Chapter 3 · PDF file© 2011 Cengage Learning Engineering. All Rights Reserved. 3 - 1 ......

Chapter 3:Chapter 3:

Atomic and Ionic Atomic and Ionic ArrangementsArrangements

© 2011 Cengage Learning Engineering. All Rights Reserved.© 2011 Cengage Learning Engineering. All Rights Reserved.

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Chapter 3: Atomic and Ionic Arrangements


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Learning Objectives

1. Short-range order versus long-range order2. Amorphous materials3. Lattice, basis, unit cells, and crystal structures4. Allotropic or polymorphic transformations5. Points, directions, and planes in the unit cell6. Interstitial sites7. Crystal structures of ionic materials8. Diffraction techniques for crystal structure analysis



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Figure 3.1 - Levels of Atomic Arrangements in Materials



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Short-Range Order versus Long-Range Order

Short-range order (SRO) A material displays short-range order (SRO), if the special

arrangement of the atoms extends only to the atoms nearest neighbors.

Tetrahedral structure in silica satisfies the requirement that four oxygen ions be bonded to each silicon ion.



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Figure 3-2



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Short-Range Order Versus Long-Range Order


Long-range order Atomic arrangement that extends over length scales ~>100nm

Crystalline

materials

Atoms or ions of materials that form a regular repetitive, grid-like pattern in three dimensions

Polycrystalline material

Many small crystals with varying orientations in space

These smaller crystals are known as grains

Grain boundaries Regions between crystals, where the crystals are in misalignment

X-ray diffraction or electron diffraction

Techniques used for the detection of long range order in crystalline materials

Liquid crystals Liquid crystal polymers behave as amorphous materials (liquid-like) in one state


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Figure 3.4 - Classification of Materials Based on the Type of Atomic Order



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Lattice, Basis, Unit Cells, and CrystalStructures

Lattice: A collection of points that divide space into smaller equally sized segments.

Basis: A group of atoms associated with a lattice point (same as motif).

Unit cell: A subdivision of the lattice that still retains the overall characteristics of the entire lattice.

Crystallography: The formal study of the arrangements of atoms in solids.

Lattice points: Points that make up the lattice. The surroundings of each lattice point are identical.



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Figure 3.5 - Lattice and Basis



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Crystal structure: The arrangement of the atoms in a material into a regular repeatable lattice. The structure is fully described by a lattice and a basis.

Bravais lattices: The fourteen possible lattices that can be created in three dimensions using lattice points.

Crystal systems: Cubic, tetragonal, orthorhombic, hexagonal, monoclinic, rhombohedral and triclinic arrangements of points in space that lead to fourteen Bravais lattices and hundreds of crystal structures.



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Figure 3.6 - The Fourteen Types of Bravais Lattices



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Figure 3.7 - The Unit Cell



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Figure 3.8



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Table 3.1 – Characteristics of the Seven Crystal Systems



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Figure 3.9



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Figure 3.11 - The Relationships Between the Atomic Radius and the Lattice Parameter in Cubic Systems



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Relationship between the lattice parameter (a0) and atomic radius (r)


0a = 2r

0

4ra =

3

0

4ra =

2

For SC

For FCC

For BCC


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Coordination

number

Number of atoms touching a particular atom, or the number of nearest neighbors for that particular atom

Packing factor (Number of atoms/cell) (Volume of each atom)

Volume of unit cell

Kepler’s conjecture The geometry which has a maximum achievable packing factor ~0.74

Density (Number of atoms/cell) (Atomic mass)

(Volume of unit cell) (Avogadro’s number)


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Figure 3.13 - The Hexagonal Close-Packed (HCP) Structure (Left) and its Unit Cell



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Table 3.2 - Crystal Structure Characteristics of Some Metals at Room Temperature



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Allotropic or Polymorphic Transformations

Allotropy: The characteristic of an element being able to exist in more than one crystal structure depending on temperature and pressure.

Polymorphism: Compounds exhibiting more than one type of crystal structure.

Iron BCC crystal structure at room temp, which changes to FCC at 912 C

Ceramic materials, such as silica (SiO2) and zirconia (ZrO2), are polymorphic.

Ceramic components made from pure zirconia typically will fracture as the temperature is lowered and as zirconia transforms from the tetragonal to monoclinic form because of volume expansion.



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Figure 3.14



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Figure 3.16 - Equivalency of Crystallographic Directions of a Form in Cubic Systems



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Table 3.3 - Directions of the Form <110> in Cubic Systems



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Points, Directions, and Planes in the Unit Cell


Repeat distance Distance between the lattice points along a particular direction

Linear density Number of lattice points per unit length along a particular direction

Packing fraction Fraction of space in a unit cell occupied by atoms


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Figure 3.17



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Figure 3.18 - Crystallographic Planes and Intercepts



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Table 3.4 - Planes of the Form {110} in Cubic Systems



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Figure 3.23



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Points, Directions, and Planes in the Unit Cell

Isotropic and anisotropic behavior A material is crystallographically anisotropic if its properties depend

on the crystallographic direction along which the property is measured. A material is crystallographically isotropic if the properties are

identical in all directions.



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Interstitial Sites


Interstitial sites Small holes between the usual atoms into which smaller atoms may be placed

Cubic site Gives a coordination number of 8. Occurs in the SC structure at the body-centered position

Octahedral sites Gives a coordination number of 6. Atoms contacting the interstitial atom form an octahedron

Tetrahedral sites Gives a coordination number of 4


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Figure 3.25 - The Location of the Interstitial Sites in Cubic Unit Cells



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Table 3.6 - The Coordination Number and the Radius Ratio



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Figure 3.26 - The Sodium Chloride Structure


MgO, CaO FeO has the same structure.


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Figure 3.27 - The Zinc Blende Structure (ZnS)



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Figure 3.32 – Diamond Cubic Structure


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