2012/04/23

STRUCTURES DERIVED FROM CUBIC CLOSE PACKING (CCP)

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STRUCTURES DERIVED FROM HEXAGONAL CLOSE PACKING (HCP)

CsCl Cesium Chloride

NiAs Nickel Arsenide

ZnS Wurtzite (High T Form)

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CRYSTAL PLANES & MILLER INDICES Since a crystal has an ordered 3-D periodic arrangement of atoms (ions or molecules) the atomic planes in any crystal can be related to the unit cell. One can label each set of planes uniquely by considering their (fractional) intersection with the unit cell axes a,b,c and converting these to INTEGERS h, k, and l. e.g. the planes that intersect the baxis at ½ and are parallel to a and c. ( a/ , b/2, c/) are defined by the MILLER INDiCES (0 2 0)

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2012/04/23

PRINCIPLE OF XRD

EXPRESSIONS FOR D-SPACINGS IN THE

X-Ray beams collide with a solid and interaction with electrons of the particular solid takes place. Interference is possible when the wavelength of the incoming X-ray is comparable to the separation between the atoms. When an ordered array of scattering centres are present, the reflected X-rays will show interference maxima and minima. Typical wavelengths used for X-ray experiments lie between 0.6 and 1.9Å.

DIFFERENT CRYSTAL SYSTEMS

 Cubic

1 h2  k 2  l 2  d2 a2

 Tetragonal

1 h2  k 2 l 2   2 d2 a2 c

 Orthorhombic

1 h2 k 2 l 2    d 2 a 2 b2 c2

 Hexagonal

1 4  h 2  hk  k 2  l 2     c 2 d 2 3  a2 

 Monoclinic

1 1  h 2 k 2 sin 2  l 2 2hl cos        2 ac  d 2 sin 2   a 2 b2 c

 Triclinic

Even more complex

A TYPICAL PXRD PATTERN

Bragg’s Law

n  2d sin For CUBIC structures we can now show that: 7

sin2  

2 4a

2

h

2

 k2  l2



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BASICALLY

► ►

►

The d-spacings of lattice planes depend on the size of the unit cell and determine the position of the peaks. The line width and shape of the peaks may be derived from conditions of measuring and properties - like particle size - of the sample material . The intensity of each peak is caused by the crystallographic structure, i.e. the position of the atoms within the unit cell and their thermal vibration.

Analytical applications of PXRD ► Identification

of unknowns. purity. ► Determination of lattice parameters. ► Determination of crystallite size. ► Variable temperature studies. ► Quantitative Analysis ► Structure determination and refinement. ► Phase

BASIC STRUCTURE TYPES 12

Ie – the ones you need to know and/or be familiar with.

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2012/04/23

CHARACTERISTIC 

STRUCTURES OF IONIC SOLIDS

These structures are prototypes of a wide range of solids. Slide 14 23/04/2012

Slide 13

IONIC SOLIDS WITH FORMULA MX

Only one type of anion & one type of cation Several different structures depending on relative sizes of ions



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Simplest ionic compounds



Slide 16



CsCl Cesium Chloride

Slide 15

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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)

NaCl Rock Salt (Halite)

Slide 17

•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+

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2012/04/23

Slide 19 23/04/2012

•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

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)

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NiAs Nickel Arsenide 

•HCP As with Ni in all Octahedral holes •Lattice: Hexagonal - P

HCP equivalent of halite structure

Slide 22

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•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)

Slide 21

ZnS Zinc Blende (Sphalerite)

MANY STRUCTURES ARE BASED ON LINKED OCTAHEDRA.

Slide 24 23/04/2012

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ZnS Wurtzite (High T Form)

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•HCP S2- with Zn2+ in half Tetrahedral holes (only T+ {or T-} filled) •Lattice: Hexagonal - P

SOLIDS WITH GENERAL FORMULA MX2

Slide 27 23/04/2012

•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)

Slide 26

Slide 25

•CCP S2- 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

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CaF2 Fluorite / {Na2O Anti-Fluorite}

Slide 30

Slide 29

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•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

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2012/04/23

Ionic oxides : ReO3 and WO3

Also : CdCl2  Rutile  

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MIXED OXIDE STRUCTURES

Ionic oxides BaTiO3

BaTiO3(cubic or tetragonal) (CaTiO3, SrTiO3 and mixed oxides. See S&A)

Perovskite – ABO3  Spinel – AB2O4  Ilmenite – ABO3 

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

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Completion of the Practical assignment associated with this course will assist you with becoming familiar with the various structure types you are expected to be familiar with.

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