mae 91 week 2 discussion slides

8/18/2019 MAE 91 Week 2 Discussion Slides

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E54 Discussion

Week 2 Arunima Bhattacharjee

Department of Chemical Engineering andMaterial Science

arunima !uci"edu

#


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$ui%

2


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$uestion #

&

What is the name of thecrystal structure shown

below?

A) SC

B) BCCC) FCCD) HCP


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$uestion 2

4

What is the coordinationnumber of the structure

shown below?

A) 2

B)C) !D) "2


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$uestion &

5

What is the name of thecrystal structure shown

below?

A) SC

B) BCCC) FCCD) HCP


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$uestion 4

'

What is the #ro#er notationfor a sin$le direction in a FCC

structure?

A) %)

B) &'C) (D) *+


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$uestion 5

(

A)%""2)B)%""")C)%""-)D)%"-2)

hich #lane does the hi$hli$hted structure re#resen


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)opics

*


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Cr+stalline Materials

, Cr+stal Structure - Metals and Ceramics

, Atomic .acking /raction 0A./1 andDensit+


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Cr+stal Structure

, Cr+stal Structure - .eriodic arrangement of atoms in a ordered

structure" Due to minimi%ation of energies"3nit cell the simplest repeating unit in acr+stal

- attice Arra+ of infinitel+ repeating atoms in &6D space

- Basis 7ector0s1 coordinates of atoms relati8eto the lattice point

, Cr+stal Structure 9 attice : Basis

#;


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Cr+stal Structure 0Cont"1

, ( different cr+stal s+stems ut cubic andhexagonal the most common

, #4 different cr+stal structures - e?agonal

##


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Simple Cu ic 0SC1

#2

Number of Atoms in Unit Cell, ! atoms at corner with each of a atom, %! atoms) . %) / " atom, Primiti0e unit cell1 " atom #er unit cell

, a / lattice #arameter %len$th of cube ed

Coordination Number (CN), umber of nearest nei$hbors

, C / 3


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#&

Simple Cu ic 0SC1 0Cont"1Lattice Parameter (unit celledge length), a / 2rUnit Cell Volume (Cube)

, 4 c / a 5 Volume of Atoms in Unit Cell(Sphere), 4 s / r 5

, 4 s / %")Atomic Packing Factor (APF), APF / / -672, 728 of the unit cell occu#ied

by atoms


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Bod+ Centered Cu ic 0BC1

#4

Number of Atoms in Unit Cell, ! atoms at corner with each of a atom, " atom at center totally enclosed, %! atoms) . %) 9 " atom/ 2 atoms

, on:#rimiti0e unit cell

Coordination Number (CN), umber of nearest nei$hbors, C / !


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#5

Bod+ Centered Cu ic 0BC1 0Cont"1

Lattice Parameter (unit celledge length), a / rUnit Cell Volume (Cube), 4 c / a 5 / /Volume of Atoms in Unit Cell(Sphere), 4 s / r 5

, 4 s / %2) /Atomic Packing Factor (APF), APF / / -63!, 3!8 of the unit cell occu#ied

by atoms


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/ace Centered Cu ic 0/CC1

#'

Number of Atoms in Unit Cell, ! atoms at corner with each of a atom, 3 atoms at the face with each of a ato, %! atoms) . %) 9 %3 atom) . %) / atom


Coordination Number (CN), umber of nearest nei$hbors

, C / "2


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#(

Lattice Parameter (unit celledge length), a /Unit Cell Volume (Cube), 4 c / a 5 / /

Volume of Atoms in Unit Cell(Sphere), 4 s / r 5

, 4 s / % ) /

Atomic Packing Factor (APF), APF / / -6;, ; 8 of the unit cell occu#ied

by atoms %Hi$hest APF< close

#ac=ed structure)

/ace Centered Cu ic 0/CC1 0Cont"1


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>e?agonal Close .acked 0>C.1

#*

Number of Atoms in Unit Cell, "2 atoms at corner with each of a

atom, 2 atoms at the face with each of a

atom, 5 atoms mid:#lane totally enclosed, %"2 atoms) . %) 9 %2 atom) . %) 9 5

atoms/ 3 atoms


Coordination Number (CN), umber of nearest nei$hbors, C / "2


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>e?agonal Close .acked 0>C.1 0Cont"1

#

Lattice Parameter (unit celledge length), >wo #arameters %a c), a /, c@a / "6355

Unit Cell Volume ( e!agon), 4 h /%3) %c) /%3) &"6355%2r)'Volume of Atoms in Unit Cell(Sphere), 4

s / r 5

, 4 s / %3) /Atomic Packing Factor (APF), APF / / -6;, ; 8 of the unit cell occu#ied

by atoms %Hi$hest APF< close


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Densit+ Calculations

2;


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2#

Densit+ Calculations 0Cont"1

inear Densit+ ≡ D 93nit length of direction 8ector

@um er of atoms centered on a direction


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22

Densit+ Calculations 0Cont"1

.laner Densit+ ≡ .D 9 Area of the plane

@um er of atoms centered on a plane

%"--) Plane on FCC

a / r


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Cr+stal Directions and .lanes

, dentif+ing and Dra=ing Directions - Cu ic s+stems

, dentif+ing and Dra=ing .lanes - Miller indices

- Cu ic and he?agonal s+stems

2&


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dentif+ing Directions

24

Procedure for dentifyin$ Directions"6 Determine 0ector com#onents & nal%head)

initial%tail)'26 Con0ert the indi0idual translations into &u0w'

notation, ee# si$n %bar) and con0ert fractions to lowest

inte$ers, Ese brac=ets &' with ( re#resentin$ a family of

directions

Gam#les


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Dra=ing Directions

25

Procedure for Drawin$ Directions"6 Place the ori$in so the direction is inside the unit

cell, e$ati0e or #ositi0e?

26 Co0ert the &u0w' notation into 0ectors from theori$in, Bar / ne$ati0e si$n and reduce to fraction

56 Pro ect the &u0w' inside the unit cell and connect

the ori$in to nal #osition

Gam#les

&"


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dentif+ing .lanes 0Cu ic1

2'

Procedure for dentifyin$ Planes %Cubic)"6 Place the ori$in so it does not lay on the #lane26 Determine where the #lane intersects the G


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Cu ic E?ample 0 dentif+ing1

2(

4" Miller ndices 0;2;1

#" ntercepts ∞ "@2 ∞

2" eciprocals "@∞ "@%"@2) "@∞- 2 -

&" eduction - 2 -

x y z Plane "

4" Miller ndices

#" ntercepts "@2 :"@2 "2" eciprocals "@%"@2) :"@%"@2) "

2 :2 "&" eduction 2 :2 "

x y z

(221)

Plane 2


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2*

Dra=ing .lanes 0Cu ic1

Procedure for Drawin$ Planes %Cubic)"6 Place the ori$in so it does not lay on the #lane

, e$ati0e or #ositi0e?26 Con0ert miller indeG notation to G


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2

Cu ic E?ample 0Dra=ing1

% %2"2

%) %)


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&;

dentif+ing .lanes 0>e?agonal1

Procedure for dentifyin$ Planes %HeGa$onal)"6 Place the ori$in so it does not lay on the #lane26 Determine where the #lane intersects the a "


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>e?agonal E?ample 0 dentif+ing1

i = − (h + k ) = − (0 + 0) = 0

4. No fractions to clear

," h = 0, k = 0, l = 2

," Convert to 4 index system ( hkil ) by

1. Intercepts ∞ ∞ 1 22. !eciprocals 1 ∞ 1 ∞ 1 (1 2)

0 0 2". !ed#ction 0 0 2

a1 a 2 z

(0002) >his is the #lane


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&2

Procedure for Drawin$ Planes %HeGa$onal)"6 Con0ert miller indeG notation to a "


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&&

>e?agonal E?ample 0Dra=ing1

% %

a 2

a "

a 5

I


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$uestions

&4

mae 91 week 2 discussion slides

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