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Inorganic Structural Chemistry > Stacking > Flashcards

Stacking Flashcards

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1
Q

What is the formula for space filling?

A

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
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2
Q

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

A

In a hexagonal patter.

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3
Q

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

A

Each sphere has six adjacent sphere.

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4
Q

What is the stacking sequence of hcp?

A

ABABAB….

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5
Q

What is stacking sequence of ccp?

A

ABCABCABC…

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6
Q

What is a colloquial name for ccp?

A

Copper type

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7
Q

What is a colloquial name for hcp?

A

Magnesium type

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8
Q

What is a colloquial name for bcc?

A

Tungsten type

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9
Q

What are the planes of closest packed planes in ccp?

A

111

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10
Q

What is the coordination polyhedron for a sphere in ccp?

A

Cuboctahedron

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11
Q

What is the coordination polyhedron for a sphere in hcp?

A

Anticuboctahedron

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12
Q

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

A

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).

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13
Q

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

A

…ABAC…
Jagondzinski: hc
Zhadnov: 22

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

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14
Q

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

A

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.

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15
Q

What is the symmetry principle?

A

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

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16
Q

What is an order-disorder structure with stacking faults?

A

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

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17
Q

What is the space filling of close packed structures?

A

74.05%

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18
Q

What is the space filling of body centered cubic packing?

A

68.02%

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19
Q

What does the Goldschmidt rule say?

A

Increased temperatures favour structures with lower coordination numbers.

20
Q

Which elements show structures types of their own?

A

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

21
Q

What is the optimal structure for Mn?

A

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

22
Q

What is the coordination number of elemental Ga?

A

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.

23
Q

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

A
  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.
24
Q

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)?

A

They will form disordered alloys with each other.

25
Q

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

A

Around 15%.

26
Q

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

A

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

27
Q

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

A

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

28
Q

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

A

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).

29
Q

In intermetallic compounds, how will the atoms arrange themselves?

A

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

30
Q

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

A

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

31
Q

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

A

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

32
Q

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

A
  1. Hexagonal (central M atom surrounded hexagonally by X)

2. Rectangular (M atoms form a rectangle with a rhombus of X in between).

33
Q

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

A

Linear chains.

34
Q

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

A

AuCu3

35
Q

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

A

SnNi3

36
Q

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

A

TiAl3

37
Q

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

A

TiCu3

38
Q

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

A

AuCu

39
Q

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

A

AuCd

40
Q

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

A

CsCl type

41
Q

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

A

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.

42
Q

What are superstructures of CsCl type?

A

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

43
Q

Draw a superstructure of CsCl

A

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.

44
Q

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

A 
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)
45
Q

What is an Laves phase?

A

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.

Inorganic Structural Chemistry (13 decks)

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