How many nearest neighbours are there for an atom in a hexagonal close-packed crystal structure?

Assign the Bravais lattice type for the following unit-cell structure.

What are the Miller indices of the following planes?

The mineral forsterite, Mg₂SiO₄, has an orthorhombic crystal structure with lattice parameters a = 4.762 Å, b = 10.225 Å and c = 5.994 Å.  Calculate the separation of the (121) lattice planes.

The spacing between the (220) planes of spinel, MgAl₂O₃, is 2.86 Å.  Calculate the glancing angle at which diffraction would be observed from these planes if CoK_a1 radiation of energy 6932 eV is used as the X-ray source. 

In an experiment to determine the unit-cell dimensions of magnetite, Fe₃O₄, which has a cubic crystal lattice, CuK_a radiation of wavelength 154 pm was used to record the X-ray diffraction pattern.  Diffraction was observed from the (200) planes at a glancing angle of 10.6°.  Calculate the unit cell parameter. 

Use the following data to calculate the lattice enthalpy at 298 K of iron (III) oxide, Fe₂O₃(s).  All values refer to a temperature of 298 K.

Enthalpy of sublimation of Fe(s): +370 kJ mol^–1

First ionization enthalpy of Fe(g): +768 kJ mol^–1
Second ionization enthalpy of Fe(g): +1566 kJ mol^–1

Third ionization enthalpy of Fe(g): +2960 kJ mol^–1

Enthalpy of dissociation of O₂(g): +498 kJ mol^–1

Enthalpy of electron attachment to O(g): –141 kJ mol^–1
Enthalpy of electron attachment to O^–(g): +844 kJ mol^–1

Enthalpy of formation of Fe₂O₃(s) from Fe(s) and O₂(g): –824 kJ mol^–1

Use the following data to calculate the lattice enthalpy at 298 K of potassium iodide, KI(s).  All values refer to a temperature of 298 K.

Enthalpy of sublimation of K(s): +81 kJ mol^–1

Ionization enthalpy of K(g): +418 kJ mol^–1

Enthalpy of atomization of I₂(g): +214 kJ mol^–1

Enthalpy of electron attachment to I(g): –295 kJ mol^–1

Enthalpy of formation of KI(s) from K(s) and ½I₂(g): –328 kJ mol^–1

Use the Born–Mayer equation to estimate the lattice energy of zinc blende, ZnS, given that the distance between the nearest neighbour ions in the crystal is 2.343 Å.  The Madelung constant for a zinc blende structure is 1.638.

The electrical conductivity of a new material was measured at different temperatures and found to vary as below.  What is the best description of the conduction properties of the material?