EGM 1 MatScie Intro Part3 Crystalline Structure

Pamantasan ng Lungsod ng MaynilaCollege of Engineering and Technology

Engineering Sciences Department

ENGR. ELAINE G. MISSION, M.Sc.

Material Science and Engineering

PART3: STRUCTURE OF CRYSTALLINE SOLIDS

Objectives:

To identify the different crystal structures in solid materials

To determine the relationship between the crystal structures and properties of

materials

To differentiate the crystalline and amorphous structured material

AY 2014-2015 Compiled by: Engr. Elaine Mission 2

Some Important Terms

Crystalline material in which the atoms are situated in a repeating or periodicarray over large atomic distances.

Noncrystalline (Amorphous) materials which lack a systematic and regular arrangement of atoms over relatively large atomic distances. Sometimes called

Supercooled Liquid because their atomic structure resembles that of a liquid.

Grains small crystals


Crystal Structure the manner in which atoms, ions, or molecules are spatially arranged.

Isotropic properties are independent of the direction of measurement.

Anisotropy is the directionality dependence of properties.


Some Important Terms

Lattice a three-dimensional array of points coinciding with atom positions (or sphere center)

Unit Cells the basic structural unit or building block of the crystal structure and defines the crystal structure by virtue of its geometry and the atom positions within.

Crystal Structure/Lattice

Most properties of the crystalline solids depend on the crystal

structure.

Atomic hard-sphere model

Atoms (or ions) in the crystalline structure, assumed to be in

the form of solid spheres having well-defined diameters, touch

the nearest-neighbor atoms.


Unit Cells

Unit Cells are usually in the form of parallelepipeds or

prisms having three sets of parallel faces


Unit Cells

The Unit Cells is the small pattern found in the structure which is

repeated throughout the whole structure of the crystalline.


Metallic Crystal Structures

Atomic Bonding : Metallic

Properties : Nondirectional

Number of nearest-neighbor : large number

Atomic Packing : Dense

Copper crystal structure


Atomic Radii of Some Metals


Metallic Crystal Structures

Three Simple Crystal Structures:

1. Face-centered cubic

2. Body-centered cubic

3. Hexagonal close-packed


Atomic Packing Factor (APF)

APF is the sum of the sphere volumes of all atoms within

a unit cell divided by the unit cell volume.

Coordination NumberCoordination number is the number of nearest-neighbor or

touching atoms.


Face-Centered Cubic Crystal

Structure (FCC)

FCC is a crystal structure which has a unit cell in the

form of cubic geometry, with atoms located at each of

the corners and the centers of all the cube faces.



Structure (FCC)

a = 2R2

a2 + a2 = (4R)2

2a2 = 16R2

a2 = 8R2

Cube Edge :



Structure (FCC)

4 x



Structure (FCC)

Atomic Packing Factor

Coordination Number = 12


Body-Centered Cubic Crystal

Structure (BCC)

BCC is a crystal structure which has a unit cell

in the form of cubic geometry, with atoms

located at all eight corners and a single atom at

the cube center.



Structure (BCC)

a = 4R/3

a2 + (2a)2 = (4R)2

3a2 = 16R2

a2 = 16/3R2

Cube Edge :



Structure (BCC)

2 x



Structure (BCC)




Hexagonal Close-Packed

Crystal Structure (HCP)

HCP is a crystal structure which has a unit cell

in the form of hexagonal geometry, with atoms

located at all twelve corners, at the center of

the two base and one at every pair of parallel

faces.




a2 + c2 = (4R)2

c/a = 1.633

a2 + (1.633a)2 = (4R)2

2.633a2 = (4R)2

a = 4R/2.633

(ideal example)




6 x


Theoretical Density ()

Density is the ratio of mass per unit volume

of substance.

n = number of atoms associated with each unit cell

A = atomic weight

V = volume of the unit cell

N = Avogadros number (6.022 x 1023 atoms/mol)


Polymorphism

Polymorphism is the phenomenon when a

material may have more than one crystal

structure.

AllotropyAllotropy is polymorphism occurring in one

elemental solid.


Crystal Systems

The concept of crystal systems is used to classify

crystal structures on the basis of unit cell

geometry.

Lattice Parameters

The parameter use as basis of unit cell which

include the unit cell edge lengths (a, b, c)and

interaxial angles (, , ).


Crystal Systems

1. Cubic

2. Hexagonal

3. Tetragonal

4. Rhombohedral (Trigonal)

5. Orthorhombic

6. Monoclinic

7. Triclinic


1. Cubic System

FluoriteAY 2014-2015 Compiled by: Engr. Elaine Mission 28

2. Hexagonal System

CorundumAY 2014-2015 Compiled by: Engr. Elaine Mission 29

3. Tetragonal System

RutileAY 2014-2015 Compiled by: Engr. Elaine Mission 30

4. Rhombohedral (Trigonal)

System

CerussiteAY 2014-2015 Compiled by: Engr. Elaine Mission 31

5. Orthorhombic System

BariteAY 2014-2015 Compiled by: Engr. Elaine Mission 32

6. Monoclinic System

BoronAY 2014-2015 Compiled by: Engr. Elaine Mission 33

7. Triclinic System

RhodoniteAY 2014-2015 Compiled by: Engr. Elaine Mission 34

Crystallographic Point Coordinates

The position of any point located within

a unit cell may be specified in terms of

its coordinates as fractional multiples of

the unit cell edge lengths.

P(a, b, c)

P(0.5a, 0.75b, 0c)


Crystallographic Directions

A crystallograpic direction is defined

as a line between two points, or a

vector.


Crystallographic Planes

The orientation of planes for a crystal

structure is specified by three MILLER

INDECES as (hkl)


Crystallographic Planes


Linear Densities (LD)

LD is defined as the number of atoms per unit

length whose centers lie on the direction vector

for a specific crystallographic direction

For a particular material with equivalent

direction, it has an identical linear densities.

The units of linear density are reciprocal length

(1/m)


Planar Densities (PD)

PD is taken as the number of atoms per unit area

that are centered on a particular

crystallographic plane.

For a particular material with equivalent

crystallographic planes, it has an identical

planar densities.

The units of linear density are reciprocal area

(1/m 2)


Single Crystals

Single crystals are the result when a crystalline

solid have a perfect periodic and repeated

arrangement of atoms that extends throughout

the entirety of the specimen without

interruption. Usually have flat faces.

PolycrystallinePolycrystalline is the collection of many grains.

Grain BoundaryGrain Boundary is an atomic mismatch within

the region where two grains meet.


Polycrystalline Single Crystals

If grains are randomly oriented then it is

isotropic.

If grains are textured then it is anisotropic.

Properties strictly are anisotropic.


X-ray Diffraction

Diffraction is a consequence of specific phase

relationships established between two or more

waves that have been scattered by the obstacles.

Diffraction occurs when a wave encounters a

series of regularly spaced obstacles that are:

1. capable of scattering the wave

2. have spacings that are comparable in

magnitude to the wavelength

Diffractometer is an apparatus used to determine

the angles at which diffraction occurs for

powdered specimens.


Diffraction

Mutually Reinforced

The waves form are added forming a wave with the

additive amplitude.


Diffraction

Partially Reinforced

The waves form are partially added forming a wave

with the additive amplitude.


Diffraction

Destructive Interfere

The waves form are interfere with each other

causing them to cancel each other.


X-ray Diffraction

X-rays are a form of electromagnetic radiation

that have high energies and short wavelengths

(wavelengths on the order of the atomic

spacings for solids).

When a beam of x-rays impinges on a solid

material, a portion of this beam will be

scattered in all directions by the electrons

associated with each atom or ion that lies

within the beams path.


Braggs Law

n = 2dsin

Braggs law provide a simple expression relating

the x-ray wavelength and interatomic spacing to

the angle of the diffracted beam.


Factors Crystalline Materials NoncrystallineMaterials

Packing Atoms pack in periodic and 3D array

Atoms have no periodic packing

Materials Usually in metals,many ceramics and

some polymers

Usually in complex structures and rapid cooling substances

Comparison


EGM 1 MatScie Intro Part3 Crystalline Structure

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