Sinclair- Band Theory and Transition Metals

Question 1

Why does free electron theory break down for transition metals?

Answer 1

d valence orbitals, especially 3d series, are more contracted than valence s and p orbitals and don’t overlap strongly. The d band has high density states due to 10 electrons/atom that can be accommodated within a narrow energy range. So electron- electron repulsion effects become important.

Question 2

Energy vs density of states N(E) for TM

Answer 2

Starts on y-axis with some energy. Curves up then there is a bulge out to the right which comes back in at the top and increases again. The lines leading into and out of the bulge look like they would have followed the same original shape. Bulge is where d band is.

Question 3

Describe the bonding character at different energies in TMs

Answer 3

Bonding orbitals in character below the narrow d band. Non-bonding in character in d band. Anti-bonding in character above d band.

Question 4

Describe the d band

Answer 4

Becomes narrower across 3d metals due to an increased effective nuclear charge across the series which causes the d orbitals to contract so they overlap less strongly with each other. Within a d band, states near bottom are bonding between the adjacent atoms and states near the top are anti-bonding. Expect maximum bonding from d electrons to be found near middle of series when d band is half full.

Question 5

Sublimation energy

Answer 5

Equal to the bond strength in the solid. Energy to convert solid directly into gas.

Question 6

Expected trend for sublimation energy vs elements across the TM series

Answer 6

Forms a dome shape.

Question 7

Sublimation trend across 3d and 4d series

Answer 7

Dome shape but with local minimum in bind strength at d5, d6 (more pronounced for 3d which also has lower dome).

Question 8

Orbital character in d band across d series

Answer 8

On left the e- have bonding orbital character in d band. On right e- have anti-bonding orbital character in d band

Question 9

Why are there local minima for 3d and 4d series?

Answer 9

Due to strong magnetic effects (electron localisation) and the lower values for the 3d series reflect poorer overlap of orbitals and weaker bonding.

Question 10

What can electrical properties of TM oxides (TMOs) range from and to?

Answer 10

Insulators to superconductors

Question 11

Structure of TMOs

Answer 11

Most have rocksalt structure apart from CuO and ZnO. Still exhibit big variation in their electrical properties.

Question 12

What determines the electrical properties in TMOs?

Answer 12

The number of d electrons and band structure

Question 13

The spatial orientation of the five d orbitals

Answer 13

xy: like balloons out into the xy plane from the origin but don’t cross any axes.
xz, yz: same as xy but in xz and yz plane respectively.
z^2: two balloons go up and down z axis, ring in xy plane.
x^2-y^2: 4 balloons out along x and y axes

Question 14

Energy of d orbitals for isolated or free M2+ ion (in gas phase)

Answer 14

The five atomic d orbitals are degenerate (same energy) and can contain a maximum of 10e-/atom

Question 15

Energy of d orbitals in MO rocksalt solid

Answer 15

Structure made from regular MO6 octahedra where M2+ surrounded by 6 O2- ions. All orbitals now higher in energy but in particular the d sub(z^2) and d sub(x^2-y^2) (e sub g set) are higher in energy compared to the other three orbitals (t sub 2g set). Because electrons that occupy eg orbitals feel greater repulsion from O2- ions.

Question 16

Crystal field splitting (CFS)

Answer 16

The energy of splitting between the t2g and eg orbitals. Depends on type of metal ion, it’s charge and the type and charge on the anion.

Question 17

Example of TiO

Answer 17

Is a d2 cation. The dxy, dyz and dxz orbitals overlap between diagonally closest Ti2+ atoms. This overlap of these orbitals leads to a t2g band. Extent of orbital overlap decreases with atomic number (narrows d band width). This band can hold 6 e-/atom but only holds 2 so is 1/3 full and there is metallic conduction within band.

Question 18

Example of NiO

Answer 18

Is d8 cation. No direct M-M bonding via dx^2-y^2 and dz2 orbitals. These go vertical and horizontal from each Ni so point directly to oxide ions and so can’t overlap to form an eg band. e- localised on individual Ni2+ ions so insulator. Is anti-ferromagnetic insulator (AFMI). The unpaired electrons in eg orbitals can couple with electrons in p-orbitals of adjacent O2- ions (super-exchange mechanism)

Question 19

Antiferromagentic insulator

Answer 19

Like NiO. One electron in an eg orbital couples with one from p orbital of O2- ion so have opposite spins. The p orbital is full so two electrons belonging to O2- have opposite spins. Next Ni on other side also couples so has opposite spin to that other electron from O2-. Results in alternating spins between nearest Ni2+ ion along a row