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Two suitcases, packed by two people are here. You can guess which was packed by whom?
The point to note is that the neatly packed suitcase holds much more dresses and in a neat manner for ready use after than the unorganized loosely filled suitcase.
The below image shows a certain number of balls stacked over the gaps. They are arranged in a way to minimize the empty spaces between the balls and maximum utility of the available space in the box to accommodate more number of balls in the box.
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In crystalline solids, the constituent particles are close-packed, leaving very less vacant spaces. In measuring the efficiency of packing, the particles are assumed to be spheres of identical size.
Let us understand close packing in 1D, 2D, and 3D.
Close packing in 1-D
There is only one way of arranging spheres in a one-dimensional, close-packed structure, which is to arrange them in a row touching each other. Each sphere in this configuration is in contact with two of its neighbours. A particle's coordination number is the sum of its nearest neighbours' numbers. Thus, in one-dimensional close-packed arrangement, the coordination number is 2.
In a one-dimensional, tightly packed structure, there is only one way to arrange spheres, and that is to arrange them in a row touching one another. In this arrangement, each sphere has two neighbours with whom it can make contact. The coordination number of a particle is equal to the sum of the numbers of its closest neighbours. Therefore, the coordination number in a one-dimensional close-packed arrangement is two.
Close packing in 2-D
A two-dimensional, close-packed structure can be generated by placing rows of close-packed spheres next to one another,
By arranging rows of closely packed spheres next to each other, a two-dimensional structure can be created. say on a table. The arrangement of spheres is done by stacking the rows of closely packed spheres in two possible ways.
● Square close packing
● Hexagonal close-packing
The spheres of the second row are placed in contact with the first one such that the spheres of the second row are exactly parallel to those of the first row. The spheres of the two rows are aligned along length and breadth of a square at right angle. If we call the first row an A-type row, then the second row, being exactly the same as the first one, is also of A type. Similarly, we can place more rows to obtain an AAA type of arrangement.
The second row's spheres are positioned in close proximity to the first row so that they are perfectly parallel to one another. The spheres of the two rows are at a right angle alignment along the length and width of a square. If the first row is an A-type row, then the second row is also an A type row because they are identical to one another. Similarly, we can add more rows to create an arrangement resembling AAA.
Each sphere in this configuration is in contact with four of its neighbours. As a result, the coordination number in two-dimensional square close packing is 4, and a square is created by joining the centres of these four immediately adjacent spheres. Hence, this packing is known as square close packing in two dimensions.
The arrangement here places four of each sphere's neighbours in contact with it. Because of this, the coordination number for two-dimensional square close packing is four, and a square is formed by connecting the centres of these four immediately adjacent spheres. The two-dimensional term for this packing is square close packing.
In this close packing, the second row is placed in the gap of the first row in a staggered manner such that its spheres fit in the depressions of the first row.
In this close packing, the second row is arranged in the opening left by the first row in a staggered fashion so that its spheres fit in the depressions of the first row.
They can be obtained by stacking two-dimensional layers one above the other The different ways of forming 3D close packing are given as follows:
a) From 2D square close packing
b) From 2D hexagonal close packing
c) BCC close packing
From 2D square close packing
From 2D Hexagonal close packing
A three-dimensional close-packed structure can be generated by placing 2D hexagonal close-packed layers one over the other.
By stacking 2D hexagonal close-packed layers on top of one another, a three-dimensional close-packed structure can be created.
It can be observed that all the triangular voids of the first layer are not covered by the spheres of the second layer.
It is clear that the spheres of the second layer do not completely enclose all of the triangular voids of the first layer. Here, out of the six voids/depressions around each sphere (in one hexagonal unit cell) in the first layer A, only three are directly covered by placing spheres of the second layer B.
putting the third layer on top of the second
When the third layer is placed over the second layer, there are two possibilities, which are given as follows:
● Covering tetrahedral voids
● Covering octahedral voids
Covering tetrahedral voids
Tetrahedral voids of the second layer (blue) may be covered by the spheres of the third layer (yellow). In this case, the spheres of the third layer are exactly aligned with those of the first layer. As a result, the sphere pattern is repeated in alternate levels. ABAB... pattern is a common way to write this pattern. The acronym HCP stands for hexagonal tightly packed structure. Many metals, including magnesium and zinc, have this kind of atom arrangement.
The spheres of the third layer may cover the tetrahedral voids of the second layer (blue) (yellow). In this instance, the spheres from the third and first layers are perfectly lined up. The result is that alternate levels of the sphere pattern are repeated. This pattern is frequently written as the ABAB... pattern. Hexagonal closely packed structure is referred to by the abbreviation HCP. This type of atom arrangement can be found in many metals, such as Mg and Zn.
There are two types of voids, and they are as follows:
(i) Tetrahedral void
(ii) Octahedral void
Tetrahedral voids
If the sphere of layer B (second layer) is placed over the triangular void of layer A (first layer), the type of void formed is known as a tetrahedral void. A sphere placed in the void will touch four spheres, three from the first layer and one from the second layer, forming a tetrahedral structure.
Octahedral void
Octahedral void
If the triangular void of layer B is placed above the triangular void of the layer A, the void formed is known as an octahedral void.
In this figure, we can see that triangular void formed by three blue spheres of one layer stacked above the triangular void formed by the three red spheres of another layer, forming an octahedral void.
A unit cell is obtained by finding the repeating units or arrangements which, on repeating in every direction, forms the HCP packing.
Drawing hexagons of the first layer and continuing it in every direction forms layer A. In the next layer B, the spheres forming a triangle (as shown by three blue spheres) are the repeating units.
The unit cell is then obtained by joining the hexagonal repeating units of the two A layers with the triangular repeating units of B layer in between them. The obtained unit cell is known as a hexagonal
close packing unit cell.
Coordination number of spheres in HCP:
Placing the third layer
The completely different arrangement of red, yellow, and blue spheres one over the other forms an ABCABC pattern, the red spheres (A), followed by the blue spheres (B), and then the yellow spheres (C) from the bottom.
● The packing in Ca, Sr, Cu, Ag, Au, etc., follows this type of arrangement.
Unit cell in Cubic close packing
Let us consider that a sphere in the first layer (A) is in the corner and the spheres of layer B, which are above the sphere of layer A, are at the face centre of the faces of the unit cell and also at the corner. The other face centres are occupied by the spheres of layer C and even some corner are also occupied by layer C. Finally, the last corner is occupied by the sphere of another layer A, forming an FCC unit cell.
Coordination of particles in FCC
Body Centred Close packing (BCC)
Q1. In which of the following states of matter constituent particles are absolutely closely packed?
A. Solid
B. Liquid
C. Gas
D. Plasma
Answer: (A)
Solution: In solid state, the constituent particles are closely packed and held together by strong force of attraction between them. The constituent particles only oscillates to their mean position. Hence, solids have a definite shape and volume.
The constituent particles of a solid are tightly packed and held together by a strong force of attraction. Only oscillation at the mean position is allowed for the constituent particles. Solids, therefore have a distinct shape and volume.
Q2. What will be the coordination number, if the particles are arranged in one dimensional close packing?
A. 1
B. 2
C. 3
D. 4
Answer: (B)
Solution: The constituent particles are arranged in a row in one dimensional close packing, each particles are in contact with two other particles. Hence, the coordination number in one dimensional close packing is 2.
Each constituent particle is in contact with two other particles and is arranged in a row in a one-dimensional close packing. Consequently, in one-dimensional close packing, the coordination number is two.
Q3. In how many ways, you can arrange two particles to get a two dimensional close packing?
A. 3
B. 1
C. 2
D. 5
Answer: There are two ways through which we can generate two dimensional close packing from one dimensional close packing
We can create two-dimensional close packing from one-dimensional close packing in two different ways.
Hence, correct option is C
Q4. Voids in two-dimensional hexagonal close packed structure are ___________ in shape.
A. rectangular
B. triangular
C. hexagonal
D. circular
Answer: When one row of a one-dimensional structure is placed below another in such a way that the spheres of the second row fit into the depressions of the first row, generating triangular voids between them, a two-dimensional hexagonal close packed structure is generated.
A two-dimensional hexagonal close packed structure is created by stacking rows of a one-dimensional structure so that the spheres of the second row fit into the depressions of the first row, creating triangular voids between them.
Corect option is C.
Q1. Which close packing arrangement is the most efficient one?
Answer: In both cubic and hexagonal closest packing, the arrangement efficiently takes up 74 percent of the space. The second layer of spheres is placed on half of the depressions of the previous layer, similar to hexagonal closest packing.
Q2. Are FCC and CCP similar?
Answer: Face Centered Cubic (FCC) and Cubic Close Packed (CCP) are two more names for the same lattice.
Q3. Which metal shows hexagonal close packing?
Answer: Titanium, zirconium, magnesium, and other hexagonal close-packed (HCP) metals and alloys are widely employed in a range of industrial industries.
Q4. What does "close packing" in solid structures mean?
Answer: The packing is done so that the constituent particles will leave the least amount of vacant space between them by utilizing the maximum amount of space that is available. Closed packing is the name for this style of packaging.