Question 1. 

Part (a)

(i)  Discuss how transmission electron microscopy (TEM) can provide information complementary to that which can be obtained from standard X-ray or neutron diffraction methods, giving suitable examples.

(ii)  The intensity of a Bragg reflection is given by:

Briefly explain the origin of each term clearly stating which provide information about the material measured.

Part (b)

(i) MgO crystallises in a face centred cubic lattice.  Two possible crystal structures are Rocksalt (motif Mg: 0,0,0 & O: ½,½,½) and Zinc blende (motif Mg: 0,0,0 & O: ¼,¼,¼).Given that for the allowed Bragg

reflections :

Derive general expressions for |F_hkl|² for both structures in terms of the atomic scattering factors and Miller indices.  Show that this can be reduced to the following expressions for the following sets of Bragg peaks:

(ii) The observed ratio of the intensities of the (420) and (331) Bragg peaks is ~6.5.  The values of the atomic X-ray scattering factors are f_Mg = 4.6, f_O = 2.2 for the 420 reflection and  f_Mg = 4.8, fO = 2.2 for the 331 reflection, you may ignore other contributions to the angular dependence of the intensity.  Both reflections have the same multiplicity.  What is the structure of MgO?

(iii) The figure  bellow shows  the 29 Si MAS NMR spectrum of  a number of silicate minerals. In each case the four coordinate net is contained within the curly brackets.  Given that cristobalite contains only silicon next nearest neighbours, comment on the degree silicon to aluminium order and potential arrangements in the remaining examples.

Part (c)

Using the following defect equilibria, construct a Brouwer diagram for AgI. Assume that the concentration of Frenkel defects is significantly greater than that of electrons and holes in the stoichiometric compound.

Question 2.

Part (a)

TiO₂ crystallises in a tetragonal cell, with atoms at positions Ti 0,0,0 and ½,½,½ O at x,x,0  -x,-x,0 ½+x,½-x,½ and ½-x,½+x,½ Given: 

Derive a general expression for the scattering factor, you may find the following useful:

Part (b)

Given the systematic absences for the tetragonal system  on the next two pages deduce the space group.

cos a ( ) = cos -a ( )
sin -a ( ) = -sin a ( )
cos a + b ( ) = cos a ( ) cos b ( ) - sin a ( ) sin b ( )
sin a + b ( ) = sin a ( ) cos b ( ) + cos a ( ) sin b ( )