Structures of Solids Flashcards
Define polymorphism? What makes a structure a crystal?
Isomerism between solid structures e.g diamond and graphite
Crystals have translational periodicity in 3 dimensions, the structure appears identical after a shift of some distance in any dimension
What are lattice points? What is a crystal lattice?
Points within a crystal with identical environments, meaning each point can be mapped onto each other by translations only
Crystal lattice= set of all lattice points, as a set of points which are evenly spaced
What is a unit cell? What is the difference between primitive and centred unit cells?
A parallelepiped (3d) or parallelogram with lattice points at its vertices
Primitive= 1 type of lattice point / unit cell
Centred= 2 + lattice points / unit cell
What is the conventional unit cell?
Smallest unit cell within a structure reflecting the underlying symmetry of the lattice
What are the properties of a cubic, tetragonal, orthorhombic, monoclinic and triclinic lattice?
Cubic: X=Y=Z, all 90 degrees
Tetragonal: X=Y not equal to Z, all 90 degrees
Orthorhombic: all different length, 90 degrees
Monoclinic: all different length, 1 set not at 90 degree
Triclinic: all different lengths and not at 90 degrees
What is the motif? What is the crystal structure?
Motif= Set of atoms we assign to each lattice point, so the recurring structural unit associated with each lattice point
Crystal Structure= motif x (crystal) lattice
What is a close packing structure in 2d?
Close packing is when the atoms/ions are packed so they are touching each other in 2d, with small gaps arising from the circular shape
How has the 2d packing efficiency of close packed structures been calculated?
Or use a parallelogram
How have the 3d close packed structures been formed?
Layering of each of these 2d layers on top of each other, falling into the holes of the layer below
There is a choice between the type of holes, up or down, and the layering of these will determine if the structure is HCP or CCP
How is the structure of HCP originated? And what is the nearest neighbour coordination?
CP with an ABAB structure
The first layer is directly below the 3rd layer
Relative to the A layer, only one set of holes have been used
12 nearest neighbours, with a the same environment above and below, but different to in the plane
How is the structure of CCP originated? And what is the nearest neighbour coordination?
CP with an ABCABC structure
The first layer is not directly below the 3rd layer, instead the first and fourth
So relative to the A layer, both sets of holes have been used
12 nearest neighbours, with the triangles above and below facing the opposite direction
By looking at the diagonal, a simplification can be made such that CCP becomes a face centred cubic
And so all 12 nearest neighbours are in the same environment
How has the efficiency of CCP been calculated?
Remember, for CCP, the spheres touch across a diagonal of a face
Use number of spheres per unit cell, and a way to calculate lattice parameters into r or vice versa
What are the nearest neighbour lengths for BCC?
8 neighbours are nearest neighbour length, from corners
And 6 at 1.5x Rnn from the other centres
So in total, 12 neighbours
What are examples of metals that are BCC?
All G1
V and below
Cr and below
Ba
What are examples of metals that are HCP?
Sc and below
Ti and below
Be/Mg
What are examples of metals that are CCP?
Ni and below
Cu and below
Ca/Sr
How do you count the number of atoms in a unit cell?
Corners= 1/8
Faces= 1/2
Edges= 1/4
What is the coordination number? What is the coordination geometry?
CN= number of neighbouring ions of opposite charges e.g 4
Geometry= arrangement of neighbours around an ion e.g tetrahedral
How do the number of holes in CCP/HCP relate to the unit cells?
In both HCP and CCP, there are the same number of octahedral holes as spheres
And twice as many tetrahedral holes as spheres
What is the stability limit and what are the critical values?
Cations will fit into the holes of an anion lattice
At the stability limit, the cations need to be large enough so that they fit in the holes and the anions are just touching
Cations slightly larger than this will fit and push the anions apart slightly, reducing repulsion and stabilising them
All based on r+ / r-
Tetrahedral stable when > 0.225
Octahedral > 0.414
Cubic > 0.732
Not always followed
How has the tetrahedral stability limit been calculated?
Use tetrahedral geometry and cosine rule
How has the octahedral stability limit been calculated?
Use positioning, effectively 2d, with the cation in between two anions and below one
How has the cubic stability limit been calculated?
Use diagonal for r+ value
And the anions are touching as the x/y so use these to calculate the diagonal of the face
What is polarisability?
The tendency for electron distribution in an anion or cation to be influenced by other ions
~ r / n , where n is charge
What does it mean for an ion to be polarising or polarisable? What properties do these types of ions possess?
Polarisable= large ions with small charges e.g Cs
Polarising= small ions with large charges e.g most halides
What happens in terms of lattice structure is both ions are both polarising or both polarisable?
Both polarising- cations surround anions
Both polarisable- anions surround cations
What is the anti-fluorite structure? Including coordination number and geometry, and examples?
M2X, CCP, all Td holes filled, 4
e.g Li2O- most G1 oxides and sulfides
Results in [LiO4] tetrahedra
and [LiO8] cubes
What is the Zinc Blend structure?Including coordination number and geometry
MX, CCP, 1/2 Td holes filled, 4
Altering tetrahedral holes 2 (1/4) and 2 (3/4) to enable full coordination of all
e.g ZnS
Both anion/cation tetrahedra
What is the Wurtzite structure? Including coordination number and geometry
MX, HCP, 1/2 Td holes filled, 4
5/8 and 1/8 central- only one possible to avoid M-M contact
Both tetrahedra
e.g ZnS
What are examples of Zinc Blend/ Wurtzite?
Cu halides
ZnO/ZnS (small G6)
What is the rock salt structure? Including coordination number and geometry, and examples?
MX, CCP, all Od holes filled, 6
Both form octahedra
G1 Halides, 2+ TM oxide, G2 dications
What is the NiAs structure? Including coordination number and geometry, and examples?
MX, HCP, all Od holes filled
e.g 3d TM with G5/G6 e.g NiAs, over CCP as some degree of metal-metal covalency
[NiAs6] octahedra
[AsNi6] trigonal prisms
What can help you with determine the geometry of shapes in unit cells?
The geometry must match the stoichiometry
e.g if MX, and 6 coordinate, both must have a shape with 6 ions
e.g M2X, and so td filled, must be MX4, and so double for X so MX8
What is the rutile structure? Including coordination number and geometry, and examples?
MX2, distorted HCP, with half filled Od holes filled, 6
See unit cell below
e.g TiO2
[TiO6] octahedra
[OTi3] triangles
e.g TM dioxides NiO2, VO2
MnF2/O2, most TM difluorides
CaCl2 distorted variant of rutile
What is the CsI structure? Including coordination number and geometry, and examples?
MX
Primitive cubic packing, with a central cubic hole, see plan
Both cubes, cation in all cubic holes
e.g CsCl, CsBr, NH4Cl
What is the fluorite structure? Including coordination number and geometry, and examples?
Similar to anti-fluorite, but this time the anions are in the tetrahedral holes and cations surrounding, or effectively in 1/2 the cubic holes
so 8 coordination of the metal ion
e.g CaF2
[CaF8] cubes and [CaF4] tetrahedra
e.g Ln/Ac dioxides
(What is the cristobalite structure?)
MX2
4 coordinate with 1/4 td holes filled
e.g SiO2
[SiO4] tetrahedra, and [OSi2] linear rods
Why is there no M2X HCP structure?
Distance between the tetrahedral holes is too small for all to be filled comparative to CCP
Why does a large difference in polarisability lead to 2d structures?
Polarising ions deform electron density so that the polarisable ion only coordinates on one side (electron deficient), see diagram
What is the CdCl2 structure?
CCP of Cl- with 1/2 Od holes filled
[CdCl6] octahedra
[ClCd3] trigonal pyramids
See drawing below, but diagonal of Cd
What is the CdI2 structure?
HCP of I- with Cd2+ in half the Od holes
[CdI6] octahedra
[ICd3] trigonal pyramids
See below, chains
What are examples of the CdCl2/I2 structure?
Most Mg/ 3d dichlorides/bromides/iodides
but not Cr
What is the Cs2O structure?
Anti-CdCl2
Cs occupies Cl sites, and O occupies Cd sites, switched
In polyhedral representation, what types of structures are possible? How do they affect M-M distance and what are the impacts?
Corner sharing- maximises M-M distance
Then edge sharing
And face sharing minimises M-M distance
e.g NiAs is face-sharing octahedra, which encourages covalency
What would NH4F be predicted for structure? What is it actually and why? What about NH4Cl?
r+/r- ~ G1 halides, as NH4+ moderately sized and F- small, so predicted rocksalt
But as NH4+ can form hydrogen bonds, Wurtzite structure as Td symmetry enables this to still occur
Even smaller but CsCl structure to enable hydrogen bonding, directing interactions
How can isoelectronic solids be used for structure determination?
Isoelectronic solids will likely share similar structures, especially when their is a degree of covalency
e.g MgB2 and Li3N, both similaqr to graphite
What are zeolites? What compounds are used in lithium batteries?
Si O compounds, covalently bonded, into rings and cyclic structures, balls
Lix CoO2
What are complex oxides and examples?
Will contain a metal at different oxidation states
e.g hematite Fe2O3
What are perovskites?
Complex oxides in the form ABO3
where A is a 12 coordinate cation, usually G1/2
And B is 6 coordinate cation, typically TM
e.g SrTiO3
e.g KNbO3
