Unit Cell

Question 1

What is a unit cell and name the 3 types?

Answer 1

The smallest unit that has total symmetry of the crystal - Simple Cubed

• Body Centred Cube
• Face Centred Cube

Question 2

Where does Slip occur?

Answer 2

• Deformation under loading occurs on certain crystalline
  planes and in certain crystallographic directions
• Slip occurs in close packed directions

Question 3

What is the ‘Theoretical Density’ equation

Answer 3

Density = (Mass of Atoms in Unit Cell) / (Total Volume of Unit Cell)

rho = (nA/VN)

n = Atoms per unit cell (#)
A = Atomic mass (g/mol)
V = Volume per unit cell (cm^3)
N = Avogadro's Number 
 6.023E23 (atoms/mol)

Question 4

What is the ‘Atomic Packing Factor’ equation?

Answer 4

Atomic Packing Factor = (Volume of Atoms in Unit Cell) / (Volume of unit cell)

APF = ((atoms/unit cell)*(volume/atom)) / (volume/unit cell)

Question 5

What are ‘Coordination Numbers’ and ‘ Close Packed Directions’?

Answer 5

Coordination Numbers - The number of spheres which are touching a particular sphere is known as coordination number.

Close Packed Directions -
Direction through unit cell which passes through the largest number of atoms. (Eg FCC = 4r)

Question 6

What are the steps for attaining the Miller Indices of a plane?

Answer 6

1. Choose the origin O in the unit cell or a new O’ with axes X’, Y’ and Z’
2. Find the intercepts, from O to a intercept, from O to b intercept and from O to c intercept
3. Take reciprocals of intercept position
4. Clean up
   - Reduce multiples
   - Eliminate fractions
   - Use ͞ above negative integer in indices
   - Place round brackets around integers

Question 7

What are the steps for drawing a plane given Miller Indices?

Answer 7

1. Select origin O at 0,0,0 (OR if they are negative at O’= X’, Y’, Z’)
2. Take reciprocal of indices to get 1/h, 1/k, 1/l, which will be the intercepts
3. Mark intercepts along x, y, z axes at a, b and c
4. Draw plane by connecting intercepts

Question 8

What the equations of Linear Density and Planar Density ?

Answer 8

LD = (number of atoms centred on direction vector) / (length of direction vector)
PD = (number of atoms centred on a plane) / (area of plane)

Question 9

How are Miller Indices for directions attained?

Answer 9

A vector r passing from the origin to a lattice
point can be written as:
 r = r1 a + r2 b + r3 c
where, a, b, c → basic vectors and
 miller indices → [r1 r2 r3]

[ ] = directions
( ) = planes