How to calculate packing efficiency of cubic unit cell of diamond ?

Diamond structure is ZnS type structure  in which carbon atoms forms  a face centred cubic (FCC/CCP) lattice as well as  four out of eight (50%) or alternate tetrahedral voids are occupied by carbon atoms. Every atom in this structure is surrounded tetrahedrally by four other. No discrete molecule can be discerned (identified) in diamond .the entire crystal is giant molecule a unit cell of which is shown as below.

Note : Only those atoms which form four covalent bond produce a repeated 3D structure using only covalent bonds.

Lattice of Diamond is ZnS type structure.

(1) C- form FCC/CCP (4-atoms)

(2) C- atoms present at the (50%) alternative tetrahedral voids (4-atoms)

(3) Total Number of one lattice unit is eight (8) hence molecular formula of diamond is (C8) (i.e. Z= 8)

(4) Number of C-C bond in lattice cell is = 4×4= 16

(5) Number of C-C bond per carbon atom is 16/8=2

(6) The distance between two Corbin atom is d_C-C = a√3/4 and the radius of carbon atom = dc-c/2 = r_c = a√3/2x4

(8) Packing efficiency (PE = π√3/10= 0.34 or 34%):

(9) Voids = 66 % 

Additional Information: 

Related Questions:

What are the normal spinel structures?

What are the inverse spinel structures?

How to calculate radius ratio of square Voids?

How to calculate radius ratio triangular voids?

How to calculate packing fraction or packing efficiency of two dimensional (2D) hexagonal packing solid atoms?

The coordination number of Al in the crystalline state of AlCl3 is .... (IIT-JEE 2009)

The number of hexagonal faces that are present in truncated octahedron is .... (IIT-JEE 2011)

What are structural information of Dimomd ?

In diamond, carbon atoms occupy FCC/CCP lattice point as well as alternate tetrahedral voids. If edge length of unit cell is 3.56pm, the radius of carbon atom is ?

The edge length of unit cubic cell of diamond is 356.7 pm and this cubic unit cell contains 8 carbon atoms calculate (A) Distance between two carbon atoms, assuming them to spheres in contact (B) Radius of carbon atoms (C) Fraction of the total volume that is occupied by the carbon atoms.

The edge length of unit cubic cell of diamond is 356.7 pm and this cubic unit cell contains 8 carbon atoms calculate (A) Distance between two carbon atoms, assuming them to spheres in contact (B) Radius of carbon atoms (C) Fraction of the total volume that is occupied by the carbon atoms.

 (A) Distance between two carbon atoms:

(B) Radius of carbon atoms:

(C) Fraction (Packing efficiency) of the total volume that is occupied by the carbon atoms:

Related Questions:

What are the normal spinel structures?

What are the inverse spinel structures?

How to calculate radius ratio of square Voids?

How to calculate radius ratio triangular voids?

How to calculate packing fraction or packing efficiency of two dimensional (2D) hexagonal packing solid atoms?

The coordination number of Al in the crystalline state of AlCl3 is .... (IIT-JEE 2009)

The number of hexagonal faces that are present in truncated octahedron is .... (IIT-JEE 2011)

What are structural information of Dimomd ?

In diamond, carbon atoms occupy FCC/CCP lattice point as well as alternate tetrahedral voids. If edge length of unit cell is 3.56pm, the radius of carbon atom is ?

In diamond, carbon atoms occupy FCC/CCP lattice point as well as alternate tetrahedral voids. If edge length of unit cell is 3.56pm, the radius of carbon atom is ?

 We know that in diamond structure the distance between two carbon atoms is

Related Questions:

What are different stacking pattern of atoms in simple cubic cell (SCC) , body cubic cell (BCC) and face centred cell (FCC) unit lattice cell ?

What is the effect of temperature and pressure on crystal structure of Caesium Chloride?

What is the number of atoms on one unit cell of HCP?

If the total number of atoms per unit cell in an hcp structure and a bcc structure gets halved, then ratio of percentage voids in hcp and bcc structures is

If silver iodide crystallizes in a zinc blende structure with I- ions forming the lattice then calculate fraction of the tetrahedral voids occupied by Ag+ ions.

Sodium metal crystallizes In body centered cubic lattice with the cell edge, a= 4.29 A.What is the radius of sodium atom? (III-.JEE 1994)

A metal crystallizes into two cubic phases, face centered cubic (fcc) and body centered cubic (bcc), whose unit cell lengths are 3.5 A° and 3.0 A°, rcspcctively. Calculate the ratio of densities of fcc and bcc. (IIT-JEE 1999)

A metallic element crystallizes into a lattice containing a sequence of layers ABABAB....Any packing of spheres leaves out voids in the lattice. What percentage by volume of this lattice is empty space? ( IIT-.IEF 2006)

The coordination number of Al in the crystalline state of AlCl3 is .... (IIT-JEE 2009)

The number of hexagonal faces that are present in truncated octahedron is .... (IIT-JEE 2011)

What are structural information of Dimomd ?

What are coordination number (nearest neighbour) in a BCC at distance of (a√3/2) and next nearest neighbour at distance (a) and next to next nearest neighbour at distance (a√2) ?.

What are coordination number (nearest neighbour) in a SCC at distance of it lattice parameter (a) and next nearest neighbour at distance (a√2) and next to next nearest neighbour at distance (a√3) ?.

Crystal lattice Structure of Oxides:

• (1) Spinel Structure: 
• (2) Corundum (Al2O3) type Structure:
• (3) Rutile (TiO2) type Structure:
• (4) Pervoskite (ABO3) type structure:

Related Questions:

What are different stacking pattern of atoms in simple cubic cell (SCC) , body cubic cell (BCC) and face centred cell (FCC) unit lattice cell ?

What is the effect of temperature and pressure on crystal structure of Caesium Chloride?

What is the number of atoms on one unit cell of HCP?

If the total number of atoms per unit cell in an hcp structure and a bcc structure gets halved, then ratio of percentage voids in hcp and bcc structures is

If silver iodide crystallizes in a zinc blende structure with I- ions forming the lattice then calculate fraction of the tetrahedral voids occupied by Ag+ ions.

Sodium metal crystallizes In body centered cubic lattice with the cell edge, a= 4.29 A.What is the radius of sodium atom? (III-.JEE 1994)

A metal crystallizes into two cubic phases, face centered cubic (fcc) and body centered cubic (bcc), whose unit cell lengths are 3.5 A° and 3.0 A°, rcspcctively. Calculate the ratio of densities of fcc and bcc. (IIT-JEE 1999)

A metallic element crystallizes into a lattice containing a sequence of layers ABABAB....Any packing of spheres leaves out voids in the lattice. What percentage by volume of this lattice is empty space? ( IIT-.IEF 2006)

The coordination number of Al in the crystalline state of AlCl3 is .... (IIT-JEE 2009)

The number of hexagonal faces that are present in truncated octahedron is .... (IIT-JEE 2011)

What are structural information of Dimomd ?

What are coordination number (nearest neighbour) in a BCC at distance of (a√3/2) and next nearest neighbour at distance (a) and next to next nearest neighbour at distance (a√2) ?.

What are coordination number (nearest neighbour) in a SCC at distance of it lattice parameter (a) and next nearest neighbour at distance (a√2) and next to next nearest neighbour at distance (a√3) ?.

How to calculate radius ratio of square Voids?

How to calculate radius ratio triangular voids?

How to calculate packing fraction or packing efficiency of two dimensional (2D) hexagonal packing solid atoms?

Corundum (Al2O3) type Structure:

This type structure is exhibited by oxides of trivalent metals for examples Fe₂O₃, Al₂O₃, Cr₂O₃, Mn₂O₃ etc.

General formula is M₂O₃:

In Corundum  Structure:

O^-2 = ions forms HCP unit cell:

M⁺³ = Occupied  2/3 (66.66%) of octahedral voids (OV): and 33.33% OV are empty and TVs are 100% empty.

In Hexagonal close packing (HCP): Formula determination:

O^-2 = HCP = O₆

M⁺³=2/3 x 6 = M₄

=M₄O₆  or  M₂O₃

Related Questions:

What are the normal spinel structures?

What are the inverse spinel structures?

What are different stacking pattern of atoms in simple cubic cell (SCC) , body cubic cell (BCC) and face centred cell (FCC) unit lattice cell ?

What is the effect of temperature and pressure on crystal structure of Caesium Chloride?

What is the number of atoms on one unit cell of HCP?

If the total number of atoms per unit cell in an hcp structure and a bcc structure gets halved, then ratio of percentage voids in hcp and bcc structures is

If silver iodide crystallizes in a zinc blende structure with I- ions forming the lattice then calculate fraction of the tetrahedral voids occupied by Ag+ ions.

Sodium metal crystallizes In body centered cubic lattice with the cell edge, a= 4.29 A.What is the radius of sodium atom? (III-.JEE 1994)

A metal crystallizes into two cubic phases, face centered cubic (fcc) and body centered cubic (bcc), whose unit cell lengths are 3.5 A° and 3.0 A°, rcspcctively. Calculate the ratio of densities of fcc and bcc. (IIT-JEE 1999)

A metallic element crystallizes into a lattice containing a sequence of layers ABABAB....Any packing of spheres leaves out voids in the lattice. What percentage by volume of this lattice is empty space? ( IIT-.IEF 2006)

The coordination number of Al in the crystalline state of AlCl3 is .... (IIT-JEE 2009)

The number of hexagonal faces that are present in truncated octahedron is .... (IIT-JEE 2011)

What are structural information of Dimomd ?

What are coordination number (nearest neighbour) in a BCC at distance of (a√3/2) and next nearest neighbour at distance (a) and next to next nearest neighbour at distance (a√2) ?.

What are coordination number (nearest neighbour) in a SCC at distance of it lattice parameter (a) and next nearest neighbour at distance (a√2) and next to next nearest neighbour at distance (a√3) ?.

Rutile (TiO2) type Structure:

This type of structure is represented by TiO₂ and other example are includes MnO₂ , SnO₂ , MgF₂, NiF₂ etc 

In Rutile structure:

O^-2  = ions forms hexagonal cubic packing (HCP).

M⁺⁴ =Tetravalent cations are occupied 50 % (1/2) of octahedral voids (OV) while all the tetrahedral voids (TO) are empty.

HCP= Lattice points (LP) = O^-2= 6

M⁺⁴ ions = OV (50%) =6 x 1/2 = 3

M₃O₆ = MO₂

It means each HCP unit cell certain three (M⁺⁴ ) and  six (O^-2 )ions

Related Questions:

What are the normal spinel structures?

What are the inverse spinel structures?

What are different stacking pattern of atoms in simple cubic cell (SCC) , body cubic cell (BCC) and face centred cell (FCC) unit lattice cell ?

What is the effect of temperature and pressure on crystal structure of Caesium Chloride?

What is the number of atoms on one unit cell of HCP?

If the total number of atoms per unit cell in an hcp structure and a bcc structure gets halved, then ratio of percentage voids in hcp and bcc structures is

If silver iodide crystallizes in a zinc blende structure with I- ions forming the lattice then calculate fraction of the tetrahedral voids occupied by Ag+ ions.

Sodium metal crystallizes In body centered cubic lattice with the cell edge, a= 4.29 A.What is the radius of sodium atom? (III-.JEE 1994)

A metal crystallizes into two cubic phases, face centered cubic (fcc) and body centered cubic (bcc), whose unit cell lengths are 3.5 A° and 3.0 A°, rcspcctively. Calculate the ratio of densities of fcc and bcc. (IIT-JEE 1999)

A metallic element crystallizes into a lattice containing a sequence of layers ABABAB....Any packing of spheres leaves out voids in the lattice. What percentage by volume of this lattice is empty space? ( IIT-.IEF 2006)

The coordination number of Al in the crystalline state of AlCl3 is .... (IIT-JEE 2009)

The number of hexagonal faces that are present in truncated octahedron is .... (IIT-JEE 2011)

What are structural information of Dimomd ?

What are coordination number (nearest neighbour) in a BCC at distance of (a√3/2) and next nearest neighbour at distance (a) and next to next nearest neighbour at distance (a√2) ?.

What are coordination number (nearest neighbour) in a SCC at distance of it lattice parameter (a) and next nearest neighbour at distance (a√2) and next to next nearest neighbour at distance (a√3) ?.

Pervoskite (ABO3) type structure:

ABQ₃ is a proto type solid where A is a divalent cation  and B is a tetravalent cation.

A⁺² = Divalent cations

B⁺⁴ =Tetravalent cations

In Pervoskite structure:

A⁺² = placed at corner of cubic unit cell

O^-2 = placed at all the face centre

That means A⁺² and O^-2 ions combinelly form CCP/FCC like structure  and

B⁺⁴ = Tetravalent cations occupy the central octahedral voids (25% of total OV) i.e centre of the centre of the unit cell so general formula is ABO₃

Other examples are BaTiO₃, SrTiO₃

Related Questions:

What are the normal spinel structures?

What are the inverse spinel structures?

What are different stacking pattern of atoms in simple cubic cell (SCC) , body cubic cell (BCC) and face centred cell (FCC) unit lattice cell ?

What is the effect of temperature and pressure on crystal structure of Caesium Chloride?

What is the number of atoms on one unit cell of HCP?

If the total number of atoms per unit cell in an hcp structure and a bcc structure gets halved, then ratio of percentage voids in hcp and bcc structures is

If silver iodide crystallizes in a zinc blende structure with I- ions forming the lattice then calculate fraction of the tetrahedral voids occupied by Ag+ ions.

Sodium metal crystallizes In body centered cubic lattice with the cell edge, a= 4.29 A.What is the radius of sodium atom? (III-.JEE 1994)

A metal crystallizes into two cubic phases, face centered cubic (fcc) and body centered cubic (bcc), whose unit cell lengths are 3.5 A° and 3.0 A°, rcspcctively. Calculate the ratio of densities of fcc and bcc. (IIT-JEE 1999)

A metallic element crystallizes into a lattice containing a sequence of layers ABABAB....Any packing of spheres leaves out voids in the lattice. What percentage by volume of this lattice is empty space? ( IIT-.IEF 2006)

The coordination number of Al in the crystalline state of AlCl3 is .... (IIT-JEE 2009)

The number of hexagonal faces that are present in truncated octahedron is .... (IIT-JEE 2011)

What are structural information of Dimomd ?

What are coordination number (nearest neighbour) in a BCC at distance of (a√3/2) and next nearest neighbour at distance (a) and next to next nearest neighbour at distance (a√2) ?.

What are coordination number (nearest neighbour) in a SCC at distance of it lattice parameter (a) and next nearest neighbour at distance (a√2) and next to next nearest neighbour at distance (a√3) ?.

How to calculate radius ratio of square Voids?

How to calculate radius ratio triangular voids?

How to calculate packing fraction or packing efficiency of two dimensional (2D) hexagonal packing solid atoms?