Structure of Crystalline and Glassy Materials Flashcards
What is a metal?
Metals and alloys composed of one or more metallic elements and often small amounts of non-metallic elements.
Atoms are arrayed in an order manner and metals are relatively dense compared to polymers and ceramics.
Relatively stiff and strong but are ductile and resistant to fracture.
Large number of delocalised electrons.
What is a polymer?
Organic compounds chemically based on C, H and other non-metallic elements. Very large molecular structure. Low densities. Generally very chemically inert. Often soften or decompose at low temps.
What is a ceramic?
An inorganic non-metallic solid.
What is a semiconductor?
Have an electrical conductivity higher than insulators but lower than conductors.
Electrical conductivity increases rapidly with temperature.
Electrical conductivity can increase with dopants.
What are glasses?
Non-crystalline amorphous solids.
What are the primary chemical bonds in solids?
Ionic, covalent and metallic.
Give an example of a secondary type of bonding in solids.
Van der Waals
What are the several types of attraction bond forces between atoms?
Non-directional: metallic (strong), VdW (weak).
Covalent
Ionic (non-directional)
Repulsion forces between atoms are due to what?
Atoms being pushed together causing the energy of electrons to rise.
Electrostatic repulsion of overlapping charges.
Pauli Principle – no more than two electrons per state, so some are pushed to higher states when atoms become close together.
Materials with large bond energies have what kind of melting temperatures?
High Tm.
What is the key characteristic of bonds in ceramics and semiconductors?
Bonding is directional.
What is a directional bond?
A bond between specific atoms that may only exist in the direction of the two atoms.
The actual covalent bond is the sum of possible atomic energy states available so orbital combinations are…
hybrids.
p and d orbitals represent a directed what?
Distribution of electron density which is important for directionality of bonding.
How do covalent bonds form?
When two atoms are sufficiently close their electron orbitals/wave functions change. The bonding state has a lower energy than the energies of the separated atoms.
Hybridisation is what?
The promotion of electrons in an atom to allow hybrid bonds to form allowing the bonded product to take occupy a less energetic state.
Why are ionic bonds non-directional?
The magnitude of the bond is equal in all directions around ion.
In many ceramics and semiconductors, is bonding ionic or covalent?
It is an intermediate where it is partially ionic and partially covalent, the amount of each depends on the electronegativity of the elements.
Pauling’s empirical formula for bond character (electronegativity difference):
p = 16|Xa-Xb|+3.5|Xa-Xb|^2
An electronegativity difference of what corresponds to a 50% ionic character?
About 2.1
Why aren’t ionic substances malleable?
A displacement of an atomic unit will result in stronger reclusive forces between anions and cations.
Where are VdW present?
In solid inert gases or as intermolecular bonds between atoms or groups of atoms which themselves are joined by primary (intramolecular) bonds.
K/σ where K is thermal conductivity and σ is electrical conductivity is similar for what type of materials?
Metals.
Thermal conductivity by the vibration of atoms equation:
K = Cvl/3
Where
C is heat capacity per unit volume
v is phonon velocity
l is mean free path between collisions
Phonon velocity formula:
v = sqrt(E/ρ)
Where
E is Young Modulus
ρ is density
In crystalline materials, each atom is bonded too…
…it’s nearest neighbour atom.
What is long range order?
The special atomic arrangement that extends over length scales > 10nm in crystalline materials.
What re the lattice parameters of a unit cell?
a, b, c, α, β and γ.
What are the seven crystal systems?
Cubic, tetragonal, orthorhombic, hexagonal, rhombohedral (trigonal), monoclinic and triclinic.
How many Bravais Lattices are there?
14
Why do metals tend to close pack?
Their bonding is non directional so there are minimal restrictions as to number and positions of nearest neighbours.
What is the ideal axial ratio (c/a) in HCP?
sqrt(8)/3 = 1.633
For HCP if c/a > 1.633 what are the mechanical properties?
Favours basal plane sliding when in polycrystalline form (slow mechanical strength).
For HCP if c/a < 1.633 what are the mechanical properties?
Better mechanical properties with prismatic plane sliding favoured (in addition to basal plane).
Equation for theoretical density:
ρ=(nA)/VcNa = Mass of Atoms in Unit Cell/Total Volume of Unit Cell
Where are tetrahedral interstices in FCC?
Between a corner and two face centring sites.
Where are octahedral interstices in FCC?
At the midpoints of each edge and in the centre of the unit cell.
Where are octahedral interstices in BCC?
At the centres of the faces and the midpoints of the edges.
Where are tetrahedral interstices in BCC?
Between the centres of the faces and midpoints of the edges.
Where is the cubic interstitial site in Cubic P?
At the body centre of the cell.
Weiss Zone Law:
If a plane (hkl) belongs to a zone [UVW] (if the direction [uvw] is parallel to the plane (hkl)) then hU+kV+lW=0
What is the direction of two planes (h1k1l1) and (h2k2l2) intersecting?
The cross product:
U=(k1l2-k2l1), V=(h2l1-h1l2), W=(h1k2-h2k1)
In 3D space, how are the zone axis and zone related?
They are 90º to each other.
What is the addition rule for planes lying in the same zone?
p(h1k1l1)+q(h2k2l2) lie in the zone [UVW] if (h1k1l1) and (h2k2l2) both lie in the zone [UVW]
In ionic crystals how do ions tend to arrange themselves?
So that each ion can have as many nearest neighbours of opposite charge as possible.
For ceramics which atomic bonding is predominately ionic, what can the structure be said to be comprised of?
Electrically charged ions instead of atoms.
What are AX structures?
Structures with the chemical formula AX where A is positive ion and X is negative.
What is [m–n] coordination?
Every A atom has m nearest neighbours of X and every X has n nearest neighbours of A.
Example of [8–8] coordination:
CsCl in a similar structure to BCC where it is primitive cubic with motif of Cs (0,0,0) and Cl (0.5,0.5,0.5)
Example of [6–6] coordination:
NaCl with two interleaved FCC lattices.
Give examples of [4–4] coordination:
Zincblende and Wurtzite both ZnS.
What is the structure of Zincblende?
FCC with motif of S (0,0,0) and Zn (0.25,0.25,0.25) in half of the tetrahedral interstices (4).
What is the structure Wurtzite?
Hexagonal P with S (0,0,0) (2/3,1/3,1/2) and Zn (0,0,3/8) (2/,1/3,7/8) or HCP of S with Zn in half of the tetrahedral sites.
What two factors influence the crystal structures in ceramics?
The magnitude of the electrical charge on each of the component ions.
The relative sizes of the cations and anions (radius ratio criterion).
Stable ceramic structures form when what happens with anions and cations?
The anions surrounding the cation are all in contact with that cation.
What is the radius ratio criterion?
rs/rl or radius of cation/radius of anion
The closer the radius ratio criterion is to 1, what can be said?
The greater the coordination is.
What are some exceptions to the radius ratio criterion and coordination rules?
Some ceramics have lower coordination than their rs/rl would suggest due to increased covalent character.
Size of ion depends on several factors such as coordination. ionic radii are often given for coordination 6, the radius is greater for 8 and less for 4.
Charge on ion also influences radius.
What else must be considered apart from hard sphere limit to determine structure?
The electrostatic binding energy.
Potential energy per ion:
V=-q^2/(4πεr)
How is binding energy over the whole crystal found?
α/r = Σ((-1)^nZn)/rn between n=1 and infinity
U=αV
What is the total lattice energy equation?
U=-αq^2/4πεr1
What factor influences binding energy?
Coordination.
What are AX2 structure’s coordinations?
[8–4] [6–3] [4–2]
What is the relationship between coordination and radius ratio criterion?
The smaller the rs/rl the lower the coordination numbers.
Describe the [8–4] coordination for CaF2 (the fluorite structure):
Ca2+ ions form FCC lattice whilst the F- ions fill all the tetrahedral interstices.
Describe the [6–4] coordination for TiO2 (the rutile structure):
Ti4+ occupies cell corners and body centre and each Ti is surrounded by six O2- and each O2- is surrounded by 3 Ti4+.
Describe the [4–2] coordination for SiO2 (the β-crystobalite structure):
Si ions occupy cube corners, face centres and half of the tetrahedral interstices (Zn and S sites in zincblende) and O ions halfway between pairs of Si ions.
Pauling’s first rule:
A coordinating polyhedron of anions is formed about each cation. The sum of the radii determines the cation – anion distance, and the radius ratio determines the coordination number. (Assumes ions are hard spheres).
Pauling’s second rule:
In a stable coordinated structure the total strength of the valency bonds which reach an anion from all the neighbouring cations is equal to the charge of the anion. (i.e. electrical neutrality is preferred).
Pauling’s third rule:
The existence of edges, and particularly faces, common to two anion polyhedra in a coordinated structure decreases its stability; this effect is large for cations with high valency and small coordination number, and is especially large when the radius ratio approaches the lower limit of the stability of the polyhedron.
eg: CsCl (large coordination) – polyhedra share faces.
NaCl (intermediate coord.) – polyhedra share edges.
ZnS (small coord.) – polyhedra share corners.
Violation of this rule usually means structure is not ionic.
Pauling’s fourth rule:
In a crystal containing different cations, this of high valency and small coordination tend not to share polyhedron elements with each other. (Only displayed in more complex structures such as perovskite. High temperature semiconductors are an example).
Pauling’s fifth rule:
The number of essentially different kinds of constituent in a crystal tends to be small.
Directionality of covalent bonding limits what?
The number of nearest neighbours.
What is the hybridised state of every carbon in diamond?
sp3
Is diamond a close packed structure?
No as each carbon atom has four nearest neighbours (close packed structures have 12).
What is the difference between diamond structure and the [4–4] zincblende structure?
The zincblende structure is caused by small radius ratio whereas diamond structure is caused by sp3 hybridisation.
What is the hybridised state of carbon in a graphite structure?
sp2
What happens to the pz orbital in graphite?
It is perpendicular to the sp2 plane and rehybridises with the pz orbital of neighbouring carbon atoms to form bonds.
Do Si and Ge show graphite structure?
No it is special to carbon.
Solid forms of inert gases have what structure?
Close packed structures
Which close packed structures do the inert gases form?
He (at very low T) is HCP the others (Ne, Ar, Kr, Xe) form fcc.
What is the coordination of the halogens?
They have local coordination of 1 as diatomic molecules.
What is the structure of Group 6 elements?
Most elements have several polymorphs.
What is the structure and coordination of S8 at RT?
A puckered ring with local coordination of 2.
Selenium and tellurium are what structure at RT and what is their coordination?
They form infinite helical chains with trigonometry symmetry attached to neighbouring chains by VdW and have a local coordination of 2.
Oxygen is the only element in Group 6 to have a local coordination of what?
1 rather than 2.
