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Structure and its types

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NabeelBhutta1

This document provides an overview of crystal structures and bonding in materials. It discusses topics such as the differences between crystalline and amorphous solids, unit cells, lattice structures, metallic crystal structures like body centered cubic and face centered cubic, atomic packing factors, and anisotropic vs isotropic materials. The key concepts covered include how crystal structures are composed of a periodic arrangement of points in a lattice, with atoms attached at each lattice point, and how properties can differ based on crystal structure and orientation.

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Bonding & Structure Course : Engineering Materials Course Code: ID-301 Credit Hours: 3 Topic : Department of Chemical Engineering NFC Institute of Engineering & Technology, Multan
Agenda • Why we study structures • Crystal Structure • Types of Solids • Lattice • Unit Cell • Lattice Parameters & Constants • Classification of Lattices • Metallic Crystal Structures • Atomic Packing Factor • Coordination Number • Stacking Sequences • Comparisons • Anisotropy • Isotropy
Why we Study Crystal Structure ? • Properties Changes • Slip Systems Like Diamond & Graphite Deformation Occurs by shear stress DiamondGraphite
Crystal Structure • The structure of all crystals can be described in term of a lattice, with the group of atoms attached to every lattice point • Basis (Motif) • Lattice + Motif = Crystal
Types of Solids • Crystalline • Amorphous Long Range Order, Repetitive Manner, Periodic Arrangement, High Bond Energy, Closed Packed Structure, Sharp Melting Point, Cleavage Property, (Ex: NaCl, CsF, Diamond ..) Short Range Order, Random Manner, Non Periodic Arrangement, Lower Bond Energy, Less Dense Packed, Less Melting Point, Cleavage Property, (Ex: Glass, Rubber, Plastic ..)
• Poly-crystalline • Single Crystal • If a crystalline material consists of only one large crystal, we refer to it as a single crystal. Single crystals are useful in many electronic and optical applications • Atoms are in a repeating or periodic array over the entire extent of the material • Object composed of randomly oriented crystals, formed by rapid solidification • Comprised of many small crystals or grains
Formation of Polycrystalline Material
Difference Between Lattice & Crystal • A 3D arrangement of atoms • It’s physical object (ex: weight, density..) • A 3D periodic arrangement of points • It’s geometric Concept (ex: triangle, Square..)
Energy and Packing of Crystalline & Amorphous Structure Dense, regular-packed structures tend to have lower energy
Lattice + Motif (Basis) = Crystal ? • A three dimensional periodic array of points conceding with atoms position. Lattice
Unit Cell • A region of space which can generate the entire lattice or (crystal) by repetition through lattice translation. • The small repeat entities of crystal structure called unit cell. • Its help us to describe the crystal structure may be primitive and non primitive Characterized by 1) Types of atoms & their radii 2) Cell dimension 3) No: of atoms/unit cell 4) Coordination number 5) APF (Atomic packing factor)
Square Unit Cell Hexagonal Unit Cell
Crystal Lattice Squares Rectangles Hexagons
Lattice Parameters • Interaxial angles 1 2 What do you think which steps are correct ? Lattice Parameter Lattice Parameter Unit Cell Unit Cell Lattice Lattice Motif Crystal Crystal
Classification of Lattices • 7 Crystal Systems or unit cell & 14 Bravais Systems • Crystal Systems are 1) Cubic 2) Tetragonal 3) Orthorhombic 4) Rhombohedral 5) Hexagonal 6) Monoclinic 7) Triclinic
Structure and its types
Metallic Crystal Structure • The atomic bonding in this group of materials is metallic and thus non-directional in nature • For metals, using the hard-sphere model for the crystal structure, each sphere represents an ion core • Three principle crystal structures for metals are: 1) Body Centered Crystal (BCC) 2) Face Centered Crystal (FCC) 3) Hexagonal Closed Packed (HCP)
Body Centered Cubic No: of atoms/unit cell : 2 Coordination no : 8 APF = 0.68 Ex: Cr, Molybedenum, Tantalum. Fe (alpha)
Face Centered Crystal No: of atoms/unit cell : 4 Coordination no : 12 APF = 0.74 Ex: Al, Cu, Pb, Ni, Ag, Pt
Hexagonal Closed Packed No: of atoms/unit cell : 6 Coordination no : 12 APF = 0.74 Ex: Beryllium, Cadmium, Titanium, Magnesium
Atomic Packing Factor • Packing Efficiency • It tell us how tightly atoms are packed • The packing factor or atomic packing fraction is the fraction of space occupied by atoms, assuming that the atoms are hard spheres. The general expression for the packing factor is APF = ð‘µð’ ð’ð’‡ ð’‚ð’•ð’ð’Žð’” ð’‘ð’†ð’“ ð’–ð’ð’Šð’• ð’„ð’†ð’ð’ ð’™ ð‘½ð’ð’ð’–ð’Žð’† ð’ð’‡ ð’†ð’‚ð’„ð’‰ ð’‚ð’•ð’ð’Ž ð‘½ð’ð’ð’–ð’Žð’† ð’ð’‡ ð’–ð’ð’Šð’• ð’„ð’†ð’ð’
Steps To Calculate Atomic Packing Factor 1 2 4 3 Calculate Number of Atoms Calculate Volume of Atoms Calculate Atomic Radius Steps Calculate Area of Cube
Atomic Packing Factor (BCC) APF = ð‘𑜠ð‘œð‘“ ð‘Žð‘¡ð‘œð‘šð‘  ð‘ð‘’ð‘Ÿ ð‘¢ð‘›ð‘–ð‘¡ ð‘ð‘’ð‘™ð‘™ ð‘¥ ð‘‰ð‘œð‘™ð‘¢ð‘šð‘’ ð‘œð‘“ ð‘’ð‘Žð‘â„Ž ð‘Žð‘¡ð‘œð‘š ð‘‰ð‘œð‘™ð‘¢ð‘šð‘’ ð‘œð‘“ ð‘¢ð‘›ð‘–ð‘¡ ð‘ð‘’ð‘™ð‘™ • Coordinate Number : 8 • Number of Atoms : 2 • Volume of Atom : 4 3 ðœ‹ð‘Ÿ3 = 8.373ð‘Ÿ3 • Volume of Unit Cell : ð‘Ž3 • Atomic Radius : √3 4 a
Atomic Packing Factor (BCC) • Radius Calculation : ð¶2 = ð´2 + ðµ 2 ð´ð·2 = ð´ð¶2 + ð¶ð·2 As; AD = 4r ð´ð¶2 = ð´ðµ2 + ðµð¶2 ð´ð¶2 = ð‘Ž2 + ð‘Ž2 ð´ð·2 = ð´ð¶2 + ð¶ð·2 4ð‘Ÿ2 = 2ð‘Ž2 + ð‘Ž2 16ð‘Ÿ2 = 3ð‘Ž2 r = √3 4 a a = 4𑟠√4 v=12.32ð‘Ÿ3
• Volume of atom = 8. ðŸ‘ðŸ•ðŸ‘𒓠👠• Volume of unit cell = 1ðŸ. ðŸ‘ðŸð’“ 👠Atomic Packing Factor (BCC) APF = ð‘𑜠ð‘œð‘“ ð‘Žð‘¡ð‘œð‘šð‘  ð‘ð‘’ð‘Ÿ ð‘¢ð‘›ð‘–ð‘¡ ð‘ð‘’ð‘™ð‘™ ð‘¥ ð‘‰ð‘œð‘™ð‘¢ð‘šð‘’ ð‘œð‘“ ð‘’ð‘Žð‘â„Ž ð‘Žð‘¡ð‘œð‘š ð‘‰ð‘œð‘™ð‘¢ð‘šð‘’ ð‘œð‘“ ð‘¢ð‘›ð‘–ð‘¡ ð‘ð‘’ð‘™ð‘™ APF = 8.373ð‘Ÿ3 12.32ð‘Ÿ3 APF = 0.68 or 68%
Atomic Packing Factor (FCC) APF = ð‘𑜠ð‘œð‘“ ð‘Žð‘¡ð‘œð‘šð‘  ð‘ð‘’ð‘Ÿ ð‘¢ð‘›ð‘–ð‘¡ ð‘ð‘’ð‘™ð‘™ ð‘¥ ð‘‰ð‘œð‘™ð‘¢ð‘šð‘’ ð‘œð‘“ ð‘’ð‘Žð‘â„Ž ð‘Žð‘¡ð‘œð‘š ð‘‰ð‘œð‘™ð‘¢ð‘šð‘’ ð‘œð‘“ ð‘¢ð‘›ð‘–ð‘¡ ð‘ð‘’ð‘™ð‘™ • Coordinate Number : 12 • Number of Atoms : 4 • Volume of Atom : 4 3 ðœ‹ð‘Ÿ3 8.373ð‘Ÿ3 • Volume of Unit Cell : ð‘Ž3 • Atomic Radius : ð‘Ž 2√2
Atomic Packing Factor (FCC) APF = ð‘𑜠ð‘œð‘“ ð‘Žð‘¡ð‘œð‘šð‘  ð‘ð‘’ð‘Ÿ ð‘¢ð‘›ð‘–ð‘¡ ð‘ð‘’ð‘™ð‘™ ð‘¥ ð‘‰ð‘œð‘™ð‘¢ð‘šð‘’ ð‘œð‘“ ð‘’ð‘Žð‘â„Ž ð‘Žð‘¡ð‘œð‘š ð‘‰ð‘œð‘™ð‘¢ð‘šð‘’ ð‘œð‘“ ð‘¢ð‘›ð‘–ð‘¡ ð‘ð‘’ð‘™ð‘™ APF = 4 ð‘¥ ( ð‘Ž 2 2 )3 4 3 ð‘¥ 3.14 ð‘Ž3 APF = 0.74 or 74%
Atomic Packing Factor (HCP) • Coordinate Number : 12 • Number of Atoms : 6 • Volume of Atom : 4 3 ðœ‹ð‘Ÿ3 8.373ð‘Ÿ3 • Volume of Unit Cell : 𑉠= ðµ ð‘¥ ð» • Atomic Radius : ð‘Ž = 2𑟠• c/a : 1.633
Atomic Packing Factor (HCP) APF = ð‘𑜠ð‘œð‘“ ð‘Žð‘¡ð‘œð‘šð‘  ð‘ð‘’ð‘Ÿ ð‘¢ð‘›ð‘–ð‘¡ ð‘ð‘’ð‘™ð‘™ ð‘¥ ð‘‰ð‘œð‘™ð‘¢ð‘šð‘’ ð‘œð‘“ ð‘’ð‘Žð‘â„Ž ð‘Žð‘¡ð‘œð‘š ð‘‰ð‘œð‘™ð‘¢ð‘šð‘’ ð‘œð‘“ ð‘¢ð‘›ð‘–ð‘¡ ð‘ð‘’ð‘™ð‘™ • Volume of unit cell : V = B x H Base of triangle = 1 2 x a x asin60 = 3ð‘Ž2 4 x 6 = 3 3 2 ð‘Ž2 x c
Atomic Packing Factor (HCP) APF = 6 ð‘¥ 4 3 ð‘¥ 3.14 ð‘¥ ð‘Ÿ3 3 3 2 ð‘Ž2 ð‘¥ ð‘ ð‘Ž = 2ð‘Ÿ ð‘Žð‘›ð‘‘ ð‘ ð‘Ž = 1.633 = 6 ð‘¥ 4 3 ð‘¥ 3.14 ð‘¥ ( ð‘Ž 2 )3 3 3 2 ð‘Ž2 ð‘¥ ð‘ = 12.55ð‘Ž 10.392ð‘ = 1.207 0.612 APF = 0.74 or 74% APF = ð‘𑜠ð‘œð‘“ ð‘Žð‘¡ð‘œð‘šð‘  ð‘ð‘’ð‘Ÿ ð‘¢ð‘›ð‘–ð‘¡ ð‘ð‘’ð‘™ð‘™ ð‘¥ ð‘‰ð‘œð‘™ð‘¢ð‘šð‘’ ð‘œð‘“ ð‘’ð‘Žð‘â„Ž ð‘Žð‘¡ð‘œð‘š ð‘‰ð‘œð‘™ð‘¢ð‘šð‘’ ð‘œð‘“ ð‘¢ð‘›ð‘–ð‘¡ ð‘ð‘’ð‘™ð‘™
FCC Stacking Sequence
Closed Packed Crystal
Comparison of FCC, BCC, HCP Crystal Structure Coordination Number Packing Factor Closed Packed Direction BCC FCC HCP 8 12 12 0.68 0.74 0.74 Body Diagonal Face Diagonal Hexagonal Side
• An anisotropic material is a material which does not behave the same way in all directions. Take wood for example. Wood is very strong along the grain. Against the grain, however, it will easily break. • A different chemical bonding in all directions is also a condition for anisotropy • Poly Crystal (Property Vary with Direction) Anisotropy
Figure 7-1 Anisotropic materials: (a) rolled material, (b) wood, (c) glass-fiber cloth in an epoxy matrix, and (d) a crystal with cubic unit cell.
• The opposite of an anisotropic material is an isotropic material. Most metals (steel, aluminum) are isotropic materials. They respond the same way in all directions. • Substances in which measured (physical)properties are independent of the direction of measurement are isotropic. • Ex : Single Crystal ( Properties do not vary with direction) • Real Materials (Isotropic) Isotropy

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Structure and its types

  • 1. Bonding & Structure Course : Engineering Materials Course Code: ID-301 Credit Hours: 3 Topic : Department of Chemical Engineering NFC Institute of Engineering & Technology, Multan
  • 2. Agenda • Why we study structures • Crystal Structure • Types of Solids • Lattice • Unit Cell • Lattice Parameters & Constants • Classification of Lattices • Metallic Crystal Structures • Atomic Packing Factor • Coordination Number • Stacking Sequences • Comparisons • Anisotropy • Isotropy
  • 3. Why we Study Crystal Structure ? • Properties Changes • Slip Systems Like Diamond & Graphite Deformation Occurs by shear stress DiamondGraphite
  • 4. Crystal Structure • The structure of all crystals can be described in term of a lattice, with the group of atoms attached to every lattice point • Basis (Motif) • Lattice + Motif = Crystal
  • 5. Types of Solids • Crystalline • Amorphous Long Range Order, Repetitive Manner, Periodic Arrangement, High Bond Energy, Closed Packed Structure, Sharp Melting Point, Cleavage Property, (Ex: NaCl, CsF, Diamond ..) Short Range Order, Random Manner, Non Periodic Arrangement, Lower Bond Energy, Less Dense Packed, Less Melting Point, Cleavage Property, (Ex: Glass, Rubber, Plastic ..)
  • 6. • Poly-crystalline • Single Crystal • If a crystalline material consists of only one large crystal, we refer to it as a single crystal. Single crystals are useful in many electronic and optical applications • Atoms are in a repeating or periodic array over the entire extent of the material • Object composed of randomly oriented crystals, formed by rapid solidification • Comprised of many small crystals or grains
  • 8. Difference Between Lattice & Crystal • A 3D arrangement of atoms • It’s physical object (ex: weight, density..) • A 3D periodic arrangement of points • It’s geometric Concept (ex: triangle, Square..)
  • 9. Energy and Packing of Crystalline & Amorphous Structure Dense, regular-packed structures tend to have lower energy
  • 10. Lattice + Motif (Basis) = Crystal ? • A three dimensional periodic array of points conceding with atoms position. Lattice
  • 11. Unit Cell • A region of space which can generate the entire lattice or (crystal) by repetition through lattice translation. • The small repeat entities of crystal structure called unit cell. • Its help us to describe the crystal structure may be primitive and non primitive Characterized by 1) Types of atoms & their radii 2) Cell dimension 3) No: of atoms/unit cell 4) Coordination number 5) APF (Atomic packing factor)
  • 14. Lattice Parameters • Interaxial angles 1 2 What do you think which steps are correct ? Lattice Parameter Lattice Parameter Unit Cell Unit Cell Lattice Lattice Motif Crystal Crystal
  • 15. Classification of Lattices • 7 Crystal Systems or unit cell & 14 Bravais Systems • Crystal Systems are 1) Cubic 2) Tetragonal 3) Orthorhombic 4) Rhombohedral 5) Hexagonal 6) Monoclinic 7) Triclinic
  • 17. Metallic Crystal Structure • The atomic bonding in this group of materials is metallic and thus non-directional in nature • For metals, using the hard-sphere model for the crystal structure, each sphere represents an ion core • Three principle crystal structures for metals are: 1) Body Centered Crystal (BCC) 2) Face Centered Crystal (FCC) 3) Hexagonal Closed Packed (HCP)
  • 18. Body Centered Cubic No: of atoms/unit cell : 2 Coordination no : 8 APF = 0.68 Ex: Cr, Molybedenum, Tantalum. Fe (alpha)
  • 19. Face Centered Crystal No: of atoms/unit cell : 4 Coordination no : 12 APF = 0.74 Ex: Al, Cu, Pb, Ni, Ag, Pt
  • 20. Hexagonal Closed Packed No: of atoms/unit cell : 6 Coordination no : 12 APF = 0.74 Ex: Beryllium, Cadmium, Titanium, Magnesium
  • 21. Atomic Packing Factor • Packing Efficiency • It tell us how tightly atoms are packed • The packing factor or atomic packing fraction is the fraction of space occupied by atoms, assuming that the atoms are hard spheres. The general expression for the packing factor is APF = ð‘µð’ ð’ð’‡ ð’‚ð’•ð’ð’Žð’” ð’‘ð’†ð’“ ð’–ð’ð’Šð’• ð’„ð’†ð’ð’ ð’™ ð‘½ð’ð’ð’–ð’Žð’† ð’ð’‡ ð’†ð’‚ð’„ð’‰ ð’‚ð’•ð’ð’Ž ð‘½ð’ð’ð’–ð’Žð’† ð’ð’‡ ð’–ð’ð’Šð’• ð’„ð’†ð’ð’
  • 22. Steps To Calculate Atomic Packing Factor 1 2 4 3 Calculate Number of Atoms Calculate Volume of Atoms Calculate Atomic Radius Steps Calculate Area of Cube
  • 23. Atomic Packing Factor (BCC) APF = ð‘𑜠ð‘œð‘“ ð‘Žð‘¡ð‘œð‘šð‘  ð‘ð‘’ð‘Ÿ ð‘¢ð‘›ð‘–ð‘¡ ð‘ð‘’ð‘™ð‘™ ð‘¥ ð‘‰ð‘œð‘™ð‘¢ð‘šð‘’ ð‘œð‘“ ð‘’ð‘Žð‘â„Ž ð‘Žð‘¡ð‘œð‘š ð‘‰ð‘œð‘™ð‘¢ð‘šð‘’ ð‘œð‘“ ð‘¢ð‘›ð‘–ð‘¡ ð‘ð‘’ð‘™ð‘™ • Coordinate Number : 8 • Number of Atoms : 2 • Volume of Atom : 4 3 ðœ‹ð‘Ÿ3 = 8.373ð‘Ÿ3 • Volume of Unit Cell : ð‘Ž3 • Atomic Radius : √3 4 a
  • 24. Atomic Packing Factor (BCC) • Radius Calculation : ð¶2 = ð´2 + ðµ 2 ð´ð·2 = ð´ð¶2 + ð¶ð·2 As; AD = 4r ð´ð¶2 = ð´ðµ2 + ðµð¶2 ð´ð¶2 = ð‘Ž2 + ð‘Ž2 ð´ð·2 = ð´ð¶2 + ð¶ð·2 4ð‘Ÿ2 = 2ð‘Ž2 + ð‘Ž2 16ð‘Ÿ2 = 3ð‘Ž2 r = √3 4 a a = 4𑟠√4 v=12.32ð‘Ÿ3
  • 25. • Volume of atom = 8. ðŸ‘ðŸ•ðŸ‘𒓠👠• Volume of unit cell = 1ðŸ. ðŸ‘ðŸð’“ 👠Atomic Packing Factor (BCC) APF = ð‘𑜠ð‘œð‘“ ð‘Žð‘¡ð‘œð‘šð‘  ð‘ð‘’ð‘Ÿ ð‘¢ð‘›ð‘–ð‘¡ ð‘ð‘’ð‘™ð‘™ ð‘¥ ð‘‰ð‘œð‘™ð‘¢ð‘šð‘’ ð‘œð‘“ ð‘’ð‘Žð‘â„Ž ð‘Žð‘¡ð‘œð‘š ð‘‰ð‘œð‘™ð‘¢ð‘šð‘’ ð‘œð‘“ ð‘¢ð‘›ð‘–ð‘¡ ð‘ð‘’ð‘™ð‘™ APF = 8.373ð‘Ÿ3 12.32ð‘Ÿ3 APF = 0.68 or 68%
  • 26. Atomic Packing Factor (FCC) APF = ð‘𑜠ð‘œð‘“ ð‘Žð‘¡ð‘œð‘šð‘  ð‘ð‘’ð‘Ÿ ð‘¢ð‘›ð‘–ð‘¡ ð‘ð‘’ð‘™ð‘™ ð‘¥ ð‘‰ð‘œð‘™ð‘¢ð‘šð‘’ ð‘œð‘“ ð‘’ð‘Žð‘â„Ž ð‘Žð‘¡ð‘œð‘š ð‘‰ð‘œð‘™ð‘¢ð‘šð‘’ ð‘œð‘“ ð‘¢ð‘›ð‘–ð‘¡ ð‘ð‘’ð‘™ð‘™ • Coordinate Number : 12 • Number of Atoms : 4 • Volume of Atom : 4 3 ðœ‹ð‘Ÿ3 8.373ð‘Ÿ3 • Volume of Unit Cell : ð‘Ž3 • Atomic Radius : ð‘Ž 2√2
  • 27. Atomic Packing Factor (FCC) APF = ð‘𑜠ð‘œð‘“ ð‘Žð‘¡ð‘œð‘šð‘  ð‘ð‘’ð‘Ÿ ð‘¢ð‘›ð‘–ð‘¡ ð‘ð‘’ð‘™ð‘™ ð‘¥ ð‘‰ð‘œð‘™ð‘¢ð‘šð‘’ ð‘œð‘“ ð‘’ð‘Žð‘â„Ž ð‘Žð‘¡ð‘œð‘š ð‘‰ð‘œð‘™ð‘¢ð‘šð‘’ ð‘œð‘“ ð‘¢ð‘›ð‘–ð‘¡ ð‘ð‘’ð‘™ð‘™ APF = 4 ð‘¥ ( ð‘Ž 2 2 )3 4 3 ð‘¥ 3.14 ð‘Ž3 APF = 0.74 or 74%
  • 28. Atomic Packing Factor (HCP) • Coordinate Number : 12 • Number of Atoms : 6 • Volume of Atom : 4 3 ðœ‹ð‘Ÿ3 8.373ð‘Ÿ3 • Volume of Unit Cell : 𑉠= ðµ ð‘¥ ð» • Atomic Radius : ð‘Ž = 2𑟠• c/a : 1.633
  • 29. Atomic Packing Factor (HCP) APF = ð‘𑜠ð‘œð‘“ ð‘Žð‘¡ð‘œð‘šð‘  ð‘ð‘’ð‘Ÿ ð‘¢ð‘›ð‘–ð‘¡ ð‘ð‘’ð‘™ð‘™ ð‘¥ ð‘‰ð‘œð‘™ð‘¢ð‘šð‘’ ð‘œð‘“ ð‘’ð‘Žð‘â„Ž ð‘Žð‘¡ð‘œð‘š ð‘‰ð‘œð‘™ð‘¢ð‘šð‘’ ð‘œð‘“ ð‘¢ð‘›ð‘–ð‘¡ ð‘ð‘’ð‘™ð‘™ • Volume of unit cell : V = B x H Base of triangle = 1 2 x a x asin60 = 3ð‘Ž2 4 x 6 = 3 3 2 ð‘Ž2 x c
  • 30. Atomic Packing Factor (HCP) APF = 6 ð‘¥ 4 3 ð‘¥ 3.14 ð‘¥ ð‘Ÿ3 3 3 2 ð‘Ž2 ð‘¥ ð‘ ð‘Ž = 2ð‘Ÿ ð‘Žð‘›ð‘‘ ð‘ ð‘Ž = 1.633 = 6 ð‘¥ 4 3 ð‘¥ 3.14 ð‘¥ ( ð‘Ž 2 )3 3 3 2 ð‘Ž2 ð‘¥ ð‘ = 12.55ð‘Ž 10.392ð‘ = 1.207 0.612 APF = 0.74 or 74% APF = ð‘𑜠ð‘œð‘“ ð‘Žð‘¡ð‘œð‘šð‘  ð‘ð‘’ð‘Ÿ ð‘¢ð‘›ð‘–ð‘¡ ð‘ð‘’ð‘™ð‘™ ð‘¥ ð‘‰ð‘œð‘™ð‘¢ð‘šð‘’ ð‘œð‘“ ð‘’ð‘Žð‘â„Ž ð‘Žð‘¡ð‘œð‘š ð‘‰ð‘œð‘™ð‘¢ð‘šð‘’ ð‘œð‘“ ð‘¢ð‘›ð‘–ð‘¡ ð‘ð‘’ð‘™ð‘™
  • 33. Comparison of FCC, BCC, HCP Crystal Structure Coordination Number Packing Factor Closed Packed Direction BCC FCC HCP 8 12 12 0.68 0.74 0.74 Body Diagonal Face Diagonal Hexagonal Side
  • 34. • An anisotropic material is a material which does not behave the same way in all directions. Take wood for example. Wood is very strong along the grain. Against the grain, however, it will easily break. • A different chemical bonding in all directions is also a condition for anisotropy • Poly Crystal (Property Vary with Direction) Anisotropy
  • 35. Figure 7-1 Anisotropic materials: (a) rolled material, (b) wood, (c) glass-fiber cloth in an epoxy matrix, and (d) a crystal with cubic unit cell.
  • 36. • The opposite of an anisotropic material is an isotropic material. Most metals (steel, aluminum) are isotropic materials. They respond the same way in all directions. • Substances in which measured (physical)properties are independent of the direction of measurement are isotropic. • Ex : Single Crystal ( Properties do not vary with direction) • Real Materials (Isotropic) Isotropy