Structures of Solids Flashcards
(53 cards)
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
