The directional bond angle in
diamond is 109.50. The
structure of diamond is better known as diamond cubic (DC). Unit cell of a DC is shown in figure. It contains a total of
18 atoms. Of these, 8 are placed on corners of the cube, one on each of the six
faces and four completely inside. The two inside atoms are placed at
three-fourth (3/4) and other two at one-fourth (1/4) distance above the base
when the height of unit cell is unity i.e. 1. These four atoms are placed on body
diagonal, and are not the lattice points.
Diamond is the hardest known solid. Its hardness on
Moh’s scale is 10. Other geometrical details are given as below:
Besides diamond, the DC structure also exists in
silicon, germanium, grey tin ect.
Q.11. Discuss the crystal structure of sodium
chloride and cesium chloride.
Ans. Structures of sodium chloride and cesium
chloride:-
Sodium
chloride (NaCl) is an ionic solid having BCC structure. In electrical
engineering applications, it is use in glazing of dielectrics. Besides, it is
used in washing soda, soap and preparation of freezing mixture. The cation in
this structure is sodium (Na) and the anion is chlorine (Cl).
Sodium forms positive and chloride forms negative
ions in the structure of sodium chloride. The ions are arranged alternately.
Each ion is surrounded by equal number of ions of the opposite sign. The exact
number of surrounding ions is decided by the relative sizes of the ions. The
ionic radius of Cl- is 
while that of Na+
is . Only 6 Cl- ions can be
surrounded by one Na+ ion. The central Cl- ion is
surrounded by 6 Na+ ions
at the centres of the cube faces. A close inspection reveals that two FCC
structures are superimposed. The scheme is shown in figure.
while that of Na+is . Only 6 Cl- ions can be
surrounded by one Na+ ion. The central Cl- ion is
surrounded by 6 Na+ ions
at the centres of the cube faces. A close inspection reveals that two FCC
structures are superimposed. The scheme is shown in figure.
Structure of cesium chloride (CsCl) is similar to
NaCl with the exception that ions are nearly of the same size which is not the
case with NaCl. Hence 8 Cl- ions
can be packed around each Cs+ ion to form a BCC structure. CsCl is not
strictly BCC as its centre and corner atoms are different. Structure of a unit
cell of CsCl is shown in figure. In it, chlorine atoms are placed on eight
corners and cesium atom is placed at the centre.
Structures of other simple ionic solids such as MgO,
BaO, SrO, CaO, CaF2 (calcium
fluoride), NaF, NaBr and NaI ect. are of
NaCl type. Halides such as LiCl, LiBr, LiI adopt NaCl type structure
having coordination number = 6.
Q.12. What is primitive cell? (AKTU. 2013-14)
Ans. A primitive cell is a unit cell built on the primitive basis of the direct lattice, namely a crystallographic basis of the vector lattice L such that every lattice vector t of L may be obtain as an integral linear combination of the basis vector a, b, c.
Q.13. Determine inter-planer spacing of a
lattice plane in a simple cubic lattice with edge 2
which cuts the axes in intercepts ratio 3:4:5. (AKTU. 2013 - 14)
which cuts the axes in intercepts ratio 3:4:5. (AKTU. 2013 - 14)
Ans. The
inter planer spacing of the lattice plane is
Q.9. What do you understand by transition
temperature? (AKTU. 2015 - 16)
Ans. Transition
temperature is the temperature at which a material changes from one crystal
state (allotrope) to another. For example, when rhombic sulfur is heated above
95.6°C it changes form into monoclinic sulfur. When cooled below 95.6°C it
reverts to rhombic sulfur.
In the case of ferroelectric or ferromagnetic
crystals a transition temperature may be known as the Curie temperature.
