MME 323: MATERIALS SCIENCE WEEK 3 :

FUNDAMENTAL of CRYSTALLOGRAPHY*

Adhi Primartomo, PhDEmail: primartomo_a@jic.edu.saOffice: Room 191 – JIC Academic Building* Source: Materials Science and Engineering; 9th Edition;

W.D.Callister; Wiley; 2011

https://sites.google.com/site/primartomo/file-cabinet

~ LECTURE OUTLINE ~

Chapter 3: Fundamental of Crystallography (page 47 - 69)*

• Why Study Fundamental of Crystallography?• Fundamental Concepts,• Unit Cells,• Crystal Systems,• Crystallographic Points, Directions and Planes• Single Crystal & Polycrystalline Materials,• Anisotropy & Isotropy.

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~ Week 3 Learning Objective ~

After studying this chapter, you should be able to:• Describe the difference in atomic structure between

Crystalline and Noncrystalline materials,• Define the crystal structure, lattice, unit cell, lattice

parameters and crystal system,• Describe the points, directions and planes in the unit

cell,• Distinguish between single crystal and polycrystalline

materials,• Define isotropy and anisotropy with respect to

materials properties.

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WHY STUDY FUNDAMENTAL OF CRYSTALLOGRAPHY?

(page 48)

The properties of materials directly related to their crystal structures:

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Magnesium (Mg):silvery white color, light weight metal, highly flammable when powdered.

Gold (Au): yellow color, very dense metal, most malleable of

all metals.

FUNDAMENTAL CONCEPTS(page 48-49)

Solid materials are classified according to the regularity with which atoms or ion are arranged with respect to one another.

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• Crystalline:

?• Noncrystalline:

?

• Crystal structure:

?• Lattice:

?

UNIT CELLS(page 49)

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• Unit Cell:

?

Unit Cell

Lattice

CRYSTAL SYSTEMS(page 50)

There are many different possible crystal structure so, it’s convenient to divide them into groups according to unit cell configurations or atomic arrangements.

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• Lattice parameters:?

• Crystal systems:?

Figure: Unit Cell with its Lattice Parameter

CRYSTAL SYSTEMS(page 50)

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All together there are 7 possible combinations of lattice parameters (crystal systems) and so 14 types of Unit Cells:

Cubic Structure a = b = c α = β = γ = 900

Tetragonal Structure a = b ≠ c α = β = γ = 900

Orthorhombic a ≠ b ≠ c α = β = γ = 900

Rhombohedral a = b = c α = β = γ ≠ 900

Hexagonal Structure a = b ≠ c α = β = 900 γ = 1200

Monoclinic a ≠ b ≠ c α = γ = 900 ≠ β Triclinic a ≠ b ≠ c α ≠ β ≠ γ ≠ 900

Figure: Unit Cell with its Lattice Parameter

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Figure: 7 Crystal Systems and their 14 Bravais Lattice

CRYSTALLOGRAPHIC POINTS, DIRECTION,& PLANES (page 51-65)

When dealing with crystalline materials, it’s necessary to specify a particular lattice point, a crystallographic direction and some crystallographic plane of atoms

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Point Coordinates: (page 52)

o qa = lattice position referenced to x axis,

o rb = lattice position referenced to y axis,

o sc = lattice position referenced to z axis.

Figure: The way in which q, r and s coordinates at point P are determined

CRYSTALLOGRAPHIC POINTS, DIRECTION,& PLANES (page 51-65)

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Examples 3.1 & 3.2: (page 52-53)

Z

Y

X

0

Z

Y

X

0

CRYSTALLOGRAPHIC POINTS, DIRECTION,& PLANES (page 51-65)

Line directed between two points (vector)

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Crystallographic Directions: (page 54)

o Using a right-handed coordinate system, determine the coordinates of two points that lie on the direction,

o Subtract the coordinates of “tail” point from the coordinates of the “head” point to obtain the number of lattice parameters traveled in the direction of each axis of the coordinate system,

o Clear fractions and reduce the results obtained from subtraction to lowest integers,

o Enclose the number in square brackets […]. Negative sign represented with bar sign over the number.

CRYSTALLOGRAPHIC POINTS, DIRECTION,& PLANES (page 51-65)

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Examples 3.3 & 3.4: (page 55-56)

Z

Y

X

0

Z

Y

X

0

CRYSTALLOGRAPHIC POINTS, DIRECTION,& PLANES (page 51-65)

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The crystallographic planes are specified by thee miller indices

Crystallographic Planes: (page 60)

o Identify the points at which the plane intercept the x, y and z coordinates in term of no. of lattice parameters,

o If the plane passes through the origin, the origin of the coordinated must be moved !!

o Take reciprocals of these intercepts,o Clear fractions but do not reduce to lowest integers,o Enclose the resulting number with parentheses (…).

Negative sign represented with bar sign over the number.

CRYSTALLOGRAPHIC POINTS, DIRECTION,& PLANES (page 51-65)

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Examples 3.6 & 3.7: (page 61-63)

Z

Y

X

0

Z

Y

X

0

CRYSTALLOGRAPHIC POINTS, DIRECTION,& PLANES (page 51-65)

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X

Z

Y

Z

Y

X

Z

X(100) (101) (112)

Some important Planes of a Cube:

CRYSTALLOGRAPHIC POINTS, DIRECTION,& PLANES (page 51-65)

CRYSTALLINE & NONCRYSTALLINE MATERIALS (page 65-68)

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Polycrystalline Materials: (page 65)

Most crystalline solids are polycrystalline

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Polycrystalline Materials: (page 65)

Nuclei

Dendrites

LiquidLiquid

Dendrites

Crystal

Liquid

Grains

Grain Boundaries

Formation of Grains during Solidification

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Polycrystalline Materials: (page 65)

Microstructure of Steel

Grain

Grain Boundary

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Polycrystalline Materials: (page 65)

• Grain: ??

• Grain Boundaries : ??

• Polycrystalline material: ??

Single Crystalline Materials: (page 65) Materials in which the atomic order extends uninterrupted over the entire of material.Examples: Single Crystal Silicon (used in semiconductor),

Single Crystal Nickel (used in Turbine Blade)

ANISOTROPY & ISOTROPIC (page 67)

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The properties of crystalline structure of some substance depend on the crystallographic direction in which measurement are taken.

• Anisotropy: ??

• Isotropic: ??

END OF PRESENTATION