Lecture 2 : Crystal lattices and unit cell ; Number of atoms in a unit cell ; Packing In Solids: One And Two Dimensions

Show that in a cubic close packed structure, eight tetrahedral voids are present
per unit cell.

With the help of a labelled diagram show that there are four octahedral voids
per unit cell in a cubic close packed structure.

Match the type of packing given in Column I with the items given in Column II.
Column I                                                           Column II
(i) Square close packing in                                      (a) Triangular voids
two dimensions
(ii) Hexagonal close packing                                    (b) Pattern of spheres is repeated in
in two dimensions every fourth layer
(iii) Hexagonal close packing in                                (c) Coordination number 4
three dimensions 
(iv) Cubic close packing in                                       (d) Pattern of sphere is repeated in
three dimensions alternate layers

Match the items given in Column I with the items given in Column II.
Column I                                                                 Column II
(i) Mg in solid state                                                   (a) p-Type semiconductor
(ii) MgCl2 in molten state                                            (b) n-Type semiconductor
(iii) Silicon with phosphorus                                          (c) Electrolytic conductors
(iv) Germanium with boron                                         (d) Electronic conductors

Match the type of unit cell given in Column I with the features given in
Column II.
Column I                                                     Column II
(i) Primitive cubic unit cell                        (a) Each of the three perpendicular
edges compulsorily have the different
edge length i.e; a≠b≠c.
(ii) Body centred cubic unit cell                    (b) Number of atoms per unit cell is one.
(iii) Face centred cubic unit cell                    (c) Each of the three perpendicular
edges compulsorily have the same
edge length i.e; a = b = c
(iv) End centred orthorhombic                        (d) In addition to the contribution from
unit cell the corner atoms the number of atoms
present in a unit cell is one.
                                                             (e) In addition to the contribution from
the corner atoms the number of
atoms present in a unit cell is three.

Note : In the following questions match the items given in Column I with
the items given in Column II. In some questions more than one item of
Column I and Column II may match.

 Match the defects given in Column I with the statements in given Column II.
Column                                                          I Column II
(i) Simple vacancy defect                                  (a) shown by non-ionic solids and
increases density of the solid.
(ii) Simple interstitial defect                            (b) shown by ionic solids and decreases
density of the solid.
(iii) Frenkel defect                                        (c) shown by non ionic solids and density
of the solid decreases
(iv) Schottky defect                                      (d) shown by ionic solids and density of
the solid remains the same.

In a compound, nitrogen atoms (N) make cubic close packed lattice and metal
atoms (M) occupy one-third of the tetrahedral voids present. Determine the
formula of the compound formed by M and N?

Calculate the number of atoms in a cubic unit cell having one atom on each corner and two atoms on each body diagonal.

Gold crystallizes in an FCC unit cell. What is the length of a side of the cell(r=0.144mm)

Explain

(i) The basis of similarities and differences between metallic and ionic crystals.

(ii) Ionic solids are hard and brittle.

Name the parameters that characterize a unit cell.

Give the significance of a 'lattice point'.