Stacking Oranges. Packing atoms together Long Range Order. What controls the nearest number of atoms? Hard Sphere Model. Hard Sphere Model.

Size: px

Start display at page:

Download "Stacking Oranges. Packing atoms together Long Range Order. What controls the nearest number of atoms? Hard Sphere Model. Hard Sphere Model."

Mavis Cross
6 years ago
Views:

{ Stacking atoms together Crystal Structure Stacking Oranges Packing atoms together Long

.. atoms pack in periodic, 3D arrays typical of: -metals -many ceramics -some polymers

.. atoms have no periodic packing occurs for: -complex structures -rapid cooling

noncrystalline SiO2 Adapted from Fig. 3.18(b), Callister 6e.

Atoms in a crystal represented by hard sphere each atom is surrounded by as many other

e minimum energy state Gives rise to coordination number number of contacting neighbours

1 { Stacking atoms together Crystal Structure Stacking Oranges Packing atoms together 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 crystalline SiO2 Adapted from Fig. 3.18(a), Callister 6e. 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 Hard Sphere Model What controls the nearest number of atoms? Relative atom size # of atoms around each atom Hard Sphere Model Directionality of bond Atoms All same size Different size Nondirectional bond Directional bond Nondirectional bond Metals Covalent Ceramics Ionic Ceramics 1

Simple case - Nondirectionally bonded atoms of equal size How can these oranges pack?

# of bonds per unit vol maximised hence bonding energy per unit volume minimised Two such close packed

Such a structure is said to be CLOSE PACKED face centred cubic FCC Hexagonal close packed HCP These names come

Closed-Packed Crystal Structure - HCP HCP Tetrahedral site Octahedral site Figure 1.

2 Simple case - Nondirectionally bonded atoms of equal size How can these oranges pack? 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 Two such close packed arrangements 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 These names come from the geometry that results Accounts for about 2/3 of all metals All the noble metals at low T Hexagonal Closed-Packed Crystal Structure - HCP HCP Tetrahedral site Octahedral site 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,

3 Face-Centered Cubic (FCC) Consider atoms as hard spheres. Close packing of atoms fc c Body-Centered Cubic (BCC) HCP FCC From Callister 6e resource CD. BCC Coordination Number =? Simple Cubic Number of atoms per unit cell? 3

4 Scott of the Antarctic Disintegration of tin dishes and cutlery in cold weather expeditions, kerosene containers (Captain Robert Scott's Antarctic expedition) Imperfections { What can go wrong? Vacancies: First Direct Experimental Observation What can go wrong? 4

How many vacancies in, say, 1m 3 of Cu at 1000 C? pure elements not possible max purity 99.9999% 1 atom in 10 6 is impurity imperfection in crystal structure where can these foreign atoms go?

5 How many vacancies in, say, 1m 3 of Cu at 1000 C? pure elements not possible max purity % 1 atom in 10 6 is impurity imperfection in crystal structure where can these foreign atoms go? Interstitial Foreign atom Substitute Foreign atom Interstitial Substitute Interstitial Foreign atom Substitute Remember, these imperfections are not always detrimental Give rise to: substitutional solid solutions interstitial solid solutions Provide unique properties unobtainable with the parent metals 5

6 Summary Remember or Cu Sn bronze rods? impurities Line Defects Dislocation motion occurs most readily on TEM of titanium dark lines are dislocations X dislocations aid plastic deformation three types edge screw mixed Dislocations are formed -solidification - plastic deformation - thermal stresses from cooling Slip planes Close packed planes smoothest surface for slipping And close packed directions smoothest surface for slipping 6

Ions pack together as densely as possible to lower overall energy

cation are all in contact with the cation. More than 1 type of atom?

167 nm r Na = 0.097 nm r Cl = 0.181 nm r Cl = 0.181 nm radius ratio = 0.

7 Ions pack together as densely as possible to lower overall energy electrostatic attraction in all directions cations want to maximize # of neighboring anions and vice versa. Limitations to dense packing: relative sizes of ions and necessity to maintain charge neutrality Charge neutrality e.g. Ca Ca 2+ F F - CaF 2 Stable configuration when anions surrounding a cation are all in contact with the cation. More than 1 type of atom? Ionic Ceramics Linear triangular tetrahedral CsCl NaCl r Cs = nm r Na = nm r Cl = nm r Cl = nm radius ratio = 0.92 radius ratio = structure: SC structure: FCC octahedral cubic And, of course, a co-ordination ordination # of 12 gives HCP or FCC Example MgO MnS LiF FeO Coordination # And Ionic Radii Coordination # increases with Issue: How many anions can you arrange around a cation? Examples: Ionic Ceramics 7

Directionally bonded atoms of equal size Materials with directional bonds have geometry

Position and number of neighbours rigidly fixed by directional nature of bonds Energy is

these are non-crystalline The results are quite different structures to ionic ceramics

8 Directionally bonded atoms of equal size Materials with directional bonds have geometry controlled by bond angles, e.g. diamond BCC metals have some covalency to their bond SiC Example: Covalent Ceramics Position and number of neighbours rigidly fixed by directional nature of bonds Energy is minimised, not by dense packing, but by forming chains, sheets or 3D networks often these are non-crystalline The results are quite different structures to ionic ceramics and also different properties Covalent Ceramics Examples: Covalent Ceramics Generally more complex than metals Will be predominately ionic or covalent CaF 2 89% ionic MgO 73 NaCl 67 Al 2O 3 63 SiO2 51 Si 3N 4 30 ZnS 18 SiC 12 Ceramic Structures 8

9 Metals Ceramics Comparison metals v ceramics 9

Order in materials. Making Solid Stuff. Primary Bonds Summary. How do they arrange themselves? Results from atomic bonding. What are they?

Order in materials. Making Solid Stuff. Primary Bonds Summary. How do they arrange themselves? Results from atomic bonding. What are they? Making Solid Stuff Primary Bonds Summary What are they? Results from atomic bonding So the atoms bond together! Order in materials No long range order to atoms Gases little or no interaction between components