§2.4 Crystal Structure and Complex Lattice

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§2.4 Crystal Structure and Complex Lattice. Ⅰ.Crystal structure is the real arrangement of atom in crystals Crystal structure = Space lattice + Basis or structure unit. +. =. Fe. Al. - PowerPoint PPT Presentation

Transcript of §2.4 Crystal Structure and Complex Lattice

  • 2.4 Crystal Structure and Complex Lattice.Crystal structure is the real arrangement of atom in crystals

    Crystal structure Space lattice + Basis or structure unit

  • Fe : Al = 1 : 1The difference between space lattice and crystal structure

  • 23 atoms / cell

  • 1. BCC

    Example: -Fe , V, Nb, Ta, Cr, Mo, W, alkali metals n = 2 atoms/cell CN=8

    The number of nearest neighbours around each atom is called Coordination Number..Typical crystal structures of metals

  • Packing fraction

    To determine, The atom is looked as a hard sphere, and the nearest neighbours touch each other.

    For BCC,

  • 2. FCC

    Example: -Fe , Al , Ni , Pb , Cu , Ag , Au , stainless steal n= 81/8+61/2=4 atoms/cell CN=12

  • 3. HCP Example: Be, Mg, Zn, Cd, Zr, Hf Ti( low temperature)

    n CN12 0.74

  • 4. Summary

    Structurea0 vs. rAtoms per cellCoordination NumberPacking factorExamplesSC160.52Polonium (Po),-MnBCC280.68Fe,Ti,W,Mo,Nb,Ta,K,Na,V,Zr,CrFCC4120.74Fe,Cu,Au,Pt,Ag,Pb,NiHCP2120.74Ti,Mg,Zn,Be,Co,Zr,Cd

  • 2.5 Interstices in typical crystals of metals. Two types of Interstitials in typical crystals Octahedral interstitial Tetrahedral interstitialDefinition: In any of the crystal structures, there are small holes between the usual atoms into which smaller atoms may be placed. These locations are called interstitial sites.

  • 1. Octahedral interstitialBCC

  • FCC

  • HCP

  • 2. Tetrahedral interstitialBCC

  • FCC

  • HCP

  • .Determination of the sizes of interstitialsDefinition: By size of an interstitial we mean diameter of the maximum hard sphere which can be accommodated in the interstitial without distorting the lattice.

  • Octahedral interstitial

    condition for touching

  • For BCC

    For FCC

  • Tetrahedral interstitialHLADCBinterstitialhost atom

  • For BCCFor FCC

  • Summary

    nCNintersticesdi/daoct.tete.oct.tete.BCC280.6866/2=31212/2=60.150.29FCC4120.7444/4=188/4=20.410.22HCP6120.7466/6=11212/6=20.410.22

  • Examples and DiscussionsBoth FCC and BCC are close-packed structures while BCC is more open?The interstitial atoms most likely occupy the oct. interstitial position in FCC and HCP, while in BCC two types of interstitial can be occupied equally.

  • 3. The solid solubility in BCC is much lower than in FCC.4. Diffusion of interstitial atoms in BCC diffusion is much faster than in FCC or HCP at same temperature.5. Determine the relationship between the atomic radius and the lattice parameter in SC, BCC, and FCC structures when one atom is located at each lattice point.

  • 6. Determine the density of BCC iron, which has a lattice parameter of 0.2866nm.Solution: For a BCC cell, Atoms/cell = 2 a0 = 0.2866nm = 2.866108cm Atomic mass = 55.847g/mol Volume of unit cell = a03 = 23.5410 24cm3/cell Density

  • ExerciseDetermine the coordinates of centers of both the octahedral and the tetrahedral interstitials in HCP referred to a, b and c.

  • 4. Prove that the A-face-centered hexagonal lattice is not a new type of lattice in addition to the 14 space lattices.

    5. Draw a primitive cell for BCC lattice.Thanks for your attention !