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Understanding Crystalline and Amorphous Solids in Materials Science

Explore the types and structures of crystalline and amorphous solids, including metallic, covalent, molecular, and ionic crystals. Learn about closest packing in hcp and fcc structures, X-ray analysis, band theory, and the electron sea model in materials science.

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Understanding Crystalline and Amorphous Solids in Materials Science

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  1. Chapter 16 Solids

  2. Types of SolidsCrystalline solids 1. Shows a sharp melting point. 2. Have a regular, ordered structure composing of identical repeating units having the same orientation throughout the crystal.

  3. Types of Crystalline solids Metallic crystals－are composed of bonded metal atoms; example are Na, Cu, Fe, and alloys. Covalent crystals－consisted of an infinite network of atoms held together by covalent bonds, no individual molecules being present. Example are dismond, graphite, SiC and SiO2.

  4. Types of Crystalline solids Molecular crystals－are composed of individual molecules. Example are Ar, CO2 and H2O Ionic crystals－consisted of an array of positive and negative ions; example are NaCl, MgO, CaCl2 and KNO3

  5. Types of SolidsAmorphous solids 1. An amorphous solid does not have a characteristic crystals shape. 2. When heated, it softens and melts over a wide temperature range.

  6.  Structure of Metals • Simple Cubic (簡單立方) • Hexagonal Closest Packed (HCP) (六方最密堆積) • Face-Centered Cubic (FCC) (面心立方) • Body-Centered Cubic (BCC) (體心立方)

  7. Closest Packing hcp and fcc The hcp and fcc structures are closely related : they are both based upon stacking layers of atoms, where the atoms are arranged in a close- packed hexagonal manner within the individual layer.

  8. The atoms of the next layer of the structure will preferentially sit in some of the hollows in the first layer - this gives the closest approach of atoms in the two layers and thereby maximizes the cohesive interaction.

  9. When it comes to deciding where the next layer of atoms should be positioned there are two choices - these differ only in the relative positions of atoms in the 1st and 3rd layers.

  10. ABABA.. packing sequence of the hcp structure ABCABC.. packing sequence of the fcc structure

  11. Closest Packing hcp and fcc These hcp and fcc structures share common features : (a) The atoms are close packed (b) Each atom has 12 nearest neighbours.

  12. Hcp structure The ..ABABA.. packing sequence of the hcp structure gives rise to a three-dimensional unit cell structure whose symmetry is more immediately related to that of the hexagonally- close packed layers from which it is built.

  13. The unit cell for the hexagonal closest-packed structure has a diamond-shaped or hexagonal base with sides of equal length. • The volume is the product of the area of the base and the height of the cell.

  14. c = 4r(2/3)1/2 b=2r a=2r

  15. An actual STM image of a Ni surface. Note the hexagonal arrangement of atoms. This image is the property of IBM Corporation.

  16. Fcc structure The ..ABCABC.. packing sequence of the fcc structure gives rise to a three-dimensional structure with cubic symmetry.

  17. FCC structure

  18. Coordination Numbers (CN)=12 • Net number of spheres in unit cell =(8×1/8)+(6×1/2)=4

  19. Bcc structure • The bcc structure has very little in common with the fcc structure - except the cubic nature of the unit cell. Most importantly, it differs from the hcp and fcc structures in that it is not a close-packed structure. • The structure of the alkali metals are cheracterized by a bcc unit cell.

  20. BCC structure

  21. Coordination Numbers (CN)=8 • Net number of spheres in unit cell =(8×1/8)+(1×1)=2

  22. For a FCC structure For a BCC structure Packing Efficiency

  23. Packing Efficiency of HCP Structure • The unit cell is characterized by three lengths (a, b, c) and three angles (a, b, g). • The quantities a and b are the lengths of the sides of the base of the cell and g is the angle between these two sides. • The quantity c is the height of the unit cell. • The angles a and b describe the angles between the base and the vertical sides of the unit cell.

  24. Packing Efficiency of HCP Structure • In the hexagonal closest-packed structure, a = b = 2r and c = [4(2/3)1/2]r, where r is the atomic radius of the atom. • a = b = 90o and g = 120o • The volume of the hexagonal unit cell: V = 8(2)1/2r3

  25. g=120o a=90o c = 4r(2/3)1/2 b=90o b=2r a=2r

  26. X-Ray Analysis of Solids

  27. Bragg equation: nl=2dsinq

  28. X-ray crystal diffraction

  29. X-ray power diffraction Cu(111) Cu(100)

  30. Band Theory • Consider a molecule with two atomic orbitals. The result must be that two molecular orbitals will be formed from these atomic orbitals: one bonding and one anti-bonding, separated by a certain energy.

  31. Band Theory • If this is expanded to a molecule with three atoms, assuming 1 atomic orbital for each, then the result must be that 3 molecular orbitals will be formed.

  32. Now , let's take it to 10 atoms. This will produce 10 molecular orbitals: 5 bonding and 5 anti-bonding. As the number of molecular orbitals increases, the energy difference between the lowest bonding and the highest anti-bondig increases, while the space between each individual orbital decreases.

  33. Consider a metal with an infinite number of atoms. This will form an infinite number of molecular orbitals so close together they blur into one another forming a band.

  34. Electron sea model

  35. Empty MOs Filled MOs

  36. Fermi Level/ Fermi Energy • At absolute zero, electrons pack into the lowest available energy states and build up a "Fermi sea" of electron energy states. The top of that "Fermi sea" of electrons is called the Fermi energy or Fermi level. • The Fermi level is the surface of that sea at absolute zero where no electrons will have enough energy to rise above the surface.

  37. Metal Alloys • Definition: A substance that contains a mixture of elements and has metallic properties. • Substitutional alloy • Interstitial alloy

  38. Substitutional alloy • Definition: Some of the host metal atoms are replaced by other metal atoms of similar size. • Vacancy Diffusion: Vacancy diffusion involves the migration of an atom from a typical lattice position to a vacancy lattice site.

  39. Vacancy Diffusion Atomic migration by a mechanism of vacancy migration. Materials flow (the atom) is opposite the vacancy flow direction.

  40. Interstitial alloy • Definition: The solute metal atoms occupy holes in the close-packed structure of the solvent metal. • Interstitial diffusion: Interstitial diffusion involves the movement of an atom from a typical lattice position to an empty space between the lattice atoms called interstitial site.

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