does diffraction occur?
BCC: h+k+l = even #
FCC: h,k,l are either all even or all odd
HCP: when (h+2k)/=3n (n is any integer)
What is anisotropy?
When properties vary with direction
ex: wood shows different strength or conductivity properties along different axes due to its grain structure.
When are single crystals anisotropic?
Always!!
When are polycrystals anisotropic?
If grains are randomly oriented: isotropic
If grains are properly oriented: anisotropic
What are examples of amorphous solids?
glasses and most polymers
How does an amorphous structure form?
When fast solidification does not allow time for atoms/molecules to reorganize into lower energy states (crystals), the solid is left in an amorphous state.
How does the transition between solid crystals and liquid occur in crystal structures?
Before and after melting: atomic vibrations increase with temperature causing slower volume expansion
At melting: crystals begin to form/unform which causes sudden volume change
How does the transition between solid crystals and liquid occur in amorphous structures?
At Tm, the liquid turns into a supercooled liquid (basically solid but not in a crystalline structure so that atoms/molecules can technically still move around)
At Tg, the supercooled liquid becomes a glass where the solid becomes hard and brittle.
What are the three types of defects in crystals?
- Vacancies (point defects)
- Dislocations (line defects)
- Grain boundaries (surface defects)
What is a vacancy defect?
When an atom within a crystal structure is missing
What is an interstitial impurity?
When there is an extra atom (typically of another kind) where there should be a vacancy.
what is a self interstitial defect?
When there is an extra atom in the crystal structure where there should be a vacancy according to the crystal structure
What is a substitutional impurity defect?
When a wrong atom replaces a right atom in the correct spot
How do vacancy defects promote diffusion?
extra space allows atoms increased mobility thus facilitating movement of atoms
what are the consequences of point defects?
Induce local strain by distorting the plane of atoms
How do vacancies affect thermal expansion?
Vacancies provide extra space within the lattice structure, allowing more freedom for neighboring atoms to move. This increased freedom can lead to a more pronounced expansion response to changes in temperature –> increase in the thermal expansion.
What is a dislocation defect?
A type of line defect around which atoms are misaligned –> if a crystal is a stack of planes of atoms, then a dislocation defect would be like rotating or pushing the top half of the stack slightly over
What are the two types of dislocation defects + explanations?
- edge dislocation: extra half plane of atoms inserted in a crystal structure
2 screw dislocation: spiral planar ramp resulting from shear deformation.
What is a grain boundary?
interface or boundary separating two crystalline grains within a material
How do grain boundaries form?
Solidification: When a material solidifies from a molten state, it forms grains. During this process, atoms or molecules arrange themselves into ordered structures and form nuclei which grow into crystals. The boundaries between these growing grains become the grain boundaries.
What are some properties of grain boundaries?
Low density:
- high mobility
- high diffusivity
- high chemical reactivity
How do grain boundaries affect the hardness of a material?
Dislocations allow for plastic deformation. Grain boundaries impede the movement of these dislocations, making the material harder. Small grains result in a stronger material
Why do large grain materials have less energy than fine grain materials?
The boundary area/unit volume is smaller in large grains (same volume of material but bigger grains)
what is an interstitial solid solution?
When a solute (substitutional interstitial) ion is within the solvent (normal atom) lattice
What is a substitutional solid solution?
when one substitutional atom replaces an original atom in a crystal.
What are the conditions for a substitutional solid solution?
- atomic radius of substitution atom must be within 15% of normal atom
- they must have proximity on the periodic table (similar properties)
- they must have the same crystal structure when in pure crystals
- substitutional atom must have a high valency
What does the lever rule show?
the relative amounts of a material in the liquid and solid phase at equilibrium.
How does cooling speed affect equilibrium of a binary system?
Slow cooling allows an equilibrium structure in which the entire solid has a uniform concentration of the two species
Faster cooling causes cored structures in which certain layers contain varying concentrations.
What causes cored structures in solids?
Diffusion is a difficult
(long) process in solids,
leading to non
homogeneities if the
cooling time is too fast and insufficient time is given to allow the solid to gain an equilibrium structure.
