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Universitas Negeri Jakarta Pertemuan 3 CLOSE PACKING STRUCTURE Iwan Sugihartono, M.Si Jurusan Fisika, FMIPA Universitas Negeri Jakarta 1

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Page 1: Pertemuan 3   close packing

Universitas Negeri Jakarta

Pertemuan 3

CLOSE PACKING STRUCTURE

Iwan Sugihartono, M.SiJurusan Fisika, FMIPAUniversitas Negeri Jakarta

1

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Outline

Crystals

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Crystal structure basics

unit cells

symmetry

lattices

Some important crystal structures and properties

close packed structures

octahedral and tetrahedral holes

basic structuresferroelectricity

Diffraction

how and why - derivation

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Objectives

By the end of this section you should:

• understand the concept of close packing

• know the difference between hexagonal and cubic close packing

• know the different types of interstitial sites in a close packed structure

• recognise and demonstrate that cubic close packing is equivalent to a face centred cubic unit cell

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Packing

Can pack with irregular shapes

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Two main stacking sequences:

If we start with one cp layer, two possible ways of adding a second layer (can have one or other, but not a mixture) :

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Two main stacking sequences:

If we start with one cp layer, two possible ways of adding a second layer (can have one or other, but not a mixture) :

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Let’s assume the second layer is B (red). What about the third layer?

Two possibilities:

(1) Can have A position again (blue). This leads to the regular sequence …ABABABA…..

Hexagonal close packing (hcp)

(2) Can have layer in C position, followed by the same repeat, to give …ABCABCABC…

Cubic close packing (ccp)

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Hexagonal close packed Cubic close packed

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No matter what type of packing, the coordination number of each equal size sphere is always 12

We will see that other coordination numbers are possible for non-equal size spheres

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

Metals usually have one of three structure types:ccp (=fcc, see next slide), hcp or bcc (body centred cubic)

Sc Ti V Cr Mn Fe Co Ni Cu Zn

Y Zr Nb Mo Tc Ru Rh Pd Ag Cd

La Hf Ta W Re Os Ir Pt Au Hg

hcp

ccp = fcc

bcc

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ccp = fcc ?

Build up ccp layers (ABC… packing)

Add construction lines -can see fcc unit cell

c.p layers are oriented perpendicular to the body diagonal of the cube

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Hexagonal close packed structures (hcp)

hcp bcc

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Recurring themes...

Foot and mouth virus

Body centred cubic

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Packing Fraction

We (briefly) mentioned energy considerations in relation to close packing (low energy configuration)

Rough estimate - C, N, O occupy 20Å3

Can use this value to estimate unit cell contents

Useful to examine the efficiency of packing - take c.c.p. (f.c.c.) as example

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Calculate unit cell side in terms of r:

2a2 = (4r)2

a = 2r 2

Volume = (16 2) r3

Face centred cubic - so number of atoms per unit cell =corners + face centres = (8 1/8) + (6 1/2) = 4

So the face of the unit cell looks like:

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Packing fraction

The fraction of space which is occupied by atoms is called the “packing fraction”, , for the structure

spaceavailable

atomsby occupied space =

4

4

3

16 2 3 2074

3

3

r

r.

For cubic close packing:

The spheres have been packed together as closely as possible, resulting in a packing fraction of 0.74

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Group exercise:

Calculate the packing fraction for a primitive unit cell

A = 2 r

52,01

3

3

34

a

r

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Mencari Fraksi Packing

Jumlah atom efektif dalam unit cell = 12(1/6)+2(1/2)+3=6

%7474,060sin

3/420

3

caa

r

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Primitive

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Close packing

Cubic close packing = f.c.c. has =0.74

Calculation (not done here) shows h.c.p. also has =0.74 -equally efficient close packing

Primitive is much lower: Lots of space left over!

A calculation (try for next time) shows that body centred cubic is in between the two values.

THINK ABOUT THIS! Look at the pictures - the above values should make some physical sense!

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Hitunglah efisiensi packing dan kerapatan dari NaCl bila diberikan data sebagai

berikut:

Jari-jari ion Na = 0,98 A

Jari-jari ion Cl = 1,81 A

Massa atom Na = 22,99 amu

Massa atom Cl = 35,45 amu

?Solusinya:

Parameter kisi, a = 2 (Jari-jari ion (Na + Cl)) = 5.58 A

Fraksi Packing:

= Volume ion yang ada dalam sebuah unit cell

Volume unit cellnya

= 4 (4/3) phi (r3Na + r3

Cl) / a3 = 66,3 %

Density:

= Massa unit cell / Volumenya

= 2234 kg m-3

1 amu = 1,66 x 10-27 kg

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Summary By understanding the basic geometry of a

cube and use of Pythagoras’ theorem, we

can calculate the bond lengths in a fcc

structure

As a consequence, we can calculate the

radius of the interstitial sites

we can calculate the packing efficiency for

different packed structures

h.c.p and c.c.p are equally efficient packing

schemes

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THANK YOU

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