3 (New)the Structure of Crystalline Solids

8/13/2019 3 (New)the Structure of Crystalline Solids

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Chapter 3: The Structure of Crystalline Solids

EAT 102

NUR FITRIAH BT ISA


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WHY STUDY The Structure of Crystalline Solids?

The properties of some material are directly

related to their crystal structures.

Furthermore, significant property differences

exist between crystalline end non crystalline

materials having the same composition.

e.g.: Crystal structure of Mg is much more

brittle than that of the crystal structure of gold


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UNIT CELL

Atoms in crystalline solidsare positioned in orderly

and repeated patterns

Atoms in non crystalline (amorphous) solids aredistributed randomly and disordered

crystalline SiO2

Non crystalline SiO2


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METALLIC CRYSTAL STRUCTURE

Most common metals exist in at least one of threerelatively simple crystal structures

Face-centered cubic (FCC) Body centered cubic (BCC)

Atoms located at each of the

corners and the centers of all

the cube faces.

Atoms located at all eight corners and a

single atom at the cube center.

1 2


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The Hexagonal Close-Packed Crystal Structure (HCP)


The top and bottom faces of the unit cell consist of six

atoms that form regular hexagons and surround asingle atom in the center. Another plane that provides

three additional atoms to the unit cell is situated

between the top and bottom planes.

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FCC

BCC

HCP


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Two other important characteristics of a crystal structure are the

coordination number and the atomic packing factor (APF) where


Crystal

Structure

FCC BCC HCP

Coordination

number

12 8 12

APF 0.74 0.68 0.74a

(unit cell

length)

Defined in

terms of

parallelpiped

No. of atoms

per unit cell

4 2 4

Coordination number = number of nearest-neighbor or touching atoms.


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DENSITY COMPUTATIONS

A knowledge of the crystal structure of a metallic solid permitscomputation of its theoretical density, p through the relationship


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Q1 : Determine Unit Cell Volume

Tutorial 2: Questions and Learning

Guides

Q2 : Density Computations


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CRYSTAL SYSTEM

x, y, z coordinate system is established with

its origin at one of the unit cell corners

Edge lengths are defined as a, b, and c.

Interaxial angles are , ,

Both FCC and BCC structures belong to the

cubic crystal system,

whereas HCP falls within hexagonal


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LATTICE PARAMETERS RELATIONSHIP FOR

SEVEN CRYSTAL SYSTEM


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LATTICE PARAMETERS RELATIONSHIP FOR

SEVEN CRYSTAL SYSTEM


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POINT COORDINATES

P = generalized point coordinates

a = unit cell length (parallel to x-axis)

b = unit cell length (parallel to y-axis)

c = unit cell length (parallel to z-axis)

qa = distance along x-axis

x axis

[q r s]

y axis z axis

rb = distance along y-axis

sc = distance along z-axis


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Guides

Q3 : Location of Point Having Specified

Coordinates

z

x

ya b

c

000

Q4 : Specification of a Coordinates


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Guides

Q5 -7: Directions within a unit Cell

Q8 : Determination of Directional Indices

Q9 : Construction of Specified

Crystallographic Directions


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Guides

Q10 :Determination of Planar (Miller) Indices

Intercepts : a, a, a

Fractional intercepts : 1 , 1 , 1

Miller Indices : (111)


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Intercepts : a, a,

Fractional intercepts : 1 , 1 ,


EXAMPLE (110) SURFACE


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EXAMPLE (210) SURFACE

Intercepts : a, a,

Fractional intercepts : , 1 ,



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Linear and Planar Densities

Linear Density:Directional equivalency is related to the atomic linear density in the

sense that equivalent directions have identical linear densities.

The direction vector is positioned so as to pass through atom centers.

The fraction of line length intersected by these atoms is equal to the

linear density.

Planar Density:Crystallographic planes that are equivalent have the same atomic planar

density. The plane of interest is positioned so as to pass through atom

centers.Planar density is the fraction of total crystallographic plane area that is

occupied by atoms.

3 (New)the Structure of Crystalline Solids

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