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TFY4255 Materials Physics 2007

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orderanisotropy isotropy

disorder

Increasing symmetry

SOLIDS LIQUIDS GAS Liquid crystals

Quasi crystals Glasses

Amorphous solids

FractalsCrystals

Single crystals

Polycrystals

Crystal structure and symmetry

Defects, such as point defects, dislocations, stacking faults, twins, grain boundaries, secondary phases etc.

Electronic structure

Lattice vibrations (fonons)

Material properties

TFY4255 Materials Physics 2007

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Fractals:

The Sierpinski gasket

The Fractal Structure of Broccoli Romanesco

A fractal is characterized by self-similar, and the structure looks identical at all length scales

TFY4255 Materials Physics 2007

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Defects in crystals:

Point defects:• Interstitials

• Impurity atoms

• Vacancies (empty lattice sites)

• Schottky defects (pair of cation and anion vacancies in ionic solids)

• Frenkel defects (cation or anion interstitial plus a vacancy)

Interstitial:

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Schottky defect in NaCl: Frenkel defect in NaCl:

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Dislocations

a) Edge dislocations:

• Extra plane/layer of atoms which ends in the interior of the crystal

• The Burger’s vector is perpendicular to the dislocation line

b) Screw dislocations:

• A screw dislocation transforms successive planes of atoms into the surface of a helix

• The Burger’s vector is parallel to the dislocation line

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4 3 6 2

3 6 2

3 2 33 3/ 2

NaAlH Na AlH Al HNa AlH NaH Al H

+ +

+ +

Example of dislocations:

The final product is H2O instead of CO2

Electrolysis of H2O

Natural gas

AlanateProton exchange membrane (PEM) fuel cell

H2

H2

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Sample: NaAlH4 + 10 mol% TiCl3; PM & No cycles

NaAlH4 + xTiCl3 (ball milling) →(1-3x)NaAlH4 + 3xNaCl + 3xAl + xTi + 6xH2

(111)

High resolution image showing crystalline particles embedded in an amorphous matrix. (b) A filtered inverse Fourier transform image of the rectangular area in (a). (111) dislocations are evident.

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Ti L, O K

Al K

Ti Kα

Ti Kβ EDS: Energy dispersive spectroscopy

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Sample: NaAlH4 + 10 mol% Ti 65 nm; PM & 2 cycles; fully desorbed

Pure Ti

TiH2

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(002)(110)

Ti:

Hexagonal, P63/mmc

TiH2:

Tetragonal, I4/mmm

a = 3.17 Å, c = 4.396 Å

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(101)

High resolution image of the edge of a TiH2 particle, showing the (101) lattice planes. There are numerous (101) edge dislocations, which can more clearly be located in the inverse Fourier transform image.

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Phase diagrams:

A eutectic or eutectic mixture is a mixture of two or more phases at a composition that has the lowest melting point, and where the phasessimultaneously crystallise from molten solution at this temperature.

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Grains and precipitates

200 nm 200 nm200 nm

La0.5Sr0.5Fe0.5Co0.5O3-δ La0.7Sr0.3Co0.5O3-δ LaCoO3

Secondary phase with Co3O4

Located at triple junctions

5 nm

Upper grain oriented in the [111]h = [110]c zone axis

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La0.5Sr0.5Fe0.5Co0.5O3-δ

2.86 Å

4.67 Å

000 111

2-20

Co3O4: Cubic spinel structure, a = 8.08 Å

CoO: Cubic rock salt structure, a = 4.26 Å

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Needle shaped precipitates in Al.