Crystal Structure (2008) (CHAPTER 1)

8/12/2019 Crystal Structure (2008) (CHAPTER 1)

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Crystal structure


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Learning Objective

Students should be able to:

Differentiate between crystalline, noncrystalline, single crystaland polycrsytal.

Derive the relationship between unit cell edge length andatomic radius for face centered and body centered cubic

Compute density and atomic packing factors for crystal

Specify the miller indices for crystallography plane anddirection

Relate the crystal structure with material properties


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Fundamental Concept

a crystal structure is a unique arrangement

of atoms in a crystal.

Composed of a unit cell


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Crystal Structure

Crystal structure

Crystalline MaterialNoncrsytalline material

(Amorphous)

Single Crystal polycrystal


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Crystalline Material

Crystalline material-atoms, molecules or ion

packed in a regularly ordered, repeating pattern,

extending in 3 spatial dimension.

Single crystal-the periodicity of the pattern

extends throughout a certain piece of material.

Polycrystalline material-comprised of many

single crystal or grain


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atoms pack in periodic, 3D arrays typical of:

Crystalline materials...

-metals

-many ceramics

-some polymers

atoms have no periodic packing

occurs for:

Noncrystalline materials...

-complex structures-rapid cooling

crystalline SiO2

noncrystalline SiO2"Amorphous" = Noncrystalline

Adapted from Fig. 3.18(a),

Callister 6e.

MATERIALS AND PACKING


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Polycrystalline material

grains

Crystalline Amorphous


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Single Crystals

-Properties vary withdirection: anisotropic.

-Example: the modulus

of elasticity (E) in BCC iron:

Polycrystals

-Properties may/may not

vary with direction.

-If grains are randomly

oriented: isotropic.(Epoly iron= 210 GPa)

-If grains are textured,

anisotropic.

200 mm

SINGLE VS POLYCRYSTALS


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Unit cell- smallest structural unit or building

block that can describe the crystal structure.Repetition of the unit cell generates the entire

crystal.

Primitive unit cell- smallest possible unit cell onecan construct.

Lattice parameters-spacing between unit cellsin various direction.

Unit cell


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Unit Cells?


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Concept test

which one is

unit cell


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Crystal system

Point group of lattice

7 unique crystal system Cubic

Hexagonal Tetragonal

Rhombohedral

Orthorhombic

Monoclinic

Triclinic

By adding additional lattice point to 7 basic shapes form 14Bravais lattice


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Metallic crystal structure

Most found crystal structure in common metal Body centered cubic (BCC)

Face centered Cubic (FCC)

Hexagonal close-packed (HCP)

Simple cubic (SC) one lattice point at each of the eight corners

a= lattice parameter

a=2r

n= no. of atom per unit cell

n= 1

coordination no : no of

adjacent atom that touch

atom at lattice point= 6


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Body Centered Cubic (BCC)

3

4ra

n = 2

coordination no: 8
http://www.uncp.edu/home/mcclurem/lattice/vrml/bcc1.wrl


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Face Centered Cubic (FCC)

n= 4

coordination no = 12

22ra


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Hexagonal Close PackedStructure

c/a =1.633


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Atomic Packing Factor (APF)

Efficiency of atomic arrangement in a unit cell.

Exercise: calculate APF for SC,BCC and FCCcrystal structure

Vc

nVs

APF

cellunitofvol.

spherex vol.ofatomofno.


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Theoretical density

ex; If a hypothetical metal crystalline with BCC

crystal structure. Calculate its density. GivenA= 26.98 amu/atom, atomic diameter0.286nm

AcNV

nA

so'no.avogadrxcell)/unitcell(cmunitofvol.

(g/mol)weightatomicxatomofno.3


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Polymorphism allotropic

transformation

the ability of a solid material to exist in more

than one form or crystal structure.

Example: Carbon and iron


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Allotropy: Carbon

Graphite Diamond


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Allotropy : iron


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Crystallography Direction and Plane

(by using miller indices)


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Crystallography direction

Line between two

point or a vector

Axis x y z

Head (H) 0 1 1

Tail (T) 0 0 1

Projection

(H-T)

0 1 0

Enclosed [ O 1 O]

Enclosed in squarebracket


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Lets do another example

Axis x y z

Head (H) 1 0

Tail (T) 0 1 1

Projection

(H-T)

1 - -1

Reduction

(x 2)

2 -1 -2

Enclosed [ 2 ]1 2


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Try it by yourself!!

(0,0,0)

Axis x y z

Head (H)

Tail (T)

Projection

(H-T)

Reduction(x )

Enclosed [ ]

You have to come to the class to get more examples.


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Crystallography Plane

The procedure:

1. If the plane passes through the selected origin

Another parallel plane must be constructed OR

Establish new origin

2. Determine either the plane is intersects or parallels with three axes.

3. Get the reciprocals.

4. If necessary, reduce the number.

5. Enclosed with parentheses , ( )

Remember the integer in enclosure is not separated by commas


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Example:

Axis x y z

Intercepts 1

reciprocals 0 1 0

Reduction(if necessary)

- - -

Enclosed ( 0 1 0 )

Reciprocal: 1/(value)


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Example 2:

Axis x y z

Intercepts 1 1

reciprocals 1 1 0


- - -

Enclosed ( 1 1 0 )


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Try it by yourself!!

(0,0,0)

You have to come to the class to get more examples

Axis x y z

Intercepts

reciprocals


Enclosed ( )

Crystal Structure (2008) (CHAPTER 1)

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