part 1 solid state, defects, diffraction

8/13/2019 Part 1 Solid State, Defects, Diffraction

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Solid State Physics- Branch of condensed matter physics

dealing with properties of solids

especially crystals

Classifications of solids:

1. Crystals2. Amorphous

Descriptions of over-all structure:

1. Lattice- Regular arrangement of mathematical

points in 3D described by the unit of

repetition of the crystal

- Lattice constantdistance betweentwo lattice points

2. Basis- The arrangement of atoms at each

lattice point

- Could range from atom to largemolecules

3. Unit cell- Three dimensional cell constructedfrom adjacent lattice points that best

describes the crystal structure

- Building block of a crystalline structure- Repeats itself to form the lattice

Metallic Crystals

- Tend to be densely packed- Made of heavy elements- Bonding is not directional- Neighbor distances tend to be small in

order to lower bond energy

Atomic packing factor:

Counting for some unit cells:

Vertex = 1/8 atom

Edge = atom

Face = atom

Body = 1 atom

1. Simple Cubic Structure (SC)- Close packed directions are

cube edges

- Coordination # = 6 (# ofnearest neighbors)

- # of atoms: = (1/8*8) = 2

2. Body Centered CubicStructure (BCC)

- Closed pack directions arecube diagonals

- Coordination # = 8- # of atoms = (1/8*8 + 1) =

2

Examples:

1: Using the hard sphere model, find the

length a of the unit BCC cell. Assume

radius of the atom is R.


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2. Determine the maximum radius of the

sphere B which can be placed into a BCC

structure without affecting the position of the

other spheres. (Ans: 0.155A)

3. Determine the actual volume occupied by the

spheres in an BCC structure as % of total

volume. This is called packing density or atomic

packing factor. (Ans: 0.68). Find also the

coordination number .(8)

3. Face centered cubicstructure (FCC)

-

Close packed directions areface diagonals

- Coordination # = 12- # of atoms = (1/8*8 + 1/2*4

+ 1) = 4

1: Using the hard sphere model, find the length

a of the unit cell of an FCC structure. Assume

radius of the atom is R.

2. Determine the maximum radius of the

sphere B which can be placed into an FCC

structure without affecting the position of the

other spheres. Assume the radii of sphere A is A

and radius of B is B. (Ans: 0.41A)

3. Determine the actual volume occupied by the

spheres in an FCC structure as % of total

volume. This is called packing density or atomicpacking factor. (Ans: 0.74)

4. Hexagonal closed packed- Formed by two hexagons and one

atom at the center of the hexagons

- The hexagons are separated by threeatoms fitting into the sites

- # of atoms = 6- Coordination # = 12


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Theoretical density:

n = number of atoms/unit cell

Vc = volume/unit cell (cm^3/unit cell)

A = atomic weight (g/mol)

Na = Avogadros number (6.023x10^23

atoms/mol)

Example 1: Compute the theoretical density of

copper based on the following information.

Crystal structures:

Polymorphism

- Same compound occurring in more thanone crystal (example: silica)

Allotropy

- Polymorphism in elemental solids (e.g.carbon)

Defects

A. Point defects1. Vacancyunoccupied lattice point2. Interstitialextra atom not in regular

lattice position

3. Substitutionaloccupancy of a latticepoint by impurity

4. Antisitea host atom occupies positionof another host atom

Types of vacancy:1.A. Schottky Defect

- an atom transfers from a lattice site in the

interior to a lattice site on the surface of a

crystal

1.B. Frenkel Defect

- atom is transferred from a lattice site to an

interstitial position

n = number of vacancies

N = total number of atoms

Ev = enthalpy of formation

T = temp in K

Kb = Boltzmann Constant (1.38x10^-23 J/atomK

OR 8.62x10^-5eV/atomK)

Example: Suppose that the energy required to

remove a sodium atom from the inside of a

sodium crystal to the boundary is 1 eV.

Calculate the concentration of Schottky

vacancies at 300K.

Schottky defect in ionic crystals:

Frenkel defect:

B. Line defects

- dislocations

1. Edge dislocationan extra plane of atoms

squeezed into a part of the crystal lattice

2. Screw dislocationa step or ramp is formed

by the displacement of the atoms in a plane in

the crystal

3. Stacking faulta change in the stacking

sequence over a few atomic spacings

4. Twin regiona change over many atomic

spacings


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part 1 solid state, defects, diffraction

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