Materials Science. Why?

Transcription

1 Materials Science and Engineering, 2012 Compiled by Greg Heness & Mike Cortie Chapter 3 Crystalline Structure - Perfection, pp Materials Science A knowledge of this material is needed for diverse areas of chemistry, physics and nanotechnology Modern materials science is largely based on these concepts Metals are tough and strong crumple zone, aluminium foil, paper clips Ceramics are brittle and strong window glass, concrete Polymers are tough and weak plastic bags, containers bottles Why? Long Range Order Crystalline materials... atoms pack in periodic, 3D arrays typical of: -metals -many ceramics -some polymers Short Range Order Noncrystalline materials... atoms have no periodic packing occurs for: -complex structures -rapid cooling "Amorphous" = Noncrystalline Si crystalline SiO2 Adapted from Fig. 3.18(a), Callister 6e. Oxygen noncrystalline SiO2 Adapted from Fig. 3.18(b), Callister 6e. From Callister 6e resource CD. Atoms in a crystal represented by hard sphere each atom is surrounded by as many other atoms as possible i.e minimum energy state Gives rise to coordination number number of contacting neighbours any one atom has This is a function of directionality of bond and relative atom sizes 1

2 Number of atoms around each atom is a function of directionality of bond and relative atom sizes Atoms All same size Different size Nondirectional bond Directional bond Nondirectional bond Metals Covalent Ceramics Ionic Ceramics Metals & noble elements expect to solidify in closest packed arrangement as possible WHY? # of bonds per unit vol maximised hence bonding energy per unit volume minimised What is the maximum number of spheres that can pack around one sphere? Such a structure is said to be CLOSE PACKED face centred cubic FCC Hexagonal close packed HCP Figure 1.4 The hexagonal close-packed (hcp) crystal structure: (a) unit cell; and (b) single crystal with many unit cells. Source: W. G. Moffatt, et al., The Structure and Properties of Materials, Vol. 1, John Wiley & Sons, These names come from the geometry that results Accounts for about 2/3 of all metals All the noble metals at low T 2

3 Face-Centered Cubic (FCC) A B A C B A fc c these are obviously different arrangements. In the lab you will get to work with models and you will see how these two are actually hexagonal closest packed (left) and face centered cubic (right) Body-Centered Cubic (BCC) This is the complex unit cell of a shape memory alloy. We have obtained the atomic positions for this by analysing diffraction patterns made by X- rays and neutrons. (more on this later) From Callister 6e resource CD. Coordination Number =? BCC? Number of atoms per unit cell? 3

4 The unit cell describes the outer shape of the repetitive unit. There are seven possibilities known as crystal systems Within each is one or more potential lattices of the same shape. There are actually 14 possible lattices. The unit cell describes the outer shape of the repetitive unit. There are seven possibilities known as crystal systems Within each is one or more potential lattices of the same shape. There are actually 14 possible lattices. A measure of the volume occupied by an atom in a unit cell APF = APF = APF = # 4r FCC BCC 1. Calculate the effective radius ρ of the void space using trigonometry AND the hard-sphere model with the radius r for the host atom (for metals) or ions (for ionic crystals). 2. Any element with atomic/ionic radius less than or equal to ρ can occupy that interstitial site. 3. If the element has radius larger than ρ, then it will cause some distortion to the crystal structure 4. The increased energy due to distortion will limit the number of interstitial sites that can be occupied (example: carbon in iron). 4

5 CsCl NaCl r Cs = nm r Na = nm r Cl = nm r Cl = nm radius ratio = 0.92 radius ratio = structure: SC structure: FCC The NaCl structure is FCC The basis consists of one Na atom and one Cl atom, Atom positions: Cl : 000 ; ½½0; ½0½; 0½½ Na: ½½½; 00½; 0½0; ½00 Each atom has 6 nearest neighbours of the opposite kind Often described as 2 interpenetrating FCC lattices (CsBr, CsI, RbCl, AlCo, AgZn, BeCu, MgCe, RuAl, SrTl) The CsCl structure is BCC The basis consists of one Cs atom and one Cl atom, with each atom at the center of a cube of atoms of the opposite kind There is on unit of CsCl in each unit cube Atom positions: Cs : 000 Cl : ½½½ (or vice-versa) Each atom has 8 nearest neighbours of the opposite kind SiO 4 4 SiO 4 4 5

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