Structures of Simple Inorganic Solids

Dr S.J. Heyes

Problem Set from the 1st Year Inorganic Chemistry Course

Michaelmas Term 1999 / Hilary Term 2000

If you have any comments please contact stephen.heyes@chem.ox.ac.uk

Problems Set.

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Questions

1.

• Draw a perspective sketch of a unit cell of the cubic close-packed structure, consisting of spheres of only one size.

   

• Indicate the orientation of the close-packed layers in your diagram. What is the stacking sequence of close-packed layers?

   

• Calculate the percentage of the total volume which is occupied by spheres.

   

• Describe other crystal structures that can be formed by the packing of equal spheres.

   

• Show by means of a sketch the positions of octahedral and tetrahedral holes in a cubic close-packed lattice.

   

• Give examples of binary compounds which exhibit structures where some or all of these octahedral and/or tetrahedral holes are filled by another element.

2.

Compare and contrast the structures of the following pairs of solids. Include descriptions of the structures and particularly discuss the reasons for their adoption.

(a) NaCl & CsCl.

(b) NiO & NiAs.

(c) TiO₂ (Rutile) & CdI₂.

(d) ZnS (Zinc Blende) & BeO.

(e) C (Diamond) & C (Graphite).

 

3.

• Differentiate clearly between the terms lattice and crystal structure.

• What structures might you expect the following compounds to adopt. Give your reasons.
  • SrCl₂
  • ZnO
  • CoTe
  • MgO
  • Cs₂O

• Plans of unit cells of several common A_nB_m crystal structures are shown below

  {viewed down the c-axis in each case. Heights of the atoms above the z = 0 plane are expressed as fractions of c.}

1. Identify the formula units, A_nB_m, and the structure type in each case.
2. Give an example of another compound that adopts each structure.
3. State the coordination about A and B in each case.

4.

• Explain how the "Radius Ratio Rules" may be used to rationalize or predict the structures of simple ionic solids.

• At room temperature and atmospheric pressure all the alkali metal halides adopt the rock salt (NaCl) structure except cesium compounds CsCl, CsBr and CsI. Comment on this in the light of the following ionic radii:

	Li+	Na+	K+	Rb+	Cs+
rM+/pm	60	95	133	149	169
	F-	Cl-	Br-	I-
rX-/pm	136	181	195	216

• What changes would you expect on increase in pressure? 

5.

• The NiAs structure is shown in plan view below:-

• Identify the coordination numbers and geometries of Ni and As and show the coordination environment of each on a plan diagram.

• If the structure is regarded as constructed of NiAs_x polyhedra, describe how these polyhedra are linked together.

• The delafossite structure of CuFeO₂ is shown in the plan view below:-

1. Draw a perspective sketch of the unit cell roughly to scale (remember that c = 6a) and show the positions of the O and Cu ions. Hence identify the arrangement of O ions around Cu ions.
2. Using the same approach as for NiAs, identify the arrangement of O ions around the Fe ion at (0,0,1/2). Show the coordination of O around Fe on a plan diagram.
3. With the aid of a plan diagram, demonstrate that each O ion is surrounded by one Cu ion and three Fe ions in a roughly tetrahedral arrangement.
4. Describe how the OCuFe₃ tetrahedra are linked together in the delafossite structure.

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Solids Page Lecture1 Lecture 2 Lecture 3 Lecture 4 Problems Set Help