Crystalstructures for Class

7/25/2019 Crystalstructures for Class

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Learning objectives

After the chapter is completed, you will be ableto answer:

Difference between crystalline and

noncrystalline structures Different crystal systems and crystal structures

Atomic packing factors of different cubic crystalsystems

Difference between unit cell and primitive cell Difference between single crystals and polycrystals


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Short-range order- The regular and predictablearrangement of the atoms over a short distance - usuallyone or two atom spacings.

Long-range order (LRO)- regular repetitive arrangementof atoms in a solid which e!tends over a very largedistance.

"ose-#instein condensate ("#$)- newly e!perimentallyveri%ed state of a matter in which a group of atoms

occupy the same &uantum ground state.

Section 3.1Short-Range Order versus

Long-Range Order


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What is space lattice?

Space lattice is the distribution of points in3D in such a way that every point hasidentical surroundings, i.e., it is an infinitearray of points in three dimensions inwhich every point has surroundingsidentical to every other point in the array.


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Common materials: with various viewpoints

Glass: amorphous

Ceramics

Crystal

Graphite

PolymersMetals


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Metals and alloysCu, Ni, Fe, NiAl (intermetallic compound), Brass (Cu-Zn alloys)

Ceramics (usually oides, nitrides, car!ides)Alumina (Al"#$), Zirconia (Zr"#$)

Polymers (thermoplasts, thermosets) (%lastomers)Polythene, Poly&inyl chloride, Polypropylene

Common materials: examples

Based on %lectrical Conduction

ConductorsCu, Al, NiAl

'emiconductorsGe, 'i, GaAs

nsulatorsAlumina, Polythene

Based on *uctility

*uctileMetals, Alloys

BrittleCeramics, nor+anic Glasses, Ge, 'i

* some special polymers could be conducting


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MA%A.' 'C%NC% / %NGN%%NGMA%A.' 'C%NC% / %NGN%%NG

P01'CA. M%C0ANCA. %.%C#-

C0%MCA.

%C0N#.#GCA.

2%tracti&e

2Castin+

2Metal Formin+23eldin+2Po4der Metallur+y

2Machinin+

2'tructure

2Physical

Properties

Science of 'etallurgy

2*e5ormation

Beha&iour

2hermodynamics2Chemistry2Corrosion

he !road scienti5ic and technolo+ical se+ments o5 Materials 'cience are sho4n

in the dia+ram !elo46

o +ain a comprehensi&e understandin+ o5 materials science, all these aspects

ha&e to !e studied6


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Lattice the underlying periodicity of the crystal

Basis Entityassociatedwith each lattice points

Lattice how to repeat

Motif what to repeat

Crystal =Lattice+

MotifMotiforBasis:typically an atom or a group of atoms associated with each lattice point

Definition 1

Translationally periodicarrangement ofmotifs

Crystal

Translationally periodicarrangement ofpoints

Lattice
http://lattice.ppt/http://motifs.ppt/http://motifs.ppt/http://motifs.ppt/http://motifs.ppt/http://lattice.ppt/


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An array of points such that every point has

identical surroundings

In Euclidean space

infinite array

We can have 1D, 2D or 3D arrays (lattices)

Space Lattice

Translationally periodic arrangement of points in space is called a lattice

or

A lattice is also called a Space Lattice
http://lattice.ppt/http://lattice.ppt/


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Unit cell:A unit cell is the sub-division of the

space lattice that still retains the overallcharacteristics of the space lattice.Primitive cell:the smallest possible unit cell of alattice, having lattice points at each of its eight

vertices only.A primitive cell is a minimum volume cellcorresponding to a single lattice point of a structurewith translational symmetry in 2 dimensions, 3dimensions, or other dimensions.A lattice can be characterized by the geometry of itsprimitive cell.


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Crystal Systems

7 crystal systems

14 crystal lattices

nit cell+nit cell+ smallest repetitive volumewhich contains the complete latticepattern of a crystal.

a, b, and care the lattice constants


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$rystal systemsCubic Three equal axes, mutually perpendicular

a=b=c ===90

Tetragnal Three perpendicular axes, nly t! equal

a=b"c ===90

#exagnal Three equal cplanar axes at 1$0 and a %urth unequalaxis perpendicular t their plane

a=b"c == 90 =1$0

&hmbhedral Three equal axes, nt at right angles

a=b=c =="90

'rthrhmbic Three unequal axes, all perpendicular

a"b"c ===90(nclinic Three unequal axes, ne % !hich is perpendicular t the

ther t!

a"b"c ==90"

Triclinic Three unequal axes, n t! % !hich are perpendicular

a"b"c " ""90


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Someengineering applications re&uiresingle crystals

--diamond single crystals *or arasives

--turine lades


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1are due to lo2 packing density !only )o has this st

Close-packed directionsare cue edges.

Coordination ' 4 ! nearest neighors$

Simple $ubic Structure (S$)


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ari *rasad


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ari *rasad


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+ Coordination,

&toms touch each other along cue diagonals.--Note+ &ll atoms are identical5 the center atom is shaded di6erently only *or ease o* vie2ing.

7ody Centered CuicStructure !7CC$

ex+ Cr, /, 8e !$, 9antalum, (olydenu

atoms:unit cell+ ; center < = corners


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tomic *ac/ing 0actor "$$

a

&)8 '

>

3

! 3a:> $3

atoms

unit cell atom

volume

a3

unit cell

volume

length ' >R'

Close-packed directions+

3 a

&)8 *or a ody-centered cuic structure ' ?.4=

aR

a2

a$


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Coordination ' ;

&toms touch each other along *ace diagonals.

--Note+ &ll atoms are identical5 the *ace-centered atomsdi6erently only *or ease o* vie2ing.

8ace Centered Cuic Structure!8CC$

ex+ &l, Cu, &u, ), Ni, )t, &g

> atoms:unit cell+ 4 *ace x ;: < = corners


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ari *rasad


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&)8 *or a *ace-centered cuic structure ' ?.@>

&tomic )acking 8actor+ 8CC

maximum achievable APF

&)8 '

>3 ! a:>$3>

atoms

unit cell atomvolume

a3

unit cell

volume

Close-packed directions+

length ' >R' a

nit cell contains+ 4 x ;: < = x ;:=

'> atoms:unit cella

$ a


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SC-coordination number

6


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BCC-coordination number

8


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FCC-coordination number

4+4+4=12


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ari *rasad


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(c) "77$ Broo8s9Cole Pu!lishin+ 9 homson .earnin+

Figure 3.11 Thefourteen tpes of!ra#ais latticesgrouped in se#encrstal sstems.The actual unitcell for ahe$agonal sstemis shown inFigures 3.1% and

3.1&.


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HCP-coordination number

3+6+3=12


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9heoretical Density,

2here n' numer o* atoms:unitcell

A'atomic 2eightVC' Aolume o* unit cell ' a

3*or

cuic N&' &vogadroBs numer

' 4.?3 x ;?3atoms:mol

Density '

'

VCN

A

nA

'

Cellnito*Aolume9otal

Cellnitin&tomso*(ass


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Documents

Crystalstructures for Class