unit cell of crystal lattice

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Crystal lattice or three dimensional lattice

The regular arrangement of the constituent particles in a crystalline solid is called stereoscopic lattice or crystal lattice.

 

Unit Cell :-

The smallest unit of the whole crystalline number whose repeating the same number of times in all directions reproduces the crystal structure is called unit cell.

Characteristics of a unit cell:-

(1) The three dimensions of a unit cell are shown by a, b, c, this param may or may not be perpendicular to each other.

(2) The angles between the three angles of a unit cell are represented by alpha, beta, gamma.
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Hence, a unit cell is represented by 6 parameters a,b,c,alpha,beta,gamma

Types of Unit Cells :- It is divided into two parts
(1) primitive or simple unit cell (2) centered unit cell\

(1) Primal or Simple Unit Cell :- The unit cell in which the constituent particles are located at the corners is called primitive or simple unit cell.

 

In this, 8 constituent particles are present at 8 angles of the unit cell and the contribution of each particle is (1 x 8) for one of its cells.

So total number of constituent particles = 8×[1/8】= 1 particle

 

(2) Centered Unit Cell :- The unit cell in which the constituent particles are present at positions other than the corners is called concentrated unit cell.
It is divided into three parts.

(1) Intracentred/Body Centered Unit Cell (BCC)
(2) Face Centered Unit Cell (FCC)
(3) End Centered Unit Cell (ECC)

(1) Intracentred/Body Centered Unit Cell (BCC) :- The unit cell in which the constituent particles are located at the center other than the corners is called intermolecular unit cell.

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In this, 8 constituent particles are present at the 8 corners of the unit cell, whose contribution is 8×[⅛]=1 and the contribution of the particle at the center is 1, so the total number of constituent particles in the unit cell is 2.

(2) Face Centered Unit Cell (FCC) :- The unit cell in which the constituent particles are located at the center of each face except at the corners is called face centered unit cell.

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In this, eight particles are present at the eight corners of the unit cell, whose contribution is 8×(⅛) = 1 and the contribution of the particles located at the center of all the 6 faces is 6×(1/2/) =3

Hence, the total number of constituent particles in the unit cell is 4.

(3) End-centered unit cell (ECC) :- The unit cell in which the constituent particles are located on any two opposite faces other than the corners is called end-centered unit cell.

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In this, 8 constituent particles are present at 8 corners of the unit cell, the contribution of the day is 8×[⅛] =1 and the contribution of the angles at the center of the two opposite faces is 2×(1/2) =1 so the unit cell is The total number of constituent particles in

Nibid Congestion (C.P) : – During crystal formation, the constituent particles are arranged in such a way that there is minimum free space between them so that the density is high and stability is high.

Seamless packaging is divided into three parts
A – one dimensional seamless packaging
B – two dimensional smooth packaging
C – three dimensional smooth packaging

A – One Dimensional Neighboring Condensation :- In this type of seamless packaging the constituent particles (sphere) are arranged in a line in such a way that one sphere touches the other two adjacent spheres, hence the packaging capacity of this smooth packaging is 2.

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B – Two dimensional unidirectional packaging :- Two dimensional unidirectional packaging is divided into two parts
(1) square – seamless packaging
(2) hexagonal smooth packing

(1) Square-Nibid packaging : – In this type of seamless packaging, the second row is placed on the first row in such a way that the shells of the second row are located immediately above the circles of the first row, similarly other rows are kept.

If the first row is called A, then the second, third and other rows will also be called A.
So AAAA…….. some sort of arrangement is obtained
In this arrangement, each sphere touches four adjacent spheres whose centers are joined to form a square, hence it is called a square-neighboring complex.
The coordination number of this smooth packaging is 4.

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(2) Hexagonal Nimble Compression : – In this type of smooth packaging, the second row is arranged on the first row in such a way that the shells of the second row come in the depression (trough) made of the first row’s balls, in this case the shells of both the rows do not lie in a line
If the arrangement of the first row is called A, then the arrangement of the second row is called B.
The third row is called A because of its similarity to the first row, thus the arrangement of ABABAB….. is obtained.

In the same arrangement, a sphere touches other 6 adjacent spheres whose centers are joined to form a hexagon. The coordination number of such a smooth clustering is 6.

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C – three dimensional smooth packaging : – This type of smooth packaging is obtained as follows

(1) Two-dimensional square, three-dimensional, non-contiguous packaging of layers: – In this type of non-uniform packaging, the second layer is placed on the first layer in such a way that the shells of the second layer are located just above the first layer, in this way other layers also are kept
If the first layer is called A, then the second layer will also be called A.
So AAAAAA…… type of arrangement is obtained.

The lattice thus obtained is called simple cubic lattice and its unit cell is called simple cubic unit cell.

 

(2) Two-dimensional Hexagonal Nimble Packed Layers with Three Dimensional

Nimble Complexes :- In this nimble packaging, the layers can be arranged as follows

(1) Laying the second layer on the first layer : – The second layer is placed on the first layer in such a way that the shells of the second layer are placed on the shell of the first layer in such a way that the shells of the second layer are formed by the depression ( get into the trough
In this case, the spheres of the two layers are not on the same line.

Therefore, if the arrangement of the properties of the first layer is called A, then the arrangement of the spheres of the second layer is called B.
In this arrangement tetrahedral spacing (hole) as well as octahedral spacing are obtained.

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Laying the third layer on the second layer :- They are kept in two ways

(1) – Covering of tetrahedral voids – The third layer is placed on the second layer in such a way that the spheres of the third layer lie just above the tetrahedral voids, in this case the arrangement of the spheres of the third layer is the same as that of the first layer, hence the third layer will be called A, in this way, these layers are repeated in an alternate order, which gives ABABAB… is 74%
e.g. mg and zn

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Covering of octahedral voids : – The third layer is placed on the second layer in such a way that the shells of the third layer completely cover the octahedral voids of the second layer
In this situation, the third layer, the second layer, the spheres of the first layer are not in a line, that is, the arrangement of the three layers is different, so if the arrangement of the spheres of the third layer is called C, then the structure of ABCABCABC… would be obtained. This structure is called Cubic Nict Balanced Structure (ccp) or Face Centered Nict Complex Structure (fcc).

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