5.Crystal Solid Structures

7/31/2019 5.Crystal Solid Structures

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STATES OF AGGREGATION

ANDCRYSTAL STRUCTURES


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Any material may be in either of thefollowing state. Gas state

Liquid state

Solid state

The state of a material is governed by: Type of bond

Energy of bond

Stability of bond

Sizes of atoms Temperature

Pressure


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GAS STATE

Each individual molecule of a gas has an order.

However, the overall structure has no order.

Intermolecular bonding in gases is built by Van

der Waals bonding which is a weak bond.

Atoms are in continuous motion at high speeds

which prevents them of having a fixed shape.

The random movement of atoms will lead thegas to fill any container into which it isintroduced.


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LIQUID STATE

Liquids have more orderly structure than gases.

However, this order is short ranged.

The bond b/w particles is weak & limited. So,

liquids can take the shape of the containereasily.

The thermal expansion of liquids is less thanthat of gases.


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1. Liquids derived from Crystalline solids:

These consist of small group of atoms still

arranged in a crystalline structure. However,bonds are not strong enough for them to form arigid mass.

2. Liquids derived from amorphous solids:

These are composed of large molecules which areflexible & mobile. The major difference b/w two

liquid types is their melting point. First one has adefinite melting point because all the bonds in theX-talline structure have the same strength & breakdown at the same temperature.


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SOLID STATE

Solid materials are classified according to theregularity with which atoms or ions arearranged with respect to one another.

Crystalline Solids Amorphous Solids

In crystalline materials atoms are situated

in a repeating or periodic array over largeatomic distances. (long range order)

In amorphous materials long range order

do not exist


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The type of bond also affects the type of solid

Ionic and Metallic Bonds Crystalline

Covalent Bonds Amorphous

While passing from liquid state to solid state

there is no definite dividing line. (Gels are inbetween)

Gels are formed by very fine particles of solidtrapping liquid molecules within themselves.

According to the type, strength and number of

bonds, gels may be more liquid or more solid.


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CRYSTALLINE SOLIDS

In a crystalline solid, particles which may be(atoms, molecules or ions) are surrounded by likeneighbors according to a definite geometricalrepetitive pattern.

When describing crystalline structures, atoms orions are thought of as being solid spheres having

well-defined diameters.


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An example of the hard sphere model is theatomic arrangement of some common elemental

metals shown in the figure.

In this example:

All atoms are identical. Sometimes the termlattice is used in thecontext of crystal

structures.Space-Lattice: 3-Darrays of points in spacecoinciding with atom

positions.


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Unit cell: is the smallest unit of a spacelattice which repeats itself to form thelattice.

In other words space-lattice is formed byface to face packing of unit cells.


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Unit Cell Configurations

1. Simple Unit Cell: Lattice points are at every

corner of the cell.

2. Base Centered Unit Cell: Extra lattice points inthe center of two parallel faces.

3. Body Centered Unit Cell:An extra lattice pointsin the interior.

4. Face Centered Unit Cell: Extra lattice points at thecenter of each face.


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CRYSTAL

SYSTEMS

Based on unit cell

configurations andatomic arrangements


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Face Centered Cubic (FCC) Structure

Two representations of a unit cell


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Atomic Packing Factor

Atomic packing factor shows us how dense the unit cell is:

volumecellunitTotalcellunitainatomsofVolumeAPF

APF = 1 ......... Unit cell is filled with atomsAPF = 0 ......... Unit cell is empty


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Atomic Packing Factor of FCC

22

)4(222

ra

raa

A

D

a

a B

GH

E

C

r

r

2r

F

Remember!!!Atoms are hard spheres and they touch oneanother along cube diagonal for an FCC structure.

Number of atoms per unit cell:

Face atoms 6 x 1/2 = 3

Corner atoms 8x1/8 = 1

Total number of atoms in the unit cell = 4

216)22(333 rraVc

Volume of unit cell, Vc


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Atomic Packing Factor of FCC

A

D

a

a B

GH

E

C

r

r

2r

F

74.0

216

)3/4(*)4(3

3

APF

r

rAPF

volumecellunitTotal

cellunitainatomsofVolumeAPF


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How many atom are in the bcc unit

cell?

aR

1 atom in core +

8 x 1/8(atoms on corner)=2 atoms

ADF =

a3

43 ( 3a/4)32

atomsUnit cell

atombody

Birimhcre

Body of unit cell

3

3

3

3

)3

4(

3/..4.23/.4.2

R

R

a

RAPF

volumecellunitTotal

cellunitainatomsofVolumeAPF

68.0APF


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DENSITY COMPUTATION

Since the entire crystal can be generated by therepetition of the unit cell, the density of a crytalline

material can be calculated based on the density of

the unit cell.

cV

nM

: Density of the unit cell

n : Number of atoms in the unit cell

M : Mass of an atom

Vc : Volume of the cell

Mass of an atom is given in the periodic table in atomic mass units

(amu) or gr/mol. To convert (amu) to (gr) use avagadros number.


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DENSITY COMPUTATION

Avagadros number, NA= 6.023x1023

atoms/molTherefore,

AcNVnA

: Density of the unit cell

n : Number of atoms in the unit cell

A: Atomic mass

Vc : Volume of the cell

NA: Avagadros number


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EXAMPLE

Crystal structure = FCC: 4 atom/unit cell Atomic mass = 63.55 g/mol (1 amu = 1 g/mol)

Atomic diameter = 0.128 nm (1 nm = 10 cm)

Vc= a3; for FCC, a = 4R/ 2 ; V

c= 4.75 x 10-23cm3

Therocical result Cu= 8.89 g/cm3Real result

Cu= 8.89 g/cm3

AcNV

nA


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Characterictics of some lements at oC

ElementAluminum

ArgonBarium

BerylliumBoronBromineCadmium

CalciumCarbonCesiumChlorineChromiumCobalt

CopperFlourineGalliumGermaniumGoldHelium

Hydrogen

SymbolAl

ArBa

BeBBrCd

CaCCsClCrCo

CuFGaGeAuHe

H

Atomic mass26.98

39.95137.339.01210.8179.90112.41

40.0812.011132.9135.4552.0058.9363.5519.0069.7272.59196.974.003

1.008

Density.

(g/cm3)2.71

------3.5

1.852.34------8.65

1.552.251.87------7.198.9

8.94------5.905.3219.32------

------

Cyristal str

fcc------bccHSPRhomb------HSP

fccHexbcc------bccHSP

fcc------Ortho.Dia. cubicfcc------

------

Atomic diameter

(nm)0.143

------0.2170.114------------0.149

0.1970.0710.265------0.1250.125

0.128------0.1220.1220.144------

------


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POLYCRYSTALLINE MATERIALS

Most crystalline solids are composed of many smallcrystals or grains termed as polycrystalline.

During the solidification of a polycrystalline solids,

the crystallization may start at various nuclei withrandom crystallographic orientations.

Upon solidification, grains of irregular shapes may

form.The structure will have grain boundaries that could

be seen under a microscope.


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Stage 1 Stage 2

Stage 3 Stage 4


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POLYMORPHIC TRANSFORMATION

Materials having the same chemical composition can

have more than one crystal structure. These are called

allotropic or polymorphic materials.

Allotropyfor pure elements.

Polymorphism for compounds.

These transformations result in changes in the

properties of materials and form the basis for the heat

treatment fo steels and alloys.


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Carbon may exist in two forms:

POLYMORPHISM

Graphite

( 2D layers)

Diamond

(3D structure)


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POLYMORPHISM

Iron (Fe) may also exist in several forms:

BCC at room temperature iron FCC at 910C iron

BCC at above 1400C iron

Above 1539C liquid

Upon heating an iron from room temperature to

above 910C, its crystal structure changes fromBCC to FCC accompanied by a contraction(reduction in volume).

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5.Crystal Solid Structures