![qa
rb
sc
Crystallographic
Points, Directions, and Planes
Crystallographic Direction
is a vector defined by a set of 3
numbers that specifies its
direction as reduced lowest set
of integers.
y
z
x
[u v w]
y
z
x
ac
b
ua
vb
wc
2](https://image.slidesharecdn.com/materialsscienceengineering1-200510002058/75/materials-science-and-engineering-1-82-2048.jpg?cb=1670663182)
![Crystallographic
Points, Directions, and Planes
Crystallographic Direction
is a vector defined by a set of 3
numbers that specifies its
direction as reduced lowest set
of integers.
[u v w]
Antiparallel Direction
y
z
x
y
z
x
ac
b
ua
vb
wc
2](https://image.slidesharecdn.com/materialsscienceengineering1-200510002058/75/materials-science-and-engineering-1-84-2048.jpg?cb=1670663182)
![<u v
w>
Crystallographic
Points, Directions, and Planes
Crystallographic Direction
is a vector defined by a set of
3 numbers that specifies its
direction as reduced lowest set
of integers.
[u v w]
Family
x y
z
[0 1 0]
[0 0 1]
[-1 0 0]
<1 0 0>
2](https://image.slidesharecdn.com/materialsscienceengineering1-200510002058/75/materials-science-and-engineering-1-85-2048.jpg?cb=1670663182)
![[u’v’w’]
Crystallographic
Points, Directions, and Planes
Crystallographic Direction
is a vector defined by a set of
3 numbers that specifies its
direction as reduced lowest set
of integers.
Miller–Bravais Coordinate
System
z
a1
a2
a3
Basal Plane
[u v t w]
𝑢 = 1
3
2𝑢′−𝑣′
𝑣 = 1
3
2𝑣′−𝑢′
𝑡 = − 𝑢+𝑣
𝑤 = 𝑤′
2](https://image.slidesharecdn.com/materialsscienceengineering1-200510002058/75/materials-science-and-engineering-1-86-2048.jpg?cb=1670663182)
![Sample Problem 15
Determine the linear density of
Molybdenum BCC [101] (for Mo:
R=0.1363 nm)
2.25 nm-1
2](https://image.slidesharecdn.com/materialsscienceengineering1-200510002058/75/materials-science-and-engineering-1-95-2048.jpg?cb=1670663182)
Materials Science and Engineering 1
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the fundamentals of materials science and some approach on understanding this field
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- 4. Fundamental Concepts e e e e e e = 1.602 x10-19 C -e -e -e -e -e SHIFT 7 2 3 1
- 5. Fundamental Concepts e = 1.602 x10-19 C SHIFT 7 2 3 Atomic Number (Z) the number of protons within the nucleus. equal to number of electrons in complete atoms. H 1 Hydrogen U 92 Uranium 1
- 6. Fundamental Concepts Mass Number (A) is expressed as: where N = number of neutrons 𝐴 = 𝑍 + 𝑁 Isotopes atoms of the same element that have different atomic masses. 𝑍 𝐴 𝐸 𝑛± 1
- 7. Sample Problem 1 An atom having a charge of +2e has 54 electrons. How many neutrons are there if the atom’s mass number is 131? 75.00 1
- 8. Fundamental Concepts Atomic Mass is the mass of an atom. 𝐴 𝑚 = 𝑍𝑚 𝑝 + 𝑁𝑚 𝑛 (Am) Atomic Mass Unit “amu” is defined as 1 12 of the atomic mass of Carbon-12. 1 𝑎𝑚𝑢 𝑎𝑡𝑜𝑚 = 1 𝑔 𝑚𝑜𝑙 Atomic Weight is the weighted average of the atomic masses of an atom’s naturally occurring isotopes. 𝐴 𝑤 = 𝐴 𝑚 % 𝑎𝑡 (Aw) SHIFT 7 0 1 SHIFT 7 0 2 1
- 9. Sample Problem 2 Carbon occurs in nature as a mixture of 12C and 13C. The isotopic mass of 13C is 13.003 amu. The atomic weight of carbon is 12.011 amu. What is the atom percentage of 12C in natural carbon? 98.90% 1
- 10. Fundamental Concepts Mole the quantity of substance corresponding to 6.022 x1023 atoms or molecules. “mol” Avogadro’s Number 𝑁𝐴 = 6.022 × 1023 (NA) SHIFT 7 2 4 1
- 11. Electrons in Atoms Bohr Atomic Model an early atomic model, in which electrons are assumed to revolve around the nucleus in discrete orbitals. 1
- 12. Electrons in Atoms Wave-Mechanical Model atomic model in which electrons are treated as being wave-like. Orbital Electron Electron Cloud 1.0 1
- 13. Electrons in Atoms Quantum Numbers a set of four numbers, the values of which are used to label possible electron states. n l m s Principal is related to the distance of an electron from the nucleus, or its position. (n) K L M N O P Q 1 2 3 4 5 6 7Electron State one of a set of discrete, quantized energies that are allowed for electrons. 1
- 14. Electrons in Atoms Quantum Numbers a set of four numbers, the values of which are used to label possible electron states. n l m s Orbital signifies the subshell and is related to its shape. (l) s p d f 0 1 2 3 1
- 15. Electrons in Atoms Quantum Numbers a set of four numbers, the values of which are used to label possible electron states. n l m s Magnetic is related to the orientation of orbitals within each subshells in the presence of a magnetic field. (m) s p d f 0 - 1 0 1 - 2 - 1 0 1 2 - 3 - 2 - 1 0 1 2 3 1
- 16. Electrons in Atoms Quantum Numbers a set of four numbers, the values of which are used to label possible electron states. n l m s Spin is related to electron’s spin moment. (s) − 𝟏 𝟐 𝟏 𝟐 𝑁𝑒 = 2𝑛2 1
- 17. Electrons in Atoms Electron Configuration the manner in which possible electron states are filled with electrons. Aufbau Principle states that electrons enter orbitals of lowest energy first. 1s 2s 3s 4s 5s 6s 7s 2p 3p 4p 5p 6p 7p 3d 4d 5d 6d 4f 5f Ground State a normally filled electron energy state from which an electron excitation may occur. Differentiating Electron the last electron that enters an orbital which makes an atom configuration different from other atoms. Valence Electrons the electrons in the outermost occupied shell, which participate in interatomic bonding. 1
- 18. Electrons in Atoms Electron Configuration the manner in which possible electron states are filled with electrons. Pauli Exclusion Principle the postulate that for an individual atom, at most two electrons, which necessarily have opposite spins, can occupy the same state. 1
- 19. Electrons in Atoms Electron Configuration the manner in which possible electron states are filled with electrons. Hund’s Rule states that when orbitals are of about the same energy, each orbital is filled with parallel spins before any of them is filled with the opposite spin electrons. 1
- 20. Sample Problem 3 Determine the set of quantum numbers for the differentiating electron of Oxygen. 2, 1, -1, -1/2 1
- 21. Electrons in Atoms Electron Configuration the manner in which possible electron states are filled with electrons. Hund’s Rule states that when orbitals are o about the same energy, each orbital is filled with parallel spins before any of them is filled with the opposite spin electrons. 1
- 22. The Periodic Table Periodic Table the arrangement of chemical elements with increasing atomic number according to the periodic variation in electron structure. 1
- 23. Representative Elementss-blockp-block ** * 118 Og 117 Ts 116 Lv 115 Mc 114 Fl 113 Nh 112 Cn 111 Rg 110 Ds 109 Mt 108 Hs 107 Bh 106 Sg 105 Db 104 Rf 103 Lr 102 No 101 Md 100 Fm 99 Es 98 Cf 97 Bk 96 Cm 95 Am 94 Pu 93 Np 92 U 91 Pa 90 Th 89 Ac 88 Ra 87 Fr 86 Rn 85 At 84 Po 83 Bi 82 Pb 81 Tl 80 Hg 79 Au 78 Pt 77 Ir 76 Os 75 Re 74 W 73 Ta 72 Hf 71 Lu 70 Yb 69 Tm 68 Er 67 Ho 66 Dy 65 Tb 64 Gd 63 Eu 62 Sm 61 Pm 60 Nd 59 Pr 58 Ce 57 La 56 Ba 55 Cs 54 Xe 53 I 52 Te 51 Sb 50 Sn 49 In 48 Cd 47 Ag 46 Pd 45 Rh 44 Ru 43 Tc 42 Mo 41 Nb 40 Zr 39 Y 38 Sr 37 Rb 36 Kr 35 Br 34 Se 33 As 32 Ge 31 Ga 30 Zn 29 Cu 28 Ni 27 Co 26 Fe 25 Mn 24 Cr 23 V 22 Ti 21 Sc 20 Ca 19 K 11 Na 12 Mg 4 Be 3 Li 1 H 18 Ar 10 Ne 2 He 17 Cl 9 F 16 S 15 P 14 Si 13 Al 5 B 6 C 7 N 8 O * ** Alkali Alkaline Earth Transition Lanthanoid Actinoid Post-transition Metalloid Nonmetal Halogen Noble Gas 1 2 3 4 5 6 7 Period IIA IA IIIA VAIVA VIIAVIA VIIIA IIIB IB IIBIVB VB VIB VIIB VIIIB 1
- 24. f-blockTransition ElementsInner Transition Elements ** * 118 Og 117 Ts 116 Lv 115 Mc 114 Fl 113 Nh 112 Cn 111 Rg 110 Ds 109 Mt 108 Hs 107 Bh 106 Sg 105 Db 104 Rf 103 Lr 102 No 101 Md 100 Fm 99 Es 98 Cf 97 Bk 96 Cm 95 Am 94 Pu 93 Np 92 U 91 Pa 90 Th 89 Ac 88 Ra 87 Fr 86 Rn 85 At 84 Po 83 Bi 82 Pb 81 Tl 80 Hg 79 Au 78 Pt 77 Ir 76 Os 75 Re 74 W 73 Ta 72 Hf 71 Lu 70 Yb 69 Tm 68 Er 67 Ho 66 Dy 65 Tb 64 Gd 63 Eu 62 Sm 61 Pm 60 Nd 59 Pr 58 Ce 57 La 56 Ba 55 Cs 54 Xe 53 I 52 Te 51 Sb 50 Sn 49 In 48 Cd 47 Ag 46 Pd 45 Rh 44 Ru 43 Tc 42 Mo 41 Nb 40 Zr 39 Y 38 Sr 37 Rb 36 Kr 35 Br 34 Se 33 As 32 Ge 31 Ga 30 Zn 29 Cu 28 Ni 27 Co 26 Fe 25 Mn 24 Cr 23 V 22 Ti 21 Sc 20 Ca 19 K 11 Na 12 Mg 4 Be 3 Li 1 H 18 Ar 10 Ne 2 He 17 Cl 9 F 16 S 15 P 14 Si 13 Al 5 B 6 C 7 N 8 O * ** Alkali Alkaline Earth Transition Lanthanoid Actinoid Post-transition Metalloid Nonmetal Halogen Noble Gas 1 2 3 4 5 6 7 Period IIA IA IIIA VAIVA VIIAVIA VIIIA IIIB IB IIBIVB VB VIB VIIB VIIIB d-block 1
- 25. Diatomic Elements ** * 112 Cn 111 Rg 110 Ds 109 Mt 108 Hs 107 Bh 106 Sg 105 Db 104 Rf 103 Lr 102 No 101 Md 100 Fm 99 Es 98 Cf 97 Bk 96 Cm 95 Am 94 Pu 93 Np 92 U 91 Pa 90 Th 89 Ac 88 Ra 87 Fr 86 Rn 85 At 84 Po 83 Bi 82 Pb 81 Tl 80 Hg 79 Au 78 Pt 77 Ir 76 Os 75 Re 74 W 73 Ta 72 Hf 71 Lu 70 Yb 69 Tm 68 Er 67 Ho 66 Dy 65 Tb 64 Gd 63 Eu 62 Sm 61 Pm 60 Nd 59 Pr 58 Ce 57 La 56 Ba 55 Cs 54 Xe 53 I 52 Te 51 Sb 50 Sn 49 In 48 Cd 47 Ag 46 Pd 45 Rh 44 Ru 43 Tc 42 Mo 41 Nb 40 Zr 39 Y 38 Sr 37 Rb 36 Kr 35 Br 34 Se 33 As 32 Ge 31 Ga 30 Zn 29 Cu 28 Ni 27 Co 26 Fe 25 Mn 24 Cr 23 V 22 Ti 21 Sc 20 Ca 19 K 11 Na 12 Mg 4 Be 3 Li 1 H 18 Ar 10 Ne 2 He 17 Cl 9 F 16 S 15 P 14 Si 13 Al 5 B 6 C 7 N 8 O * ** Alkali Alkaline Earth Transition Lanthanoid Actinoid Post-transition Metalloid Nonmetal Halogen Noble Gas 1 2 3 4 5 6 7 Period IIA IA IIIA VAIVA VIIAVIA VIIIA IIIB IB IIBIVB VB VIB VIIB VIIIB 118 Og 117 Ts 116 Lv 115 Mc 114 Fl 113 Nh Noble MetalsRefractory Metals 1
- 26. The Periodic Table Periodic Table the arrangement of chemical elements with increasing atomic number according to the periodic variation in electron structure. Electropositive the tendency of an atom to release valence electrons. Electronegative the tendency of an atom to accept valence electrons. 1
- 27. Bonding Forces and Energies FA FR r 𝐹 𝑁 = 𝐹𝐴 + 𝐹𝑅 ro ro corresponds to the separation distance at the minimum of the potential energy curve. 1
- 28. Bonding Forces and Energies ER EA r ro corresponds to the separation distance at the minimum of the potential energy curve. Eo Bonding Energy the energy required to separate two atoms to an infinite separation.𝐸 𝑁 = 𝐸𝐴 + 𝐸 𝑅 (Eo) 𝐸 𝑁 = − 𝐴 𝑟 + 𝐵 𝑟 𝑛 1
- 29. Sample Problem 4 For a given ion pair the following relations are given: -5.32 eV 𝐸𝐴 = − 1.436 𝑟 𝐸 𝑅 = − 7.32 × 10−6 𝑟8 where EA and ER in eV and r in nm. Determine the magnitude of the bonding energy between the two ions 1
- 30. Bonding Forces and Energies Primary Bonds interatomic bonds that are relatively strong and for which bonding energies are relatively large. Secondary Bonds interatomic and intermolecular bonds that are relatively weak and for which bonding energies are relatively small. Chemical Physical 1
- 31. Primary Atomic Bonds Ionic Bonds a coulombic interatomic bond that exist between two adjacent and oppositely charged ions. 11 Na 17 Cl 18 Ar 10 Ne Electrovalent 1
- 32. Primary Atomic Bonds Ionic Bonds a coulombic interatomic bond that exist between two adjacent and oppositely charged ions. 11 Na 17 Cl 18 Ar 10 Ne Coulombic Force a force between charged particles like ion; attractive if opposite charged NaCl (salt) Non-directional 1
- 33. Primary Atomic Bonds Ionic Bonds a coulombic interatomic bond that exist between two adjacent and oppositely charged ions. 11 Na 17 Cl 18 Ar 10 Ne Attractive Energy 𝐸𝐴 = − 𝑉1 𝑉2 𝑒2 4𝜋𝜖 𝑜 1 𝑟 SHIFT 7 2 3 IA VIIA SHIFT 7 3 2 1
- 34. ** * 112 Cn 111 Rg 110 Ds 109 Mt 108 Hs 107 Bh 106 Sg 105 Db 104 Rf 103 Lr 102 No 101 Md 100 Fm 99 Es 98 Cf 97 Bk 96 Cm 95 Am 94 Pu 93 Np 92 U 91 Pa 90 Th 89 Ac 88 Ra 87 Fr 86 Rn 85 At 84 Po 83 Bi 82 Pb 81 Tl 80 Hg 79 Au 78 Pt 77 Ir 76 Os 75 Re 74 W 73 Ta 72 Hf 71 Lu 70 Yb 69 Tm 68 Er 67 Ho 66 Dy 65 Tb 64 Gd 63 Eu 62 Sm 61 Pm 60 Nd 59 Pr 58 Ce 57 La 56 Ba 55 Cs 54 Xe 53 I 52 Te 51 Sb 50 Sn 49 In 48 Cd 47 Ag 46 Pd 45 Rh 44 Ru 43 Tc 42 Mo 41 Nb 40 Zr 39 Y 38 Sr 37 Rb 36 Kr 35 Br 34 Se 33 As 32 Ge 31 Ga 30 Zn 29 Cu 28 Ni 27 Co 26 Fe 25 Mn 24 Cr 23 V 22 Ti 21 Sc 20 Ca 19 K 11 Na 12 Mg 4 Be 3 Li 1 H 18 Ar 10 Ne 2 He 17 Cl 9 F 16 S 15 P 14 Si 13 Al 5 B 6 C 7 N 8 O * ** Alkali Alkaline Earth Transition Lanthanoid Actinoid Post-transition Metalloid Nonmetal Halogen Noble Gas 1 2 3 4 5 6 7 Period IIA IA IIIA VAIVA VIIAVIA VIIIA IIIB IB IIBIVB VB VIB VIIB VIIIB 118 Og 117 Ts 116 Lv 115 Mc 114 Fl 113 Nh Ionic Pairs 1
- 35. Sample Problem 5 Calculate the attractive energy between a Ca+2 and an O-2 ion, the centers of which are separated by a distance of 12.5 Å (units in eV) 13.83 eV 1 J = 1.602 x10-19 eV 1 nm = 10 Å 1
- 36. Primary Atomic Bonds Ionic Bonds ionic materials are characteristically hard and brittle, furthermore, electrically and thermally insulative. the predominant bonding in ceramic materials is ionic. 1
- 37. Primary Atomic Bonds Covalent Bonds an interatomic bond that is formed by the sharing of electrons between neighboring atoms. 6 C 1 H 10 Ne Molecular 1
- 38. Primary Atomic Bonds Covalent Bonds an interatomic bond that is formed by the sharing of electrons between neighboring atoms. 6 C 1 H 2 He 10 Ne CH4 (methane) Directional Number of Covalent Bonds 8 − 𝑉 Percent Ionic Character %𝑖𝑐 = 1 − 𝑒− 𝑋1−𝑋2 2 4 × 100% 1
- 39. ** * 112 Cn 111 Rg 110 Ds 109 Mt 108 Hs 107 Bh 106 Sg 105 Db 104 Rf 103 Lr 102 No 101 Md 100 Fm 99 Es 98 Cf 97 Bk 96 Cm 95 Am 94 Pu 93 Np 92 U 91 Pa 90 Th 89 Ac 88 Ra 87 Fr 86 Rn 85 At 84 Po 83 Bi 82 Pb 81 Tl 80 Hg 79 Au 78 Pt 77 Ir 76 Os 75 Re 74 W 73 Ta 72 Hf 71 Lu 70 Yb 69 Tm 68 Er 67 Ho 66 Dy 65 Tb 64 Gd 63 Eu 62 Sm 61 Pm 60 Nd 59 Pr 58 Ce 57 La 56 Ba 55 Cs 54 Xe 53 I 52 Te 51 Sb 50 Sn 49 In 48 Cd 47 Ag 46 Pd 45 Rh 44 Ru 43 Tc 42 Mo 41 Nb 40 Zr 39 Y 38 Sr 37 Rb 36 Kr 35 Br 34 Se 33 As 32 Ge 31 Ga 30 Zn 29 Cu 28 Ni 27 Co 26 Fe 25 Mn 24 Cr 23 V 22 Ti 21 Sc 20 Ca 19 K 11 Na 12 Mg 4 Be 3 Li 1 H 18 Ar 10 Ne 2 He 17 Cl 9 F 16 S 15 P 14 Si 13 Al 5 B 6 C 7 N * ** Alkali Alkaline Earth Transition Lanthanoid Actinoid Post-transition Metalloid Nonmetal Halogen Noble Gas 1 2 3 4 5 6 7 Period IIA IA IIIA VAIVA VIIAVIA VIIIA IIIB IB IIBIVB VB VIB VIIB VIIIB 118 Og 117 Ts 116 Lv 115 Mc 114 Fl 113 Nh Covalent Pairs 8 O 1
- 40. Sample Problem 6 Determine the percent ionic character of the ceramic Fe3O4 given that 1.8 and 3.5 are the electronegativities of iron and oxygen respectively. 51.45% 1
- 41. Primary Atomic Bonds Covalent Bonds covalent materials can be hard as in diamond or may be very weak as with bismuth. the predominant bonding in polymeric materials is covalent. 1
- 42. Primary Atomic Bonds Metallic Bonds an interatomic bond involving the sharing of nonlocalized valence electrons. 18 Ar 26 Fe 36 Kr Ion Cores Sea of Electrons Non-directional 1
- 43. Primary Atomic Bonds Metallic Bonds these bonds may be weak (mercury) or strong (tungsten) metallic materials are good conductors of both electricity and heat. 1
- 44. Secondary Atomic Bonds Fluctuating Induced Dipole Bonds bonds that exist between atoms having short-lived distortions of its electrical symmetry caused by constant vibrational motion. Van Der Waals Bonding exists when there is some separation of positive and negative portions of an atom or molecule. 18 Ar 1
- 45. Secondary Atomic Bonds Fluctuating Induced Dipole Bonds bonds that exist between atoms having short-lived distortions of its electrical symmetry caused by constant vibrational motion. London Forces 1
- 46. a molecule in which there exist a permanent electric dipole moment by virtue of the asymmetrical distribution of positively and negatively charged regions. Secondary Atomic Bonds Polar Molecule – Induced Dipole Bonds bonds that exist between polar molecules and the affected nonpolar ones. 1 H 17 Cl 1
- 47. Secondary Atomic Bonds Polar Molecule – Induced Dipole Bonds bonds that exist between polar molecules and the affected nonpolar ones. 1
- 48. Secondary Atomic Bonds Permanent Dipole Bonds bonds that exist between polar molecules. Dipole ForcesHydrogen Bonding the strongest van der waals bond. 1 H 9 F 7 N 8 O 1
- 49. ENDofChapter1 1
- 50. The Structure of Crystalline Solids CHAPTER 2 2
- 51. Fundamental Concepts Atomic Hard Sphere Model a model in which spheres representing nearest-neighbor atoms touch one another. Solid Materials: Crystalline Solids Amorphous Solids 2
- 52. Crystal StructureUnit Cell Fundamental Concepts Crystalline Solid is one in which the atoms are situated in a repeating or periodic array over large atomic distances. Amorphous Solid long-range atomic order is absent. the manner in which atoms, ions, or molecules are spatially arranged. the basic structural unit of a crystal structure. 2
- 53. means a three-dimensional array of points coinciding with atom positions Unit Cell the basic structural unit of a crystal structure. Fundamental Concepts Crystalline Solid is one in which the atoms are situated in a repeating or periodic array over large atomic distances. Lattice 2
- 54. Crystal Systems Lattice Parameters the combination of unit cell edge lengths and interaxial angles that defines the unit cell geometry. y z x ac b α β γCrystal System a scheme in which crystal structures are classified by unit cell geometry. 2
- 55. Crystal Systems Crystal System: Cubic a b c α β γ x x x 90o 90o 90o x x x θ θ θ x x x Rhombohedral θ θ θ 2
- 56. Crystal Systems Crystal System: Tetragonal a b c α β γ x x x 90o 90o 90o x x x y y 2
- 57. 120o y y Crystal Systems Crystal System: Hexagonal a b c α β γ x x 90o 90o 90o x x120o Orthorhombic 2
- 58. Orthorhombic 90o y y Crystal Systems Crystal System: a b c α β γ x x 90o 90o x x z z 2
- 59. z 90o y y Crystal Systems Crystal System: a b c α β γ x 90o 90o z x θ Monoclinic θ 2
- 60. z 90o y y Crystal Systems Crystal System: a b c α β γ x 90o z x θ Triclinic θ φ φ 2
- 61. z 90o y y Crystal Systems Crystal System: a b c α β γ x z x θ Triclinic φ θ φ ψ ψ 2
- 62. Metallic Crystal Structures Pointers: - the hard spheres represents the ion cores of metals. - cubic and hexagonal crystal systems are the predominant structures in common metals Coordination Number the number of atomic or ionic nearest neighbors. Atomic Packing Factor the fraction of the unit cell occupied by atoms. (APF)(Nc) 2
- 63. the fraction of the unit cell occupied by atoms. Atomic Packing Factor Metallic Crystal Structures Pointers: - the hard spheres represents the ion cores of metals. - cubic and hexagonal crystal systems are the predominant structures in common metals 𝐴𝑃𝐹 = 𝑁 4 3 𝜋𝑟3 𝑉𝑢 (APF) 2
- 64. Metallic Crystal Structures Face-Centered Cubic a crystal structure found in some of the common elemental metals; where within the cubic unit cell, atoms are located at all corner and face- centered positions. (FCC) 2
- 65. Metallic Crystal Structures Face-Centered Cubic (FCC) Face-Centered AtomsCorner Atoms Parameter Value Coordination Number Atomic Packing Factor Edge Length “f(r)” 12 2
- 66. Sample Problem 7 Determine the APF of FCC structure. 0.74 2
- 67. Metallic Crystal Structures Face-Centered Cubic (FCC) Parameter Value Coordination Number Atomic Packing Factor Edge Length “f(r)” 12 0.74 4𝑟 2 FCC Metals at Room Temperature Aluminum (Al) Nickel (Ni) Copper (Cu) Platinum (Pt) Gold (Au) Silver (Ag) Lead (Pb) 2
- 68. Metallic Crystal Structures Body-Centered Cubic a common crystal structure found in some elemental metals; where within the cubic unit cell, atoms are located at corner and cell center positions. (BCC) 2
- 69. Metallic Crystal Structures Body-Centered Cubic (BCC) Body-Centered AtomCorner Atoms Parameter Value Coordination Number Atomic Packing Factor Edge Length “f(r)” 8 2
- 70. Sample Problem 8 Determine the APF of BCC structure. 0.68 2
- 71. Metallic Crystal Structures Body-Centered Cubic (BCC) Parameter Value Coordination Number Atomic Packing Factor Edge Length “f(r)” 8 0.68 4𝑟 3 BCC Metals at Room Temperature Chromium (Cr) Tungsten (W) Iron (Fe) Molybdenum (Mo) Tantalum (Ta) 2
- 72. Metallic Crystal Structures Hexagonal Close-Packed a crystal structure found for some metals. It is of hexagonal geometry and is generated by the stacking of close-packed planes of atoms. (HCP) 2
- 73. Midplane Interior Atoms Metallic Crystal Structures Center Face AtomsCorner Atoms Parameter Value Coordination Number Atomic Packing Factor Height/Edge Length 12 Hexagonal Close-Packed (HCP) 0.74 1.6330 HCP Metals at Room Temperature Cadmium (Cd) Cobalt (Co) Titanium (Ti) Zinc (Zn) 2
- 74. Metallic Crystal Structures Simple Cubic a crystal structure, which Polonium (Po) only have, consists of only corner atoms. 2
- 75. Metallic Crystal Structures Simple Cubic Parameter Value Coordination Number Atomic Packing Factor Edge Length “f(r)” 8 0.52 4𝑟 4 Simple Cubic Metal Polonium (Po) 2r 2
- 76. Density Computations Theoretical Density the density of a given unit cell which intrinsically represents the whole solid with no regard to imperfections. 𝜌𝑡 = 𝑚 𝑎 𝑉𝑢 = 𝐴 𝑤 𝑛 𝑉𝑢 = 𝐴 𝑤 𝑁 𝑁 𝐴 𝑉𝑢 𝜌𝑡 = 𝑁𝐴 𝑤 𝑉𝑢 𝑁 𝐴 = 𝐴𝑃𝐹 𝐴 𝑤 4 3 𝜋𝑟3 𝑁 𝐴 (ρt) 2
- 77. Sample Problem 9 The unit cell for a uranium has orthorhombic symmetry, with a, b, and c lattice parameters of 0.286, 0.587, and 0.495 nm, respectively. If its density, atomic weight, and atomic radius are 19.05 g/cm3, 238.03 g/mol, and 0.1385 nm, respectively, compute the atomic packing factor. 0.54 2
- 78. Density Computations Theoretical Density the density of a given unit cell which intrinsically represents the whole solid with no regard to imperfections. 𝜌𝑡 = 𝑁𝐴 𝑤 𝑉𝑢 𝑁 𝐴 = 𝐴𝑃𝐹 𝐴 𝑤 4 3 𝜋𝑟3 𝑁 𝐴 (ρt) 2
- 79. Polymorphism and Allotropy Polymorphism the ability of a solid material to exist in more than one form or crystal structure. Allotropy the term used for polymorphism of elemental solids. Graphite Diamond 2
- 80. Crystallographic Points, Directions, and Planes Point Coordinate set of 3 numbers that specifies the location of a point inside a unit cell as fractional multiples of the edge lengths. y z x ac b qa rb sc q r s 2
- 81. Sample Problem 10 Locate the body-centered atom of Niobium BCC having an atomic radius of 0.143 nm. 𝟏 𝟐 𝟏 𝟐 𝟏 𝟐 2
- 82. qa rb sc Crystallographic Points, Directions, and Planes Crystallographic Direction is a vector defined by a set of 3 numbers that specifies its direction as reduced lowest set of integers. y z x [u v w] y z x ac b ua vb wc 2
- 83. Sample Problem 11 Determine the indices for the direction shown below. 𝟑 𝟔 𝟏 y z x 1 3 1 2 , 1 2 2
- 84. Crystallographic Points, Directions, and Planes Crystallographic Direction is a vector defined by a set of 3 numbers that specifies its direction as reduced lowest set of integers. [u v w] Antiparallel Direction y z x y z x ac b ua vb wc 2
- 85. <u v w> Crystallographic Points, Directions, and Planes Crystallographic Direction is a vector defined by a set of 3 numbers that specifies its direction as reduced lowest set of integers. [u v w] Family x y z [0 1 0] [0 0 1] [-1 0 0] <1 0 0> 2
- 86. [u’v’w’] Crystallographic Points, Directions, and Planes Crystallographic Direction is a vector defined by a set of 3 numbers that specifies its direction as reduced lowest set of integers. Miller–Bravais Coordinate System z a1 a2 a3 Basal Plane [u v t w] 𝑢 = 1 3 2𝑢′−𝑣′ 𝑣 = 1 3 2𝑣′−𝑢′ 𝑡 = − 𝑢+𝑣 𝑤 = 𝑤′ 2
- 87. Sample Problem 12 Determine the indices for the direction shown below. 𝟏 𝟏 𝟐 𝟑 z a1 a2 a3 2
- 88. Crystallographic Points, Directions, and Planes Crystallographic Plane is a plane defined by a set of 3 numbers called Miller Indices that specifies its position inside the cell as reciprocals of its intersections with the axes. (h k l) y z x ac b ha kb lc 2
- 89. Sample Problem 13 Determine the Miller indices for the plane shown below. 𝟎 𝟏 𝟐 y z x 2
- 90. (h k l){h k l} Crystallographic Points, Directions, and Planes Crystallographic Plane is a plane defined by a set of 3 numbers called Miller Indices that specifies its position inside the cell as reciprocals of its intersections with the axes. Family x y z (0 1 2) (2 0 -1) {0 1 2} (1 -2 0) 2
- 91. (h’k’l’) Crystallographic Points, Directions, and Planes Crystallographic Plane is a plane defined by a set of 3 numbers called Miller Indices that specifies its position inside the cell as reciprocals of its intersections with the axes. Hexagonal Crystals z a1 a2 a3 (h k i l) 𝑖 = − ℎ+𝑘 𝑙 = 𝑙′ ℎ = ℎ′ 𝑘 = 𝑘′ 2
- 92. Sample Problem 14 Determine the Miller indices for the plane shown below. 𝟏 𝟏 𝟐 𝟐 z a1 a2 a3 2
- 93. (h’k’l’) Crystallographic Points, Directions, and Planes Crystallographic Plane is a plane defined by a set of 3 numbers called Miller Indices that specifies its position inside the cell as reciprocals of its intersections with the axes. Hexagonal Crystals z a1 a2 a3 (h k i l) 𝑖 = − ℎ+𝑘 𝑙 = 𝑙′ ℎ = ℎ′ 𝑘 = 𝑘′ 2
- 94. Linear and Planar Densities Linear Density defined as the number of atoms per unit length whose centers lie on the direction vector for a specific crystallographic direction. (LD) 𝐿𝐷 = 𝑁 𝐿 2
- 95. Sample Problem 15 Determine the linear density of Molybdenum BCC [101] (for Mo: R=0.1363 nm) 2.25 nm-1 2
- 96. Linear and Planar Densities Linear Density defined as the number of atoms per unit length whose centers lie on the direction vector for a specific crystallographic direction. (LD) 𝐿𝐷 = 𝑁 𝐿 Planar Density defined as the number of atoms per unit area that are centered on a particular crystallographic plane. 𝑃𝐷 = 𝑁 𝐴 2
- 97. Sample Problem 16 Determine the planar density of Copper FCC (110) (for Cu: R=0.1280 nm) 10.79 nm-2 2
- 98. Close-Packed Crystal Structures Close-Packed Planes of Atoms planes having a maximum atom or sphere packing density. 0.74 is the most efficient packing of equal-sized spheres or atoms. 2 FCC HCP
- 99. Close-Packed Crystal Structures Close-Packed Planes of Atoms planes having a maximum atom or sphere packing density. 0.74 is the most efficient packing of equal-sized spheres or atoms. 2 B B B B B B B B B B BB B B B B B B C C C C C C C C C A A A A A A A A A A A A A A A
- 100. Close-Packed Crystal Structures 2 A A B C A {1 1 1} B C A FCC A B A {0 0 0 1} B HCP
- 101. Crystalline Materials Single Crystal a crystalline solid for which the periodic and repeated atomic pattern extends throughout its entirety without interruption. 2 Anisotropy the directionality of properties.
- 102. Crystalline Materials Polycrystalline is a collection of multiple crystals with different orientations. 2 Isotropy having identical properties in all crystallographic directions. Grain Grain Boundary
- 103. X-ray Diffraction Diffraction constructive interference of waves that are scattered by atoms of a crystal. 2 Constructive Interference Destructive Interference X-ray a form EM radiation that have high energy and short wavelength (order of atomic spacings)
- 104. X-ray Diffraction Diffraction constructive interference of waves that are scattered by atoms of a crystal. 2 X-ray a form EM radiation that have high energy and short wavelength (order of atomic spacings) Bragg’s Law a relationship that stipulates the condition for diffraction by a set of crystallographic planes. 𝑛𝜆 = 2 𝑑ℎ𝑘𝑙 sin 𝜃
- 105. X-ray Diffraction 2 Bragg’s Law a relationship that stipulates the condition for diffraction by a set of crystallographic planes. 𝑛𝜆 = 2 𝑑ℎ𝑘𝑙 sin 𝜃 𝑑ℎ𝑘𝑙 = 𝑎 ℎ2+𝑘2+𝑙2 (hkl) (hkl) θ θ dhkl λ θθ
- 106. Sample Problem 17 For BCC iron, compute the lattice parameter (a) in angstrom. It has a diffraction angle of 124.26o for the (220) set of planes. Also, assume that monochromatic radiation having λ = 0.179 nm is used, and the order of reflection is 1. 2.86 Å 2
- 107. X-ray Diffraction Diffractometer is an apparatus used to determine the angles at which diffraction occurs for powdered specimens 2 TS C θ 2θ
- 108. 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 Diffraction Angle X-ray Diffraction Diffractometer is an apparatus used to determine the angles at which diffraction occurs for powdered specimens 2 TS θ 2θ C (111) (200) (220) (311) (222) (400) Intensity
- 109. Non Crystalline Solids Non Crystalline Solid their atomic structure resembles that of a liquid. 2 rapidly cooling through the freezing temperature favors its formation.
- 110. ENDofChapter2 2
- 111. Materials Science and Engineering – An Introduction (7th Edition) by William D. Callister, Jr. Materials Science and Engineering Source
- 112. Steradia n