Stacking

Question 1

What is the formula for space filling?

Answer 1

SF = 1/V * 4π / 3 Σ Zi * r_i^3

V = volume of unit cell
Z_i = number of atom i
r_i = ionic radius of atom i

Question 2

How are spheres arranged in the plane to form closest packing?

Answer 2

In a hexagonal patter.

Question 3

How many spheres are adjacent to any sphere in a closest packed plane?

Answer 3

Each sphere has six adjacent sphere.

Question 4

What is the stacking sequence of hcp?

Answer 4

ABABAB….

Question 5

What is stacking sequence of ccp?

Answer 5

ABCABCABC…

Question 6

What is a colloquial name for ccp?

Answer 6

Copper type

Question 7

What is a colloquial name for hcp?

Answer 7

Magnesium type

Question 8

What is a colloquial name for bcc?

Answer 8

Tungsten type

Question 9

What are the planes of closest packed planes in ccp?

Answer 9

111

Question 10

What is the coordination polyhedron for a sphere in ccp?

Answer 10

Cuboctahedron

Question 11

What is the coordination polyhedron for a sphere in hcp?

Answer 11

Anticuboctahedron

Question 12

What other stacking sequences than hcp and ccp can we have for closest packing?

Answer 12

In theory infinite, however only a few are observed. Some lanthanoids have different sequences, such as La, Pr, Nd and Pm with a ..ABAC.. stacking (double hexagonal, hc, 22). Sm has …ABACACBCB… (hhc, 21).

Question 13

What is the double-hexagonal closest-packing of spheres?

Answer 13

…ABAC…
Jagondzinski: hc
Zhadnov: 22

This is the stacking sequence that La, Pr, Nd and Pm takes.

Question 14

What is the packing trend of increasing f-electrons among the lanthanoids?

Answer 14

La (57), Pr (59), Nd (60), Pm (61) has hc.
Sm (62) has hhc.
Gd (64), Tb (65), Dy (66), Ho (67), Er (68), Tm (69), Lu (71) has h

So increasing hexagonality with higher f-electrons.

Ce (58, c), Eu (63, i) and Yb (70, c) are exceptions. Eu and Yb can be rationalised with an analysis of the the electron configuration.

Question 15

What is the symmetry principle?

Answer 15

Among several feasible structure types those having the highest symmetry are normally favored.

Question 16

What is an order-disorder structure with stacking faults?

Answer 16

Order within the planes, but lack of ordering in the stacking. A more or less statistical stacking sequence.

Question 17

What is the space filling of close packed structures?

Answer 17

74.05%

Question 18

What is the space filling of body centered cubic packing?

Answer 18

68.02%

Question 19

What does the Goldschmidt rule say?

Answer 19

Increased temperatures favour structures with lower coordination numbers.

Question 20

Which elements show structures types of their own?

Answer 20

Ga, Sn, Bi, Po, Mn, Pa, U, Np and Pu.

Question 21

What is the optimal structure for Mn?

Answer 21

There seems to be none. It has many polymorphic forms with peculiar structures.

Question 22

What is the coordination number of elemental Ga?

Answer 22

1+6. One Ga is significantly closer than the others. This is interpreted as a metal structure of Ga-Ga pairs with a covalent bond. Low melting point indicates an unstable structure.

Question 23

When alloys are cooled slowly, in which ways can a segregation occur?

Answer 23

1. Metals crystallise separately (complete segregation)
2. Two kinds of solid sollutions crystallize, a solution of metal 1 in metal 2 and vice versa (limited miscibility)
3. An alloy with a specific composition cyrstallises; its composition may differ from that of the liquid (formation of an intermetallic compounds). The composition of the liquid can change during the crystallisation process and further intermetallic compounds with other compositions may crystallise.

Question 24

What is likely to happen if you have two atoms that are chemically related and of nearly the same size (e.g. Au and Ag)?

Answer 24

They will form disordered alloys with each other.

Question 25

For two chemically related atoms, what is the approximate limit of relative size for them to form solid solutions?

Answer 25

Around 15%.

Question 26

For atoms of different size, what is the more likely structure when mixing them?

Answer 26

Structures with ordered atomic distributions. This structure is favoured energetically as the amount of lattice energy is larger.

Question 27

How can the principle of most efficient space filling be applied to solid solutions of atoms of different sizes?

Answer 27

If they have different sizes, and ordered structure will always provide a more efficient space filling.

Question 28

What can be said about the stoichiometry of solid state combination of atoms of different sizes?

Answer 28

As they tend to form ordered structures, they will have definite compositions. They will form an intermetallic compounds. Also compounds that have complete miscibility in the solid state (e.g. Cu and Au) will form ordered alloys at certain compositions (AuCu and AuCu3).

Question 29

In intermetallic compounds, how will the atoms arrange themselves?

Answer 29

They have a tendency to be surrounded by atoms of the different kind (though less pronounced than in ionic compounds).

Question 30

What is the condition for an atom in an intermetallic compound to be surrounded only by different atoms?

Answer 30

MXn, n ≥ 3. In compounds with n < 3, it can't be fulfilled for any of the two atoms.

Question 31

How can one simply describe the structure of a closest packed intermetallic compound?

Answer 31

As the composition is usually fulfilled within the hexagonal layers, it is sufficient to describe the hexagonal layer and the stacking sequence.

Question 32

Which are the most important kinds of ordering we can have in the hexagonal layers of MX3 compounds?

Answer 32

1. Hexagonal (central M atom surrounded hexagonally by X) | 2. Rectangular (M atoms form a rectangle with a rhombus of X in between).

Question 33

What is the the most important kind of ordering we have in the hexagonal layers of MX compounds?

Answer 33

Linear chains.

Question 34

What is an example of hexagonal arrangement of MX3 compound with cubic stacking?

Answer 34

AuCu3

Question 35

What is an example of hexagonal arrangement of MX3 compound with hexagonal stacking?

Answer 35

SnNi3

Question 36

What is an example of rectangular arrangement of MX3 compound with cubic stacking?

Answer 36

TiAl3

Question 37

What is an example of rectangular arrangement of MX3 compound with hexagonal stacking?

Answer 37

TiCu3

Question 38

What is an example of linear arrangement of MX compound with cubic stacking?

Answer 38

AuCu

Question 39

What is an example of linear arrangement of MX compound with hexagonal stacking?

Answer 39

AuCd

Question 40

What is the name of the body-centered cubic type packing of alloys?

Answer 40

CsCl type

Question 41

With two body-centered cubic metals of roughly same atomic radii, what kind of alloy will be formed?

Answer 41

Disordered alloys may form (e.g. K and Rb), but the formation of ordered alloys is usually favoured. At higher temperatures the tendency towards disordered structure increases.

Question 42

What are superstructures of CsCl type?

Answer 42

When CsCl type structures are multiplied (2x2x2 supercell) where different atoms occupy the atomic positions.

Question 43

Draw a superstructure of CsCl

Answer 43

Draw a 2x2x2 supercell. Alternating of the (0,0,0) position of regular CsCl is an a-site and b-site. Alternating in the (1/2, 1/2, 1/2) position of regular CsCl is a c-site and d-site.

Question 44

Give some examples of structures that can be represented with the CsCl superstructure.

Answer 44

``` Fe3Al (Al at a, Fe at b, c, d) NaTl (Tl at a and c, Na at b, d) Diamond (C at a and c, vacancy at b, d) Zinc Blende (Zn at a, S at c, vacancy at b, d) NaCl (Na at a, Cl at b) ```

Question 45

What is an Laves phase?

Answer 45

A compound with the composition MM'2 where M is larger than M'. Considered to have CsCl-superstrucutre with M in a, c and M'4 in b and d. M'4 form corner sharing tetrahedra Example: MgCu2 Other polytypes exist, such as Mg in hexagonal diamond.