crystal slides
TRANSCRIPT
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METE 327 Physical Metallurgy Copyright 2008 Loren A. Jacobson !"#!08
Crystal $y%%etries
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METE 327 Physical Metallurgy Copyright 2008 Loren A. Jacobson !"#!08
&hy shoul' (e be intereste')
*%portant physical properties 'epen' on crystalstructure
Con'ucti+ity
Magnetic properties $ti,,ness
$trength
These properties also o,ten 'epen' on crystalorientation
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METE 327 Physical Metallurgy Copyright 2008 Loren A. Jacobson !"#!08
$o%e *%portant Ter%s ,or Crystals
Crystal $tructure -ra+ais lattices
$y%%etry operations
-asis o, Close Pace'$tructures
Miller *n'ices Planes /irections
$tereographicProection
$tan'ar' Proection Principal Metal $tructures
1-CC CC 4CP
*onic Crystals
/ia%on' $tructure
T(inne' Crystals
*so%orphis%
Poly%orphis%
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METE 327 Physical Metallurgy Copyright 2008 Loren A. Jacobson !"#!08
-ra+ais Lattices 5"6 Total
Cubic1abc all angles 90o Tetragonal1ab !c all angles90o :rthorho%bic1a!b!c all angles90o ;ho%bohe'ral1abc three e> a!b!c no angles nor 90o
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METE 327 Physical Metallurgy Copyright 2008 Loren A. Jacobson !"#!08
Cubic -ra+ais Lattices
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METE 327 Physical Metallurgy Copyright 2008 Loren A. Jacobson !"#!08
Tetragonal an' :rthorho%bic
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METE 327 Physical Metallurgy Copyright 2008 Loren A. Jacobson !"#!08
:rthorho%bic ;ho%bohe'ral
4e=agonal
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METE 327 Physical Metallurgy Copyright 2008 Loren A. Jacobson !"#!08
Monoclinic Triclinic
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METE 327 Physical Metallurgy Copyright 2008 Loren A. Jacobson !"#!08
Miller *n'icesA Con+enient &ay to *'enti,y
Crystal Planes an' /irections or Planes the in'e= is the
reciprocal o, the +alue o, the
intersection o, the plane (ith aparticular a=is con+erte' to (holenu%bers.
or /irections the in'e= is the a=is
coor'inate o, the en' point o, the+ectorcon+erte' to nearest (holenu%bers.
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METE 327 Physical Metallurgy Copyright 2008 Loren A. Jacobson !"#!08
Miller *n'ices 5'irections
h,k,an'l re,er to principal a=esx,yan' z. /irections are in'icate' by s"00@?0>"0@ an' ?00>"@ The ,irst three are principal a=es
=y an' D.
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METE 327 Physical Metallurgy Copyright 2008 Loren A. Jacobson !"#!08
Miller *n'ices 5planes
Planes are in'icate' byparentheses 5hl an' ,a%ilies o,planes by curly bracets hlF.
E=a%ple o, a plane ,a%ily is as,ollo(s "00F 5"00 50"0 500"5>"00 50>"0 an' 500>" These are all si= ,aces o, a cube.
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METE 327 Physical Metallurgy Copyright 2008 Loren A. Jacobson !"#!08
Calculating Miller *n'e= ,or planes
x
z
Intercepts= 0.5, 1, 1/3
Index = (213)
Intercepts= -1, 1, 0.5
Index = (-112)
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METE 327 Physical Metallurgy Copyright 2008 Loren A. Jacobson !"#!08
Calculating Miller *n'e= 'irections
End coordinates= 0.5,0.5,1
Index = [112]
End=0,1,0.5
Index=[021]
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METE 327 Physical Metallurgy Copyright 2008 Loren A. Jacobson !"#!08
4e=agonal Miller>-ra+ais *n'ices
a1
a2
a3
c!ree a directions,as s!o"n, p#$s c
Indices are%
(!,&,-(!'&), #)
!e p#ane s!o"n is%
(11-20)
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METE 327 Physical Metallurgy Copyright 2008 Loren A. Jacobson !"#!08
:ther Crystal CharacteriDation
*t is o,ten i%portant to 'eter%ine crystalorientation.
$ingle crystals.
*n'i+i'ual grains in a polycrystal *, there is a pre,erre' grain orientation
this is re,erre' to as Gte=tureH.
:ne %etho' is to e%ploy the $tereographic
Proection.
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METE 327 Physical Metallurgy Copyright 2008 Loren A. Jacobson !"#!08
$tereographic Proection
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$o%e Cubic Crystal Planes
001 #ane
110 #ane
111 #ane
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METE 327 Physical Metallurgy Copyright 2008 Loren A. Jacobson !"#!08
Crystal $y%%etries
Translational $y%%etry1a %o+e o, one cellin each o, 3 a=is 'irections restores thestructure.
;otational $y%%etry1rotation o, speci,icangle 590o "20o "80o restores the structure.
Mirror $y%%etry1re,lection across a planerestores the structure.
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METE 327 Physical Metallurgy Copyright 2008 Loren A. Jacobson !"#!08
A si%ple Cubic $tructure5illustrating translational sy%%etry
The cubic unit cell
Eight unit cells the starto, a crystal structure.
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METE 327 Physical Metallurgy Copyright 2008 Loren A. Jacobson !"#!08
;otational $y%%etry Cubic
o$r-*o#d
+otation
"o-o#d
+otation
!ree-o#d+otation
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METE 327 Physical Metallurgy Copyright 2008 Loren A. Jacobson !"#!08
"00F Poles o, a Cubic Crystal
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METE 327 Physical Metallurgy Copyright 2008 Loren A. Jacobson !"#!08
*nterplanar Angles
oints on t!e sp!ere are intersectionso* p#ane nora#s.
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METE 327 Physical Metallurgy Copyright 2008 Loren A. Jacobson !"#!08
Calculating *nterplanar Angles5Cubic Crystals
os = h1h
2+ k
1k
2+ l
1l2
-------------------------- +((h
1
2 + k1
2+ l1
2)(h2
2
+ k
2
2+ l2
2))
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METE 327 Physical Metallurgy Copyright 2008 Loren A. Jacobson !"#!08
Calculating *nterplanar $pacing5Cubic Crystals
1/d2 = (h2+ k2+ l2)/ a2
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METE 327 Physical Metallurgy Copyright 2008 Loren A. Jacobson !"#!08
$tan'ar' 500" Cubic Proection
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METE 327 Physical Metallurgy Copyright 2008 Loren A. Jacobson !"#!08
The $tan'ar' $tereographic Triangle
se*$# *or s!o"in crysta# axis orientations.
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METE 327 Physical Metallurgy Copyright 2008 Loren A. Jacobson !"#!08
Metallic -on'ing
Ialence or outer electrons o, %etallic ato%s are 'istribute' throughoutthe structure. Positi+ely charge' %etal ions are 'istribute' (ithin thisGseaH o, electrons.
This allo(s %etals to be electrical con'uctors.
There are secon' nearest neighbor interactions that in,luence thecrystal structure
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METE 327 Physical Metallurgy Copyright 2008 Loren A. Jacobson !"#!08
-o'y Centere' Cubic 5-CC Metals
-e, r,o, , -i,
-4r
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METE 327 Physical Metallurgy Copyright 2008 Loren A. Jacobson !"#!08
ace>Centere' Cubic 5CC Metals
$, #, 6i, 7,
-e
4 l Cl P ' 54CP
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METE 327 Physical Metallurgy Copyright 2008 Loren A. Jacobson !"#!08
4e=agonal Close>Pace' 54CPMetals
8e, , 4n, d, -i, -4r
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METE 327 Physical Metallurgy Copyright 2008 Loren A. Jacobson !"#!08
;elation -et(een CC an' 4CP
8
8..
.
88
8..
.
-CC t 4CP T , ti
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METE 327 Physical Metallurgy Copyright 2008 Loren A. Jacobson !"#!08
-CC to 4CP Trans,or%ation
#ose ac&ed 8 p#ane 9110: 7ecoes#ose ac&ed ; p#ane (0002).
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METE 327 Physical Metallurgy Copyright 2008 Loren A. Jacobson !"#!08
-CC to 4CP Trans,or%ation 52
1.ariants o* ;.)
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METE 327 Physical Metallurgy Copyright 2008 Loren A. Jacobson !"#!08
Types o, Trans,or%ations
/isplaci+e (hich %eans that ato%s 'onot ha+e to %o+e +ery ,ar an' o,ten ashear 'isplace%ent can lea' ,ro% onecrystal structure to another.
;eplaci+e (hich %eans that ato%s (ill%o+e so%e 'istance to their ne(locations an' so longer range 'i,,usionis re
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METE 327 Physical Metallurgy Copyright 2008 Loren A. Jacobson !"#!08
a
7
a
7
c = a x 7
a 1
7 3
7 3= a1x a2 a3 (a1x a2)
a3a 2
c ab sin a
c a = b a b ab cos a
Iector Multiplication E=a%ples
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METE 327 Physical Metallurgy Copyright 2008 Loren A. Jacobson !"#!08
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METE 327 Physical Metallurgy Copyright 2008 Loren A. Jacobson !"#!08