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Chapter 3: Structures of Metals & Ceramics

Chapter 3: Structures of Metals & Ceramics Structures The properties of some materials are directly related to their crystal structures. Significant property differences exist between crystalline and noncrystalline materials having the same composition. Energy and Packing Energy

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Chapter 3: Structures of Metals & Ceramics

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  1. Chapter 3: Structures of Metals & Ceramics

  2. Structures • The properties of some materials are directly related to their crystal structures. • Significant property differences exist between crystalline and noncrystalline materials having the same composition.

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

  4. Materials and Packing Crystalline materials... • atoms pack in periodic, 3D arrays • typical of: -metals -many ceramics -some polymers crystalline SiO2 Si Oxygen Noncrystalline materials... • atoms have no periodic packing • occurs for: -complex structures -rapid cooling "Amorphous" = Noncrystalline noncrystalline SiO2

  5.  Metallic Crystal Structures • How can we stack metal atoms to minimize empty space? 2-dimensions vs.

  6. Metallic Crystal Structures • 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. • - The “electron cloud” shields cores from each other • They have the simplest crystal structures.

  7. Simple Cubic Structure (SC) • Rare due to low packing density (only Po has this structure) • Close-packed directions are cube edges. • Coordination # = 6 (# nearest neighbors)

  8. Atomic Packing Factor (APF) volume atoms atom 4 a 3 unit cell p (0.5a) 3 R=0.5a volume close-packed directions unit cell contains 8 x 1/8 = 1 atom/unit cell Volume of atoms in unit cell* APF = Volume of unit cell *assume hard spheres • APF for a simple cubic structure = 0.52 1 APF = 3 a

  9. Body Centered Cubic Structure (BCC) • Atoms touch each other along cube diagonals. All atoms are identical. ex: Cr, W, Fe (), Tantalum, Molybdenum • Coordination # = 8 2 atoms/unit cell: 1 center + 8 corners x 1/8

  10. Atomic Packing Factor: BCC a 3 a 2 Close-packed directions: R 3 a length = 4R = a atoms volume 4 3 p ( 3 a/4 ) 2 unit cell atom 3 APF = volume 3 a unit cell • APF for a body-centered cubic structure = 0.68 a

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

  12. c03prob

  13. Atomic Packing Factor: FCC 2 a Unit cell contains: 6 x1/2 + 8 x1/8 = 4 atoms/unit cell a atoms volume 4 3 p ( 2 a/4 ) 4 unit cell atom 3 APF = volume 3 a unit cell • APF for a face-centered cubic structure = 0.74 maximum achievable APF Close-packed directions: 2 a length = 4R =

  14. Hexagonal Close-Packed Structure (HCP – another view)

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

  16. ABAB... Stacking Sequence c03f30

  17. X-Ray Diffraction

  18. Detector Xray-Tube Xray-Tube Sample Metal Target (Cu or Co) Detector X-Ray Diffractometer sample d – distance between the same atomic planes λ – monochromatic wavelength θ – angle of diffracto- meter Bragg´s Equation d = λ/2 sinθ

  19. c03tf01

  20. nA VCNA Mass of Atoms in Unit Cell Total Volume of Unit Cell  = Theoretical Density, r Density =  = where n = number of atoms/unit cell A =atomic weight VC = Volume of unit cell = a3 for cubic NA = Avogadro’s number = 6.022 x 1023 atoms/mol

  21. R a 2 52.00 atoms g  = unit cell mol atoms 3 a 6.022x1023 mol volume unit cell Theoretical Density, r • Ex: Cr (BCC) A(atomic weight) =52.00 g/mol n = 2 atoms/unit cell R = 0.125 nm a = 4R/ 3 = 0.2887 nm theoretical = 7.18 g/cm3 ractual = 7.19 g/cm3

  22. - - - - - - + + + - - - - - - unstable - F 2+ Ca + CaF : 2 anions cation - F A X m p m, p values to achieve charge neutrality Factors that Determine Crystal Structure 1.Relative sizes of ions – Formation of stable structures: --maximize the # of oppositely charged ion neighbors. stable stable 2.Maintenance of Charge Neutrality: --Net charge in ceramic should be zero. --Reflected in chemical formula:

  23. Atomic Bonding in Ceramics CaF2: large SiC: small • Bonding: -- Can be ionic and/or covalent in character. -- % ionic character increases with difference in electronegativity of atoms. • Degree of ionic character may be large or small:

  24. Coordination # and Ionic Radii r cation r anion r ZnS cation (zinc blende) r anion NaCl (sodium chloride) CsCl (cesium chloride) • Coordination # increases with To form a stable structure, how many anions can surround a cation? Coord # linear < 0.155 2 triangular 0.155 - 0.225 3 tetrahedral 0.225 - 0.414 4 octahedral 0.414 - 0.732 6 cubic 0.732 - 1.0 8

  25. c03tf03

  26. Computation of Minimum Cation-Anion Radius Ratio a • Determine minimum rcation/ranionfor an octahedral site (C.N. = 6) Measure the radii (blue and yellow spheres) a= 2ranion Substitute for “a” in the above equation

  27. Example Problem:Predicting the Crystal Structure of FeO • Answer: Cation Ionic radius (nm) 3+ Al 0.053 2 + Fe 0.077 3+ Fe 0.069 2+ Ca 0.100 based on this ratio, -- coord # = 6 because 0.414 < 0.550 < 0.732 -- crystal structure is similar to NaCl Anion 2- O 0.140 - Cl 0.181 - F 0.133 • On the basis of ionic radii, what crystal structure would you predict for FeO?

  28. Rock Salt Structure Same concepts can be applied to ionic solids in general. Example: NaCl (rock salt) structure rNa = 0.102 nm rCl = 0.181 nm • rNa/rCl = 0.564 • cations (Na+) prefer octahedralsites

  29. MgO and FeO MgO and FeO also have the NaCl structure O2- rO = 0.140 nm Mg2+ rMg = 0.072 nm • rMg/rO = 0.514 • cations prefer octahedral sites So each Mg2+ (or Fe2+) has 6 neighbor oxygen atoms

  30. AX Crystal Structures AX–Type Crystal Structures include NaCl, CsCl, and zinc blende Cesium Chloride structure:  Since 0.732 < 0.939 < 1.0, cubicsites preferred So each Cs+ has 8 neighbor Cl-

  31. AX2 Crystal Structures Fluorite structure • Calcium Fluorite (CaF2) • Cations in cubic sites • UO2, ThO2, ZrO2, CeO2 • Antifluorite structure – • positions of cations and anions reversed

  32. ABX3 Crystal Structures • Perovskite structure • Ex: complex oxide • BaTiO3

  33. SUMMARY • Atoms may assemble into crystalline or amorphous structures. • 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. • We can predict the density of a material, provided we know the atomic weight, atomic radius, and crystal geometry (e.g., FCC, BCC, HCP). • Interatomic bonding in ceramics is ionic and/or covalent. • Ceramic crystal structures are based on: -- maintaining charge neutrality -- cation-anion radii ratios.

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