Solid State Flashcards
solid state chem triangle
composition, properties and structure
uses of solid state structures?
- batteries (LiCoO2)
- zeolites (catalytic cracking)
- magnetic material
- silicons for solar cells ((CH3NH3)PbI3, (GaAs))
explain lithium ion batteries
lithium elemental give off an electron that can go through the external circuit to power an appliance, and so the lithium cation in the cell travels to the cathode where it can be recharged and the process reversed
local structure of ruby?
aluminium oxide that is colourless to light in single crystal, but colour centres can form in the material which absorb light and so they are red
unit cell of concrete?
Ca2SiO4 polymorphs
the reactive chemical bonds towards water in order to produce cement
pigments? eg CdS
red to yellow piments, as they have the right optical properties. the brightness increases when grinded, this si cause of a larger surface area caused by cutting up (this is the micro structure that is impacted, not just the unit cell) larger particles would be duller
what is glass?
no a crystalline structure. highly disordered amorphous structure
energetics of crystals
- enthalpy (H) overrides entropy effect
- ordering is good for the structure
unit cell composition?
a lattice and a motif
lattice?
periodic arrangement of identical points
motif?
an arrangement of atoms associated with lattice points.
a physical object
shapes of lattice?
there are 7 different shapes of lattice, and can get 14 different lattices combined with motifs to get 230 different “face groups”
unit cell?
minimum repeated unit which makes up the infinite structure
hexagonally close packed equation for c? (cosine rule)
c = sqrt(a^2 + b^2 - 2ab*cos(y))
primative unit cell?
the corners are in 3 other unit cells
how many lattice points per unit cell in primative unit cell?
one (in 4 unit cells)
triangle unit cells?
nooooo, if it gets translated there is void space that defies making it a unit cell
lattice energy of rock salt?
lattice energy gets bigger based on charge difference and the distance between the anion and cations,
structures of metals and ionic solids?
cubic close packed (including face centred cubic)
hexagonally close packed
primative cubic
body centred cubic
face centred cubic / cubic close packed (F) ?
sqrt (2) for the full length of the unit cell
lattice points of corners and faces
ABC packing of layers
4 atoms in the unit cell
CN = 12, 74% packing
hexagonal close packing?
ABA packing
coordinated of the central atoms: origin 0,0,0, 1/3A,2/3B,1/2C
hexagonal lattice is primative, adding the extra motif makes it hexagonally close packed
gives 2 atoms in unit cell
CN = 12, 74% packing
primative cubic (P)
there is no empty space between the 4 corner atoms (ie atoms would touch)
CN = 6, 52% packing
body centred cubic (I)
sqrt(3) for the body diagonal length
2 atoms in the unit cell
4x radius = length of the body diagonal
CN = 8, 68% packing
equation for density of unit cell?
density = mass/volume
density (g/cm3) =(number of atoms in unit cell)(atomic weight of atoms (g)) / (volume of unit cell (cm3))(avogadros number (mol-1))
Angstroms (Å)?
1 A = 1x10^-10 m = 1x10^-8 cm
which structures go beyond close packing?
hexagonally close packed and face centred cubic
interstitial sites?
tetrahedral and octahedral sites, that occupy the 26% vacancy in the hcp and fcc structures
in each close packed unit cell how many T and O sites?
tetrahedral x2, has 4 fold coordination
octahedral x1, has 6 fold coordination
octahedral sharing in close packed structures?
corner sharing (1 anion)
dimer: M2X11
As a chain: MX5 (MX4X2/2)
face sharing (3 anion)
as a dimer: M2X9
as a chain: MX3 (MX6/2)
edge sharing (2 anion)
as a dimer: M2X10
as a chain: M2X10(MX2X4/2)
atomic coordinated of structures in FCC?
cp atoms (FCC): (0,0,0); (1/2,1/2,0); (0,1/2,1/2); (1/2,0,1/2)
^all of the other 12 are just symmetrical positions
O sites: (0,0,1/2); (1/2,0,0); (0,1/2,0); (1/2,1/2,1/2)
T+ : (3/4,1/4,1/4); (1/4,3/4,1/4); (1/4,1/4,3/4); (3/4,3/4,3/4)
^half of the tetrahedral sites
T−: (1/4,1/4,1/4); (3/4,3/4,1/4); (3/4,1/4,3/4); (1/4,3/4,3/4)
all possible location of tetrahedral/octahedral in a FCC?
see notes document -
white = fcc (1 unit cell)
blue = octahedral
yellow = tetrahedral
hexagonally close packed layer convention?
ABA, stacking along the c-axis
symmetry plane is B
tetrahedral holes in HCP?
described as T+ and T-
share common faces with each other along c-direction
four tetrahedral sites per HCP unit cell
octahedral sites in HCP?
share common face with each other in c-direction
two octahedral sites per unit cell
octahedral sites @ (0,0,0) and (0,0,1/2)
close packed sites @ (1/3,2/3,1/4) and (2/3,1/3,3/4) - such that they add up to 1.
relationship between T+ and T- in FCC?
they do not share a common face, they are on diagonals
there is 4 of each in each unit cell by breaking up into 8 mini cubes
octahedral sites in FCC?
at cell edges and cell body centre, giving 4 per unit cell
relationship between O and T in FCC?
O sites share FACES with T sites
O sites share EDGES with O sites
T+ sites share EDGES with T- sites
one O site and two of each T site
cubic close packed complex examples?
- rocksalts
- zinc blende
- anti fluorite
Rant about rocksalt?
- NaCl
- All O sites FILLED
-All T sites EMPTY
-Cubic structure
-Only has one lattice parameter which is the same value
-on corner are chlorine ANIONS, close packed so FCC structure
-octahedral gives one atom of the sodium anion
-coordination of 6:6
-a = 5.64 Å
-in this case anion and cations could be swapped and the structure remains equivalent
rant about zinc blende?
-ZnS
-All T+ sites are FILLED (4/8)
- means that half of the tetrahedral sites occupied by zinc cations
- the sulfur anions occupy the FCC sites
-All other sites are empty
-Coordination of 4:4
-this is the diamond structure, but when all sites are carbons
rant about antifluorite?
-Li2O
-All T+ and T- sites are FILLED
-O sites are EMPTY
-Coordination of 4:8
-has cubic eight fold coordination
Fluorite structure?
-fluorite has the structure of all T sites filled and O sites empty. MX2. ABC layers
Structure matches CaF2 (calcium difluoride)
-anions are large and cations are small (often found in tetrahedral sites)
**** but this is the reverse in this molecule, where the Li cation is actually larger than the O
-can something fit in these gaps? but cant throw off the balance between the charges
-there can be ions that fit between the ion structure
hexagonally close packed complex structures?
-nickel arsenide
- wurtzite
rant about nickel arsenide?
-NiAs
-All O sites filled
-All T sites are empty
-Is the HCP version of CCP rocksalt (rocksalt has empty tetrahedral sites)
-The nickel is octahedrally coordinated
-Arsenic is trigonal prismatic coordinated (6CN)
(in rock salt both are octahedral coordinated)
-Repeating layers of ABAB
-Coordination 6:6 for both structures of central atom
- a = 3.60 Å and c = 5.01
- Because of the different ENVIRONMENT the anions and cation cannot be swapped
ionic vs covalent environment based on anions and cations
o Ni polyhedra favoured for less ionic due to metal metal contact
o As polyhedra close structure has covalent properties
- Because of the different ENVIRONMENT the anions and cation cannot be swapped
compare NiAs vs NaCl
different stacking
NiAs- ABABAB
NaCl - ABCABCA
locations of octahedral sites different
octahedral sharing
NiAs - share faces
NaCl - share edges
bonding of the material
NiAs - covalent, short distance between Ni-Ni
NaCl - ionic, no contact between Na-Na
ramble about wurtzite?
-All T+ (or T-) sites are filled
-All other sites are empty (O)
-This is comparable to zinc blende
-Has a network of corner sharing on the tetrahedral sites
-c axis can be longer or shorter, so structure has. A degree of flexibility
-has coordination 4:4
-poly morphs can have the same composition but different structures
caesium chloride - NOT CLOSE PACKED?
this is primative CsCl
- Cs in body centred with CN=8
coordination of 8:8
what is CsCl?
Cl (0,0,0) and Cs (1/2, 1/2, 1/2)
- large cation that cannot fit in octahedral or tetrahedral, then getting an eight-fold coordination of both the cations and anion
-this is NOT body centred
-based on a square lattice of ions
-so relatively large void spaces and more of them
-CsCl is comparable to antifluorite, fluorite and CaF2
Spinel structure?
AB2O4
what is spinel?
where both T and O sites are occupied in FCC, but they dont all have to be filled
4x anions, and a total of 8 tetrahedral sites available, but only 1/8 possible tetrahedral sites are occupied
and only 1/2 of the octahedral sites are filled with
not possible to fill them all cause then cations would be too close to each other
spinel vs inverse spinel?
Spinel = [A]tet[B2]octO4
(MgAl2O4, CoCr2O4, Mn3O4)
Inverse spinel = [B]tet[AB]octO4
(Fe3O4, NiFe2O4)
what is special about inverse spinel?
where the B cation can have multiple charges, can choose between the tetrahedral and octahedral sites
if ions A and B in spinel are first row TM need to consider CFSE…
will a too large cation fit in the respective site (tetrahedral smaller)?
then consider the energy difference between a tetrahedral CFSE and a octahedral CFSE and the ligand its is paired with the 0.4/0.6 values. the lowest energy one will be the preferred site for the cation
what is perovskites?
ABO3
very common and versatile
very conductive
where B is large cation and A is small cation
-A has coordination 12 (close packed structure)
-B has coordination 6 (octahedral)
ratio rule (1)
ratio: cationic radii/anionic radii
rm/rx
coordination number 6, minimum cation size?
= 0.414
= sqrt(2) -1
coordination number 8, minimum cation size?
=0.732
= sqrt(3) -1
coordination number 4, minimum cation size? eg tetrahedral
=0.225
= (sqrt(3)/sqrt(2)) -1
the coordination number prefers which cation size?
4: 0.225 <rM/rX < 0.414
6: 0.414< rM/rX < 0.732
8: rM/rX > 0.732
exception to radius rule (1)
O^2- because this gets too covalent
ionic radii trend?
R decrease across the period
R increase down the group
- note at the bottom there is a inert pair effect and relativistic contractions
ionic radii are additive cause they elastic spheres
further ionic radii trends?
radii decreases with charge (removing more electrons) for a specific coordination number
radius decrease with increasing oxidation state (adding more electrons)
increasing coordination number, increases with coordination number (as spread further apart to accommodate more bonds)
for given oxidation state, radius decrease across period (if the same oxidation state follow trend of getting more pulled in
for 3d elements, high spin has a greater radius than low spin states
diagonal relationships, where there are near enough equal radii (cause there is an increase in oxidation state but there is more pull from nucleus with more electrons)
absolute values of ionic radii?
bond length = sum of two ionic radii
considering the effective nuclear charge
radii is inversely proportional to effective charge
values of shielding used in effective nuclear charge?
n = 0.35
n-1 = 0.85
n-2 onwards = 1
Zeff equation?
Z - (shielding values)
shielding values = no. e- in the n * n constant for shielding
after calculating the ratio of Zeff between the ionic bond…?
have the bond length value, must be split up by the ratio of cation/anion
units are given in question - in not assume Å
defects in inorganic crystals?
intrinsic and extrinsic
intrinsic defects in inorganic crystals?
- thermodynamics
- changes to packing of layers
- absences… pair imbalances.. but occurs at low concentrations so usually overall balance out
defects in NaCl?
1 in 10^5 in NaCl at room temperature
extrinsic defects in inorganic crystals?
-doping (replacing), changed properties, composition and structure - usually controlled
- cations/anions of different size or chemistry
- vaccines of a site
-cations/anions can be put on unoccupied sites (interstitials)
substitution defects?
NaCl and KCl can be substituted, to any ratio that will produce same crystal structure
substitution defect, ionic size difference?
15-20%, ideally similar sized
substitution defects, temperature dependancy?
chromium is much bugger than aluminium, and there a change to stabilisation and this is not a favourable substitution but the x value is temperature dependant - so can do at high temperatures to give it a greater chance of working
vacancy defects? both cation and anion…
when there is a cation vacancy:
cation
- cation for cation of higher charge
anion
- anion for anion of lower charge
when there is an anion vacancy:
cation
- cation for cation of lower charge
anion
- anion for anion of higher charge
interstitial defects? cations and a less common anion version
cation interstitial
- cations of lower charge
- anions of higher charge - but this is not possible due to size restraints
(anion vacancy = cation interstitial)
anion interstitial
- cation of lower charge only
electrostatic valance rules for inorganic crystals?
electrostatic bond strength is “s” per M-X bond
charge of central cation/anion neighbours
strength of interaction increases as distance decreases (get closer = stronger bonds
interaction of CaF2
For CaF2, s(Ca-F) = ¼; four bonds to F-
this is done by:
1xCa2+ = 1x2 = 2, 8xF1- = 8x1 = 8
2/8 = ¼ for s(Ca-F)
x = 1
(Coord: Ca:F = 8:4) known due too the charges on the atoms
Oxyanions?
The oxy-anions XO4n-
X = Al, Si, P, S, Cl
bond valance sum?
Vi = sum-j sij
sij = exp [(r0 – dij)/0.37Å]
r0 constant for a given i-j pair
dij is the i-j bond length (units Å)
Rationalises why bond length
decreases with Coord. No.
rattling cation effect?
displacement in the octahedral structure to give a short and long bond, this swaps and give alternating long and short
atom at centre gets called under bonded, but really cause cation is too small
as bond length increases, bond valance decreases
bond valance method?
checking to see which charge on the cations in the structure
- given the bond distances
- calculate s for each charge
= exp(known length - fraction length)/0.37 - sum s, (snumber of bonds that length)+(snumber of bonds that length)
the value of bond valance sub is rounded and that number suggests which oxidation state should be on the structure
