CHEC 501 Structure and Energetics solids Ionic...

© Dr. Rajesh Chakrabarty, RGU 1

CHEC 501 Structure and Energetics in Metallic and Ionic solids

Rajesh Chakrabarty Department of Chemistry

Rajiv Gandhi University Rono Hills, Doimukh

Ionic Solids

n  Ions of opposite charge surround each other

n  Larger (usually anion) forms the unit cell and the smaller ions goes into the ‘holes’

Ionic Solids

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Ionic Crystal Structure Types

Formula Type and fraction of sites occupied

ccp hcp

AX All octahedral Rock Salt (NaCl) Nickel Arsenide (NiAs)

Half tetrahedral (T+ or T-) Zinc Blende (ZnS) Wurtzite (ZnS)

AX2

All Tetrahedral Fluorite (CaF2) Anti-Fluorite (Na2O)

Not known

Half octahedral (ordered framework)

Anatase (TiO2) Rutile (TiO2)

Half octahedral (Alternate layers full/ empty)

Cadmium Chloride (CdCl2)

Cadmium iodide (CdI2)

AX3 One-third octahedral YCl3 BiI3

A3X All octahedral & All Tetrahedral Li3Bi Not known

Ionic Solids : AX type

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Cesium Chloride Structure: CsCl

•  Chloride ions occupy the corners of a cube, with a cesium ion in the center (called cubic hole) or vice versa.

•  Cl- = 0.96Cs+ size (0.73r in center is ideal) •  Both ions have a coordination number of 8, with the two ions

fairly similar in size •  Rare structure, need big cation (Cs, Tl only cations known with

this structure)

Cesium Chloride Structure: CsCl

Coordination: 8:8 (cubic)

Unit cell of CsCl = Cs+ (174 pm) = Cl- (181 pm)

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Cesium Chloride Structure: CsCl

Number Cs atoms per unit cell:

                     1                                =  1  atom  per  unit  cell  Central  atom                              

Number Cl atoms per unit cell:

(8  ×  1/8)          =  1  atom  per  unit  cell  Corner  atoms      

Total number CsCl molecules per unit cell (Z) = 1

Rock Salt Structure: NaCl

n  NaCl structure can be viewed as a face-centered cubic (fcc) array of the anions, with the cations in all of the octahedral holes (or vice versa)

n  Large size difference of ions facilitate this structure (ionic radii: Na+ = 116 pm; Cl- = 167 pm)

n  Both ions have a coordination number of 6, each Cl- has six nearest Na+ neighbors and vice versa

n  Most alkali halides have this structure

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= Na+ (116 pm) = Cl- (167 pm)

Rock Salt Structure: NaCl

= Na+ = Cl-

Rock Salt Structure: NaCl

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= Na+ = Cl-

Rock Salt Structure: NaCl

= Na+ = Cl-

Rock Salt Structure: NaCl

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= Na+ = Cl-

Rock Salt Structure: NaCl

= Na+ = Cl-

Rock Salt Structure: NaCl

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= Na+ = Cl-

Na+ Cl- Unit cell of NaCl

Rock Salt Structure: NaCl

= Na+ = Cl-

Can be viewed as a face-centered cubic (fcc) array of the anions, with the cations in all of the octahedral holes, or

Rock Salt Structure: NaCl

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= Na+ = Cl-

As a face-centered cubic (fcc) array of the cations with anions in all of the octahedral holes

Coordination: 6:6 (octahedral)

Rock Salt Structure: NaCl

Na+ Cl-

Number Na atoms per unit cell:

1                          +          (12  ×  1/4)      =  4  atoms  per  unit  cell  central                    edge      atom                          atoms      

Number Cl atoms per unit cell:

(6  ×  1/2)    +        (8  ×  1/8)      =  4  atoms  per  unit  cell  Face                            corner      atom                          atoms      

Total number NaCl molecules per unit cell (Z) = 4

Rock Salt Structure: NaCl

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Zinc Blende or Spalerite Structure: ZnS

n  The anions (S2-) ions are in a face-centered cubic (fcc) arrangement, with cations (Zn2+) in ½ of the tetrahedral holes

n  Alternate: Zn and S each in (fcc) lattices combined so each ion is in a Td hole of the other lattice

n  Stoichiometry: only ½ of the Td holes are occupied and ½ are vacant

Zinc Blende or Spalerite Structure: ZnS

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All Td hole occupied Half of the Td hole occupied Zinc Blende (ZnS) Structure

Zinc Blende or Spalerite Structure: ZnS

Coordination: 4:4 (tetrahedral)

Ionic radii: Zn2+ = 74 pm; S2- = 170 pm

Zinc Blende or Spalerite Structure: ZnS

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Number Zn atoms per unit cell:

4                            =  4  atoms  per  unit  cell  central                          atom                                

Number S atoms per unit cell:

(6  ×  1/2)    +        (8  ×  1/8)      =  4  atoms  per  unit  cell  Face                            corner      atom                          atoms      

Total number ZnS molecules per unit cell (Z) = 4

Zinc Blende or Spalerite Structure: ZnS

Wurtzite Structure: ZnS

n  Rarer than Zinc Blende structure for ZnS; formed at higher temperatures

n  Zn and S each in (hcp) lattices combined so each ion is in a Td hole of the other lattice

n  Stoichiometry: ½ of the Td holes are vacant other ½ are vacant

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Total number ZnS molecules per unit cell (Z) = 4

Wurtzite Structure: ZnS

Spalerite vs. Wurtzite Structure

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Ionic Solids: AX2 type

Fluorite Structure: CaF2

n  Ca2+ in (ccp) lattice with 8 F- surrounding each and occupying all Td holes

n  Alternate: F- in simple cubic lattice with Ca2+ in alternate body centers

n  Nearly perfect radius fits for this structure n  Coordination: Ca2+ 8 (cubic) : F- 4 (tetrahedral)

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Antifluorite Structure: Na2O

n  In the related Anti-Fluorite structure cation and anion positions are reversed

n  Every Td hole in the anion lattice is occupied by a cation

Fluorite Structure: CaF2

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Fluorite (CaF2) Structure

= F- (167 pm) = Ca2+ (126 pm)

Coordination: Ca2+ 8 (cubic) : F- 4 (tetrahedral)

Fluorite Structure: CaF2

Number Ca atoms per unit cell:

8                            =  8  atoms  per  unit  cell  central                          atom                                

Number F atoms per unit cell:

(6  ×  1/2)    +        (8  ×  1/8)      =  4  atoms  per  unit  cell  Face                            corner      atom                          atoms      

Total number CaF2 molecules per unit cell (Z) = 4

Coordination: Ca2+ 8 (cubic) : F- 4 (tetrahedral)

Fluorite Structure: CaF2

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Layered Structures

Nickel Arsenide: NiAs

n  Arsenic atoms forms hexagonal close packed (hcp) lattice layers exactly above each other

n  Ni atoms occupy all the Oh holes between all the layers of As atoms

n  Coordination: Ni 6 (octahedral) : As 6 (trigonal prismatic) n  Usual for MX compounds where X = Sn, As, Bi, S, Se, Te n  Example: NiS, FeS, PtSn, CoS n  These are better regarded as intermetallic phases rather than

true compounds

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Nickel Arsenide: NiAs

There are 6 Ni (orange) arranged in a trigonal prism around the central

As (green)

There are 6 As (green) arranged octahedrally around the central Ni

(brown)

Nickel Arsenide: NiAs