Bcc Fcc Primitive Cubic Unit Cell - Definition, Structure, Types, FAQs

Unit Cell

The smallest group of atoms has the same number of crystals, and where the entire lattice can be formed by three dimensions is called the Cell Unit. Crystalline Solids exhibit a normal and repetitive pattern of existing particles.

Representation of the three-dimensional design of the particles present in the crystal, in which each particle is presented as a point in space known as a crystal lattice.

FCC structure

FCC (face-centered cubic): Atoms are usually arranged at the corners and even at the center of the surface of each given cell. Atoms are considered to affect the diagonals of the face. 4 atoms in a single unit cell. Atoms are arranged in the corners of the cube, and another atom is in the center of the cube.

BCC structure

The BCC unit cell has a total number of two atoms, one in the center and one in the eight from the corners. In the FCC system, there are also eight atoms in the corners of a cell cell with one atom centered on each surface. The atom on the surface is shared with a nearby cell.

What is an FCC structure and a BCC structure?

The most direct difference between FCC crystals and BCC is in the atomic systems. The cubic structure in the center of the face has an atom in all 8 positions, and in the center of all 6 faces. The body-centered cubic structure has atoms in all eight corner positions, and one is in the center of the cube.

Primitive meaning

1. Relating to, identifying, or preserving a first-degree character in the development of the appearance or history of a particular object.

2. Very basic or non-technical in terms of comfort, ease of use, or efficiency.

"Camp accommodation was old."

Types of Unit Cell

Multiple unit cells together form a crystal lattice. Physical particles such as atoms, and molecules also exist. Each lattice point remains such particles.

1. First Cubic Cell

2. Body-centered Body Unit Cell

3.A cell unit in the center of the face

1. Primitive Cubic Unit Cell

In the first cell of the cubic unit, atoms are found only in the corners. Every atom in a corner is shared between cells in eight adjacent units. There are four unit cells in the same layer as 4 in the upper (or lower) layer. Thus, a single unit of cell has only 1 / 8th of an atom. Each subdivision in each of the following figures represents the particle center in that particular position and not its size. This building is known as the open-air building.

Atoms in the first phase of the simple cubic unit cell are found only in the corners

All the atoms in the corner are divided between the cells of the eight adjacent units

Four unit cells exist in the same layer

One unit cell is in the upper / lower layer

Thus, a single cell unit has only 18 atoms

Each subdivision in each of the following figures represents the particle center in that particular position and not its size

In each cell of the cubic unit, there are 8 atoms in the corners. Therefore, the total number of atoms in a single cell is

8 × 1/8 = 1 atom.

2. Body-centered Unit Cell (BCC)

The BCC unit cell has atoms in each corner of the cube and the atom in the center of the structure. According to this structure, the atom in the center of the body entirely belongs to the cell unit in which it is located. In the BCC unit cell, every corner has atoms. There is one atom in the center of the building. At the bottom of the drawing is an open structure.

According to this, the atom of the structure in the physical organs is entirely the cell of the unit in which it is located.

Number of atoms in a BCC cell:

Therefore, in the BCC cell, we have:

8 x 1/8 corners with each atom = 8 × 1/8 = 1 atom

1 physical center atom = 1 × 1 = 1 atom

Hence, here the total number of atoms that are present per cell unit = 2 atoms.

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3. Face-centered unit Cell (FCC)

The FCC unit cell contains atoms in all corners of the crystal lattice and in the center of each cube surface. An atomic surface atom is divided between cells in two adjacent units, and only 1/2 of each atom is in each cell.

In the FCC unit cell, atoms are present in all corners of the crystal lattice

Also, there is an atom at the center of the whole surface of the cake

This atomic center is divided between cells in two adjacent units

Only about 12 atoms are part of a cell

Number of atoms in an FCC cell

a) 8 x 1/8 corners with each atom = 8 × 1/8 = 1 atom

b) Six surface atoms × 1/2 atom per unit of cell = 3 atoms

Therefore, the total number of atoms in a cell = 4 atoms

Therefore, in the cellic unit centered on the surface, we have:

8 x 1/8 corners with each atom = 8 × 1/8 = 1 atom

Six atoms centered on the surface × 1/2 atom per unit of cell = 3 atoms

Therefore, the total number of atoms in a cell = 4.

What is Lattice?

A lattice is a three-dimensional structure, a series of periodic points, on which a crystal is formed. In 1850, M. A. Bravais showed that similar points can be arranged geographically to produce 14 types of standard patterns. These 14 space fragments are known as Bravais lattices.

The crystal lattice of solidity can be defined according to its unit cell. A crystal lattice is made up of a very large number of unit cells, where every lattice point resides in a single particle. A unit cell can be seen as a three-dimensional structure consisting of one or more atoms.

We can see the volume of this cell unit in terms of cell unit size. For example, if we have a single edge cell “a”, the unit cell volume can be given as “a³”. The unit size of a cell is given as a measure of the size and volume of the cell. The unit size of a cell is equal to the product of the number of atoms in the cell and the size of each atom in the unit cell.

Quantity of cell unit = number of atoms per cell unit × size of each atom = z × m

Where, z = number of atoms in a cell,

m = Mass for each atomic mass

Atomic mass can be given with the help of Avogadro number and molar mass as:

MNA

Where, M = molar mass

NA number = Avogadro

Cell unit volume, V = a³

=> Multiple cell unit = maximum cell unit unit cell

=> Cell unit quantity = mV = z × ma³ = z × Ma³ × NA

Therefore, with the knowledge of the number of atoms in the unit cell, the marginal length and the molar size can determine the cell density of the unit.

A general description of the cell unit size of the various cases is found below:

1. The first cell unit: In the cell of the first unit, the number of atoms in a unit is equal to one. Therefore, the size is given by:

Maximum cell unit = 1 × Ma³ × NA

2. Cells centered in a cubic unit: In a cell-centered cubic unit cell, the number of atoms in a cell is equal to two. Therefore, the size is given by:

Maximum cell unit = 2 × Ma³ × NA

3. Cube-centered cubic unit cell: In a cell-centered cubic unit cell, the number of atoms in a unit cell is equal to four. Therefore, the size of the cell unit is given as:

Maximum cell unit = 4 × Ma³ × NA

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Some Solved Examples

Question 1: Which of the following statements is true regarding primitive unit cells?

1) They contain one or more constituent particles at positions other than corners.

2) (correct) They contain constituent particles only at the corner positions.

3) They contain one constituent particle at the body-centre besides the ones at the corners.

4) They contain one constituent particle present at the centre of each face besides the ones at the corners.

Solution:

Primitive and Centred Unit Cells

Primitive Unit Cells
When constituent particles are present only on the corner positions of a unit cell, it is called a primitive unit cell.

Centred Unit Cells
When a unit cell contains one or more constituent particles present at positions other than corners in addition to those at corners, it is called a centred unit cell. Centred unit cells are of three types:

• Body-Centred Unit Cells: Such a unit cell contains one constituent particle (atom, molecule or ion) at its body-centre besides the ones that are at its corners.
• Face-Centred Unit Cells: Such a unit cell contains one constituent particle present at the centre of each face, besides the ones that are at its corners.
• End-Centred Unit Cells: In such a unit cell, one constituent particle is present at the centre of any two opposite faces besides the ones present at its corners.

Primitive unit cells are defined as unit cells that contain only constituent particles at the corner positions. This means that there are no particles at any other positions within the unit cell. Therefore, option b) is the correct statement. Option a) describes centred unit cells, while options c) and d) describe specific types of centred unit cells (body-centred and face-centred, respectively).

Hence, the answer is option (2).

Question 2:

A metal crystallises with a FCC lattice. THe edge length pf unit cell is 408 pm. The diameter of metal atom is

1) (correct) 288 pm

2) 408 pm

3) 144 pm

4) 204 pm

Solution:

For the FCC lattice,

$
\begin{aligned}
& 4 r=a \sqrt{2} \\
& r=\frac{a \sqrt{2}}{4}=\frac{408}{2 \sqrt{2}}=144 \mathrm{pm} \\
& \text { diameter }=2 r=144 \times 2=288 \mathrm{pm}
\end{aligned}
$
Hence, the answer is option (1).

Question 3: In a simple cubic cell, each point on a corner is shared by

1) 2 unit cells

2) 1 unit cell

3) (correct) 8 unit cells

4) 4 unit cells

Solution:

Crystal Lattices and Unit Cells
A portion of the three-dimensional crystal lattice and its unit cell.

In the three-dimensional crystal structure, a unit cell is characterised by:
(i) its dimensions along the three edges a, b, and c. These edges may or may not be mutually perpendicular.
(ii) angles between the edges, α (between b and c), β (between a and c), and γ (between a and b). Thus, a unit cell is characterised by six parameters a, b, c, α, β, and γ.
Primitive Unit Cells
When constituent particles are present only on the corner positions of a unit cell, it is called a primitive unit cell.

Solution

As we learnt in

Primitive unit cell -

In a primitive unit cell, constituent particles are present only in the corner positions of the unit cell.

In the simple cubic cell, each point on a corner is shared by 8 unit cells.

Hence, the answer is option (3).

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