Upload
mmiller276
View
222
Download
0
Embed Size (px)
Citation preview
7/21/2019 05 Metals Cry
1/23
Metallic Structures: Unit CellsMetallic Structures: Unit Cells
Simplifed 2D DiscussionSimplifed 2D Discussion
Unit Cell: Smallest Repeating unit that represents symmetry/order ostructure.
7/21/2019 05 Metals Cry
2/23
Metallic Structures: Unit CellsMetallic Structures: Unit Cells
z
x
y
7/21/2019 05 Metals Cry
3/23
7 systems o crystal symmetry
!"amples o the Unit Cells#
Source: R.E. Smallman, Ch1, F1.7
7/21/2019 05 Metals Cry
4/23
Source: R.E. Smallman, Ch1, F1.15
7 Systems o Crystal Symmetry$% Crystal Structures
7/21/2019 05 Metals Cry
5/23
&oint Coordinates: Determining'here atoms sit.
&oint coordinates or unit cellcenter are
a/2( b/2( c/2 ) ( )( )#
&oint coordinates or unit cellcorner are $( $( $#
*ranslation: integer multiple olattice constants identical
position in another unit cell
z
x
y
a b
c
000
111
y
z
2c
b
b
7/21/2019 05 Metals Cry
6/23
Crystallographic Directions: Mo+ing,et-een tomic &ositions
$. 0ector repositioned i necessary# topass
through origin.
2. Read o1 proections in terms ounit cell dimensions a( b( and c3. dust to smallest integer +alues%. !nclose in s4uare 5rac6ets( nocommas
uvw
8ex:1, 0, => 2, 0, 1 => [201]
-1, 1, 1
amilies o directions
z
x
l!or"#hm
-here o+er5ar represents a negati+einde"
[111]=>
y
7/21/2019 05 Metals Cry
7/23
ex: l"near $en%"#& o' l "n [110]$"rec#"on
a= 0.(05 nm
;inear Density;inear Density
;inear Density o toms ;D &roperties +ary -ith direction: anisotropic.
>!"ample: the modulus o elasticity !# in ,CC iron:
?mportance o ;inear/ &lanar Densities?mportance o ;inear/ &lanar Densities
! diagonal# < 273 @&a
! edge# < $2A @&a
7/21/2019 05 Metals Cry
9/23
Metallic Structure:Metallic Structure:
Crystallographic &lanesCrystallographic &lanes
$a#e$ 'rom F"!. *., Callister 7e.
7/21/2019 05 Metals Cry
10/23
Metallic Structure:Metallic Structure:
Crystallographic &lanesCrystallographic &lanes z
x
ya b
c
(. /"ller n$"ce% 110
examle a b cz
x
ya b
c
(. /"ller n$"ce% 100
1. n#erce#% 1 1 2. Rec"rocal% 131 131 13
1 1 0*. Re$uc#"on 1 1 0
1. n#erce#% 132 2. Rec"rocal% 13 13 13
2 0 0*. Re$uc#"on 2 0 0
examle a b c
7/21/2019 05 Metals Cry
11/23
Re+ie- o Determining &lanes CoordinatesRe+ie- o Determining &lanes Coordinates
examle a b cz
x
y
a b
c
(. /"ller n$"ce% 100
1. n#erce#% 1 2. Rec"rocal% 1 13 13
*. Re$uc#"on 1 0 0
7/21/2019 05 Metals Cry
12/23
Crystallographic &lanes
z
x
y
a b
c
(. /"ller n$"ce% 4*(
examle
1. n#erce#% 132 1 *3(
a b c
2. Rec"rocal% 13 131 13
2 1 (3*
*. Re$uc#"on 4 * (
001010,
Fam"l& o' 6lane% hkl8
100, 010,001,Ex: 1008 = 100,
7/21/2019 05 Metals Cry
13/23
Spacing 5et-een e4ui+alent planes
dhkl
=a
h2+ k
2+ l
2
'hat is the spacing 5et-een $$$#
planes in BCC =ic6el *he atomicradius is .$2% nm.
a# .2 nm5# .3A nmc# .3 nm
7/21/2019 05 Metals Cry
14/23
&lanar Density o $# ?ron
t * 9 E$2C iron has the ,CC structure.
100
Radius o iron R< .$2%$ nm
R*
*(a=
$a#e$ 'rom F"!. *.2c, Callister 7e.
2D repeat unit
6lanar en%"#& =a2
1
a#om%
2 reea# un"#
=
m2a#om%= 1.2 x 101
12
R*
*(area
2 reea# un"#
7/21/2019 05 Metals Cry
15/23
&lanar Density o $$$# ?ron
Solution cont#: $$$# plane 1 a#om "n lane3 un"# %ur'acecell
***
2
2
R*
14R
*
(
2a*ah2area =
===
atoms in plane
atoms a5o+eplane
atoms 5elo-
plane ah2*=
a2
2,re
-ea#un"#
1
= =
nm2a#om%
7.0m2
a#om%0.70 x 101
* 2R*
146lanar en%"#& =
a#om%2 reea# un"#
area
2 reea# un"#
7/21/2019 05 Metals Cry
16/23
F Coordination G < $2
F ,,... Stac6ing Se4uence
F &B < .7%
F 3D &roection F 2D &roection
$a#e$ 'rom F"!. *.*a,
Callister 7e.
He"agonal Close>&ac6ed StructureHe"agonal Close>&ac6ed Structure
HCHC
I atoms/unit cell
e": Cd( Mg( *i( Jn
F c/a< $.I33
c
a
%"#e%
9 %"#e%
%"#e% 9o##om la&er
/"$$le la&er
o la&er
7/21/2019 05 Metals Cry
17/23
F Coordination G < $2
F ,,... Stac6ing Se4uence
F &B < .7%
F 3D &roection
$a#e$ 'rom F"!. *.*a,
Callister 7e.
He"agonal Close>&ac6ed StructureHe"agonal Close>&ac6ed Structure
HCHC
F c/a< $.I33
c
a
%"#e%
9 %"#e%
%"#e%
7/21/2019 05 Metals Cry
18/23
+1;
HC& Crystallographic Directions
1.
$a#e$ 'rom F"!. *.;a, Callister 7e.
$a%he$ re$ l"ne% "n$"ca#e
roec#"on% on#o a1an$ a2axe%a1
a2
a*
-a*
2
a2
2
a1
-a*
a1
a2
zl!or"#hm
7/21/2019 05 Metals Cry
19/23
%"#e%
9 9
9
99
9 9
C %"#e%
C C
C
9
9 %"#e%
F ,C,C... Stac6ing Se4uence
F 2D &roection
BCC Stac6ing Se4uence
9 9
9
99
9 9
C C
C
C C
C
9o##om la&er
/"$$le la&er
o la&er
7/21/2019 05 Metals Cry
20/23
He"agonal Close Pac6ed
For "$eall& acAe$ hc, c3a=1.4**
c3aBn=1.;54, c3a"=1.5;7Source: R.E. Smallman, Ch1, F1.15
7/21/2019 05 Metals Cry
21/23
Stac6ing: Di1erence 5et-eenHC& .7%# and BCC .7%#
FCC: 9C9C9C
C6: 999
Source: R.E. Smallman, Ch1, F1.14
7/21/2019 05 Metals Cry
22/23
BCC +s. HC&
7/21/2019 05 Metals Cry
23/23
Source: R.E. Smallman