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.
Why is nitrogen an exception in Group 5 In terms of structure?
It is the only element in Group 5 with a local coordination of 1 (others have 3).
Arsenic, antimony and bismuth are isomorphism, what is their structure?
They are bonded in indefinitely extended puckered layer with local coordination of 3 within each layer.
What happens with the layers in Group 5 structures?
They stack to form a trigonal structure.
The forces between the sheets is primarily VdW but small metallic contribution to bonding which increases with increasing atomic number.
What is the 8–N rule?
The number of bonds (local coordination) is equal to 8 minus the group number.
What is the structure of a CO2 crystal?
Near close packed cubic arrangement with VdW between molecules.
How is CO2 bonded?
Covalently though there is some covalent character as C atoms carry positive charge whilst O atoms carry negative charge.
Why do permanent dipole moments exist in some molecules?
They have an assymetrical arrangement of positively and negatively charged regions.
What is the structure of ice?
Hexagonal structure with oxygen atoms arranged in the same way as the Zn and S in wurtzite.
What is the distribution of charge over a water molecule?
Tetrahedral.
Each water molecule has how many nearest neighbours in ice?
4.
What is the average number of nearest neighbours of a water molecule in liquid form?
4.5.
Silicon carbide has how many structures?
6, two forms have zincblende and wurtzite structure, other forms are similar to wurtzite but with more complex stacking sequences of puckered sheets.
What are the three naturally occurring forms of silica?
Quartz (below 870ºC), Tridymite (870–1470ºC) and Cristobalite (above 1470ºC).
All three forms of stable silica have what coordination?
[4–2]
Which silica structures are related to zincblende and wurtzite?
β–cristobalite is related to zincblende and tridymite is related to wurtzite.
What are the structures of α and β quartz?
α quartz is rhombohedral and is stable below 573ºC, whereas β quartz is hexagonal and is stable between 573 and 870ºC.
What percentage ionic character does Si–O have?
40%.
Both Al2O3 and Fe2O3 are polymorphous, which forms are most common?
α
α Al2O3 is corundum, precious stones such as sapphire and ruby.
α Fe2O3 is hematite.
What is the structure of α Al2O3 and Fe2O3?
[6–4] coordination in HCP arrangements with O2- occupying 2/3 of 6 coordinated interstitial sites.
What is spinel?
MgAl2O4, but is a structure found among many other oxides.
What is the structure of spinel?
Cubic close packed array of O2-, with 1/8 of tetrahedral sites filled with Mg2+ and 1/2 the octahedral sites filled with Al3+.
γ forms of Al2O3 and Fe2O3 have what structure?
Spinel structure.
What structure does perovskite (CaTiO3) have?
A cubic structure Ti on corners, Ca atom at centre and O atoms on midpoints of edges.
What is the coordination of each atom in perovskite?
12 for Ca, and 6 for both Ti and O.
Is the perovskite structure common?
Yes but often as a pseudo symmetric variant.
Many perovskites are ferroelectric, what does this mean?
It can be electrically polarised in the absence of an electric field.
Some ceramics can conduct, why?
High melting points and chemical stability make good heating elements.
Resistivity of some ceramics is sensitive to applied electric fields so can be used to absorb power surges.
What can be said about the V-T curve in cooling and heating of a glass?
The curve never retraces the path it took on cooling when heating.
Dielectric ceramics can be used where?
In capacitors.
Some ceramics are piezoelectric, what is this?
Piezoelectric ceramics convert oscillating electric fields into mechanical oscillations or mechanical stress into electric polarisation.
Ceramics do not dissipate energy in transformer cores by what?
Eddy currents.
What are typical semiconductors made from?
Si or Ge
What structure do semiconductors have?
The same structure as diamond, FCC with half tetrahedral interstices filled.
Many binary compounds with group III and V or II and VI are what?
Semiconductors.
Which are more ionic, II/VI compounds or III/V?
II/VI
What is an alkali silicate glass?
A silica glass with network modifiers such as Li2O.
Each alkali ion in an alkali silicate glass creates what?
One non bridging oxygen and reduces the connectivity of the network.
What does amorphous mean?
Without form or shape?
What are most of the world’s glasses based on?
Silica
What is a glass?
An inorganic product of fusion which has been cooled to a rigid condition without crystallising.
How does a glass behave like a solid?
Density, mechanical and thermal properties are similar to solids.
How are glasses unlike crystals?
No sharp, well defined melting point.
Isotropic.
Glasses display what under heating from solid to liquid state?
Glass transition behaviour, smooth change in volume from solid to liquid with increasing temperature.
What is the glassy state?
Where a liquid is supercooled and the molecules do not have time to rearrange themselves into a crystalline form characteristic of the temperature.
What is the smooth curve between the onset and departure from the supercooled liquid line?
The glass transition range (region).
What is Tf?
The interestion of the supercooled liquid and the extrapolated glass line, fictive temperature. It is used interchangably with Tg.
What happens when a glass is heated?
It smoothly moves towards the supercooled liquid line but enters a region of increasing fluidity and relaxes towards the supercooled liquid line.
Equation for degree of polymerisation:
DP=Mn/m
Where,
m is molecular weight per repeat unit.
What is the pair distribution density?
number density at a distance r is given by: ρg(r) where g(r) is the ratio of number density at a distance r to the homogeneous density.
What does ρg(r)dr give?
dp which is the probability of fining an atom centre in dr which is a distance from the origin atom.
What are the shells in the pair density function?
Areas where the probability of finding an atom increases.
What is the pair correlation function?
h(r)=g(r)–1
centres g(r) on 0.
What is a glass network former?
The backbone of the glass network, eg, SiO2.
What is a glass network modifier?
Components in the system that change the bonding and characteristics of glass structure, eg, Li2O, Na2O, MgO.
What do NWMs do?
Convert bridging oxygens to non-bridging oxygens.
What is an alkali silicate glass?
A silica glass with network modifiers such as Li2O.
What causes polymerisation?
An indicator species R•
Why are there large elastic extensions in rubber materials?
Lots of kinks and bends in polymers can straighten out.
What is the r distance of a polymer?
The distance from end to end (it is a displacement not the full length of the polymer).
What does the r distance of a polymer show?
The confirmation of the chain.
Describe atactic configuration.
® groups are randomly positioned on the chain.
Equation to find r for a polymer:
r^2=nl^2C
C is characteristic of a particular polymer.
What is ro of a polymer?
The maximum frequency of r distances as it follows a Gaussian distribution.
How do we define molecular weight (mass) for polymers?
We use average molecular weight as each chain has a different number of repeat units so has a range of weights.
What is an alternative way of expressing average chain size?
Degree of polymerisation.
What does degree of polymerisation represent?
The average number of repeats per chain.
Equation for degree of polymerisation:
DP=Mn/m
Where,
m is molecular weight per repeat unit.
Flexibility of polymer chains can be affected by what?
Intermoleuclar forces.
What are the four kinds of molecular structure for repeat polymer units?
Linear
Branched
Cross linked
Network
What is graft sequencing in copolymers?
Where there is one long chain of a single repeat unit and the other repeat unit forms branches off the side of the chain.
What physical property results from branched chains forming during synthesis?
The polymers can’t pack as tightly so lower density.
Example of a cross linked polymer:
Vulcanised rubber.
What is distinctive about network polymers:
Their properties.
What is molecular configuration?
The arrangement of repeat units along the chain that cannot be altered unless primary bonds are reformed
If an ® group is bonded to alternate C atoms, what is its configuration?
Head to tail.
If an ® group is bonded to adjacent C atoms, what is its configuration?
Head to head.
What are the three kinds of stereoisomerism in polymers with ® groups?
Isotactic configuration
Syndiotactic configuration
Atactic configuration
Describe isotactic configuration.
® groups are all on one side of the chain.
Describe syndiotactic configuration.
® groups are on alternate sides of the chain.
Describe atactic configuration.
® groups are randomly positioned on the chain.
Dominant stereoisomerism depends on what?
The synthesis process.
What is cis- trans- isomerism?
Cis- is when different ® groups are on the same side of a double bond.
Trans- is when different ® groups are on the opposite side of the double bond.
What makes thermosetting plastics not soften on heating?
They are network or cross linked polymers.
What is the process of cross linking elastomers called?
Vulcanisation.
What causes cross linking in vulcanisation?
S compounds are added to create backbones between chains. The sites for cross links are where C atoms were doubly bonded.
What are copolymers?
Where more than one repeat unit is synthesised together.
What are the different sequences for repeat units in copolymers?
Random
Block
Alternating
Graft
What is block sequencing in copolymers?
Where repeat units are in a chain in groups similar repeat units.
What is graft sequencing in copolymers?
Where there is one long chain of a single repeat unit and the other repeat unit forms branches off the side of the chain.
What kind of crystallinity do polymers show?
Either
Amorphous
Semi-crystalline
Crystalline
What is the range of crystallinity for polymers?
From completely amorphous to about 95% crystalline.
Equation for percentage crystallinity (by weight):
ρc(ρs–ρa)/(ρs(ρc–ρa)) x100
Where
ρc is fully crystalline density
ρa is fully amorphous density
ρs is density of sample
What does the degree of crystallinity depend on?
The rate of cooling during solidification.
Simplicity of the polymer.
Whether it is linear.
The stereoisomerism (atactic are difficult to crystallise).
What is the structure of semicrystalline polymers?
Small crystalline regions (crystallites) surrounded by amorphous regions.
What shape are crystallites?
Lamella.
What are spheriulite structures?
Approximately spherical shape, lamella radially grow outwards from single nucleation site.
Which polymers undergo glass transition when heated?
Amorphous, whereas crystalline have a melting point. In semicrystalline, crystalline regions will undergo melting and crystallisation whereas amorphous regions will undergo glass transition.
3 types of structure classes on the periodic table.
Class I, II and III
What is a class I structure?
A crystalline structure in the form of one of the three typical metal structures, bcc, fcc or hcp.
What us a class III structure?
A non-close packed structure (8-N rule for coordination).
What is a class II structure?
A deformed close-packed structure with some influence from the 8-N rule.
Derive the atomic packing factors for fcc, bcc and hcp.
Check
The observed relation between atomic radius and coordination number.
As coordination number reduces so too does atomic radius.
What does a low compressibility of a metal suggest?
Strong bonding.
Which metals have the highest compressibilities?
Alkali metals.
Heat of sublimation can be used as a measure of what?
Measure of the strength of bonding in the solid.
Alloy structures can be broken down into which two main types?
Homogenous and mixtures.
What are the two types of structure a homogenously structured alloy can have?
Solid solution or intermetallic phase.
What are the two types of solid solutions.
Substituional and interstitial.
What are the types of intermetallics?
Intermetallic substituional or intermetallic (size factor, electrochemical and electronic)
What types of alloy structures can a mixture take?
Combination of pure metal, solid solution or intermediate phase.
What is a primary solid solution?
A solution that has the same crystal structure as the parent metal.
Calculate the radius ratio for all interstices in fcc and bcc.
Check
Hume Rothery rules are valid for what types of alloys?
Substitutional solid solutions.
Which HR rule is the most influential?
Atomic size factor.
What is an electron compound?
A compound with a composition expressed in terms of electron concentration (e/a ratio)
What are the characteristic e/a ratios for electron compounds?
3:2, 21:13, and 7:4
Are electron compounds stoichiometric?
No, they show a composition range.
What are electrochemical compounds?
Normal valency compounds that have fixed compositions.
When are electrochemical compounds most stable?
When there are large differences in electronegativity between constituents.
What are the two types of size factor compounds?
Laves phases and interstitial compounds.
What are interstitial phases?
Radius ratio 0.41-0.59 with small atoms (usually C or N) in interstices.
What is a Laves phase?
A size factor compound with stoichiometric composition AB2.
What is the coordination of a Laves phase like?
Higher than close-packed materials. Average coordination of 13.33.
A has 12 B neighbours and 4 A neighbours
B has 6 A neighbours and 6 B neighbours.
When do Laves phases typically exist?
When component atoms differ in size by about 22.5%.
What is a superlattice structure?
An ordered solid solution.
Example of a superlattice structure?
Cu3Au
Factors contributing towards superlattice formation.
Electrochemical interaction.
Atomic size factor.
How does long and short range order within an ordered alloy structure vary with temperature?
At great enough temperatures, long range order is destroyed, however, short range order may exist due to driving forces for order still being present.
How does order in superlattice alloys affect electrical resistivity?
Increasing T about Tc causes increase in resistivity.
How does order in superlattice alloys affect mechanical properties?
Ordering can lead to strain within lattice leading to hardening.
How does order in superlattice alloys affect magnetic properties?
Kind of ordering and degree of order can affects magnetic properties (domain size).
