crystallization
TRANSCRIPT
![Page 1: Crystallization](https://reader033.vdocuments.us/reader033/viewer/2022042817/55a8e47d1a28ab446a8b488a/html5/thumbnails/1.jpg)
![Page 2: Crystallization](https://reader033.vdocuments.us/reader033/viewer/2022042817/55a8e47d1a28ab446a8b488a/html5/thumbnails/2.jpg)
“A crystal is a solid in which atoms are arranged in some regular repetition pattern in all directions.”
“Aggregation of molecules with a definite internal structure and the external form of a solid enclosed by symmetrically arranged plane faces.”
“Structure of anything is defined as the framework of its body.”
CRYSTAL
STRUCTURES
![Page 3: Crystallization](https://reader033.vdocuments.us/reader033/viewer/2022042817/55a8e47d1a28ab446a8b488a/html5/thumbnails/3.jpg)
Lattice The underlying periodicity of the crystal
Basis Entity associated with each lattice points
Crystal = Lattice+BaseMotif or basis:
Typically an atom or a group of atoms associated witheach lattice point.
Translationally periodic arrangement of motifs.
Translationally periodic arrangement of points.
Lattice Crystal
![Page 4: Crystallization](https://reader033.vdocuments.us/reader033/viewer/2022042817/55a8e47d1a28ab446a8b488a/html5/thumbnails/4.jpg)
Crystal = Lattice (Where to repeat)+
Motif (What to repeat)
=
+
a
a
2
a
Lattice
Motif Note: all parts of the motif do not sit on the lattice
point
Crystal
![Page 5: Crystallization](https://reader033.vdocuments.us/reader033/viewer/2022042817/55a8e47d1a28ab446a8b488a/html5/thumbnails/5.jpg)
Let us construct the crystal considered before starting with an infinite array of points spaced a/2 apart
Put arrow marks pointing up and down alternately on the points:
What we get is a crystal of lattice parameter ‘a’ and not ‘a/2’!
And the motif
is: +
![Page 6: Crystallization](https://reader033.vdocuments.us/reader033/viewer/2022042817/55a8e47d1a28ab446a8b488a/html5/thumbnails/6.jpg)
A strict 1D crystal = 1D lattice + 1D motif
The only kind of 1D motif is a line segment.
Lattice
Motif
Crystal
=
+
An unit cell is a representative unit of the structure (finite part of a infinite structure) . Which when repeated gives the whole structure.
![Page 7: Crystallization](https://reader033.vdocuments.us/reader033/viewer/2022042817/55a8e47d1a28ab446a8b488a/html5/thumbnails/7.jpg)
2D crystal = 2D lattice + 2D motif
Lattice
a
b
+Motif
![Page 8: Crystallization](https://reader033.vdocuments.us/reader033/viewer/2022042817/55a8e47d1a28ab446a8b488a/html5/thumbnails/8.jpg)
Crystal
=
![Page 9: Crystallization](https://reader033.vdocuments.us/reader033/viewer/2022042817/55a8e47d1a28ab446a8b488a/html5/thumbnails/9.jpg)
3D crystal = 3D lattice + 3D motifs
CRYSTAL OR SPACE LATTICE
It is defined as an array of points in 3 dimensions in which every point has surroundings identical to every other point in array.
According to BRAVAIS there are 14 possible types of space lattice in 7 basic crystal system
![Page 10: Crystallization](https://reader033.vdocuments.us/reader033/viewer/2022042817/55a8e47d1a28ab446a8b488a/html5/thumbnails/10.jpg)
![Page 11: Crystallization](https://reader033.vdocuments.us/reader033/viewer/2022042817/55a8e47d1a28ab446a8b488a/html5/thumbnails/11.jpg)
a = b= c = = = 90º
• Simple Cubic (P) - SC
• Body Centred Cubic (I) – BCC
• Face Centred Cubic (F) - FCC
Elements with Cubic structure → SC: F, O
BCC: Cr, Fe, Nb, K, WFCC: Al, Ar, Pb, Ni, Ge
![Page 12: Crystallization](https://reader033.vdocuments.us/reader033/viewer/2022042817/55a8e47d1a28ab446a8b488a/html5/thumbnails/12.jpg)
• Cubic unit cell is 3D repeat unit • Rare (only Po has this structure)
• Coordination No. = 6
(# nearest neighbors)
SIMPLE CUBIC STRUCTURE
![Page 13: Crystallization](https://reader033.vdocuments.us/reader033/viewer/2022042817/55a8e47d1a28ab446a8b488a/html5/thumbnails/13.jpg)
• APF for a simple cubic structure = 0.52
contains 8 x 1/8 = 1 atom/unit cell
Adapted from Fig. 3.19,
Callister 6e.
Lattice constant
close-packed directions
a
R=0.5a
![Page 14: Crystallization](https://reader033.vdocuments.us/reader033/viewer/2022042817/55a8e47d1a28ab446a8b488a/html5/thumbnails/14.jpg)
BODY CENTERED CUBIC STRUCTURE
• Coordination No. = 8
(# nearest neighbors)
![Page 15: Crystallization](https://reader033.vdocuments.us/reader033/viewer/2022042817/55a8e47d1a28ab446a8b488a/html5/thumbnails/15.jpg)
aR
• APF for a body-centered cubic structure = p3/8 = 0.68
Unit cell c ontains:
1 + 8 x 1/8
= 2 atoms/unit cell
Adapted fromFig. 3.2,Callister 6e.
![Page 16: Crystallization](https://reader033.vdocuments.us/reader033/viewer/2022042817/55a8e47d1a28ab446a8b488a/html5/thumbnails/16.jpg)
Atoms are arranged at the corners and center of each cube face of the cell.◦ Atoms are assumed to touch along face diagonals
FACE CENTERED CUBIC STRUCTURE
![Page 17: Crystallization](https://reader033.vdocuments.us/reader033/viewer/2022042817/55a8e47d1a28ab446a8b488a/html5/thumbnails/17.jpg)
• Coordination No. = 12
(# nearest neighbors)
![Page 18: Crystallization](https://reader033.vdocuments.us/reader033/viewer/2022042817/55a8e47d1a28ab446a8b488a/html5/thumbnails/18.jpg)
Unit cell c ontains:
6 x 1/2 + 8 x 1/8
= 4 atoms/unit cella
• APF for a body-centered cubic structure = p/(32) = 0.74
![Page 19: Crystallization](https://reader033.vdocuments.us/reader033/viewer/2022042817/55a8e47d1a28ab446a8b488a/html5/thumbnails/19.jpg)
• ABCABC... Stacking Sequence
• FCC Unit Cell
A sites
B sites
C sites
B B
B
BB
B BC C
CA
A
• 2D Projection
![Page 20: Crystallization](https://reader033.vdocuments.us/reader033/viewer/2022042817/55a8e47d1a28ab446a8b488a/html5/thumbnails/20.jpg)
Ideally, c/a = 1.633 for close packingHowever, in most metals, c/a ratio deviates from this value
![Page 21: Crystallization](https://reader033.vdocuments.us/reader033/viewer/2022042817/55a8e47d1a28ab446a8b488a/html5/thumbnails/21.jpg)
• Coordination NO.= 12
• ABAB... Stacking Sequence
• APF = 0.74, for ideal c/a ratio of 1.633
• 3D Projection • 2D Projection
A sites
B sites
A sites
![Page 22: Crystallization](https://reader033.vdocuments.us/reader033/viewer/2022042817/55a8e47d1a28ab446a8b488a/html5/thumbnails/22.jpg)
![Page 23: Crystallization](https://reader033.vdocuments.us/reader033/viewer/2022042817/55a8e47d1a28ab446a8b488a/html5/thumbnails/23.jpg)
Close packed crystals
A plane
B plane
C plane
A plane
…ABCABCABC… packing[Face Centered Cubic (FCC)]
…ABABAB… packing[Hexagonal Close Packing (HCP)]
![Page 24: Crystallization](https://reader033.vdocuments.us/reader033/viewer/2022042817/55a8e47d1a28ab446a8b488a/html5/thumbnails/24.jpg)
Examples of elements with Cubic Crystal Structure
Po
n = 1n = 2 n = 4
Fe Cu
BCC FCC/CCPSC
C (diamond)
n = 8 DC
![Page 25: Crystallization](https://reader033.vdocuments.us/reader033/viewer/2022042817/55a8e47d1a28ab446a8b488a/html5/thumbnails/25.jpg)
a = b c = = = 90º
Simple Tetragonal Body Centred Tetragonal -BCT
Elements with Tetragonal structure → In, Sn
![Page 26: Crystallization](https://reader033.vdocuments.us/reader033/viewer/2022042817/55a8e47d1a28ab446a8b488a/html5/thumbnails/26.jpg)
Example of an element with Body Centred Tetragonal Crystal Structure
BCT
![Page 27: Crystallization](https://reader033.vdocuments.us/reader033/viewer/2022042817/55a8e47d1a28ab446a8b488a/html5/thumbnails/27.jpg)
a b c = = = 90º
Simple Orthorhombic
Body Centred Orthorhombic
Face Centred Orthorhombic
End Centred Orthorhombic
Elements with Orthorhombic structure → Br, Cl, Ga
![Page 28: Crystallization](https://reader033.vdocuments.us/reader033/viewer/2022042817/55a8e47d1a28ab446a8b488a/html5/thumbnails/28.jpg)
Element with Orthorhombic Crystal Structure
![Page 29: Crystallization](https://reader033.vdocuments.us/reader033/viewer/2022042817/55a8e47d1a28ab446a8b488a/html5/thumbnails/29.jpg)
a = b c = = 90º =120º
Elements with Hexagonal structure → Be, Cd, Co, Ti, Zn
Simple Hexagonal
![Page 30: Crystallization](https://reader033.vdocuments.us/reader033/viewer/2022042817/55a8e47d1a28ab446a8b488a/html5/thumbnails/30.jpg)
Element with Hexagonal Crystal Structure
![Page 31: Crystallization](https://reader033.vdocuments.us/reader033/viewer/2022042817/55a8e47d1a28ab446a8b488a/html5/thumbnails/31.jpg)
a = b = c
= = 90º
Elements with Trigonal structure → As, B, Bi, Hg
Rhombohedral (simple)
![Page 32: Crystallization](https://reader033.vdocuments.us/reader033/viewer/2022042817/55a8e47d1a28ab446a8b488a/html5/thumbnails/32.jpg)
Element with Simple Trigonal Crystal Structure
![Page 33: Crystallization](https://reader033.vdocuments.us/reader033/viewer/2022042817/55a8e47d1a28ab446a8b488a/html5/thumbnails/33.jpg)
a b c = = 90º
Elements with Monoclinic structure → P, Pu, Po
Simple Monoclinic End Centred (base centered) Monoclinic
![Page 34: Crystallization](https://reader033.vdocuments.us/reader033/viewer/2022042817/55a8e47d1a28ab446a8b488a/html5/thumbnails/34.jpg)
a b c
• Simple Triclinic
![Page 35: Crystallization](https://reader033.vdocuments.us/reader033/viewer/2022042817/55a8e47d1a28ab446a8b488a/html5/thumbnails/35.jpg)
Crystal System Shape of UC Bravais Lattices
P I F C
1 Cubic Cube
2 Tetragonal Square Prism (general height)
3 Orthorhombic Rectangular Prism (general height)
4 Hexagonal 120 Rhombic Prism
5 Trigonal Parallopiped (Equilateral, Equiangular)
6 Monoclinic Parallogramic Prism
7 Triclinic Parallopiped (general)
14 Bravais Lattices divided into 7 Crystal Systems
P Primitive
I Body Centred
F Face Centred
C A/B/C- Centred
A Symmetry based concept ‘Translation’ based concept
![Page 36: Crystallization](https://reader033.vdocuments.us/reader033/viewer/2022042817/55a8e47d1a28ab446a8b488a/html5/thumbnails/36.jpg)
+
Face Centred Cubic (FCC) Lattice Two Carbon atom Motif(0,0,0) & (¼, ¼, ¼)
=
Diamond Cubic Crystal