# Atomic structure

Diameter of atoms is measured using the Angstrom (10e-10 m) unit. Amorphous materials only have short order atomic arrays (1 to 10 Angstroms) while crystalline materials have short and long order arrays (~10 nm to cm). A grain is a monocristal.

1. Nanostructure (1 to 100 nm).

2. Microstructure (0.1 to 100 micrometers). Grain size are from this magnitude.

3. Macrostructure (>100 nm). Characteristics like porisity, the thickness of a layer of paint and cracks belong to this range of size.

## Structure of the atom

The nucleus contains protons and neutrons, and is surrounded by electrons. The number of protons and electrons is the same.

### Atomic number

Is the number of protons in every atom.

### Atomic mass M

The mass of protons and neutrons (the average) in the atom.

Number of atoms or molecules in a mol.

$N_A=6.022 \times 10^{23}$
atoms/mol.

#### Number of atoms in a given mass of any element

It can be calculated using the formula:

$\text{Atoms}=\frac{\text{Mass} [g] \times N_A [atoms/mol]}{\text{Atomic mass} [g/mol]}$ ### Pauli exclusion principle

Two electrons in the same atom can't have the exact same set of quantum numbers.

## Electronic structure of atoms

### Aufbau principle

Predicts the deviations of the expected order of energy levels. This is:

 1  Orbital 3  Orbital 5  Orbital 7  Orbital 9  Orbital 11 Orbital 13 Orbital Max. Electrons Shell 1s 2 Shell 2s 2p 8 Shell 3s 3p 3d 18 Shell 4s 4p 4d 4f 32 Shell 5s 5p 5d 5f 5g 50 Shell 6s 6p 6d 6f 6g 6h 72 Shell 7s 7p 7d 7f 7g 7h 7i 98 Subshell Subshell Subshell Subshell Subshell Subshell Subshell

Shells are energy levels, from 1 to 7. Subshells are s, p, d, f, g, h and i. Every subshell has orbitals. Each orbital can hold two electrons. This is:

• The s subshell has 1 orbital for a total of 2 electrons max. per subshell.
• The p subshell has 3 orbital for a total of 6 electrons max. per subshell.
• The d subshell has 5 orbital for a total of 10 electrons max. per subshell.
• The f subshell has 7 orbital for a total of 14 electrons max. per subshell.
• The g subshell has 9 orbital for a total of 18 electrons max. per subshell.
• The h subshell has 11 orbital for a total of 22 electrons max. per subshell.
• The i subshell has 13 orbital for a total of 26 electrons max. per subshell.

Each shell can have a maximum number of electrons. Calculations are like this:

• The first shell has the s subshell for a total of 2 electrons max. per shell.
• The second shell has the s and p subshells for a total of 2+6=8 electrons max. per shell.
• The third shell has the s, p and d subshells for a total of 2+6+10=18 electrons max. per shell.
• The fourth shell has the s, p, d and f subshells for a total of 2+6+10+14=32 electrons max. per shell.
• The fifth shell has the s, p, d, f and g subshells for a total of 2+6+10+14+18=50 electrons max. per shell.
• The sixth shell has the s, p, d, f, g and h subshells for a total of 2+6+10+14+18+22=72 electrons max. per shell.
• The seventh shell has the s, p, d, f, g, h and i subshells for a total of 2+6+10+14+18+22+26=98 electrons max. per shell.

The total number of electrons that a shell can hold is given by:

$2n^2$

where

$n$
is the number of the shell from 1 to 7.

## Electronic structures

The Aufbau principle brings the following:

 Sum of electrons 2 4 10 12 18 20 30 1s2 2s2 2p6 3s2 3p6 4s2 3d10 Sum of electrons 36 38 48 54 56 70 80 4p6 5s2 4d10 5p6 6s2 4f14 5d10 Sum of electrons 86 88 102 112 118 6p6 7s2 5f14 6d10 7p6

Let's see a couple of examples:

Iron: atomic number: 26. The electronic structure is:

1s2-2s2-2p6-3s2-3p6-4s2-3d6

But, cuantic numbers must be in ascending order:

1s2-2s2-2p6-3s2-3p6-3d6-4s2

Copper: atomic number 29. The electronic structure is:

1s2-2s2-2p6-3s2-3p6-4s2-3d9

But, cuantic numbers must be in ascending order:

1s2-2s2-2p6-3s2-3p6-3d9-4s2

But, d subshell must be fully occupied. We must add 1 to d subshell and substract 1 to s subshell:

1s2-2s2-2p6-3s2-3p6-3d10-4s1

## Valence

Sum of electrons of s and p subshells that belong to the most external energy level.

Mg: 1s2-2s2-2p6-3s2 ---> Valence: 2.

Al: 1s2-2s2-2p6-3s2-3p1 ---> Valence: 3.

Si: 1s2-2s2-2p6-3s2-3p2 ---> Valence: 4.

If an atom has a valence of 0, then it is inert (non reactive). Let's see:

Ar: 1s2-2s2-2p6-3s2-3p6 ---> Valence: 0. (no more atoms in s, no more atoms in p).

## Electronegativity

A highly electronegative atom accepts electrons easily. External energy levels almost full (clorine). An atom is electropositive if electronegativity <2.0. These atoms have very few electrons in the last energy level S and P and give away atoms very easily (aluminium).

## Atomic bond

### Metallic bond

Low electronegativity atoms give away electrons (electropositive elements). Relatively strong bond. Atoms give away electrons and become cations. A pool that is full of electrones is created when all atoms do the same. Electrons move freely. Mutual atraction of electrons in this pool and catondes creates the mutual attraction that creates the Metallic bond. Conductivity is a consequence of electrons moving freely. Metals are ductile because the are not directional materials.

### Covalent bond

Electrons are shared between two atoms. Strong bond. Materials are expected to be relatively hard. A directional relationship is created when covalent bond produces 3D arrays of cations with specific angles between three atoms. Diamond is 100% covalent bond and has a fusion temperature of 3550°C. Diamond ductility is limited due to the directional bond. Electrical conductivity is low because valence electrons are trapped between atoms and are not available for conduction. The most external energy level is full of electrons. Ceramics have covalent bond, but can also have ionic bond.

### Ionic bond

An electron passes from one atom to the other, creating a cation and an anion. The difference in charges creates the electrostatic attraction that creates the bond. The most external energy level is full of electrons. NaCl is pure ionic bond. Ionic bond is produced between atoms with different electronegativities.

### Van der Waals bond

It is created when atoms have unsymmetric electric charge. Dipoles are the cause of the asymmetry of the charges. Force between atoms and molecules. Is is created when the center of electric charges in the atom are unbalanced and both, positive (nucleus) and negative (electrons) are not in the center of the atom. A neutral atom doesn't have a dipole moment. Molecules or atoms where a dipole moment exists are attracted to each other by the difference in polarity (- and +). Van der Waals forces are present in all materials and can be differenciated as:

1. London forces: when two induced dipoles interact.

2. Debye interaction: when an induced and a permanent dipole interact.

3. Keesom interaction: when two permanent diploes interact (for example, between two water molecules. Bond inside the molecule is covalent). It is also called hydrogen bond.

Polymers have covalent bond between monomers and van der Waals bond between polymer chains. When binding energy is high resistence is high and fusion temperature is also high. The higher the difference between electronegativities (between ions) the higher the binding energy. Metals have lower binding energies because they have similar electronegativities. The force by type of bond is:

1. Ionic.

2. Covalent.

3. Metallic.

4. Van der Waals.

## Allotropes of carbon

Diamond, graphite, buckminsterfullerenes and carbon nanotubes are all formed by pure carbon. Their material properties are different due to different atomic arrays of their structures.