FisMat3c

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Chapter 3. The structure of crystalline solids

3.1. Crystal structures 3.1.1. Fundamental concepts

3.1.2. Unit cells3.1.3. Metallic crystal structures

3.1.4. Ceramic crystal structures3.1.5. Silicate ceramics3.1.6. Carbon

3.1.7. Polymorphism

3.2. Crystallography 3.2.1. Crystal systems

3.2.2. Crystallographic directions and planes3.2.3. Linear and planar density 3.2.4. Closed-packed crystal structures

3.3. Crystalline and noncrystalline materials 3.3.1. Single crystal

3.3.2. Polycrystalline materials3.3.3. X-ray diffraction3.3.4. Noncrystalline solids

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3.3. Crystalline and noncrystalline materials

3.3.1. Single crystal

Single crystal is a crystalline solid, when the periodic and repeatedarrangement of atoms is perfect or extends throughout the entiretyof the specimen without interruption.Single crystals exist in nature and may also be produced artificially.Examples: gem stone,

silicone and other semiconductors(electronic microcircuit purposes)

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3.3.2. Polycrystalline materials

Polycrystalline is a solid which is composed of a collection of manysmall crystals or grains.

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Physical properties of single crystals of some substances depend onthe crystallographic direction which measurements are taken.Substances in which measured properties are dependent of thedirection of measurement are anisotropy.Example: elastic modulus, electrical conductivity and index of refraction

have different values in the [100] and [111] directions.

Substances in which measured properties are independent of thedirection of measurement are isotropy.

Triclinic structures normally are highly anisotropic.The degree of anisotropic increases with the decreasing structuralsymmetry.

The grains in polycrystalline materials have a preferential crystallographicorientation (“texture”).The magnitude of a measured property represents some average of thedirectional values.

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3.3.3. X-ray diffraction

The diffraction phenomenonDiffraction occurs when a wave encounters a series of regularly spacedobstacles that

1. are capable of scattering the wave,2. have spacings that are comparable in magnitude to the wavelength.

The diffraction conceptThe phase difference between the scattered waves depend on the pathlength difference and the path length difference is an integral number of

wavelength (λ).

Constructive interference (same phase and ∆l = λ )

Destructive interference (∆l = ½ λ )

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The Bragg’s Law

The atomic spacings for solids is in the order of X-rays.X-rays are a form of EM radiation that have high energies and short λ.

sinθ2dnλ hkl

=Bragg’s Law

The magnitude of the distance between 2 adjacent and parallel planesof atoms (dhkl) is a function of the Miller indices (h, k, and l) and the

lattice parameters

222hkl

lk h

ad

++=

where d is the interplanar spacing,a is the lattice parameter

(Cubic system)

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∆l = SQ + QT = d sin θ + d sin θ

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Diffraction techniquePowder or polycrystalline specimens (C), consisting of many fineand randomly oriented particles, are exposed to monochromaticX-rays (T).A diffractometer (D) is an apparatus used to determine the angles

at which diffraction occurs for powder specimens.

D is mounted on a movable carriage that may also be rotatedabout the O axis. Carriage and specimen are

mechanically coupled in a way that arotation of the specimen

through θ is accompaniedby a 2θ rotation of D.

A recorder automatically plotsthe diffracted beam intensity

as a function of 2θ.

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Interplanar spacings for different crystal system

Cubic

Tetragonal

Orthorhombic

Hexagonal2

1

2

2

2

22

c

l

3a

kh)k 4(h−

+

++

2

1

2

222

a

lk h−

++

2

1

2

2

2

22

c

l

a

k h−

+

+

2

1

2

2

2

2

2

2

c

l

b

k

a

h−

++

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The high-intensity peaks result whenthe Bragg diffraction condition issatisfied by some set ofcrystallographic planes.

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3.3.4. Noncrystalline solids

Noncrystalline solids or amorphous are materials with lack a systematicand regular arrangement of atoms over relatively large atomic distances.

Silicon dioxide (SiO2) may exist in crystalline and noncrystalline structures.

Each silicon ion bonds to four oxygen ions for both states, but the structureis more irregular for the noncrystalline structure.

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Silicon dioxide (SiO2) in the noncrystalline state is called fused silicaor vitreous silica.Other oxides, such as B2O3 and GeO2, may also form glassystructures and polyhedral oxide structures.These materials are called network formers.

Network modifiers are usually added to silica glasses to form commonglass (for containers, windows etc).Intermediates are also usually added to silica glasses to stabilize the

network.Both modifiers and intermediates lower the melting point and viscosityof a glass so that it is easier to form in lower temperatures.

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