Table of Contents
- 1 What are HKL values?
- 2 What is the packing fraction of BCC and FCC?
- 3 Why do we use Miller indices?
- 4 How much is the packing efficiency of bcc?
- 5 What is the packing efficiency of BCC?
- 6 Why face Centred tetragonal is not possible?
- 7 Which is an example of a bcc structure?
- 8 How to generate fcc structure from SC lattice?
What are HKL values?
Equivalently, (hkℓ) denotes a plane that intercepts the three points a1/h, a2/k, and a3/ℓ, or some multiple thereof. That is, the Miller indices are proportional to the inverses of the intercepts of the plane, in the basis of the lattice vectors.
What is the packing efficiency of BCC and FCC?
Therefore, we can Summarize:
| Type of Structure | Number of Atoms | Packing Efficiency |
|---|---|---|
| Scc | 1 | 52.4% |
| Bcc | 2 | 68.04% |
| Hcp and Ccp – Fcc | 4 | 74% |
What is the packing fraction of BCC and FCC?
The packing factors of slip systems include: Hexagonal close-packed (hcp): 0.74. Face-centered cubic (fcc): 0.74. Body-centered cubic (bcc): 0.68.
How many lattice points are present in a FCC crystal is BCC crystal?
Answer: One unit cell of a face-centered cubic has 8 lattice points are corners and 6 lattice points at faces, total 14 lattice points….Answer:
| Hexagonal Close Packing | Cubic Close Packing |
|---|---|
| Volume of unit cell is 24√2r3 | Volume of unit cell =16√2r3 |
Why do we use Miller indices?
Miller indices are used to specify directions and planes. These directions and planes could be in lattices or in crystals. The number of indices will match with the dimension of the lattice or the crystal.
What is the meaning of Miller indices?
Miller indices, group of three numbers that indicates the orientation of a plane or set of parallel planes of atoms in a crystal. The reciprocals of these intercepts are computed, and fractions are cleared to give the three Miller indices (hkl).
How much is the packing efficiency of bcc?
The volume of the unit cell is given as. Therefore, packing efficiency of BCC is 68.04%.
How will you determine packing efficiency of bcc?
With the help of packing efficiency, the quantitative aspect of solid state can be done. Mathematically it is the volume occupied by atoms in a unit cell divided by the total volume of the unit cell, the whole multiplied by 100. Packing efficiency is always calculated in percentage.
What is the packing efficiency of BCC?
How do you calculate BCC?
The relation between edge length (a) and radius of atom (r) for BCC lattice is √(3a) = 4r .
Why face Centred tetragonal is not possible?
A face-centered tetragonal (FCT) lattice does have this symmetry. But we cannot replace FCC by BCT because FCC has a higher symmetry (four three-fold axes along the body diagonals) which the BCT does not have. So although a smaller unit cell is possible in this case also we do not go for it.
How many lattice points are body centered?
one lattice point
So, lattice points contributed by the corners are =8×18=1 atom. -In body-centered, one lattice point is present in the body centre of the unit cell other than the points present in the corners. SO contribution of the lattice point in a unit cell by the corners=8×18=1 and at the point center it is 1 lattice point.
Which is an example of a bcc structure?
The basis vectors are: Example: Body-centered cubic (bcc) structure The bcc structure can be generated using a sc lattice with a two-atom basis. 1e ih k l( ) F f hkl =⋅+π ++ First atom: d 1=(0,0,0) d 2=(0.5,0.5,0.5) f Second atom: f e π i (h k l) = 1, h k l =even −1, h k l =odd F hkl = 2 f h k l =even 0, h k l
Which is an example of a fcc structure?
Example: Face-Centered Cubic (fcc) Structure The fcc structure can be generated from a sc lattice with a four-atom basis. 1e e eik l ih l ih k( ) ( ) ( ) F f hkl =⋅+ + +π+ π+ π+ First atom:
How to generate fcc structure from SC lattice?
The fcc structure can be generated from a sc lattice with a four-atom basis. 1e e eik l ih l ih k( ) ( ) ( ) F f hkl =⋅+ + +π+ π+ π+ First atom: d 1=(0,0,0)