Structures of Simple Inorganic Solids

Dr S.J. Heyes

Fourth of Four Lectures in the 1st Year Inorganic Chemistry Course

Hilary Term 2000

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

Lecture 4. Oxide Structures & Networks.

1. Oxide Structures

• TiO₂ (Rutile)
• ReO₃
• CaTiO₃ (Perovskite)
• La₂CuO₄ (K₂NiF₄ structure) (high-T_c superconductors)

2. Connectivity - Topological approach to structures

e.g. non-metallic elements

• atoms
• dimers
• rings
• chains
• layers
• cages/polyhedra
• nets

e.g. Diamond (C) / Sphalerite (ZnS) / Cristobalite (SiO₂) / Cuprite (Cu₂O)

e.g. silicate minerals

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Aims of this Lecture

After studying this lecture you should be able:-

1. Describe all aspects of three common Metal Oxide structures and give examples of their adoption

• TiO₂ rutile

• ReO₃ rhenium trioxide

• CaTiO₃ perovskite

2. Identify:-

• Coordination Numbers
• Coordination Geometries
• Polyhedral Linking

from even (superficially) complex unit cell views (e.g. those of the superconducting oxides)

3. Rationalize the structures of Non-Metallic elements from the 8-N rule and the concept of Network Connectivity

4. Identify structures with the Diamond Network

METAL OXIDE STRUCTURES

Metal Oxides are some of the most important Inorganic Solids

Rutile, TiO₂

View a Quicktime Rutile Movie or Quicktime Rutile VR scenes, ball & stick or polyhedral

• Unit Cell: Primitive Tetragonal (a = b ¹ c)
• 2TiO₂ per unit cell
• Motif: 2Ti at (0, 0, 0); (¹/₂, ¹ / ₂, ¹ /₂) & 4O at ±(0.3, 0.3, 0); ±(0.8, 0.2, ¹ /₂)
• Ti: 6 (octahedral coordination)
• O: 3 (trigonal planar coordination)
• TiO₆ octahedra share edges in chains along c
• Edge-sharing Chains are linked by vertices
• Examples:
  • oxides: MO₂ (e.g. Ti, Nb, Cr, Mo, Ge, Pb, Sn)

    fluorides: MF₂ (e.g. Mn, Fe, Co, Ni, Cu, Zn, Pd)

Comparison of Rutile with Nickel Arsenide

i.e. Rutile is distorted hcp O with Ti in ¹/₂ Octahedral holes

Rhenium Trioxide, ReO₃

View a Quicktime ReO₃ Movie or Quicktime ReO₃ VR scenes, ball & stick or polyhedral

• Lattice: Primitive Cubic
• 1ReO₃ per unit cell
• Motif: Re at (0, 0, 0); 3O at (¹/₂, 0, 0), (0, ¹/₂, 0), (0, 0, ¹/₂)
• Re: 6 (octahedral coordination)
• O: 2 (linear coordination)
• ReO₆ octahedra share only vertices
• May be regarded as ccp oxide with ¹/₄ of ccp sites vacant (at centre of the cell) See the unit cell expressed with the origin at O

  - shows a defective fcc of O atoms (a face O missing)

  

• Examples:
  • WO₃ , AlF₃ , ScF₃ , FeF₃ , CoF₃ , Sc(OH)₃ (distorted)

Perovskite, CaTiO₃

View a Quicktime Perovskite A-cell Movie  or Quicktime Perovskite VR scene

 

The above link downloads the A-Cell coordinates

Download the alternative B-Cell coordinates for Perovskite

View a Quicktime Perovskite B-cell Movie or Quicktime Perovskite B-cell VR scene

also or Quicktime Perovskite VR scenes of TiO₆ octahedra and CaO₁₂ cuboctahedra

• Lattice: Primitive Cubic (idealised structure)
• 1CaTiO₃ per unit cell
• A-Cell Motif: Ti at (0, 0, 0); Ca at (¹/₂, ¹/₂, ¹/₂); 3O at (¹/₂, 0, 0), (0, ¹/₂, 0), (0, 0, ¹/₂)
• Ca 12-coordinate by O (cuboctahedral)
• Ti 6-coordinate by O (octahedral)
• O distorted octahedral (4xCa + 2xTi)
• TiO₆ octahedra share only vertices
• CaO₁₂ cuboctahedra share faces
• Ca fills the vacant ccp site in ReO₃, Þ a CaO₃ ccp arrangement

  with ¹/₄ of octahedral holes (those defined by 6xO) filled by Ti

• Examples: NaNbO₃ , BaTiO₃ , CaZrO₃ , YAlO₃ , KMgF₃
• Many undergo small distortions: e.g. BaTiO₃ is ferroelectric

The Perovskite Structure is fully predicted by Pauling's 2^nd Rule

Visit the Oxford King of the Perovskites, Dr Peter Battle

Crystallography meets modern art in the Various Pictures of Perovskites

FINDING SIMPLE PATTERNS IN MORE "COMPLEX" STRUCTURES

Using Examples of High Temperature Oxide Superconductors

La₂CuO₄ {K₂NiF₄ structure}

Doped La_2-xSr_xCuO₄ {La_2-xSr_xCuO₄ } was the first (1986) High-T_c Superconducting Oxide (T_c ~ 40 K)

for which Bednorz & Müller were awarded a Nobel Prize

La₂CuO₄ may be viewed as if constructed from an ABAB... arrangement of Perovskite cells

- known as an AB Perovskite!

Alternative Views of the La₂CuO₄ Structure

We may view the structure as based on:-

1. Sheets of elongated CuO₆ octahedra, sharing only vertices
2. Layered networks of CuO₄^6-, connected only by La³⁺ ions

Comparison of La₂CuO₄ with the related Nd₂CuO₄

• Common structural motif of vertex-linked CuO₄ squares
• This motif occurs in all the high temperature superconducting copper oxides
• The structures differ in the structure of the 'filling' in the 'sandwich' of copper oxide layers - known as Intergrowth Structures

YBa₂Cu₃O₇ - the 1:2:3 Superconductor

(the first material to superconduct at l-N₂ temperature, T_c > 77 K)

• YBa₂Cu₃O₇ can be viewed as an Oxygen-Deficient Perovskite

• Two types of Cu site

  Layers of CuO₅ square pyramids (elongation Þ essentially vertex-linked CuO₄ squares again)

  Chains of vertex-linked CuO₄ squares

  These are indicated in a Polyhedral Representation

• Information about Superconductors is available from the Chemistry IT Centre's Virtual Laboratory
• You can view pictures and movies of many more oxide superconductor structures from the site of Prof. J. McDevitt at the University of Texas, Austin.

Topological Approach to Structures - Networks

Concept of CONNECTEDNESS (P) of a network connecting structural units (atoms or groups)

e.g. Structures of Non-Metallic Elements

P = 8 - N

P = 1 e.g. I₂ DIMERS

Iodine dehybridizes to a metallic (fcc) state at high pressure

P = 2 e.g. S₈ RINGS

View a Quicktime S₈ Movie or Quicktime S₈ VR scene

Note how the packing approximates to a distorted close-packing arrangement

• apparently 11-coordinate (3 left + 5 in-plane+ 3 right)

P = 2 e.g. a-Se CHAINS

P = 3 e.g. As LAYERS

The colours in top, plan and smaller side views emphasize the layers

CARBON Allotropes with P = 3

Carbon shows both Layer and Cage Networks with P=3

Crystalmaker files for Graphite and Buckminsterfullerene are available

• Note that we have already considered the Crystallographic details of Graphite, without considering its network
• Also the C₆₀ fullerene's solid structure is not fully described by the network approach, we must also consider the arrangement of C ₆₀ molecules with respect to each other in a face-centred cubic arrangement

CARBON with P = 4 the Diamond FRAMEWORK

• The Diamond Structure is the commonest P=4 Network
• The Diamond Network has very high (cubic) symmetry
• The Properties of Diamond are reviewed in the University of Bristol's Molecule of the Month

View a Quicktime Diamond Movie or Quicktime Diamond VR scene

Structures with the Diamond FRAMEWORK

P = 4 Networks

Cuprite

The Cuprite structure may be invisaged as an interesting Framework Structure

Silicate Minerals - Networks of Tetrahedral SiO₄^4- Units

• Samples of the following minerals and many more are contained in the Collections of the University Museum at Oxford
• VRML files of silicate mineral structures are available from the University of Darmstadt

P=0, Orthosilicate, SiO₄^4-

P=1, Pyrosilicate, Si₂O₇^6-

P=2 Rings, (SiO₃^3-)_n

P=2 Chains, Pyroxene, (SiO₃^3-)_n

P = 2 & 3 Chain of Rings, Amphibole, (Si₄O₁₁^6-)_n

P=3 Layers, (Si₂O₅^2-)_n

P=4, Tectosilicate, SiO₂

e.g. Mⁿ⁺_x/n[(AlO₂)_x(SiO₂)_y].mH₂O Zeolite ZSM-5

View a Quicktime ZSM-5 Movie

ZSM-5 is considered in the Molecule of the Month feature for April 1997

Natrolite, a naturally-occuring Zeolite

Prof. Thomas Mennard of the University of Calgary, Canada has manipulable Chime structures for some of the silicates considered above

There are also VRML files for silicate structures in the Verscheidene Vorlesungen site of Prof. Caroline Röhr of the Universität Freiburg

An extensive Introduction to Zeolites from the Chemistry Department, UMIST

The Atlas of Zeolite Structures allows you to view all the known zeolite structure types, and includes files for VRML and WebLab viewers

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NOW TEST YOUR KNOWLEDGE OF STRUCTURES OF SOLIDS

by attempting the Problems Set

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Solids Page Lecture 1 Lecture 2 Lecture 3 Lecture 4 Problems Set Help