The Modern Periodic Table

C12

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mass numbersymbol

atomic number

name & atomic weight 12.011Carbon

Law of Periodicity “The properties of the elements areperiodic functions of atomic number.”

Metals – Conducting, Ductile

Metalloids - Semiconductors Ductile ?

Nonmetals – insulatorsnot ductile

Group Period

Repetition of properties

Similar chemical properties

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Crystalline SolidsCrystalline solids: Metals, ions, atoms, molecules

Constructed form crystal lattices.

Stabilized by electrostatic forces.

Identical building blocks : unit cells.

LATTICE:

X-ray diffraction is used to study crystalline solids

The lattice of regularly repeating atoms with spacing acts as a diffraction grating for the rays.

The diffraction pattern is used to establish the structure of the solid!

X-ray Diffraction

Amorphous SolidsAmorphous solids: disordered solids

Strongly resemble liquids in this lack of long-range order

Many amorphous solids can be thought of very accurately as frozen liquids.

Common examples of amorphous solid are glass, candy (sugar), plastics.

In all, there are then 5 categories of solids, 4 types of crystalline + amorphous

Type Examples Structural Units Typical Properties

Ionic NaCl, K2SO4, CaCl2, (NH4)3PO4

Positive and negative ions

Hard; brittle; high melting point; electric conductivity poor as solid & good as liquid; often water-soluble

Metallic Iron, silver, copper, other metals & alloys

Metal cations in a sea of electrons

Malleable; ductile; wide range of hardness and melting points; good electric conductivity in solid & liquid; good heat conductivity.

Molecular H2, O2, I2, H2O, CO2, CH4, CH3OH, CH3CO2H

Molecules Soft; low to moderate melting points & boiling points; poor electric conductivity in solid and liquid

Network Graphite, diamond, quartz, feldspars, mica

Atoms Wide range of hardnesses & melting points (3-dimensional bonding > 2-dimensional bonding > 1-dimensional bonding); poor electric conductivity, with some exceptions

Amorphous (glassy)

Glass, polyethylene, nylon

Molecules, ionsNo long range order

Soft, wide temperature range for melting; poor electric conductivity, with some exceptions

Summary of the Structures and Properties of Various Types of Solid Substances

Semicrystalline MaterialsContain both amorphous and crystalline regions => strong and flexible.

Examples: Plastics (polymers), Steel, Wood (cellulose), collagen (tendon)

Example: Polyvinylidenedifluoride

…-CH2-CF2-CH2-CF2-….. PVDF is semicrystalline - Similar to Teflon (-CF2-CF2-)

It has several different crystal phases, which can be modified by processing methods.

The alpha phase is non-polar

The beta phase is polar

PVDF can be processed to contain mostly the polar form, by stretching the film to several time its original length

Electrical Properties of Semicrystalline MaterialsSemicrystalline materials respond to heat, pressure and external fields.

They are used as heat and pressure sensors

Thin films can be prepared than have a permanent electric filed across them.

These are used as non-stick coatings, selective membranes, etc

Electropoled films are used by theelectronics industry, ex. speaker membranes

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Lattices and Closest PackingHow do objects naturally arrange themselves?

If a second layer is added how does that effect the arrangements?

OR

Non-closest Closest

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Lattices and Unit Cells

We will focus only on the cubic and the hexagonal crystal systems

as they describe the vast majority of metallic elements.

Mathematicians have shown that there are seven basic geometries in which unit cells can be assembled that completely fill 3-D space.

These are called the seven crystal systems

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Unit CellsIdentical building blocks : unit cells.

i) No “gaps” between them in the lattice.

ii) All have same orientation in the lattice.

iii) Cannot be arranged in a staggered fashion in the lattice.

LATTICE:

NOT: OR: OR:

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Lattices and Unit Cells

Consider the smallest possible “unit cell” :

The smallest unit cell in a lattice is called the primitive unit cell.

In general one would have to consider three-dimensions.

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Closest Packing

The marbles adopted a “closest packing” as in most metals.

Two kinds:

cubic closest packed

hexagonal closest packed.

The difference arises when a third row is added:

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Hexagon Closest PackingOrient the lattice so that the layers are more easily seen:

Note every second layer are superimposable, as shown in the

case of the red layers.

A

B

A

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Cubic Closest Packing

Every third layer is superimposible.

Note that, there is an atom at each corner of the cubeAnd, the center of each face.

It is also called face centered cubic (fcc).

A

B

C

A

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Cubic LatticesThere are three types of cubic unit cells:

Note in some cases only parts of an atoms is contained by the unit cell.

i.e. The unit cell only contains the fraction of each atom that is *inside* the

cube!

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Lattices and Unit Cells

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Co-ordination Number, Density and Metallic Radii

The number of atoms an atom contacts in the lattice is referred to as

its co-ordination number.

Determine the coordination number of the following lattices:

Simple cubic (e.g. Po) Face-centered cubic (e.g. Cu)

Body-centered cubic (e.g. Na) Hexagonal closest packed (e.g. Mg)

Lattice type is related to density.

What is the relative order of density from most to least dense?

How would you measure the density of a metal?

How could you relate the lattice type and density to the atomic radius?

1. Aluminum has a density of 2.699 g· cm–3, and the atoms are packed into a face-centered cubic unit cell. Use this information to find the radius of an aluminum atom.

EXERCISE

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23 323 1

3 23 3 8 103

Count: there are 4 Al atoms per unit cell by counting rules

4 26.986.6398 10 cm

2.699 6.022 10

For any cube, 6.6398 10 cm 4.049 10 cm 4.049 10 m

By geometry, face diag

gmol

gmolcm

mV

d

a V

102onal 4 2 4.049 10 m 143 pm

4 d r a r

Along the face diagonal, there are two half and one whole sphere

The diagonal length is (a2 + a2)1/2 and corresponds to 4 atomic radii

12 2 2 2( ) 2 2 a a a a a a

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2) Lithium has a metallic radius of 152 pm and the atoms are packed into a body-centered cubic unit cell. Calculate the density of lithium.

EXERCISE

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Cubic Lattices

Lattice Packing fraction Density (m/r3)simple cubic 0.5236 0.125body-centered cubic 0.6802 0.162face-centered cubic 0.7405 0.177

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Lattices, Density and Metallic Radii

Europium has a metallic radius of 198.4 pm and a density of 5.243 g/cm3.

Which cubic units cell is the likely for this crystal structure?