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CRYSTAL STRUCTURE- Chapter 3 (atomic arrangement) Why study this? Ductile-brittle transition in metals. Crystalline #

CRYSTAL STRUCTURE- Chapter 3 (atomic arrangement) Why study this? Ductile-brittle transition in metals. Crystalline # amorphous - transparency In gases, atoms have no order.

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CRYSTAL STRUCTURE- Chapter 3 (atomic arrangement) Why study this? Ductile-brittle transition in metals. Crystalline #

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  1. CRYSTAL STRUCTURE- Chapter 3 (atomic arrangement) Why study this? Ductile-brittle transition in metals. Crystalline # amorphous - transparency In gases, atoms have no order. If atoms bonded to each other but there is no repeating pattern (short range order) . e.g. water, glasses (AMORPHOUS - non-crystalline) If atoms bonded together in a regular 3-D pattern they form a CRYSTAL - long range order - like wall paper pattern or brick wall. Handout#3 - 221

  2. ENERGY AND PACKING • Non dense, random packing • Dense, regular packing Dense, regular-packed structures tend to have lower energy. Handout#3 - 221

  3. MATERIALS AND PACKING Crystalline materials... • atoms pack in periodic, 3D arrays • typical of: -metals -many ceramics -some polymers crystalline SiO2 Noncrystalline materials... • atoms have no periodic packing • occurs for: -complex structures -rapid cooling "Amorphous" = Noncrystalline noncrystalline SiO2 Handout#3 - 221

  4. FOR SOLID MATERIALS: Most METALS (>99%) are CRYSTALLINE. CERAMICS are CRYSTALLINE except for GLASSES which are AMORPHOUS. POLYMERS (plastics) tend to be: either AMORPHOUS or a mixture of CRYSTALLINE + AMORPHOUS (known as Semi-crystalline) Handout#3 - 221

  5. CRYSTALS Different ways of arranging atoms in crystals. Assume atoms are hard spheres and pack like pool/snooker balls (touching). Each type of atom has a preferred arrangement depending on Temp. and Pressure (most stable configuration). These patterns known as SPACE LATTICES Handout#3 - 221

  6. METALLIC CRYSTALS • tend to be densely packed. • have several 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. • have the simplest crystal structures. Handout#3 - 221

  7. 7 types of CRYSTAL SYSTEM 14 standard UNIT CELLS METALLIC CRYSTAL STRUCTURES Most metals crystallize into one of three densely packed structures: BODY CENTERED CUBIC - BCC FACE CENTERED CUBIC - FCC HEXAGONAL (CLOSE PACKED) - HCP Actual size of UNIT CELLS is VERY VERY SMALL!! Iron unit cell length (0.287 x 10-9 m) (0.287 nm) 1 mm length of iron crystal has  3.5 million unit cells Handout#3 - 221

  8. SIMPLE CUBIC STRUCTURE (SC) • Rare due to poor packing (only Po has this structure) • Close-packed directions are cube edges. • Coordination # = 6 (# nearest neighbors) Handout#3 - 221

  9. ATOMIC PACKING FACTOR • APF for a simple cubic structure = 0.52 Handout#3 - 221

  10. BODY CENTERED CUBIC STRUCTURE (BCC) • Close packed directions are cube diagonals. --Note: All atoms are identical; the center atom is shaded differently only for ease of viewing. • Coordination # = 8 Handout#3 - 221

  11. BCC STRUCTURE Atoms at cube corners and one in cube centre. Lattice Constant for BCC: e.g. Fe (BCC) a = 0.287 nm Two atoms in Unit Cell. (1 x 1 (centre)) + (8 x 1/8 (corners)) = 2 Each atom in BCC is surrounded by 8 others. COORDINATION number of 8. Packing is not as good as FCC; APF = 0.68 BCC metals include: Iron (RT), Chromium, Tungsten, Vanadium Handout#3 - 221

  12. Handout#3 - 221

  13. ATOMIC PACKING FACTOR: BCC • APF for a body-centered cubic structure = 0.68 Handout#3 - 221

  14. FACE CENTERED CUBIC STRUCTURE (FCC) • Close packed directions are face diagonals. --Note: All atoms are identical; the face-centered atoms are shaded differently only for ease of viewing. • Coordination # = 12 Handout#3 - 221

  15. FACE CENTERED CUBIC (FCC) e.g. copper, aluminium, gold, silver, lead, nickel Lattice constant (length of cube side in FCC) “a” for FCC structure: where R = atomic radius Each type of metal crystal structure has its own lattice constant. (1/8 at each corner x 8) + (½ at each face x 6 ) = 4 So 4 atoms per Unit Cell. Each atom touches 12 others. Co-ordination number = 12. Handout#3 - 221

  16. Handout#3 - 221

  17. ATOMIC PACKING FACTOR: FCC • APF for a body-centered cubic structure = 0.74 Handout#3 - 221

  18. FCC STACKING SEQUENCE • ABCABC... Stacking Sequence • 2D Projection • FCC Unit Cell Handout#3 - 221

  19. HEXAGONAL CLOSE-PACKED STRUCTURE (HCP) • ABAB... Stacking Sequence • 3D Projection • 2D Projection Adapted from Fig. 3.3, Callister 6e. • Coordination # = 12 • APF = 0.74 Handout#3 - 221

  20. HEXAGONAL CLOSE PACKED Note: not simple hexagonal but HCP Simple Hex. very inefficient; HCP has extra plane of atoms in middle. 1/6 of atom at each corner. So (1/6) x 12 corners = 2 atoms and (½) x (top + bottom) = 1 atom and (3) internal = 3 atoms Total = 6 atoms/cell Because of Hexagonal arrangement (not cubic), have 2 lattice parameters “a” , and “c” Handout#3 - 221

  21. Handout#3 - 221

  22. a = basal side = 2R c = cell height By geometry, for IDEAL HCP: but this varies slightly for some HCP Metals. HCP metals include: Magnesium, Zinc, Titanium, Zirconium, Cobalt. atomic packing factor for HCP = 0.74 (same as FCC) Atoms are packed as tightly as possible. Each atom surrounded by 12 other atoms so co-ordination number = 12. Handout#3 - 221

  23. CRYSTAL DENSITY The true density, , of material (free from defects) can be calculated knowing its crystal structure. n = number of atoms in unit cell A = Atomic Weight of element (g/mol) Vc = volume of unit cell Nav = Avogadro’s number (6.023 x 1023 atoms/mol) Handout#3 - 221

  24. e.g., copper, FCC  4 atoms/cell n = 4 Cu atoms have mass 63.5 g/mol Vol. of cell = a3 , for FCC a =2R2 Atomic radius of copper = 0.128 nm = 8.89 Mgm-3 (or 8.89 gcm-3 or 8890 kgm-3) Handout#3 - 221

  25. POLYMORPHISM / ALLOTROPY Some elements/compounds can exist in more than one crystal form. Usually requires change in temperature or pressure. Carbon: Diamond (high pressure) or Graphite (low). Can be IMPORTANT as some crystal structures more dense (better packing, higher APF) than others, so a change in crystal structure can often result in volume change of material. APF e.g. Iron 913oC FCC 0.74 911oC BCC 0.68 i.e. expands on cooling! Handout#3 - 221

  26. DENSITIES OF MATERIAL CLASSES Why? Metals have... • close-packing (metallic bonding) • large atomic mass Ceramics have... • less dense packing (covalent bonding) • often lighter elements Polymers have... • poor packing (often amorphous) • lighter elements (C,H,O) Composites have... • intermediate values Data from Table B1, Callister 6e. Handout#3 - 221

  27. CRYSTAL SYSTEMS Group crystals depending on shape of Unit Cell. x, y and z are three axes of lattice separated by angles ,  and . A unit cell will have sides of length a, b and c. (Note: for the cubic system all sides equal so a = b = c) SEVEN possible crystal systems (Table 3.2) Cubic most symmetry … … Triclinic least symmetry Handout#3 - 221

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  30. Positions in lattice Handout#3 - 221

  31. CRYSTALLOGRAPHIC DIRECTIONS • Line between two points or vector. • Using 3 coordinate axes, x, y, and z. • Position vector so that it passes through origin (parallel vectors can be translated). • Length of vector projected onto the three axes (x, y and z) is determined in terms of unit cell dimensions (a, b and c). • Multiply or divide by common factor to reduce to lowest common integers. • Enclose in SQUARE brackets with no commas [uvw], and minus numbers given by bar over number; e.g. Handout#3 - 221

  32. Handout#3 - 221

  33. Parallel vectors have same indices. Changing sign of all indices gives opposite direction. If directions are similar, (i.e., same atomic arrangements - for example, the edges of a BCC cube) they belong to a FAMILY of directions: i.e. with < > brackets can change order and sign of integers. e.g. cube internal diagonals <111> cube face diagonals <110> Handout#3 - 221

  34. HEXAGONAL CRYSTALS Use a 4-axis system (Miller-Bravais). a1, a2and a3axes in basal plane at 120 to each other and z axis in vertical direction. Directions given by [uvtw] or [a1 a2 a3 c] Can convert from three-index to four index system. t=-(u+v) Handout#3 - 221

  35. Handout#3 - 221

  36. CRYSTAL PLANES Planes specified by Miller Indices (hkl) (Reciprocal Lattice). Used to describe a plane (or surface) in a crystal e.g., plane of maximum packing. Any two planes parallel to each other are equivalent and have identical Miller indices Handout#3 - 221

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  40. To find Miller Indices of a plane: • If the plane passes through the selected origin, construct a parallel plan in the unit cell or select an origin in another unit cell. • Determine where plane intercepts axes. (if no intercept i.e.., plane is parallel to axis, then ) e.g., axis x y z intercept a b c • Take reciprocals of intercepts (assume reciprocal of  is 0): 1/a 1/b 1/c • Multiply or divide to clear fractions: (hkl) Miller indices of plane Handout#3 - 221

  41. FAMILYof planes, use {hkl} These planes are crystallographically similar (same atomic arrangements). e.g., for cube faces: {100} NOTE: In CUBIC system only, directions are perpendicular to planes with same indices. e.g., [111] direction is perpendicular to the (111) plane. HEXAGONAL CRYSTALS Four-index system similar to directions; (hkil) i = - (h+K) Handout#3 - 221

  42. ATOMIC PACKING Arrangement of atoms on different planes and in different directions. LINEAR ATOMIC DENSITIES Tells us how well packed atoms are in a given direction. If LD = 1 then atoms are touching each other. Handout#3 - 221

  43. PLANAR DENSITIES Tells us how well packed atoms are on a given plane. Similar to linear densities but on a plane rather than just a line. gives fraction of area covered by atoms. Handout#3 - 221

  44. e.g., BCC unit cell, (110) plane: 2 whole atoms on plane in unit cell. So Ac = 2(R2) AD = a, DE = a2 And so Ap = a22 Handout#3 - 221

  45. PACKING ON PLANES FCC and HCP are both CLOSE-PACKED structures. APF = 0.74 (This is the maximum if all atoms are same size). Atoms are packed in CLOSE-PACKED planes In FCC, {111} are close packed planes In HCP, (0001) is close packed Both made of close packed planes, but different stacking sequence. FCC planes stack as ABCABCABC HCP planes stack as ABABABABAB BCC is not close packed (APF = 0.68) most densely packed plane is {110} Handout#3 - 221

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  49. CRYSTALS AS BUILDING BLOCKS • Some engineering applications require single crystals: diamond single crystals for abrasives --turbine blades • Crystal properties reveal features of atomic structure. --Ex: Certain crystal planes in quartz fracture more easily than others. Handout#3 - 221

  50. SINGLE CRYSTALS This is when a piece of material is made up of one crystal; all the unit cells are aligned up in the same orientation. POLYCRYSTAL Many small crystals (grains) with different orientations joined together. Most materials/metals are POLYCRYSTALLINE. Grain boundary - Regions where grains (crystals) meet. Handout#3 - 221

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