Crystallography- Metal Structures and Silicate Chemistry

Question 1

fcc

Answer 1

Bravais lattice: cubic F
Aka ccp
Point group: m3m
Space group: Fm3m
Examples: Al, Cu, γ-Fe, Ni

Question 2

bcc

Answer 2

Bravais lattice: cubic I
Point group: m3m
Space group: Im3m
Examples: Nb, W, α-Fe, Cr

Question 3

hcp

Answer 3

Bravais lattice: hexagonal P
Point group: 6/mmm
Space group: P6sub3/mmc
Examples: Co, Be, Mg, Ti

Question 4

Trends in metal structures

Answer 4

hcp most frequent. All alkali metals and typical refractory metals are bcc. Noble metals (Pt group) are fcc. Some metals have small energy difference to the 2nd most favourite structure meaning stacking faults and phase transitions via temperature or pressure are facilitated.

Question 5

Ordered intermetallic alloy structures

Answer 5

Ordered bcc: system is cubic, Bravais primitive, has one element on corners of cube and the other in the centre, atoms alternate along space diagonal, example NiAl.
Ordered fcc: system is tetragonal, Bravais primitive, has one element for top and bottom faces and other for remaining 4 face centred midway up, alternating layers of elements, example TiAl.

Question 6

Disordered intermetallic alloys

Answer 6

Do not fulfill strict definition of crystals, can be treated by placing statistical ‘mixed elements’ at lattice points (occupancy factors), then the ordered structures would return to proper bcc and fcc and both be cubic.

Question 7

Glide systems in alloy structures

Answer 7

Determine the direction of dislocation motion. Normal bcc has (110)[111], normal fcc has (111)[110]. For the ordered intermetallic alloys the Burgers vector is twice as long as for pure metals, so plastic deformation is hindered and alloy is more brittle (not as brittle as ceramics).

Question 8

Tin structure

Answer 8

Gray α-Tin: stable under 13C, cubic, diamond-structure, semiconductor.
White β-Tin: stable above 13C, tetragonal, is distorted cubic primitive, metallic.
Both are metastable so don’t immediately change as temperature goes through 13C.

Question 9

Heusler alloy

Answer 9

ABC2. Example MnAlCu2 so no anion. Based on fcc, has all interstitials fully filled, has larger lattice parameter than normal fcc. This is first ferromagnetic alloy known without a ferromagnetic element

Question 10

What is complex stacking?

Answer 10

Anything other than ABAB, ABCABC, AAAA

Question 11

Nomenclature for cation/anion stacking sequences

Answer 11

Main (Bravais lattice) stacking is upper case roman letters ABC.
Interstitial stacking is Greek letter αβγ.
A, B and C are same chemistry
α, β, γ are also the same elements as each other
<> denotes infilled interstitials (layers entirely vacant)

Question 12

Stacking sequences for ZnS wurtzile, ZnS cubic, NiAs hexagonal, CdI2 hexagonal

Answer 12

ZnS wurtzile: AαBβ
ZnS cubic: AαBβCγ
NiAs hexagonal: AγBγ
CdI2 hexagonal: AγB<>

Question 13

Rare earth elements stacking sequences

Answer 13

Mixed stacking sequences
ABCB
Examples: La, Pr, Nd, Pm

Question 14

Complex stacking in molybdenite

Answer 14

AβA<>BγB<>. This is height of one unit cell. Is MoS2. System is hexagonal, Bravais primitive. Sheet structure, rather loose S-S cross-layer bonds so good lubricant as can exfoliate into single 2D sheets. Get pairs of hexagonal primitive layers with rather loose packing. Interstitial layers are not oct or tet but are trigonal prismatic

Question 15

Basics of silicates

Answer 15

Polymerisation via Si-O-Si bonds. Stoichiometry varies within SiOx depending on how many O shared. 1D, 2D, 3D network structures. Tetrahedra robust and angles and distances vary little and are close to ideal mathematical tetrahedron. Al can sub in silica lattices but needs extra caution to balance charge which are often in interstitial positions.

Question 16

Structures of silicates

Answer 16

Monomer is SiO4 tetrahedron. Dimer is two tetrahedra sharing one O. Trimer 3 tetrahedra forming ring. Can get other rings made of more tetrahedra linked together. Single chain and double chain (2 chains sort of cross-linked). Layer/sheet/net of many hexagon shapes seen in double chains. 3D framework can form a ball.

Question 17

How to count oxygens in silicates

Answer 17

Bridging oxygen shared by 2 tetrahedra counts 1/2

Non-bridging oxygen is unshared and counts 1

Question 18

Different Si:O ratios

Answer 18

1: 4- extreme 1, is the monomer where all O non-bridging, e.g CaSiO4, dimensionality is zero.
1: 2- extreme 2, framework SiO2, all O bridging, e.g quartz, dimensionality is 3D.
1: 3- intermediate, chain silicate SiO3, 2 O in line with chain are bridging, out of chain are non-bridging (x2), e.g MgSiO3, dimensionality 1D.
1: 2.5- intermediate, sheet silicate, 3 O in plane of sheet are bridging, other out of plane is non-bridging, e.g Na2Si2O5, dimensionality 2D

Question 19

Al as tetrahedral framework cation

Answer 19

Can replace Si. E.g NaAlSi3O8 albite feldspar, is 3D framework silicate with 4 bridging O atoms, Na fills large gaps.

Question 20

Al and Mg as octahedral cation

Answer 20

Either can fill holes in silicate polymer, especially in combination with OH- ions.

Question 21

Olivine

Answer 21

Mg2SiO4. 3D island silicate. Si:O is 1:4. No bridging O. Oxygen in near hcp packing but trigonal distorted. Si in centre of tetrahedra. Is basically ionic structure between Mg cation and negative SiO4 ions.

Question 22

Cristobalite

Answer 22

SiO2. 3D framework silicate. All 4 O shared so no non-bridging O. Si:O is 1:2. Alpha phase is tetragonal. Cubic structure and Si atoms sit on diamond lattice. Metastable a time room temperature.

Question 23

Serpentine and Kaolinite

Answer 23

Mg and Al respectively. Sheet silicates. Has SiOx tetrahedral layer. Oxygens sticking out of bottom of layer are bonded to 2 Mg or Al atoms which are octahedrally coordinated. Mg or Al atoms bonded to OH- ion as well. Lattice contants mismatch between octahedra/tetrahedra and induce curvature/rolling up

Question 24

Differences between silicate crystal and glass

Answer 24

For normal silicate glass, maintains high Si:O ratio (about 2:1) and has only few non-bridging oxygens, no long range order.
Alkali silicate glass has alkali ions that break Si-O-Si chains and form pairs with non-bridging oxygens. E.g Na+ to SiO4- charge balance