Chapter 3: Atomic and Ionic Arrangements. Chapter 3: Atomic and Ionic Arrangements Cengage Learning Engineering. All Rights Reserved.

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1 Chapter 3: Atomic and Ionic Arrangements 3-1

2 Learning Objectives Short-range order versus long-range order Amorphous materials Lattice, basis, unit cells, and crystal structures Allotropic or polymorphic transformations Points, directions, and planes in the unit cell Interstitial sites Crystal structures of ionic materials Diffraction techniques for crystal structure analysis 3-2

3 Figure Levels of Atomic Arrangements in Materials 3-3

4 Short-Range Order versus Long-Range Order Short-range order (SRO) A material displays short-range order (SRO), if the special arrangement of the atoms extends only to the atoms nearest neighbors. Tetrahedral structure in silica satisfies the requirement that four oxygen ions be bonded to each silicon ion. 3-4

5 Figure

6 Short-Range Order Versus Long-Range Order Long-range order Atomic arrangement that extends over length scales ~>100nm Crystalline Atoms or ions of materials that form a regular repetitive, grid-like pattern in three dimensions materials Polycrystalline material Many small crystals with varying orientations in space These smaller crystals are known as grains Grain boundaries Regions between crystals, where the crystals are in misalignment X-ray diffraction or electron diffraction Techniques used for the detection of long range order in crystalline materials Liquid crystals Liquid crystal polymers behave as amorphous materials (liquid-like) in one state 3-6

7 Figure Classification of Materials Based on the Type of Atomic Order 3-7

8 Lattice, Basis, Unit Cells, and Crystal Structures Lattice: A collection of points that divide space into smaller equally sized segments. Basis: A group of atoms associated with a lattice point (same as motif). Unit cell: A subdivision of the lattice that still retains the overall characteristics of the entire lattice. Crystallography: The formal study of the arrangements of atoms in solids. Lattice points: Points that make up the lattice. The surroundings of each lattice point are identical. 3-8

9 Figure Lattice and Basis 3-9

10 Lattice, Basis, Unit Cells, and Crystal Structures Crystal structure: The arrangement of the atoms in a material into a regular repeatable lattice. The structure is fully described by a lattice and a basis. Bravais lattices: The fourteen possible lattices that can be created in three dimensions using lattice points. Crystal systems: Cubic, tetragonal, orthorhombic, hexagonal, monoclinic, rhombohedral and triclinic arrangements of points in space that lead to fourteen Bravais lattices and hundreds of crystal structures. 3-10

11 Figure The Fourteen Types of Bravais Lattices 3-11

12 Figure The Unit Cell 3-12

13 Figure

14 Table 3.1 Characteristics of the Seven Crystal Systems 3-14

15 Figure

16 Figure The Relationships Between the Atomic Radius and the Lattice Parameter in Cubic Systems 3-16

17 Lattice, Basis, Unit Cells, and Crystal Structures Relationship between the lattice parameter (a0) and atomic radius (r) For SC For BCC For FCC a 0 = 2r 4r a0 = 3 4r a0 =

18 Lattice, Basis, Unit Cells, and Crystal Structures Coordination Number of atoms touching a particular atom, or the number of nearest neighbors for that particular atom number Packing factor (Number of atoms/cell) (Volume of each atom) Volume of unit cell Kepler s conjecture Density The geometry which has a maximum achievable packing factor ~0.74 (Number of atoms/cell) (Atomic mass) (Volume of unit cell) (Avogadro s number) 3-18

19 Figure The Hexagonal Close-Packed (HCP) Structure (Left) and its Unit Cell 3-19

20 Table Crystal Structure Characteristics of Some Metals at Room Temperature 3-20

21 Allotropic or Polymorphic Transformations Allotropy: The characteristic of an element being able to exist in more than one crystal structure depending on temperature and pressure. Polymorphism: Compounds exhibiting more than one type of crystal structure. Iron BCC crystal structure at room temp, which changes to FCC at 912 C Ceramic materials, such as silica (SiO2) and zirconia (ZrO2), are polymorphic. Ceramic components made from pure zirconia typically will fracture as the temperature is lowered and as zirconia transforms from the tetragonal to monoclinic form because of volume expansion. 3-21

22 Figure

23 Figure Equivalency of Crystallographic Directions of a Form in Cubic Systems 3-23

24 Table Directions of the Form <110> in Cubic Systems 3-24

25 Points, Directions, and Planes in the Unit Cell Repeat distance Distance between the lattice points along a particular direction Linear density Number of lattice points per unit length along a particular direction Packing fraction Fraction of space in a unit cell occupied by atoms 3-25

26 Figure

27 Figure Crystallographic Planes and Intercepts 3-27

28 Table Planes of the Form {110} in Cubic Systems 3-28

29 Figure

30 Points, Directions, and Planes in the Unit Cell Isotropic and anisotropic behavior A material is crystallographically anisotropic if its properties depend on the crystallographic direction along which the property is measured. A material is crystallographically isotropic if the properties are identical in all directions. 3-30

31 Interstitial Sites Interstitial sites Small holes between the usual atoms into which smaller atoms may be placed Cubic site Gives a coordination number of 8. Occurs in the SC structure at the body-centered position Octahedral sites Gives a coordination number of 6. Atoms contacting the interstitial atom form an octahedron Tetrahedral sites Gives a coordination number of

32 Figure The Location of the Interstitial Sites in Cubic Unit Cells 3-32

33 Table The Coordination Number and the Radius Ratio 3-33

34 Figure The Sodium Chloride Structure MgO, CaO FeO has the same structure. 3-34

35 Figure The Zinc Blende Structure (ZnS) 3-35

36 Figure 3.32 Diamond Cubic Structure 3-36