1. Fundamentals of materials science Amir Seyfoori نیمسال دوم سال تحصیلی 93-92 کارشناسی مهندسی پزشکی ( بیومواد )

2. مبانی ( ساختار - خواص جامدات )

3. انواع مواد مهندسی 1- فلزات : فلزات خالص آلیاژ های فلزی 2- سرامیک ها : سرامیک های سنتی سرامیک های مهندسی ( مدرن ) 3- پلیمرها : گرمانرم گرما سخت الاستومر ها 4- کامپوزیت ها : پایه فلزی پایه سرامیکی پایه پلیمری

4. Atomic Structure atom – electrons – 9.11 x 10 -31 kg protons neutrons atomic number = # of protons in nucleus of atom = # of electrons of neutral species A [=] atomic mass unit = amu = 1/12 mass of 12 C Atomic wt = wt of 6.023 x 10 23 molecules or atoms 1 amu/atom = 1g/mol C 12.011 H 1.008 etc. 4 } 1.67 x 10 -27 kg

5. Atomic Structure Valence electrons determine all of the following properties 1)Chemical 2)Electrical 3)Thermal 4)Optical 5

6. Electronic Structure Electrons have wavelike and particulate properties. – This means that electrons are in orbitals defined by a probability. – Each orbital at discrete energy level determined by quantum numbers. Quantum # Designation n = principal (energy level-shell)K, L, M, N, O (1, 2, 3, etc.) l = subsidiary (orbitals)s, p, d, f (0, 1, 2, 3,…, n -1) m l = magnetic1, 3, 5, 7 (- l to + l ) m s = spin½, -½ 6

7. Electron Energy States 7 1s1s 2s2s 2p2p K-shell n = 1 L-shell n = 2 3s3s 3p3p M-shell n = 3 3d3d 4s4s 4p4p 4d4d Energy N-shell n = 4 have discrete energy states tend to occupy lowest available energy state. Electrons... Adapted from Fig. 2.4, Callister 7e.

8. 8 SURVEY OF ELEMENTS Why? Valence (outer) shell usually not filled completely. Most elements: Electron configuration not stable. Electron configuration (stable)... 1s1s 2 2s2s 2 2p2p 6 3s3s 2 3p3p 6 (stable)... 1s1s 2 2s2s 2 2p2p 6 3s3s 2 3p3p 6 3d3d 10 4s4s 2 4p4p 6 (stable) Atomic # 18... 36 Element 1s1s 1 1Hydrogen 1s1s 2 2Helium 1s1s 2 2s2s 1 3Lithium 1s1s 2 2s2s 2 4Beryllium 1s1s 2 2s2s 2 2p2p 1 5Boron 1s1s 2 2s2s 2 2p2p 2 6Carbon... 1s1s 2 2s2s 2 2p2p 6 (stable) 10Neon 1s1s 2 2s2s 2 2p2p 6 3s3s 1 11Sodium 1s1s 2 2s2s 2 2p2p 6 3s3s 2 12Magnesium 1s1s 2 2s2s 2 2p2p 6 3s3s 2 3p3p 1 13Aluminum... Argon... Krypton Adapted from Table 2.2, Callister 7e.

9. Electron Configurations Valence electrons – those in unfilled shells Filled shells more stable Valence electrons are most available for bonding and tend to control the chemical properties – example: C (atomic number = 6) 1s 2 2s 2 2p 2 9 valence electrons

10. Electronic Configurations ex: Fe - atomic # = 10 26 valence electrons Adapted from Fig. 2.4, Callister 7e. 1s1s 2s2s 2p2p K-shell n = 1 L-shell n = 2 3s3s 3p3p M-shell n = 3 3d3d 4s4s 4p4p 4d4d Energy N-shell n = 4 1s 2 2s 2 2p 6 3s 2 3p 6 3d 6 4s 2

11. 11 The Periodic Table Columns: Similar Valence Structure Adapted from Fig. 2.6, Callister 7e. Electropositive elements: Readily give up electrons to become + ions. Electronegative elements: Readily acquire electrons to become - ions. give up 1e give up 2e give up 3e inert gases accept 1eaccept 2e O Se Te PoAt I Br He Ne Ar Kr Xe Rn F ClS LiBe H NaMg BaCs RaFr CaKSc SrRbY

12. 12 Ranges from 0.7 to 4.0, Smaller electronegativityLarger electronegativity Large values: tendency to acquire electrons. Adapted from Fig. 2.7, Callister 7e. (Fig. 2.7 is adapted from Linus Pauling, The Nature of the Chemical Bond, 3rd edition, Copyright 1939 and 1940, 3rd edition. Copyright 1960 by Cornell University. Electronegativity

13. 13 Ionic bond – metal + nonmetal donates accepts electrons electrons Dissimilar electronegativities ex: MgOMg 1s 2 2s 2 2p 6 3s 2 O 1s 2 2s 2 2p 4 [Ne] 3s 2 Mg 2+ 1s 2 2s 2 2p 6 O 2- 1s 2 2s 2 2p 6 [Ne] [Ne]

14. 14 Occurs between + and - ions. Requires electron transfer. Large difference in electronegativity required. Example: NaCl Ionic Bonding Na (metal) unstable Cl (nonmetal) unstable electron + - Coulombic Attraction Na (cation) stable Cl (anion) stable

15. 15 Ionic Bonding Energy – minimum energy most stable – Energy balance of attractive and repulsive terms Attractive energy E A Net energy E N Repulsive energy E R Interatomic separation r r A n r B E N = E A + E R =  Adapted from Fig. 2.8(b), Callister 7e.

16. 16 Predominant bonding in Ceramics Adapted from Fig. 2.7, Callister 7e. (Fig. 2.7 is adapted from Linus Pauling, The Nature of the Chemical Bond, 3rd edition, Copyright 1939 and 1940, 3rd edition. Copyright 1960 by Cornell University. Examples: Ionic Bonding Give up electronsAcquire electrons NaCl MgO CaF 2 CsCl

17. 17 C: has 4 valence e -, needs 4 more H: has 1 valence e -, needs 1 more Electronegativities are comparable. Adapted from Fig. 2.10, Callister 7e. Covalent Bonding similar electronegativity  share electrons bonds determined by valence – s & p orbitals dominate bonding Example: CH 4 shared electrons from carbon atom shared electrons from hydrogen atoms H H H H C CH 4

18. 18 Primary Bonding Metallic Bond -- delocalized as electron cloud Ionic-Covalent Mixed Bonding % ionic character = where X A & X B are Pauling electronegativities %)100( x Ex: MgOX Mg = 1.3X O = 3.5

19. 19 Arises from interaction between dipoles Permanent dipoles-molecule induced Fluctuating dipoles -general case: -ex: liquid HCl -ex: polymer Adapted from Fig. 2.13, Callister 7e. Adapted from Fig. 2.14, Callister 7e. SECONDARY BONDING asymmetric electron clouds +-+- secondary bonding HHHH H 2 H 2 secondary bonding ex: liquid H 2 H Cl H secondary bonding secondary bonding +-+- secondary bonding

20. 20 Type Ionic Covalent Metallic Secondary Bond Energy Large! Variable large-Diamond small-Bismuth Variable large-Tungsten small-Mercury smallest Comments Nondirectional (ceramics) Directional (semiconductors, ceramics polymer chains) Nondirectional (metals) Directional inter-chain (polymer) inter-molecular Summary: Bonding

21. 21 Bond length, r Bond energy, E o Melting Temperature, T m T m is larger if E o is larger. Properties From Bonding: T m r o r Energy r larger T m smaller T m EoEo =“bond energy” Energy r o r unstretched length

22. 22 Coefficient of thermal expansion (CTE),   ~ more symmetry at r o  is larger if E o is smaller. Properties From Bonding :  =  (T 2 -T 1 )  L L o coeff. thermal expansion  L length,L o unheated, T 1 heated, T 2 r o r Smaller  Larger  Energy unstretched length EoEo EoEo

23. 23 Ceramics (Ionic & covalent bonding): Metals (Metallic bonding): Polymers (Covalent & Secondary): Large bond energy large T m large E small  Variable bond energy moderate T m moderate E moderate  Directional Properties Secondary bonding dominates small T m small E large  Summary: Primary Bonds secondary bonding

24. 24 Non dense, random packing Dense, ordered packing Dense, ordered packed structures tend to have lower energies. Energy and Packing Energy r typical neighbor bond length typical neighbor bond energy Energy r typical neighbor bond length typical neighbor bond energy

25. 25 atoms pack in periodic, 3D arrays Crystalline materials... -metals -many ceramics -some polymers atoms have no periodic packing Noncrystalline materials... -complex structures -rapid cooling crystalline SiO 2 noncrystalline SiO 2 "Amorphous" = Noncrystalline Adapted from Fig. 3.22(b), Callister 7e. Adapted from Fig. 3.22(a), Callister 7e. Materials and Packing SiOxygen typical of: occurs for:

26. 26 Section 3.3 – Crystal Systems 7 crystal systems 14 crystal lattices Fig. 3.4, Callister 7e. Unit cell: smallest repetitive volume which contains the complete lattice pattern of a crystal. a, b, and c are the lattice constants

27. 27 Section 3.4 – Metallic Crystal Structures How can we stack metal atoms to minimize empty space? 2-dimensions vs. Now stack these 2-D layers to make 3-D structures

28. 28 Tend to be densely packed. Reasons for dense packing: - Typically, only one element is present, so all atomic radii are the same. - Metallic bonding is not directional. - Nearest neighbor distances tend to be small in order to lower bond energy. - Electron cloud shields cores from each other Have the simplest crystal structures. We will examine three such structures... Metallic Crystal Structures

29. 29 Rare due to low packing denisty (only Po has this structure) Close-packed directions are cube edges. Coordination # = 6 (# nearest neighbors) (Courtesy P.M. Anderson) Simple Cubic Structure (SC)

30. 30 APF for a simple cubic structure = 0.52 APF = a 3 4 3  (0.5a) 3 1 atoms unit cell atom volume unit cell volume Atomic Packing Factor (APF) APF = Volume of atoms in unit cell* Volume of unit cell *assume hard spheres Adapted from Fig. 3.23, Callister 7e. close-packed directions a R=0.5a contains 8 x 1/8 = 1atom/unit cell

31. 31 Coordination # = 8 Adapted from Fig. 3.2, Callister 7e. (Courtesy P.M. Anderson) Atoms touch each other along cube diagonals. --Note: All atoms are identical; the center atom is shaded differently only for ease of viewing. Body Centered Cubic Structure (BCC) ex: Cr, W, Fe (  ), Tantalum, Molybdenum 2 atoms/unit cell: 1 center + 8 corners x 1/8

32. 32 Atomic Packing Factor: BCC a APF = 4 3  (3a/4) 3 2 atoms unit cell atom volume a 3 unit cell volume length = 4R = Close-packed directions: 3 a APF for a body-centered cubic structure = 0.68 a R Adapted from Fig. 3.2(a), Callister 7e. a 2 a 3

33. 33 Coordination # = 12 Adapted from Fig. 3.1, Callister 7e. (Courtesy P.M. Anderson) Atoms touch each other along face diagonals. --Note: All atoms are identical; the face-centered atoms are shaded differently only for ease of viewing. Face Centered Cubic Structure (FCC) ex: Al, Cu, Au, Pb, Ni, Pt, Ag 4 atoms/unit cell: 6 face x 1/2 + 8 corners x 1/8

34. 34 APF for a face-centered cubic structure = 0.74 Atomic Packing Factor: FCC maximum achievable APF APF = 4 3  (2a/4) 3 4 atoms unit cell atom volume a 3 unit cell volume Close-packed directions: length = 4R = 2 a Unit cell contains: 6 x 1/2 + 8 x 1/8 =4 atoms/unit cell a 2 a Adapted from Fig. 3.1(a), Callister 7e.

35. 35 A sites B B B B B BB C sites C C C A B B ABCABC... Stacking Sequence 2D Projection FCC Unit Cell FCC Stacking Sequence B B B B B BB B sites C C C A C C C A

36. 36 Coordination # = 12 ABAB... Stacking Sequence APF = 0.74 3D Projection 2D Projection Adapted from Fig. 3.3(a), Callister 7e. Hexagonal Close-Packed Structure (HCP) 6 atoms/unit cell ex: Cd, Mg, Ti, Zn c/a = 1.633 c a A sites B sites A sites Bottom layer Middle layer Top layer

37. 37 Theoretical Density,  where n = number of atoms/unit cell A = atomic weight V C = Volume of unit cell = a 3 for cubic N A = Avogadro’s number = 6.023 x 10 23 atoms/mol Density =  = VC NAVC NA n An A  = Cell Unit of VolumeTotal Cell Unit in Atomsof Mass

38. 38 Ex: Cr (BCC) A = 52.00 g/mol R = 0.125 nm n = 2  theoretical a = 4R/ 3 = 0.2887 nm  actual a R  = a 3 52.002 atoms unit cell mol g unit cell volume atoms mol 6.023 x 10 23 Theoretical Density,  = 7.18 g/cm 3 = 7.19 g/cm 3

39. 39 Densities of Material Classes  metals >  ceramics >  polymers Why? Data from Table B1, Callister 7e.  (g/cm ) 3 Graphite/ Ceramics/ Semicond Metals/ Alloys Composites/ fibers Polymers 1 2 20 30 Based on data in Table B1, Callister *GFRE, CFRE, & AFRE are Glass, Carbon, & Aramid Fiber-Reinforced Epoxy composites (values based on 60% volume fraction of aligned fibers in an epoxy matrix). 10 3 4 5 0.3 0.4 0.5 Magnesium Aluminum Steels Titanium Cu,Ni Tin, Zinc Silver, Mo Tantalum Gold, W Platinum Graphite Silicon Glass-soda Concrete Si nitride Diamond Al oxide Zirconia HDPE, PS PP, LDPE PC PTFE PET PVC Silicone Wood AFRE* CFRE* GFRE* Glass fibers Carbonfibers Aramid fibers Metals have... close-packing (metallic bonding) often large atomic masses Ceramics have... less dense packing often lighter elements Polymers have... low packing density (often amorphous) lighter elements (C,H,O) Composites have... intermediate values In general

40. 40 Some engineering applications require single crystals: Properties of crystalline materials often related to crystal structure. (Courtesy P.M. Anderson) --Ex: Quartz fractures more easily along some crystal planes than others. --diamond single crystals for abrasives --turbine blades Fig. 8.33(c), Callister 7e. (Fig. 8.33(c) courtesy of Pratt and Whitney). (Courtesy Martin Deakins, GE Superabrasives, Worthington, OH. Used with permission.) Crystals as Building Blocks

41. 41 Most engineering materials are polycrystals. Nb-Hf-W plate with an electron beam weld. Each "grain" is a single crystal. If grains are randomly oriented, overall component properties are not directional. Grain sizes typ. range from 1 nm to 2 cm (i.e., from a few to millions of atomic layers). Adapted from Fig. K, color inset pages of Callister 5e. (Fig. K is courtesy of Paul E. Danielson, Teledyne Wah Chang Albany) 1 mm Polycrystals Isotropic Anisotropic

42. 42 Single Crystals -Properties vary with direction: anisotropic. -Example: the modulus of elasticity (E) in BCC iron: Polycrystals -Properties may/may not vary with direction. -If grains are randomly oriented: isotropic. (E poly iron = 210 GPa) -If grains are textured, anisotropic. 200  m Data from Table 3.3, Callister 7e. (Source of data is R.W. Hertzberg, Deformation and Fracture Mechanics of Engineering Materials, 3rd ed., John Wiley and Sons, 1989.) Adapted from Fig. 4.14(b), Callister 7e. (Fig. 4.14(b) is courtesy of L.C. Smith and C. Brady, the National Bureau of Standards, Washington, DC [now the National Institute of Standards and Technology, Gaithersburg, MD].) Single vs. Polycrystals E (diagonal) = 273 GPa E (edge) = 125 GPa

43. 43 Section 3.6 – Polymorphism Two or more distinct crystal structures for the same material (allotropy/polymorphism) titanium ,  -Ti carbon diamond, graphite BCC FCC BCC 1538ºC 1394ºC 912ºC  - Fe  - Fe  - Fe liquid iron system

44. 44 Section 3.8 Point Coordinates Point coordinates for unit cell center are a/2, b/2, c/2 ½ ½ ½ Point coordinates for unit cell corner are 111 Translation: integer multiple of lattice constants  identical position in another unit cell z x y a b c 000 111 y z 2c2c b b

45. 45 Crystallographic Directions 1. Vector repositioned (if necessary) to pass through origin. 2. Read off projections in terms of unit cell dimensions a, b, and c 3. Adjust to smallest integer values 4. Enclose in square brackets, no commas [uvw] ex: 1, 0, ½ => 2, 0, 1=> [ 201 ] -1, 1, 1 families of directions z x Algorithm where overbar represents a negative index [ 111 ] => y

46. 46 ex: linear density of Al in [110] direction a = 0.405 nm Linear Density Linear Density of Atoms  LD = a [110] Unit length of direction vector Number of atoms # atoms length 1 3.5 nm a2 2 LD  

47. 47 HCP Crystallographic Directions 1. Vector repositioned (if necessary) to pass through origin. 2. Read off projections in terms of unit cell dimensions a 1, a 2, a 3, or c 3. Adjust to smallest integer values 4. Enclose in square brackets, no commas [uvtw] [ 1120 ] ex: ½, ½, -1, 0 => Adapted from Fig. 3.8(a), Callister 7e. dashed red lines indicate projections onto a 1 and a 2 axes a1a1 a2a2 a3a3 -a3-a3 2 a 2 2 a 1 - a3a3 a1a1 a2a2 z Algorithm

48. 48 HCP Crystallographic Directions Hexagonal Crystals – 4 parameter Miller-Bravais lattice coordinates are related to the direction indices (i.e., u'v'w') as follows.    'ww t v u )vu( +- )'u'v2( 3 1 - )'v'u2( 3 1 -  ]uvtw[]'w'v'u[  Fig. 3.8(a), Callister 7e. - a3a3 a1a1 a2a2 z

49. 49 Crystallographic Planes Adapted from Fig. 3.9, Callister 7e.

50. 50 Crystallographic Planes Miller Indices: Reciprocals of the (three) axial intercepts for a plane, cleared of fractions & common multiples. All parallel planes have same Miller indices. Algorithm 1. Read off intercepts of plane with axes in terms of a, b, c 2. Take reciprocals of intercepts 3. Reduce to smallest integer values 4. Enclose in parentheses, no commas i.e., (hkl)

51. 51 Crystallographic Planes z x y a b c 4. Miller Indices (110) examplea b c z x y a b c 4. Miller Indices (100) 1. Intercepts 1 1  2. Reciprocals 1/1 1/1 1/  1 1 0 3. Reduction 1 1 0 1. Intercepts 1/2   2. Reciprocals 1/½ 1/  1/  2 0 0 3. Reduction 2 0 0 examplea b c

52. 52 Crystallographic Planes z x y a b c 4. Miller Indices (634) example 1. Intercepts 1/2 1 3/4 a b c 2. Reciprocals 1/½ 1/1 1/¾ 21 4/3 3. Reduction 63 4 (001) (010), Family of Planes {hkl} (100),(010), (001),Ex: {100} = (100),

53. 53 Crystallographic Planes (HCP) In hexagonal unit cells the same idea is used example a 1 a 2 a 3 c 4. Miller-Bravais Indices(1011) 1. Intercepts 1  1 2. Reciprocals 1 1/  1 0 1 1 3. Reduction1 0 1 a2a2 a3a3 a1a1 z Adapted from Fig. 3.8(a), Callister 7e.

54. 54 Crystallographic Planes We want to examine the atomic packing of crystallographic planes Iron foil can be used as a catalyst. The atomic packing of the exposed planes is important. a)Draw (100) and (111) crystallographic planes for Fe. b) Calculate the planar density for each of these planes.

55. 55 Planar Density of (100) Iron Solution: At T < 912  C iron has the BCC structure. (100) Radius of iron R = 0.1241 nm R 3 34 a  Adapted from Fig. 3.2(c), Callister 7e. 2D repeat unit = Planar Density = a 2 1 atoms 2D repeat unit = nm 2 atoms 12.1 m2m2 atoms = 1.2 x 10 19 1 2 R 3 34 area 2D repeat unit

56. 56 Planar Density of (111) Iron Solution (cont): (111) plane 1 atom in plane/ unit surface cell 33 3 2 2 R 3 16 R 3 4 2 a3ah2area           atoms in plane atoms above plane atoms below plane ah 2 3  a 2 2D repeat unit 1 = = nm 2 atoms 7.0 m2m2 atoms 0.70 x 10 19 3 2 R 3 16 Planar Density = atoms 2D repeat unit area 2D repeat unit

57. 57 Section 3.16 - X-Ray Diffraction Diffraction gratings must have spacings comparable to the wavelength of diffracted radiation. Can’t resolve spacings  Spacing is the distance between parallel planes of atoms.

58. 58 X-Rays to Determine Crystal Structure X-ray intensity (from detector)   c d d  n 2 sin  c Measurement of critical angle,  c, allows computation of planar spacing, d. Incoming X-rays diffract from crystal planes. Adapted from Fig. 3.19, Callister 7e. reflections must be in phase for a detectable signal spacing between planes d incoming X-rays outgoing X-rays detector   extra distance travelled by wave “2” “1” “2” “1” “2”

59. 59 X-Ray Diffraction Pattern Adapted from Fig. 3.20, Callister 5e. (110) (200) (211) z x y a b c Diffraction angle 2  Diffraction pattern for polycrystalline  -iron (BCC) Intensity (relative) z x y a b c z x y a b c

60. 60 Atoms may assemble into crystalline or amorphous structures. We can predict the density of a material, provided we know the atomic weight, atomic radius, and crystal geometry (e.g., FCC, BCC, HCP). SUMMARY Common metallic crystal structures are FCC, BCC, and HCP. Coordination number and atomic packing factor are the same for both FCC and HCP crystal structures. Crystallographic points, directions and planes are specified in terms of indexing schemes. Crystallographic directions and planes are related to atomic linear densities and planar densities.

61. 61 Some materials can have more than one crystal structure. This is referred to as polymorphism (or allotropy). SUMMARY Materials can be single crystals or polycrystalline. Material properties generally vary with single crystal orientation (i.e., they are anisotropic), but are generally non-directional (i.e., they are isotropic) in polycrystals with randomly oriented grains. X-ray diffraction is used for crystal structure and interplanar spacing determinations.