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What are Miller indices ? Determine the miller indices of a plane that makes an intercept of 1 on x axis, 2 on y axis and is parallel to z axis.

Consider a BCC lattice of identical atoms having radius R. Compute i) the number of atoms per unit cell, ii) the coordination number and iii) the packing fraction.

X - rays with a wavelength of 1.54 Angstrom are used to calculate the spacing of ( 2,0,0 ) planes in aluminium. The Bragg angle for this reflection is 22.4 degree. What is the size of the unit cell of the aluminium crystal ?

Show that the packing fraction in FCC is more than in the BCC structure.

Explain in brief how Bragg's law is useful in the analysis of the crystal structure.

Show that the FCC structure possesses maxium packing density among the three crystal structures SC, BCC and FCC.

The radius of the Polonium atom is 1.68 Angstrom and it belongs to simple cubic (SC) lattice system. If its atomic mass is 209 kg/k-mol, calculate density.

Explain the concept of space lattice. How is crystal structure of a crystal related to its space lattice ?

Consider a body centered cubic (BCC) crystal formed by identical atoms having a radius R. Determine the number of atoms per unit cell, the coordination number and the atomic packing fraction.

Nickel is characterized by a FCC lattice. The edge of the unit cell is 3.52 Angstrom. The atomic weight of nickel is 58.71 kg/k-mol. Determine the density of the metal.

Show that for BCC and FCC crystal structures, the lattice constants are given by 4r/(square root of 3) and 4r/(square root of 2) respectively, where the symbols have their usual meaning.

What are Miller indices ? Explain with example.

Gold with atomic radius 1.44 Angstrom and FCC structure is being used to determine the wavelength of X - rays. Calculate the wavelength of X - rays if the ( 1,1,1 ) plane diffracts the beam by 32.1 degree. Assume first order diffraction.

Which type of the cubic crystal structure has closest packing of atoms ? How many nearest neighbours does an atom in this type of crystal have ? Derive the relation between the atomic radius and the unit - cell dimension of this crystal.

The lattice constant of BCC iron at 20 degree centigrade is 2.87 Angstrom. The density of iron is 7870 kg/cubic metre. Determine its atomic mass.

State and prove Bragg's law of X - ray diffraction.

Find Miller indices of a set of planes with intercepts a, 2a and 3a on x, y and z axes respectively for a cubic crystal. Draw [1,2,0] plane.

Show that the FCC structure possesses maximum packing density and minium percentage of void space among the three crystal structures SC, BCC and FCC. Also find the density of crystals with this structure in terms of lattice constant.

Calculate the longest wavelength that can be analysed by rock - salt crystal of spacing 2.82 Angstrom in the first order. Explain the principle used for this.

Fill in the blanks :-
(i) The relation between atomic radius (r) and unit cell dimension (a) for FCC structure is ______.
(ii) The coordination number for a typical BCC structure is ______.
(iii) The atomic packing fraction for a simple cubic structure is ______.
(iv) The percent void space for the BCC structure is ______.

Sodium chloride has a FCC structure. The density of sodium chloride is 2180 kg/cubic metre. If the atomic weight of sodium is 23 and that of chlorine is 35.5, calculate the distance between two adjacent atoms.

What are Miller indices ? Show schematically the principal planes (1,0,0), (1,1,0) and (1,1,1) for simple cubic structure.

Deduce relation between an interplaner distance d and the Miller indices of the planes for cubic crystal.

Draw SC, BCC and FCC unit cells showing the coordinates of the atoms in these unit cells.

Obtain an expression relating the wavelength of the X - rays to the angular positions of the scattered beams and the separation of atomic planes in the crystal. Can a natural crystal be used to diffract light rays ? If not, why ?

What do you understand by Miller indices of a crystal plane ? Obtain an expression for interplaner spacing in cubic crystals.

Explain and deduce Bragg's law for X - ray diffraction.

Lead is FCC with an atomic radius r = 1.746 Angstrom. Find the spacing of :-
(i) (2,0,2) planes, (ii) (2,2,0) planes and (iii) (1,1,1) planes.

Define coordination number.

Explain and deduce Bragg's law for X - ray diffraction.

Show that the SC structure possesses a minimum percentage of packing density and maximum percentage of void space among the three cubic crystal structures.

Determine lattice constant for FCC lead crystal of radius 1.746 Angstrom. Also find the spacing of
(i) (1 1 1) planes, (ii) (2 0 0) planes and (iii) (2 2 0) planes.

Draw the following planes in a cubic unit cell :-
(112) and (120) plane.

Copper has FCC structure and atomic radius is 0.1278 nm. calculate the interplaner spacing for (1 1 1) plane and (3 2 1) plane.

Compare the unit cell properties of SC, BCC and FCC unit cell.

Derive Bragg's law of X - ray diffraction. State one of the applications of X-ray diffraction technique.

Sodium crystallizes in a cubic lattice. The edge of the unit cell is 4.3 A⁰. The density of sodium is 963 kg / m³ and its atomic weight is 23 kg / k.mol. How many atoms are contained in one unit cell ? What type of cubic unit cell does sodium form ?