2D Packing Examples

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# 2D Packing Examples - PowerPoint PPT Presentation

2D Packing Examples. Answer the following questions for both packing diagrams. Find the smallest unit that, if repeated, would give you the entire structure. This is the unit cell. Draw a box on the diagram representing the unit cell.

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2D Packing Examples

Answer the following questions for both packing diagrams.

Find the smallest unit that, if repeated, would give you the entire structure. This is the unit cell. Draw a box on the diagram representing the unit cell.

How many total atoms are inside the unit cell? Remember that only fractions of some atoms lie inside the box you drew.

Accurately draw boxes exactly 3 atoms wide. How many total atoms are in each? Which displays the greater packing density?

hole

hole

SIMPLE CUBIC PACKING

A

A

TOP VIEW

AA

unit cell: simple cubic

SCP 1 | Flash Anim | Jmol 1

BODY CENTERED CUBIC PACKING - ABAB

A

B

Unit cell: body centered cubic

Do not touch

BCP 1 | Flash Anim | Jmol 1

HEXAGONAL CLOSEST PACKING - ABAB

B

A

1200

Unit cell: hexagonal

A

7

8

4

3

6

5

C

A

1

2

B

B

Unit cell: face centered cubic

6

7

A

C

8

A

4

3

5

CUBIC CLOSEST PACKING

2

1

FCC = CCP: Jmol

CCP (FCC) 1 | Flash Anim | Jmol 1

Counting atoms in a unit cell

1. What fraction of the white colored sphere is part of a unit cell in each of the lattices shown below.

A face atom? ________

An edge atom? ________

A corner atom? ________

2. From your answers above, how many spheres below to the unit cell shown.

Simple Cubic ________

Face centered cubic ________

Body centered cubic ________

Now to some real structures. How do we know the arrangement of ions and atoms?

• X-Ray Crystallography:
• Na – bcc – what’s up with it’s 3s1 electron
• NaCl
• Bragg’s Law and diffraction
• Xray diffraction (Laue transmission) from simple cubic, bcc and fcc lattices

How do you describe salts with more than one atom type? By unit cells and holes

NaCl

Space fill

Types of Holes

109.50

3 atomse clouds in plane

• What's a tetrahedron
• What's an octahedron
• Holes: Cubic, tetrahedral, and Octahedral
• CCP and holes

Tetrahedron – 4 identicalequilateral triangles

5 atoms/e clouds in plane

SF6

Octahedron – 8 identical triangles

Determining the empirical formula from unit cell data:

A salt must be electrically neutral. If you know the charge on the cations and anions, you can determine MxNy.

Alternatively, you can use crystal data to determine the structure of the unit cell and hence the empirical formula. Determine the number of each different ion in the following unit cells. Does it correspond to the formula from charge balance?

Copper (I) chloride

4. Based on Cl- alone, what type of unit cell is this? What type of “hole” is occupied by Cu+?

Cl

Cu

2. Barium Chloride

5. Based on just Cl- alone, what type of unit cell is NaCl? What type of “hole” is occupied by Na+?

3. Rhenium oxide

Calculation of the atomic radius of a polonium atom, which forms a simple cubiccell, from macroscopic parameters. How many P atoms are in the unit cell?

• Given Polonium Data
• density 9.23 g/cm3 macroscopic meas.
• molar mass: 208.98 g
• Avogadro’s #: 6.022 x 1023 atoms/mol

r

2r

Top

Side

views

Use 2 simple equations

Solve for the following:

Vatom/Veff =

Veff (from density data) and dimensional analysis

Veff =

Vatom =

rPo =

2r

Body-Centered Cubic Unit Cell

unit

cell

a

4r

a

√2 a

a

x2 = a2 + a2

x = √2 a

Edge sphere

Do how many unit cells does the yellow sphere belong?

Corner sphere

Do how many unit cells does the yellow sphere belong?

Face sphere

Do how many unit cells does the yellow sphere belong?

A

C

B

A