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The Muppet’s Guide to:. The Structure and Dynamics of Solids. 2. Simple Crystal Structures. Bonding. or. E A is bonding dependent. Already looked at vdW and ionic. Figure adapted from Callister, Materials science and engineering, 7 th Ed. Covalent Bond.

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the muppet s guide to

The Muppet’s Guide to:

The Structure and Dynamics of Solids

2. Simple Crystal Structures

bonding
Bonding

or

EA is bonding dependent

Already looked at vdW and ionic

Figure adapted from Callister, Materials science and engineering, 7th Ed.

covalent bond
Covalent Bond

Short range interaction between pairs of atoms

Highly directional in space

Number of bonds proportional to number of valence electrons

Conduction band

(semi-conductors or insulators)

Valence band

Figure adapted from Callister, Materials science and engineering, 7th Ed.

covalent bond1
Covalent Bond

Relies on orbital overlap (hybridisation)

Total wavefunction must be anti-symmetric

s - bond

p - bond

Bonding orbital formed from overlap of symmetric wavefunctions,

Electrons must be anti-symmetric

Figure adapted from hyperphysics

covalent structures
Covalent Structures

Graphite and Graphene– sp2

Methane – sp3

Diamond,

Si, Ge – sp3

covalent materials
Covalent Materials

Si, Ge, Diamond, Organic molecules and Polymers, SiH4, CH4, H2O, HNO3, HF..

Diamond – >3550°C

Bismuth – 270°C

Range of bond energies

Strong angular preference of bonds due to overlap

sp2 hybridisation – trigonal planar structure

sp3 hybridisation – tetragonal tetrahedra

Low density materials

Open structures, polymorphs

Large lattice parameters

metallic bonds
Metallic Bonds

Complex bonding mechanism between the degenerate electrons and the ion cores but also between electrons.

Not all electrons involved in bonding – good electrical and thermal conductors

Tungsten: 3410°C Mercury: -39°C

Range of bond energies

Figure adapted from Callister, Materials science and engineering, 7th Ed.

crystal structures
Crystal Structures

How do atoms pack given their bonding?

Figures adapted from Callister, Materials science and engineering, 7th Ed.

packing fraction
Packing Fraction

Nature453, 629-632 (29 May 2008),

Physics World The secrets of random packing May 29, 2008

dense packed structures
Dense Packed Structures

Atoms modelled as incompressible spheres

In 2 D, each atom has 6 nearest neighbours

unit cell lattice and basis
Unit Cell, Lattice and Basis

A crystal is a parallelepiped that is made up of a regular repeat of some representative unit, called the unit cell.

Unit Cell: A volume of space bounded by lattice points which describe the symmetry. It is defined in terms of their axial lengths (a,b,c) and the inter-axial angles (,,).

TRANSLATIONAL SYMMETRY maps the unit cells across the entire volume of the crystal

crystal structure
Crystal Structure

Convolution of Basis and lattice

slide14

2D Bravais Lattices

A lattice is an infinite periodic set of points defined by the three basis vectors, a,b and c.

In 2D total of 5 distinct lattices

T

Lattice vector:

slide15

Bravais Lattices – 14 possible in 3D

F

I

P

I

P

P

F

I

C

P

P

R

C

T

T – trigonal

R- rhombohedral

All lattices have translational symmetry

simple metals
Simple Metals

W

W

BASIS

BCC LATTICE

slide17

Molecular crystals

BASIS

FCC LATTICE

slide18

Lattice and Basis

The basis can be convolved with the lattice in different ways due to the symmetry of the basis and lattice

slide19

SiF4

BASIS

LATTICE

NB: The point symmetries of the basis and lattice MUST be compatible!

CRYSTAL

dense packed structures1
Dense Packed Structures

Atoms modelled as incompressible spheres

In 2 D, each atom has 6 nearest neighbours

Extend to three dimensions by layering sheets on top of each other

Repeat Patterns:

ABABAB…. Hexagonal close packed

ABCABCABC… Face centred cubic

simple centred cubic
Simple Centred Cubic

AAAAAAAAAA

Stacked symmetry is cubic

P

Polonium

Centre of 4 unit cells is an octahedral site

Packing Fraction=52.4%

No. of Neighbours=6

Figure adapted from Callister, Materials science and engineering, 7th Ed.

hexagonal close packed
Hexagonal Close Packed

ABABABABAB

Cd,

Mg,

Zn

Co

P

The second layer (B) is translated with respect to the first (A) such that the atoms in layer B sit in the dimples between the atoms in layer A

Packing Fraction=74%

No. of Neighbours=12

c/a=1.663

Figure adapted from Callister, Materials science and engineering, 7th Ed.

face centred cubic
Face Centred Cubic

Noble Gases

Cu,

Ag,

Au,

Ni,

Al,

Pb

ABCABCABCABC

[111]

F

Initial stacking is the same as hcp. Then the third layer (C) is translated with respect to both the first and second such that the atoms in layer C sit in the dimples between the atoms in layer B.

Packing Fraction=74%

No. of Neighbours=12

Figure adapted from Callister, Materials science and engineering, 7th Ed.

body centred cubic
Body Centred Cubic

Cr

Fe

W

ABABABABAB

Stacked symmetry is cubic not hexagonal

I

Packing Fraction=68%

No. of Neighbours=8

tetragonal distortions
Tetragonal Distortions

In such cases the structure is usually written as bct or fct

Figure adapted from Callister, Materials science and engineering, 7th Ed.

covalent elements diamond
Covalent Elements - Diamond

Group VI elements such as C, Si and Ge

sp3 hybridisation - tetrahedra

2 FCC lattices

Packing Fraction=37%

Number of neighbours=12

http://cwx.prenhall.com

http://www.ipap.jp/jpsj/news/jpsj-nc_17-fig1.gif

diatomic ax type structures
Diatomic, AX type structures
  • The three most common AX type structures are cubic and named after the representative examples:
  • Rocksalt – NaCl
  • Caesium Chloride – CsCl
  • Zinc blende or sphalerite - ZnS

Ionic

Covalent

diatomic ax type structures1
Diatomic, AX type structures
  • The three most common AX type structures are cubic and named after the representative examples:
  • Rocksalt – NaCl
  • Caesium Chloride – CsCl
  • Zinc blende or sphalerite - ZnS

Ionic

Covalent

the rocksalt structure
The Rocksalt Structure

Structure adopted for materials with strong ionic bonds

MgO, MnS, LiF, FeO, Alkali halides and hydrides and II-VI compounds

fcc lattice

Each cation/anion is surrounded by 6 neighbours of the opposite kind in a perfect octahedral arrangement.

Figure adapted from Callister, Materials science and engineering, 7th Ed.

caesium chloride
Caesium Chloride

Resembles bcc lattice but it is not because the atom at the centre is different and so it is not a lattice point.

Primitive lattice

Each cation/anion is surrounded by 8 neighbours of the opposite kind.

Figure adapted from Callister, Materials science and engineering, 7th Ed.

zinc blende
Zinc Blende

III-V and I-VII as well as ZnS (l=18%), SiC (l=12%), CdTe, ZnTe, MnTe

A structure that resembles the Diamond structure.

Common in materials which exhibit low ionic character and thus favour sp3 hybridised bonds and tetragonal bond angles

No. of Neighbours=12

Figure adapted from Callister, Materials science and engineering, 7th Ed.