Electrical- The d Band and Dielectrics

Question 1

Where are the lowest metal orbitals for transition metal oxides?

Answer 1

Normally the d orbitals rather than the s in the pre-TM elements

Question 2

How do the d orbitals fit in with the band picture?

Answer 2

Still a VB of oxygen 2p character. The d orbitals can sometimes form a single band separated from those of the higher energy s and p orbitals of the TM. This is still above the VB. For d0 cations the d band is empty and this is the case for insulators. For some d e- containing compounds there is a partially filled d band and this is the case for metals.

Question 3

How does doping of BaTiO3 work?

Answer 3

Initially is a white band gap insulator. La3+ (donor) doping on the Ba2+ site turns it into a black semiconductor. They are similar size so La3+ replaces Ba2+ like:
Ba2+ + Ti4+ -> La3+ + Ti3+
(Ba1-xLax)TiO3 is actually (Ba1-xLax)(Ti4+(1-x)Ti3+(x))O3
Ti4+ is d0 and Ti3+ is d1. This is n-type semiconductor and an example of donor doping.

Question 4

What can be said about the valence state of a donor dopant ion?

Answer 4

It has a higher valence state than the host ion

Question 5

Band pictures for insulating and semiconducting BaTiO3

Answer 5

Insulating: full VB of O 2p. Empty CB as the Ti 3d band has no electrons in it (d0). Band gap between VB and empty d band.
Semiconducting: full VB. discrete La donor levels (ED) just below the CB. Partially filled 3d band. n-type semiconductivity.

Question 6

What is aliovalent doping?

Answer 6

Where some ions of different charge but similar size readily substitute for each other.

Question 7

Bonding trends for compounds

Answer 7

Compounds within p block have high degree of covalent bonding.
Oxides with s block elements have high degree of ionic bonding.
Oxides with d block elements have mixed bonding.

Question 8

How do ion sizes change across the periodic table?

Answer 8

Going down, cation size increases. Going right, cation size decreases. Anions (like most of group VII form) are large.

Question 9

Properties of dielectric materials

Answer 9

They are insulators. There is a complete absence of charge movement under an electric field. It is a poor conductor of electricity but an efficient supporter of electrostatic fields. Materials may be ionic, covalent or polar covalent.

Question 10

Two types of non-conductors

Answer 10

Ones we use as insulators. Ones we use in electrical circuits in devices such as capacitors

Question 11

How do capacitors work?

Answer 11

It is a device used to store charge and the simplest form is two separated parallel plates. In DC circuit, charge builds up across the two plates so it stores charge. When building a charge there is a very short lasting transient current.

Question 12

What happens when a different material is put between the plates of a capacitor?

Answer 12

The total charge stored in the capacitor will change. The change depends on the ability of the material to polarise under an electric field. The dielectric constant, or permittivity (ε), of the material determines the change in charge storage.

Question 13

Where are the positive and negative charges in the capacitor and dielectric material?

Answer 13

Next to the positive plate of the capacitor, there is an overall negative charge on that side of the dielectric. Next to the negative plate there is an overall positive charge on that side of the dielectric.

Question 14

Formula for capacitance with a vacuum between the plates

Answer 14

C0=ε0A/d
Where ε0 is permittivity of free space
A is plate area
d is plate separation

Question 15

Formula for charge stored by capacitor with vacuum between plates

Answer 15

q0=C0V

V is the potential difference between the plates

Question 16

Formula for dielectric constant of a material

Answer 16

ε’=C1/C0

Question 17

Name a dielectric material used in multi layer ceramic capacitors (MLCC)

Answer 17

BaTiO3

Question 18

Describe the layout of a MLCC

Answer 18

There are many (100-600) layers of BaTiO3 separated by thinner layers of Ni metal which is the electrode. One full active dielectric layer is equal to one layer of BaTiO3.

Question 19

Formula for capacitance in a MLCC

Answer 19

C=nε0ε’A/d
Where n is number of active dielectric layers
ε’ is relative permittivity of BaTiO3 (roughly 1000)
d is thickness of dielectric layer (1-10μm)

Question 20

Complication in manufacture of MLCCs

Answer 20

Fired body (1280°C in 5% H2) has to deal with shrinkage of ceramic due to sintering and mismatch in thermal expansion coefficients of the Ni electrode and BaTiO3 ceramics.

Question 21

What is dielectric strength?

Answer 21

The ability to withstand voltages measured in kV/mm

Question 22

Why doesn’t water have a dielectric strength?

Answer 22

Because it can conduct under any voltage due to dissociated H+ ions

Question 23

Describe the ideal perovskite structure of SrTiO3

Answer 23

General form is ABX3. It is a cubic close packed structure. There are 8 A atoms at the vertices of the cube. There are 6 X atoms on the faces of the cube like fcc. The smallest atom is B which sits in the very centre of the cube and has a coordination number of 6 due to the 6 X atoms that are close to it. The unit cell is centro-symmetric.

Question 24

How does the perovskite structure change for BaTiO3 compared to SrTiO3?

Answer 24

The Ba2+ ion is larger than Sr2+. The cubic unit cell becomes stretched into a tetragonal unit cell which is non-centrosymmetric. The Ti (B) atom no longer sits in the centre of the octahedron of oxygen ions and is slightly displaced so that one oxygen ion is further away from it than the others. There is no a dipole moment in the unit cell due to a slight excess of positive charge on the side the Ti ion has moved towards and a slight negative charge on the other side.