Topic 14: Crystalline Solids

What is it meant by an allotrope of allotropic form of an element

Elements can have more than one geometric arrangement in their solid state

Crystal lattice

Ordered geometric 3D array of points that show the symmetry of a crystal

Motif

Specific group of atoms that when multiplied and brought together can create the full crystal

Unit cell

Smallest repeating pattern that completely describes full crystal lattice

Why can a unit cell contain a fraction of atoms

Because at corners and faces they are shared with adjacent cells

Stacking pattern

3D arrangement formed with square packed atomic layers stacked one above another

Sequence AAAA Vs ABAB vs abcabc

Aaaa: simple cubic layers stacked right on top of eachlayer), ABAB : body centered cubic (stacking with atom in middle ) , abcabc : face centered cubic (stacking with atoms on faces)

What unit cells result from cubic packing squares

Simple cubic

How do edges, faces, corners contribute to unit cells?

Corner atoms share by 8 ( 1/8 each)

Face atoms are shared by 2 cells (1/2 each)

Edge atoms are shared by 4 cells (1/4) each

Center atoms not shared (1 each)

Why can cubic models be simplified

Because overlapping portions of shared atoms can be cut off

How are atoms arranged and how do they touch in a simple cubic lattice

Atoms sit at the corners and touch along the edges of the cube

How many atoms in a simple cubic cell

8 corners * (1/8) = 1 atom

What is the relationship between edge length (a) and atomic radius (R ) for simple cubic

A=2r

How is bcc unit cell generated

From abab stacking pattern where one atom is in the middle and the others follow cubic shape

How do atoms touch in bcc

They touch at the corners and one atom in the center

What is the relationship between a and r for bcc

A= 4r/sqrt 3

How many atoms per bcc cell

8 corner * (1/8) + 1 center =2

How is a fcc cell generated

Form abcabc which is stacking each layer with 9ne atom sitting in the spaces of the layer before it

How do atoms touch in fcc

Along the faces and the corners

Relationship between a and r for fcc

A = sqrt 8 r

how many atoms per fcc cell

8 corners x (1/8) + 6 faces x (1/2) = 4

Packing efficiency

Percentage of a unit cells volume actually occupied by atoms

What are packing efficiencies for simple cubic, bcc, fcc

Sc = 54.2

Bcc = 68.

fcc= 74

What is the general formula for density of a crystalline solid

P= # of particles in a per unit cell x mass per 1 particle / volume of unit cell

Volume

V=a³

What define San ionic solid

Crystalline material made up of cations and anions with usually a larger anion lattice framework

What kids of voids occur in cubic lattices

Tetrahedral holes (4 atoms surrounding) or octahedral holes (surrounded by 6 atoms)

How can formula unit be derived from ionic compound unit cell

Count cations and anions in the cell and reduce to simplest whole number ratio

Density formula for ionic compounds

P = (number of atoms for type x) (mass of 1 particle of type x) + ( number of atoms for type x) (mass of a particle of type y)/volume of cell