Estructuras cristalinas

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CHAPTER

3
Crystal Structures and Crystal Geometry
3-1

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The Space Lattice and Unit Cells
• Atoms, arranged in repetitive 3-Dimensional pattern, in long range order (LRO) give rise to crystal structure. • Properties of solids depends upon crystal structure and bonding force. • An imaginarynetwork of lines, with atoms at intersection of lines, representing the arrangement of atoms is called space lattice. Space Lattice • Unit cell is that block of atoms which repeats itself to form space lattice. • Materials arranged in short range order are called amorphous materials Unit Cell
3-2

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CrystalSystems and Bravais Lattice
• Only seven different types of unit cells are necessary to create all point lattices. • According to Bravais (1811-1863) fourteen standard unit cells can describe all possible lattice networks. • The four basic types of unit cells are
Simple Body Centered Face Centered Base Centered

3-3

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Types of Unit Cells
• Cubic Unit Cell
a=b=c α = β = γ = 900 Simple Body Centered

Face centered

Figure 3.2

• Tetragonal
a =b ≠ c α = β = γ = 900

Simple
3-4

Body Centered

After W.G. Moffatt, G.W. Pearsall, & J. Wulff, “The Structure and Properties of Materials,” vol. I: “Structure,” Wiley, 1964, p.47.)

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Types of Unit Cells (Cont..)
• Orthorhombic
a≠ b≠ c α = β = γ = 900 Simple Base Centered

Body Centered Face Centered

• Rhombohedral
a =b = c α = β = γ ≠ 900

Figure 3.2

Simple
3-5
After W.G. Moffatt, G.W. Pearsall, & J. Wulff, “The Structure and Properties of Materials,” vol. I: “Structure,” Wiley, 1964, p.47.)

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Types of Unit Cells (Cont..)
• Hexagonal
a≠ b≠ c α = β = γ = 900 Simple

• Monoclinic
a≠ b≠ c α = β = γ = 900 Simple Base Centered

• Triclinic
a≠ b≠ c α = β = γ = 900

Figure 3.2

Simple
3-6
After W.G. Moffatt, G.W. Pearsall, & J. Wulff, “The Structure and Properties of Materials,” vol. I: “Structure,” Wiley,1964, p.47.)

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Principal Metallic Crystal Structures
• 90% of the metals have either Body Centered Cubic (BCC), Face Centered Cubic (FCC) or Hexagonal Close Packed (HCP) crystal structure. • HCP is denser version of simple hexagonal crystal structure.

BCC Structure
3-7

FCC Structure
Figure 3.3HCP Structure

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Body Centered Cubic (BCC) Crystal Structure
• Represented as one atom at each corner of cube and one at the center of cube. • Each atom has 8 nearest neighbors. • Therefore, coordination number is 8. • Examples :Chromium (a=0.289 nm) Iron (a=0.287 nm) Sodium (a=0.429 nm)

Figure3.4 a&b 3-8

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BCC Crystal Structure (Cont..)
• Each unit cell has eight 1/8 atom at corners and 1 full atom at the center. • Therefore each unit cell has (8x1/8 ) + 1 = 2 atoms



Atoms contact each other at cube diagonal Therefore, lattice constant a =

4R 3

Figure 3.5

3-9

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Atomic Packing Factor of BCC Structure
Volume of atoms in unit cell Volume of unit cell

Atomic Packing Factor =

Vatoms =

 4 ΠR 3   2.    3 

= 8.373R3
3

V unit cell =

a3

=

 4R       3

= 12.32 R3

Therefore APF =

8.723 R3 = 0.68 12.32 R3

3-10

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