topic 11 - metallic bonding + crystallography (bonding in non-molecular solids)

close packing of spheres

• without directional covalent bonds electronically neutral metal atoms will pack as efficiently as possible in space

• hard, non-deformable spheres of identical radii form close packed layers

• the second layer will form identically to the first but sitting in the centre of triangles of the first layer

• types- hexagonal close packing + cubic close packing (fcc)

hexagonal close packing (HCP)

• third layer sits directly over the first layer

• spheres occupy 74% of the total volume

• “ABA” layer repeat

• two parallelograms at heights 1 + 2 with a sphere at ½ height in the centre of the triangle on one side

• coordination number = 12

unit cell

• the smallest parallel-sided volume element of a crystal structure (Atom arrangement)

cubic close packing (CCP)

• also called FCC

• third layer sits over holes in first layer

• 74% of total volume taken up by spheres

• “ABC” or “ABCA” layer repeat

• coordination number = 12

body centred cubic (BCC)

• not a close packed arrangement

• spheres occupy 68% of total volume

• spheres arranged in layers based on square rows not triangles

• second layer sits so a sphere is directly over a gap in the first and pushed the spheres slightly apart

• third layer sits directly over first

• coordination number = 8

what are the two types of solids?

• crystalline solids

• amorphous solids

crystalline solids

• atoms/ions/molecules are in an orderly array called a lattice

• a regular arrangement of atoms

• eg. NaCl, diamond, metals. CuSO₄.5H₂O

amorphous solids

• non-crystalline

• atoms/ions/molecules lie in a random jumble

• their structures are similar in character to liquids

• eg. charcoal, rubber and glass (amorphous SiO₂)

what are the 5 structures of crystalline solids

• atomic crystalline solids

• molecular crystalline solids

• ionic crystalline solids

• metallic crystalline solids

• network covalent crystalline solids

atomic crystalline solids

• individual atoms held together by dispersion forces

• noble gasses are the only example - eg. Argon crystallises in CCP structure

• physical properties : low mpt + bpt - reflect the very weak forces among atoms

molecular crystalline solids

• held together by intermolecular forces (dispersion, dipole-dipole, H-bonds)

• lattice points are occupied by individual molecules

• eg. methane crystallises in FCC structure w c of molecules centres on each lattice point

ionic crystalline solids

• participate in ionic bonding - electrons transferred between atoms to form cations and anions

• solid/ordered lattice is held together by electrostatic forces between ions

• eg. NaCl, ZnS etc

metallic crystalline solids

• metals conduct electricity freely via motion of electrons

• consider metals as a sea of electrons surrounding an array of cations held together by electrostatic interactions between electrons and cations

• interactions are maximised when cations are close packed

network covalent crystalline solids

• atoms joined by strong covalent bonds which extend throughout the solid forming a network

• hard, rigid materials

• eg. diamond + graphite

examples of metals with an HCP structure

• Be

• Cd

• Co

• Mg

• Ti

• Zn

examples of metals with an CCP structure

• Ag

• Al

• Au

• Ca

• Cu

• Ni

• Pb

examples of metals with an BCC structure

• Ba

• Cr

• Fe

• W

• Li

• Na

• K

• Rb

• Cs

delocalised electrons lead to non-directional bonding

• what properties result?

• malleable

• ductile

delocalised electrons are mobile

• what properties result?

• electrical conductivity

• thermal conductivity

alloy

• a blend of metals (or a metal and another element) that is prepared by mixing the molten components and then cooling

• the elements have ben mixed at an atomic level

• a general term for elements mixed at the atomic level is a solid solution

solid solution

• elements mixed at the atomic level

brass

• up to 40% Zn in copper

• Zn increases strength - Zn atoms are larger forming a distortion in FCC structure making it more difficult to deform/less malleable

sterling silver

• 7.5% Cu in Ag

• increases strength

• forms a distortion in CCP structure making it more difficult to deform/less malleable

stainless steel

• Fe with 13-18% Cr, 8-12% Ni and traces of C

• Cr - a sacrificial metal - oxidises preferentially over Fe

• Ni - increasing strength by distortion of structure

• C - improves strength a lot but in a different way - C is very small so sits w/i spaces in packing arrangement

what are the two types of alloys?

• substitutional

• interstitial

substitutional alloys

• atoms of solute metal randomly occupy sites in solvent metal lattice

criteria:

1. metal radii must be similar - w/i 15%

2. solute metal must tolerate the coordination environment of the host lattice

3. the electropositive characteristics of the two metals must be similar otherwise charge is transferred and the formation of a compound that is no longer metallic is likely

interstitial alloys

• some of the holes (interstices) between the metals are occupied by another element

• there is 26% of space available even in a close packed structure

crystal structure

• a name given to the unit cell and the particular arrangement of atoms within it

structure type

• a defined arrangement of atoms for example the NaCl structure type is found in many different AX atoms combinations and all have the same atomic arrangement

a unit cell explanation

• smallest imaginary volume element with all opposite sides parallel to each other that by replication and translation can produce the entire 3D array of atoms in a structure

• defined by 3D vectors (a, b, c) and the angles (alpha, beta, Y) between them

atom counting rules

• corner - 1/8 of atom is contributing to unit cell

• edge - ¼ of atom is contributing to unit cell

• face - ½ of atom is contributing to unit cell

• centre - all of atom is contributing to unit cell

cubic crystal systems

• a=b=c

• alpha=beta=Y=90 degrees

hexagonal crystal systems

• a=b does not equal c

• alpha = beta = 90 degrees

• Y = 120 degrees

centring

unit cells may have translational symmetry that applies to all atoms within it known as centring - the centring automatically generates new positions linked by the symmetry of the unit cell

centring or a primitive cell (symbol P)

• has no centring

• points only on corners

centring on a body-centred cell (symbol I)

• atoms shifted by ½ in all directions in the cell)

• ½ , ½ , ½ translation

centring on a face-centred cell (symbol F)

• atoms shifted by ½ along a and b AND ½ along a and c AND ½ along b and c

• ½ , 0, ½ translation