Close packed structuresn.ethz.ch/~nielssi/download/4. Semester/AC II... · only three close packed directions A close packed plane is at the bottom and top of the unit cell separated

Close packed structures

1 5/22/2013 L. Viciu| ACII| close packed structures

Outlook

• Close packed structures:

a) cubic close packed (c.c.p.) or face centered cubic (f.c.c.)

b) hexagonal close packed

• Materials described by close packed structures (metals, alloys, ionic compounds, covalent compounds, molecular compounds)

• Voids in close packed structures


Two ways of describing structures: 1. close packing: guiding factor = realization of maximum density

2. Space filling polyhedron: structure = polyhedra linked together by sharing corner, edges or faces

3

Examples of Packing:

Irregular shapes Regular shape

5/22/2013 L. Viciu| ACII| close packed structures

http://www.photographyontherun.com/HexagonalClosePacking.aspx

Examples of space filling polyhedron:

5/22/2013 L. Viciu| ACII| close packed structures 4

Corner shared CaF8 cubes

Edge shared Oh

Face sharing Oh

Corner shared Td

Close packed structures

1. HEXAGONAL 2. SQUARE

Two packing arrangements of atoms in 2D:

closest-packed of a single layer of spheres is the HEXAGONAL coordination of each sphere


Packing: from 2D to 3D

A B C

+ +

C.C.PFCC

=

A B

+

HCP

=

A

+

Shown displaced for clarity


In 3D, a structure is formed by stacking Close Packed Planes.

Two possible stacking sequences: 1. …ABCABC... Face centered cubic (f.c.c) 2. ...ABABAB... Hexagonal closed packed (h.c.p)


f.c.c. : …ABCABC… layers

Build up c.c.p. layers (ABC… packing)

Cubic: a=b=c, ===90ᵒ 4 atoms in the unit cell:

0, 0, 0 ½

, ½

, 0 ½

, 0, ½ 0, ½ ,

½

8

A

B

C

A


9

f.c.c. vs. b.c.c.


f.c.c.

•Close packed directions

•Close packed planes in f.c.c.

4 different sets of planes: {111}

10

b.c.c.

4 close packed directions

• No close packed planes

• Only close packed directions

y

[-110] [110] [101] [-101] [011] [0-11]


h.c.p.: …ABAB… packing

only three close packed directions

A close packed plane is at the bottom and top of the unit cell separated by 3 atoms in the cell center also part of a close packed plane

Hexagonal: a = b c, = = 90°, = 120° 2 atoms in the unit cell at: 0, 0, 0 and 2/3, 1/3, 1/2

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2/3, 1/3, 1/2


Materials described by close packed structures

1. Metals (covalent contributions to their interatomic bonding make them less well packed structures)

2. Alloys (intermetallic phases or solid solutions)

3. Ionic structures (NaCl, ZnS, Na2O, NiAs)

4. Covalent network structures (diamond, SiC)

5. Molecular structures (H2, CH4, HCl)


1. Close packed metals

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The reasons why a particular metal prefers a particular structure are still not well understood


Malleability and Ductility: characteristic of some metals

• Slip of the planes occurs more easily if on a close packed plane

• depend on the number of close packed planes and directions possessed by a structure

f.c.c. structure can undertake severe plastic deformation

f.c.c h.c.p. b.c.c.

Close packed planes 4 1 -

Close packed directions 6 3 4


f.c.c metals > h.c.p > b.c.c. (Nb which is b.c.c. is an exception)

2. Close packed alloys

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Colored Golds: FCC structures with color Pure Au yellow Cu(low) yellow Cu(high) pink Ni white Al purple In Blue Cd green


Some of these color changes can be explained by shifts in the energy levels relative to the Fermi level.

*

* intermetallics

*

3. Ionic structures

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- -

- -

- - -

-

-

- -

- - -

+

+ +

+ +

+

+

+ + +

+

+

+

• Balance of attractive and repulsive electrostatic forces

• The relative size of ions affect the structure

• Because the anions are larger they form the close packed array and

the cations are in interstices

• The cations however are often too large to fit the interstices the

anion array is expanding to accommodate them


Tetrahedral T+ Tetrahedral T- Octahedral O

Interstitials Sites

17

(red circle is above) (blue circles are above)

Interstitial sites distribution between two c.p. layers 5/22/2013 L. Viciu| ACII| close packed structures

3D


• Td sites in the f.c.c . arrangement of anions •8 Td sites in total •Location: on the body diagonals – two on each body diagonal at ¼ of the distance from each end.

T • Oh sites in f.c.c. arrangement of anions (fcc unit cell) •4 Oh sites in total

O

414

112 )(

)(

centreedge

Voids in f.c.c. structure


Examples of f.c.c structure

NaCl: Oh voids filled K2O: Td voids filled

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½

½

½ ½

½ 0,1

0,1 0,1

0,1

¼ , ¾ ¼ , ¾

¼ , ¾ ¼ , ¾


Size of Oh and Td voids in f.c.c.:

Face diagonal, a2 = 2R2 but, face diagonal is 2(R+r) 2R2 = 2(R+r) (1+r/R)=2

r/R =0.414

Body diagonal is a3 = R6 (a=R2)

but, body diagonal is also 2(R+r) R6 = 2(R+r); (1+r/R)=6/2

r/R =0.225

Oh

Td

21

*The anion radius is R while the cation radius is r


Anions are touching on the face diagonala2=2R a=R2

Anions are touching on the edge a = 2R*

Voids in h.c.p. structure

Td void

The voids are identical to the ones found in FCC

Octahedral voids occur in 1 orientation, tetrahedral voids occur in 2 orientations 22

The spacing of the close packed layers: d = 1.633r c=2x1.633r=2x1.633xa/2=1.633a

(0,0,5/8), (⅔,⅓,7/8)

(⅔, ⅓,1/8),

(0,0,3/8)

Oh void (1/3, 2/3, ¼)

(1/3, 2/3, ¾ )


A

B

A

NiAs: Oh voids filled by Ni ZnS (wurtzite): ½ Td voids filled by Zn

HCP voids Position Voids / cell

Octahedral • (⅓,⅔,¼), (⅓,⅔,¾) 2

Tetrahedral (⅔, ⅓,1/8), (0,0,3/8),

(0,0,5/8), (⅔,⅓,7/8) 4

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Examples of h.c.p. structure from A. West

A. West: Basic Solid State Chemistry and its applications 5/22/2013 L. Viciu| ACII| close packed structures

Note: Some books, including West, give the h.c.p. anions at (0,0,0) and (⅓,⅔,½). As a result, the

Oh sites are at (⅔,⅓,¼) and (⅔,⅓,¼) while Td sites are (⅓, ⅔, 1/8), (0,0,3/8), (0,0,5/8) and (⅓,⅔,7/8)

Cubic void(BCC structures)

The anion spheres are touching on the edge a = 2R Face diagonal: f=a2=2R2 Body diagonal: b = a3 = 2R3

but Body diagonal: b = 2R+2r 2R3=2(R+r) R3 = (R+r) (R+r)/R=3 (1+r/R)=3

r/R =0.732 C.N. = 8


Stable Bonding Configurations in Ionic solids

For a stable coordination the bonded cation and anion must be in contact with each other.


Radius Ratio Coordination no. Binary (AB) Structure-type

r+/r- = 1 12

none known

1 > r+/r- > 0.732 8

CsCl

0.732 > r+/r- > 0.414 6

NaCl

0.414 > r+/r- > 0.225 4

ZnS

1732.0414.0225.0/ cubicoctahedralltetrahedraanioncation Rr


4: Covalent network structures

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Diamond structure: - ½ C atoms form a c.c.p. (f.c.c) array - ½ C atoms fills the Td voids

C60 structure: f.c.c. K3C60 structure: -C60 form f.c.c array - K filles all Oh and Td voids


5. Molecular structures

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• Close packing is also important in organic crystals but it is the molecules that are close-packed rather than individual atoms

Al2Br6 structure Br form a h.c.p. array Al fills 1/6 of Td sites

2 AlBr4 Td share an edge


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Close packed structuresn.ethz.ch/~nielssi/download/4. Semester/AC II... · only three close packed directions A close packed plane is at the bottom and top of the unit cell separated