Upcoming SlideShare
×

# 972 B3102005 Cullity Chapter 2

2,649

Published on

0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

Views
Total Views
2,649
On Slideshare
0
From Embeds
0
Number of Embeds
1
Actions
Shares
0
53
0
Likes
0
Embeds 0
No embeds

No notes for slide

### 972 B3102005 Cullity Chapter 2

1. 1. Space Lattice are non-coplanar vectors in space forming a basis { }
2. 2. One dimensional lattice Two dimensional lattice
3. 3. Three dimensional lattice
4. 4. Lattice vectors and parameters
5. 5. Indices of directions
6. 6. Miller indices for planes
7. 7. Miller indices and plane spacing
8. 8. Two-dimensional lattice showing that lines of lowest indices have the greatest spacing and greatest density of lattice points
9. 9. Reciprocal lattice
10. 10. Illustration of crystal lattices and corresponding reciprocal lattices for a cubic system
11. 11. Illustration of crystal lattices and corresponding reciprocal lattices for a a hexagonal system
12. 12. If then and perpendicular to (hkl) plane
13. 13. If then and perpendicular to (hkl) plane Proof: H • ( a 1 /h- a 2 /k) = H • ( a 1 /h- a 3 /l)=0 a 1 /h• H /| H |=[1/h 0 0] • [hkl]*/| H |=1/| H |=d hkl H a 1 a 2 a 3
14. 14. Symmetry (a) mirror plane (b)rotation (c)inversion (d)roto- inversion
15. 15. Symmetry operation
16. 16. Crystal system
17. 17. The 14 Bravais lattices
18. 18. The fourteen Bravais lattices Simple cubic lattices nitrogen - simple cubic copper - face centered cubic body centered cubic Cubic lattices a 1 = a 2 = a 3 α = β = γ = 90 o
19. 19. Tetragonal lattices a1 = a2 ≠ a3 α = β = γ = 90  simple tetragonal Body centered Tetragonal
20. 20. Orthorhombic lattices a1 ≠ a2 ≠ a3 α = β = γ = 90  simple orthorhombic Base centered orthorhombic Body centered orthorhombic Face centered orthorhombic
21. 21. Monoclinic lattices a1 ≠ a2 ≠ a3 α = γ = 90  ≠ β (2nd setting) α = β = 90  ≠ γ (1st setting) Simple monoclinic Base centered monoclinic
22. 22. Triclinic lattice a1 ≠ a2 ≠ a3 α ≠ β ≠ γ Simple triclinic
23. 23. Hexagonal lattice a1 = a2 ≠ a3 α = β = 90  , γ = 120  lanthanum - hexagonal
24. 24. Trigonal (Rhombohedral) lattice a1 = a2 = a3 α = β = γ ≠ 90  mercury - trigonal
25. 25. Relation between rhombo-hedral and hexagonal lattices
26. 26. Relation of tetragonal C lattice to tetragonal P lattice
27. 27. Extension of lattice points through space by the unit cell vectors a, b, c
28. 28. Symmetry elements
29. 29. Primitive and non-primitive cells Face-centerd cubic point lattice referred to cubic and rhombo-hedral cells
30. 30. All shaded planes in the cubic lattice shown are planes of the zone{001}
31. 31. Zone axis [uvw] Zone plane (hkl) then hu+kv+wl=0 Two zone planes (h 1 k 1 l 1 ) and (h 2 k 2 l 2 ) then zone axis [uvw]=
32. 32. Plane spacing
33. 33. Indexing the hexagonal system
34. 34. Indexing the hexagonal system
35. 35. Crystal structure  -Fe, Cr, Mo, V  -Fe, Cu, Pb, Ni
36. 36. Hexagonal close-packed Zn, Mg, Be,  -Ti
37. 37. FCC and HCP
38. 38.  -Uranium, base-centered orthorhombic (C-centered) y=0.105±0.005
39. 43. AuBe: Simple cubic u = 0.100 w = 0.406
40. 44. Structure of solid solution (a) Mo in Cr (substitutional) (b) C in  -Fe (interstitial)
41. 45. Atom sizes (d) and coordination
42. 46. Change in coordination 12  8 12  6 12  4 size contraction, percent 3 3 12
43. 47. A: Octahedral site, B: Tetrahedral site
44. 48. Twin
45. 49. (a) (b) FCC annealing (c) HCP deformation twins
46. 50. Twin band in FCC lattice, Plane of main drawing is (1 ī 0)
47. 51. Homework assignment Problem 2-6 Problem 2-8 Problem 2-9 Problem 2-10
48. 52. Stereographic projection *Any plane passing the center of the reference sphere intersects the sphere in a trace called great circle * A plane can be represented by its great circle or pole, which is the intersection of its plane normal with the reference sphere
49. 53. Stereographic projection
50. 55. Pole on upper sphere can also be projected to the horizontal (equatorial) plane
51. 56. Projections of the two ends of a line or plane normal on the equatorial plane are symmetrical with respect to the center O.
52. 57. Projections of the two ends of a line or plane normal on the equatorial plane are symmetrical with respect to the center O. U L P P’ P P’ X O O
53. 58. <ul><li>A great circle representing a plane is divided to two half circles, one in upper reference sphere, the other in lower sphere </li></ul><ul><li>Each half circle is projected as a trace on the equatorial plane </li></ul><ul><li>The two traces are symmetrical with respect to their associated common diameter </li></ul>
54. 59. N S E W
55. 60. The position of pole P can be defined by two angles  and 
56. 61. The position of projection P’ can be obtained by r = R tan(  /2)
57. 62. The trace of each semi-great circle hinged along NS projects on WNES plane as a meridian
58. 63. As the semi-great circle swings along NS, the end point of each radius draws on the upper sphere a curve which projects on WNES plane as a parallel
59. 64. The weaving of meridians and parallels makes the Wulff net
60. 65. Two projected poles can always be rotated along the net normal to a same meridian (not parallel) such that their intersecting angle can be counted from the net
61. 66. P : a pole at (  1 ,  1 ) NMS : its trace
62. 67. The projection of a plane trace and pole can be found from each other by rotating the projection along net normal to the following position
63. 68. Zone circle and zone pole
64. 69. If P2’ is the projection of a zone axis, then all poles of the corresponding zone planes lie on the trace of P2’
65. 70. Rotation of a poles about NS axis by a fixed angle: the corresponding poles moving along a parallel *Pole A1 move to pole A2 *Pole B1 moves 40 ° to the net end then another 20 ° along the same parallel to B1’ corresponding to a movement on the lower half reference sphere, pole corresponding to B1’ on upper half sphere is B2
66. 71. m: mirror plane F1: face 1 F2: face 2 N1: normal of F1 N2: normal of N2 N1, N2 lie on a plane which is 丄 to m
67. 73. A plane not passing through the center of the reference sphere intersects the sphere on a small circle which also projects as a circle, but the center of the former circle does not project as the center of the latter.
68. 74. Projection of a small circle centered at Y
69. 75. Rotation of a pole A1 along an inclined axis B1: B1  B3  B2  B2  B3  B1 A1  A1  A2  A3  A4  A4 A plane not passing through the center of the reference sphere intersects the sphere on a small circle which also projects as a circle .
70. 76. Rotation of a pole A1 along an inclined axis B1:
71. 77. A 1 rotate about B 1 forming a small circle in the reference sphere, the small circle projects along A 1 , A 4 , D, arc A 1 , A 4 , D centers around C (not B 1 ) in the projection plane
72. 78. Rotation of 3 directions along b axis
73. 79. Rotation of 3 directions along b axis
74. 80. Rotation of 3 directions along b axis
75. 81. Standard coordinates for crystal axes
76. 82. Standard coordinates for crystal axes
77. 83. Standard coordinates for crystal axes
78. 84. Standard coordinates for crystal axes
79. 85. Projection of a monoclinic crystal +C -b +b -a + a x x 011 0-1-1 01-1 0-11 -110 -1-10 110 1-10
80. 86. Projection of a monoclinic crystal
81. 87. Projection of a monoclinic crystal
82. 88. Projection of a monoclinic crystal
83. 89. (a) Zone plane (stippled) (b) zone circle with zone axis ā, note [100] • [0xx]=0
84. 90. Location of axes for a triclinic crystal: the circle on net has a radius of  along WE axis of the net
85. 92. Zone circles corresponding to a, b, c axes of a triclinic crystal
86. 93. Standard projections of cubic crystals on (a) (001), (b) (011)
87. 94. d/(a/h)=cos  , d/(b/k)=cos  , d/(c/l)=cos  h:k:l=a  cos  : b  cos  : c  cos  measure 3 angles to calculate hkl
88. 95. The face poles of six faces related by -3 axis that is (a) perpendicular (b) oblique to the plane of projection
1. #### A particular slide catching your eye?

Clipping is a handy way to collect important slides you want to go back to later.