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Crystalline Structure of Metals

Crystalline Structure of Metals. ISSUES TO ADDRESS. • How do atoms assemble into solid structures?. • How does the density of a material depend on its structure?. • When do material properties vary with the atom(i.e., part) orientation?. Concept. Energy and Packing. Energy.

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Crystalline Structure of Metals

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  1. Crystalline Structure of Metals

  2. ISSUES TO ADDRESS... • How do atoms assemble into solid structures? • How does the density of a material depend on its structure? • When do material properties vary with the atom(i.e., part) orientation?

  3. Concept

  4. 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.

  5. Materials and Packing Crystalline materials... • atoms pack in periodic, 3D arrays • typical of: -metals -many ceramics -some polymers crystalline SiO2 Adapted from Fig. 3.23(a), Callister & Rethwisch 8e. Si Oxygen Noncrystalline materials... • atoms have no periodic packing • occurs for: -complex structures -rapid cooling "Amorphous" = Noncrystalline noncrystalline SiO2 Adapted from Fig. 3.23(b), Callister & Rethwisch 8e.

  6.  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

  7. 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. - Electron cloud shields cores from each other • Have the simplest crystal structures. We will examine three such structures...

  8. 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)

  9. 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

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

  11. 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 Adapted from Fig. 3.2(a), Callister & Rethwisch 8e.

  12. 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 Adapted from Fig. 3.1, Callister & Rethwisch 8e. 4 atoms/unit cell: 6 face x 1/2 + 8 corners x 1/8

  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 = Adapted from Fig. 3.1(a), Callister & Rethwisch 8e.

  14. B B B B C C C A A A B B B B B B B A sites C C C C C C B B sites sites B B B B C sites FCC Stacking Sequence • ABCABC... Stacking Sequence • 2D Projection A • FCC Unit Cell B C

  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 Adapted from Fig. 3.3(a), Callister & Rethwisch 8e. 6 atoms/unit cell • Coordination # = 12 ex: Cd, Mg, Ti, Zn • APF = 0.74 • c/a = 1.633

  16. The reason that metals form different crystal structures is to minimize the energy required to fill space • At different temperatures the same metal may form different structures

  17. 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

  18. R a 2 52.00 atoms g  = unit cell mol atoms a3 6.022x1023 mol volume unit cell Theoretical Density, r • Ex: Cr (BCC) A =52.00 g/mol R = 0.125 nm n = 2 atoms/unit cell a = 4R/ 3 = 0.2887 nm Adapted from Fig. 3.2(a), Callister & Rethwisch 8e. theoretical = 7.18 g/cm3 ractual = 7.19 g/cm3

  19. r r r metals ceramics polymers Platinum Gold, W Tantalum Silver, Mo Cu,Ni Steels Tin, Zinc Zirconia Titanium Al oxide Diamond Si nitride Aluminum Glass - soda Glass fibers Concrete PTFE Silicon GFRE* Carbon fibers Magnesium G raphite CFRE * Silicone A ramid fibers PVC AFRE * PET PC H DPE, PS PP, LDPE Wood Densities of Material Classes In general Graphite/ Metals/ Composites/ Ceramics/ Polymers > > Alloys fibers Semicond 30 Why? B ased on data in Table B1, Callister 2 0 *GFRE, CFRE, & AFRE are Glass, Metals have... • close-packing (metallic bonding) • often large atomic masses Carbon, & Aramid Fiber-Reinforced Epoxy composites (values based on 60% volume fraction of aligned fibers 10 in an epoxy matrix). Ceramics have... • less dense packing • often lighter elements 5 3 4 (g/cm ) 3 r 2 Polymers have... • low packing density (often amorphous) • lighter elements (C,H,O) 1 0.5 Composites have... • intermediate values 0.4 0.3 Data from Table B.1, Callister & Rethwisch, 8e.

  20. Crystals as Building Blocks • Some engineering applications require single crystals: -- turbine blades -- diamond single crystals for abrasives Fig. 8.33(c), Callister & Rethwisch 8e. (Fig. 8.33(c) courtesy of Pratt and Whitney). (Courtesy Martin Deakins, GE Superabrasives, Worthington, OH. Used with permission.) • Properties of crystalline materials often related to crystal structure. -- Ex: Quartz fractures more easily along some crystal planes than others. (Courtesy P.M. Anderson)

  21. Single vs Polycrystals E (diagonal) = 273 GPa E (edge) = 125 GPa • Single Crystals -Properties vary with direction: anisotropic. -Example: the modulus of elasticity (E) in BCC iron: • Polycrystals 200 mm -Properties may/may not vary with direction. -If grains are randomly oriented: isotropic. -If grains are textured, anisotropic.

  22. Grains and Grain Boundaries • When molten metal solidifies, crystals begin for form independently of each other. They have random and unrelated orientations. Each of these crystals grows into a crystalline structure or GRAIN. • The number and size of the grains developed in a unit volume of the metal depends on the rate at which NUCLEATION (the initial stage of crystal formation) takes place

  23. Characteristic of Grain Growth • Rapid cooling – smaller grains • Slow cooling – larger grains • Grain boundaries – the surfaces that separate individual grains • Grain size- at room temperature a large grain size is generally associated with low strength, low hardness, and low ductility (ductility is a solid material's ability to deform under tensile stress) • Grain size is measured by counting the number of grains in a given area or by counting the number of grains that intersect a length of line randomly drawn on an enlarged photograph of the grains

  24. Anisotropy • Metal properties are different in the vertical direction from those in the horizontal direction • It influences both mechanical and physical properties of metals • Strength is higher for metals with small grains because…

  25. Virtual Materials Science & Engineering (VMSE) • VMSE is a tool to visualize materials science topics such as crystallography and polymer structures in three dimensions

  26. VMSE: Metallic Crystal Structures & Crystallography Module • VMSE allows you to view crystal structures, directions, planes, etc. and manipulate them in three dimensions

  27. Unit Cells for Metals • VMSE allows you to view the unit cells and manipulate them in three dimensions • Below are examples of actual VMSE screen shots FCC Structure HCP Structure

  28. VMSE: Crystallographic Planes Exercises Additional practice on indexing crystallographic planes

  29. detector “1” incoming reflections must X-rays “2” be in phase for “1” a detectable signal outgoing X-rays l extra “2” distance q q travelled spacing by wave “2” d between planes X-ray nl intensity q d= c 2sin (from detector) q q c X-Rays to Determine Crystal Structure • Incoming X-rays diffract from crystal planes. Measurement of critical angle, qc, allows computation of planar spacing, d.

  30. z z z c c c y y y a a a b b b x x x X-Ray Diffraction Pattern (110) (211) Intensity (relative) (200) Diffraction angle 2q Diffraction pattern for polycrystalline a-iron (BCC) Adapted from Fig. 3.22, Callister 8e.

  31. 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).

  32. 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. • Some materials can have more than one crystal structure. This is referred to as polymorphism (or allotropy). • X-ray diffraction is used for crystal structure and interplanar spacing determinations.

  33. Mechanical Working of Metal

  34. Introduction • Mechanical working of metal is defined as an intentional deformation of metals plastically under the action of externally applied force. • Mechanical working of metals is described as: • 1. Hot working • 2. Cold working

  35. Hot Working • The working of metal above the recrystallization temperature is called hot working . Hot working of metal has following advantage : • 1. The porosity of metal largely eliminated . • 2. The grain structure of metal is refined . • 3. The mechanical properties such as toughness, ductility improved . • 4. The deformation of metal is easy.

  36. Recrystallization Temperature Recrystallization is a process in which at a certain temperature range , a new equiaxed & stress free grains are formed . Recrystallization temperature is generally defined as temperature at which complete recrystallization occurs within approximately one hour.

  37. Cold Working • Cold working refers to the process of strengthening a metal by plastic deformation. Also referred to as work hardening, the metal working technique involves subjecting metal to mechanical stress so as to cause a permanent change to the metal's crystalline structure. • The technique is most commonly applied to steel, aluminum and copper. • When these metals are cold worked permanent defects change their crystalline make-up. • These defects reduce the ability of crystals to move within the metal structure and the metal becomes more resistant to further deformation. • The resulting metal product has improved tensile strength and hardness, but less ductility.

  38. Advantages of cold working : • 1. Residual stresses set up in the metal • 2. Strength and hardness of metal are increased. • 3. Surface finish improved . • 4. Close dimensional tolerances maintained. • Disadvantages … •  Cold working distorted the material •  Requires much higher pressures than hot working .

  39. Metal forming processes •  Rolling •  Forging •  Extrusion •  Tube and Wire Drawing •  Deep Drawing

  40. Sequence of operations

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