Structures of Simple Inorganic Solids

Dr S.J. Heyes

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

Michaelmas Term 1999

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

Lecture 2. Descriptions of Simple 'Ionic' Structures.

1. Ions and ionic structures

2. 'Ionic' structures derived from occupancy of interstitial sites in close-packed structures

3. Structures described as linked polyhedra

4. Descriptions of some common structures

• NaCl (Rock Salt/Halite)
• CaF₂ Fluorite (Na₂O Anti-Fluorite)
• ZnS (Zinc Blende/Sphalerite)
• (complex ion variants)
• NiAs
• ZnS (Wurtzite)
• CdI₂
• CsCl
• MoS₂

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Aims of this Lecture

After studying this lecture you should be able:-

For these structure types:-

• NaCl halite (rock salt)

• CaF₂ fluorite

• ZnS zinc blende

• NiAs nickel arsenide

• ZnS wurtzite

• CdI₂ cadmium iodide

• CsCl cesium chloride

To do the following:-

1. Describe the structure as filling of interstitial holes in close-packing

2. Describe the structure as linked polyhedra

3. Draw the unit cell in a plan or perspective view

4. Recognise the structure from a plan or perspective view of a unit cell

5. Identify coordination numbers & geometries of atoms

6. Give examples of adoption

Ionic (and other) structures may be derived from the occupation of interstitial sites in close-packed arrangements.

Some Binary Structures derived from Hole-Filling by one atom type in CCP and HCP arrangements of another

Hole-filling doesn't just work with single-atom species!

C₆₀ molecules are arranged in a face-centred cubic arrangement. If C₆₀ is reduced with potassium metal it forms compounds such as K₃C₆₀, which is fcc C₆₀^3- molecules with K⁺ ions in all octahedral and tetrahedral interstitial sites. K₃C₆₀ is an interesting material because of its superconducting properties (T_c = 20 K) and metal fullerides are the subject of much current research, for example in the group of the University of Liverpool's Prof Matthew Rosseinsky.

Polyhedral Representations

Defining the coordination environment of an ion as a polyhedron

Polyhedral Representations of Structures by linking Coordination Polyhedra together

STRUCTURES DERIVED FROM CUBIC CLOSE PACKING (CCP)

NaCl Rock Salt (Halite)

• CCP Cl^- with Na⁺ in all Octahedral holes
• Lattice: fcc
• Motif: Cl at (0,0,0); Na at (¹/₂,0,0)
• 4NaCl in unit cell
• Coordination: 6:6 (octahedral)
• Cation and anion sites are topologically identical

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

The fcc nature of the lattice can be seen by examining just one atom of the motif at a time (i.e. just Cl or just Na)

CaF₂ Fluorite / {Na₂O Anti-Fluorite}

View a Quicktime CaF₂ Movie or Quicktime CaF₂ VR scenes, ball & stick or polyhedral

• CCP Ca²⁺ with F^- in all Tetrahedral holes
• Lattice: fcc
• Motif: Ca²⁺ at (0,0,0); 2F^- at (¹/₄,¹/₄,¹/₄) & (³/₄,³/₄,³/₄)
• 4CaF₂ in unit cell
• Coordination: Ca²⁺ 8 (cubic) : F^- 4 (tetrahedral)
• In the related Anti-Fluorite structure Cation and Anion positions are reversed

View a Quicktime CaF₂ B-cell Movie or Quicktime CaF₂ B-Cell VR scenes, ball & stick or polyhedral

ZnS Zinc Blende (Sphalerite)

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

• CCP S^2- with Zn²⁺ in half Tetrahedral holes (only T+ {or T-} filled)
• Lattice: fcc
• 4ZnS in unit cell
• Motif: S at (0,0,0); Zn at (¹/₄,¹/₄,¹/₄)
• Coordination: 4:4 (tetrahedral)
• Cation and anion sites are topologically identical

Examples of Structure Adoption

NaCl (Halite)

• Very common (inc. 'ionics', 'covalents' & 'intermetallics' )
• Most alkali halides (CsCl, CsBr, CsI excepted)
• Most oxides / chalcogenides of alkaline earths
• Many nitrides, carbides, hydrides (e.g. ZrN, TiC, NaH)

CaF₂ (Fluorite)

• Fluorides of large divalent cations, chlorides of Sr, Ba
• Oxides of large quadrivalent cations (Zr, Hf, Ce, Th, U)

Na₂O (Anti-Fluorite)

• Oxides /chalcogenides of alkali metals

ZnS (Zinc Blende/Sphalerite)

• Formed from Polarizing Cations (Cu⁺, Ag⁺, Cd²⁺, Ga³⁺...)

  • and Polarizable Anions (I^-, S^2-, P^3-, ...);

  e.g. Cu(F,Cl,Br,I), AgI, Zn(S,Se,Te), Ga(P,As), Hg(S,Se,Te)

COMPLEX-ION VARIANTS

"Fool's Gold"

The CrystalMaker files are FeS₂, SrO₂, K₂PtCl₆

STRUCTURES DERIVED FROM HEXAGONAL CLOSE PACKING

NiAs Nickel Arsenide

View a Quicktime NiAs Movie or Quicktime NiAs VR scene

• HCP As with Ni in all Octahedral holes
• Lattice: Hexagonal - P
• a = b, c Å Ã(8/3)a
• Motif: 2Ni at (0,0,0) & (0,0,¹/₂) 2As at (²/₃,¹/₃,¹/₄) & (¹/₃,²/₃,³/₄)
• 2NiAs in unit cell
• Coordination: Ni 6 (octahedral) : As 6 (trigonal prismatic)

A CrystalMaker files for NiAs emphasizing AsNi₆ trigonal prisms or NiAs₆ octahedra

Quicktime NiAs VR scenes, trigonal prisms or octahedra

An alternative unit cell origin is at As (rather than Ni)

ZnS Wurtzite

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

• HCP S^2- with Zn²⁺ in half Tetrahedral holes (only T+ {or T-} filled)
• Lattice: Hexagonal - P
• a = b, c Å Ã(8/3)a
• Motif: 2S at (0,0,0) & (²/₃,¹/₃,¹/₂); 2Zn at (²/₃,¹/₃,¹/₈) & (0,0,⁵/₈)
• 2ZnS in unit cell
• Coordination: 4:4 (tetrahedral)

Comparison of Wurtzite and Zinc Blende

CrystalMaker Clusters for Zinc Blende and Wurtzite

 

CdI₂ Cadmium Iodide

View a Quicktime CdI₂ Movie or Quicktime CdI₂ VR scenes, ball & stick or polyhedral

• HCP I with Cd in Octahedral holes of alternate layers

  This is perhaps most easily appreciated with a unit cell origin at I (the usual hcp cell representation)

• Lattice: Hexagonal - P
• Motif: Cd at (0,0,0); 2I at (²/₃,¹/₃,¹/₄) & (¹/₃,²/₃,³/₄)
• 1CdI₂ in unit cell
• Coordination: Cd - 6 (Octahedral) : I - 3 (base pyramid)

Examples of Structure Adoption

NiAs

• Transition metals with chalcogens, As, Sb, Bi

  e.g. Ti(S,Se,Te); Cr(S,Se,Te,Sb); Ni(S,Se,Te,As,Sb,Sn)

CdI₂

• Iodides of moderately polarising cations; bromides and chlorides of strongly polarising cations;

  e.g. PbI₂, FeBr₂, VCl₂

• Hydroxides of many divalent cations

  e.g. (Mg,Ni)(OH)₂

• Di-chalcogenides of many quadrivalent cations

  e.g. TiS₂, ZrSe₂, CoTe₂

CdCl₂ (CCP equivalent of CdI₂)

• Chlorides of moderately polarising cations

  e.g. MgCl₂, MnCl₂

• Di-sulfides of quadrivalent cations

  e.g. TaS₂, NbS₂ (CdI₂ form as well)

• Cs₂O has the anti-cadmium chloride structure

HCP CaF₂ ?

• No structures are known with all Tetrahedral sites (T+ and T-) filled in HCP

  i.e. there is no HCP analogue of the Fluorite/Anti-Fluorite Structure

• To explain this we note that the T+ and T- interstitial sites above and below a layer of close-packed spheres in HCP are too close to each other to tolerate the coulombic repulsion generated by filling with like-charged species.

• This is also clear from a polyhedral viewpoint. Fluorite has edge-linked FCa₄ tetrahedra, but its HCP analogue would involve face-linking of the T+ and T- tetrahedra between adjacent inter-layer gaps.
•  

NON CLOSE-PACKED STRUCTURES

CsCl Cesium Chloride

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

• Lattice: Cubic - P (N.B. Primitive!)

• Motif: Cl at (0,0,0); Cs at (¹/₂,¹/₂,¹/₂)
• 1CsCl in unit cell
• Coordination: 8:8 (cubic)
• Adoption by chlorides, bromides and iodides of larger cations,

  e.g. Cs⁺, Tl⁺, NH₄⁺

The primitive nature of the lattice can be seen by examining just one atom of the motif at a time (i.e. just Cl or just Cs)

MoS₂ Molybdenite

• Note: Hexagonal layers of S atoms are NOT Close-packed in 3D
• Lattice: Hexagonal - P
• Motif: 2Mo at (²/₃,¹/₃,³/₄) & (¹/₃,²/₃,¹/₄)
  • 4I at (²/₃,¹/₃,¹/₈), (²/₃,¹/₃,³/₈), (¹/₃,²/₃,⁵/₈) & (¹/₃,²/₃,⁷/₈)
• 2MoS₂ in unit cell
• Coordination: Mo 6 (Trigonal Prismatic) : S 3 (base pyramid)

Comparison of MoS₂ and CdI₂

the diagrams indicate that:-

• both MoS₂ and CdI₂ are LAYER structures
• MoS₂ layers are edge-linked MoS₆ trigonal prisms
• CdI₂ layers are edge-linked CdI₆ octahedra

Comparison of MoS₂ and NiAs

• S in MoS₂ / Ni in NiAs are hexagonal close-packed 2D layers
• These layers do not stack in close-packed 3D sequences
  • Ni layers in NiAs stack directly above each other in an AAAA... fashion
  • S layers in MoS₂ stack in an AABBAABB ... fashion
• Two hexagonal layers directly above each other leave TRIGONAL PRISMATIC interstitials
  • 2 per sphere
• In NiAs, As fills half the trigonal prismatic sites between all layers of Ni, in a layer sequence bcbcbc...
• In MoS₂ Mo also fills alternate trigonal prismatic sites where they occur
  • Trigonal prismatic sites only occur between directly stacked layers (AA or BB)
  • Adjacent S layers with an AB sequence have no Mo inbetween & interact by van der Waals forces
• MoS₂ cannot be described in terms of interstitial filling of a close-packed structure
• NiAs can be described as HCP As with Ni in octahedral holes (the more usual description!)

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