9. Bonding of Materials Flashcards Preview

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Flashcards in 9. Bonding of Materials Deck (32)
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1
Q

Why does the forming of bonds cause a reduction in the overall energy of the material?

A

When electron orbitals overlap, energy levels split and broaden due to Pauli’s exclusion principle. This means that the electrons populate new lower energy levels

2
Q

Why do antibonding orbitals form?

A

As the number of orbitals must be conserved, so when two atomic orbitals come together to form molecular orbitals, they will form one bonding orbital and one antibonding orbital.

3
Q

Which has a higher energy level, bonding or antibonding orbitals?

A

Antibonding orbitals, as bonding orbitals see a reduction in energy due to electron energy levels splitting due to the Pauli exclusion principle

4
Q

When might an electron enter the antibonding orbital?

A

If the electron was to become excited it could jump up to the antibonding orbital

5
Q

What is orbital hybridisation?

A

Orbital hybridisation is the concept of mixing atomic orbitals into new hybrid orbitals (with different energies, shapes, etc. than the component atomic orbitals) suitable for the pairing of electrons to form chemical bonds in valence bond theory. This was first invented to explain how carbon doesn’t do expected and form 2 bonds (CH2) but 4 bonds (CH4). The only way CH4 it can be explained is is, the 2s and the 3 2p orbitals fused together to make four, equal energy sp3 hybrid, molecular orbitals.

6
Q

How does carbon form hybrid orbitals to make CH4?

A

Carbon’s electron structure is 1s2 2s2 2p2. To make four bonds, it takes it’s 2s orbital and all 3 of the 2p orbitals to make 4 sp3 hybridised molecular orbitals. To hybridise the orbitals, it must promote one of the 2s electrons to the vacant 2p orbital, then it can hybridise them, leaving 4 molecular orbitals that are identical in energy. Each sp3 orbital has 1 electron, leaving one space free to come from the other atom in the covalent bond.

7
Q

What is an orbital diagram?

A

Electron orbital diagrams and written configurations tell you which orbitals are filled and which are partially filled for any atom.
They are drawn with each atom on the side with its respective atomic orbital, and the molecular orbitals go in between. (each orbital type eg 1s, 2s, 2p is shown as a separate diagram)

8
Q

How does hybridisation minimise the total energy?

A

By arranging as many electrons as possible in bonding orbitals

9
Q

What is the equation for the optimum number of covelent bonds?

A

X = 8 - N (for N>=4)
X = N (for N<4)
X- number of covalent bonds
N- number of valence electrons

10
Q

How does silicon hybridise?

A

Si has 2 e- in its 3p orbitals, and these are close in energy to its 2 3s e-. It is energetically favorable for the 3s and 3p orbitals to hybridise into 4 sp3 orbitals. this is what allows it to form 4 bonds and give it its tetragonal bonding geometry.

11
Q

What is electronic band structure?

A

Electronic band structure (or simply band structure) of a solid describes the range of energies that an electron within the solid may have (called energy bands, allowed bands, or simply bands) and ranges of energy that it may not have (called band gaps or forbidden bands).

12
Q

What is the Fermi level

A

The energy of the highest occupied state

13
Q

What does it mean if the Fermi energy is in the middle of a band?

A

It means that the material is a metal

14
Q

What is the tight-binding approximation?

A

The tight-binding model is an approach to the calculation of electronic band structure using an approximate set of wave functions based upon superposition of wave functions for isolated atoms located at each atomic site.

15
Q

Why does an energy band form in materials?

A

Each atom has its own ‘potential well’ with discrete energy levels. For a material with N atoms, these energy levels will form bands of N finely separate energy levels, forming an energy band (Pauli exclusion principle, no two electrons can occupy the same quantum state)

16
Q

Why are there only 2 important energy levels, and what are they?

A

All other energy levels are filled, except for the Valence band and the Conduction band

17
Q

What is the band gap?

A

The energy gap between the valence band (the highest occupied band at 0K) and the conduction band (the first empty band). In this energy gap there are no allowed electron energy levels.

18
Q

What defines a semiconductor in terms of band gap?

A

The material has a band gap and it is small (around 0.5 - 2 eV)

19
Q

What defines insulators in terms of band gap?

A

The material has a band gap and it is large (around 2 - 9 eV)

20
Q

What defines conductors in terms of band gap?

A

The material doesn’t have a band gap (the conduction and valence bad overlap)

21
Q

What defines a transparent material in terms of band gap?

A

The band gap energy is greater than that of visible light, hence no electrons can be excited by the photons enough to go up to the bottom of the conduction band

22
Q

What is the nearly free electron model?

A

The nearly free electron model (or NFE model) is a quantum mechanical model of physical properties of electrons that can move almost freely through the crystal lattice of a solid. The model is closely related to the more conceptual empty lattice approximation. The model enables understanding and calculating the electronic band structure of especially metals.

23
Q

What is the dispersion relation equation, and what can this tell us about the relationship between energy and propagation constant k?

A

ω = h(bar)*k^2 / 2m

can multiply by h(bar) to get energy, teaching us that the energy depends on k in a parabolic fashion, so a graph of E (y) and k (x) looks like a parabola (y=x^2)

24
Q

How does the free electron model reveal the band gaps in a material?

A

Interference between the right and left traveling wavefunctions causes small gaps to appear in the E vs k parabola (derived from the dispersion relaion) between the band at periodic intervals

25
Q

What is a direct band gap?

A

Where the highest occupied valence state is at the same point in k-space as the lowest unoccupied conduction state. Means that an electron can make a direct transition with a photon

26
Q

What is an indirect band gap?

A

Where the minimum band gap occurs at different k values

27
Q

What is optoelectronics, and what is the key property that allows this?

A

Optoelectronics is the study and application of electronic devices and systems that source, detect and control light.

The key property that allows this is the recombination of an electron and a hole in a semiconductor to give energy, creating a photon (as with classical mechanics, this process must conserve both energy and momentum)

28
Q

What is the equation for the photon energy released when an electron recombines into a hole in a semiconductor?

A

E(photon) = E(electron) - E(hole)
also
k(photon) = k(electron) - k(hole)
k- propagation constant

29
Q

What is the propagation constant for a photon?

A

k = ω/c

30
Q

What is the propagation constant for an electron?

A

k = sprt(2mE) / h(bar)

derived from the dispersion relation and E= h(bar) * freq

31
Q

How can recombination occur with an indirect band gap?

A

Phonons need to be absorbed which strongly lowers the probability and speed of recombination.
Phonons are thought of as lattice vibrations, or a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter

32
Q

Explain why bands form in materials using the example of a large number of carbon atoms being brought together to form a diamond crystal.

A

When the atoms are far apart each atom has valence atomic orbitals p and s which have the same energy. However when the atoms come closer together their orbitals begin to overlap. Due to the Pauli Exclusion Principle each atomic orbital splits into N molecular orbitals each with a different energy, where N is the number of atoms in the crystal. Since N is such a large number, adjacent orbitals are extremely close together in energy so the orbitals can be considered a continuous energy band. a is the atomic spacing in an actual crystal of diamond. At that spacing the orbitals form two bands, called the valence and conduction bands, with a 5.5 eV band gap between them.