Sinclair- Superconducting Transition Metal Oxides (La2CuO4 focus)

Question 1

Rules that may produce a high Tc material

Answer 1

Have an insulating parent phase (La2CuO4 is AFMI).
Unusual high oxidation states (Cu3+).
Linear B-O-B bonds (contain CuO2 planes).
Large amount of covalency in the bonding.
High oxidation states due to large (A-site) electropositive cations (Sr, Ba, La, Y).
Variable oxygen contents (YBa2Cu3O7-δ)

Question 2

Rare earth, Bi and Y ion charges

Answer 2

All always +3

Question 3

Favoured materials for industrial application

Answer 3

BiSCCO: Bi2Sr2CaCu2O8+δ (2212 or 90K phase) or
Bi2Sr2Ca2Cu3O10+δ (2223 or 110K phase)
YBCO: YBa2Cu3O7-δ (123 phase)

Question 4

How to find oxidation states of Cu in YBCO

Answer 4

Y is +3, Ba is 2+ (x2), O is 2- (x7) makes -7.
So Cu3 needs to account for +7.
Could be 2Cu2+ and Cu3+ or 2Cu3+ and Cu+
Find which one using the crystal structure and coordination number.
In this case is 2Cu2+ and Cu3+. Tc,max seems to be when Cu2.33+ is present

Question 5

Doped lanthanum cuprate

Answer 5

La2-xMxCuO4. M is Ca, Sr, Ba.
So the La3+ is partly replaced by M2+. To balance charge some Cu2+ oxidises to Cu3+ (d9 to d8)
Example: La3+ + Cu2+ -> Sr2+ + Cu3+
Becomes superconducting at T>23K

Question 6

Structure of La2CuO4

Answer 6

Alternating layers of rocksalt AO with perovskite ABO3. SC resides in the perovskite blocks so have 2D superconducting planes. So perovskite block of LaCuO3 and rocksalt block of LaO. Orthorhombic units cell a=5.363, b=5.409, c=13.17Å. Have corner sharing octahedra (not regular but elongated)

Question 7

What does band theory predict La2CuO4 to be?

Answer 7

A metal but is an insulator due to JT distortion

Question 8

Energy vs density of states N(E) for pure La2CuO4

Answer 8

Have an empty UHB and a full LHB (Cu 3d9) as half an ellipse each separated. Extending either side of LHB is semicircular band from O (2p). This is d9 Jahn-Teller distortion

Question 9

Energy vs density of states N(E) for doped La2CuO4

Answer 9

Same as pure La2CuO4 but at top of band from O 2p is empty and has holes until Ef before is reaches top of LHB.

Question 10

Where do holes come from in doped La2CuO4?

Answer 10

70% holes come from Cu2+ + h+ = Cu3+

The 30% holes come from O2- + h+ = O-

Question 11

AFM alignment in La2CuO4 (superexchange mechanism?)

Answer 11

In a linear Cu2+ - O2- - Cu2+ arrangement there is strict AFM (anti-parallel spin) alignement on adjacent Cu2+ neighbours. The Cu2+ has an outer 3(dx2-y2) orbital with one electron in. The O2- in the middle has an outer 2p orbital with two electrons (of opposite spins) in. The electron in O2- closest to a Cu2+ will cause its electron to have the opposite spin. Effect same for the Cu2+ on the other side of the O2- so the electrons in the two Cu2+ ions will have opposite spins.

Question 12

Magnetic frustration caused by O- ion in doped La2CuO4

Answer 12

Now a hole on O so only has one outer electron with one spin. The spins of the outer electrons for Cu2+ ions either side are opposite to this but the same as each other leading to ferromagnetic (parallel spin) alignment of Cu2+ nearest neighbours

Question 13

Magnetic frustration caused by oxidation to Cu3+ in doped La2CuO4

Answer 13

Consider Cu2+ - O2- - Cu3+ - O2- - Cu2+ line.
Central Cu has a hole. Leads to AFM alignment of next nearest neighbour Cu spins. Because O2- still have two electrons in outer orbital. Basically same case as pure La2CuO4 superexchange mechanism but leaping over the central Cu3+ ion

Question 14

Tc vs x graph for doped La2CuO4 with Sr

Answer 14

Basically a dome with finite x intercepts. Has peak at x=0.15 which corresponds to average Cu2.15+. There is a dip just left of the full peak. Left of peak is underdoped, peak is optimum doping, right is overdoped. Under peak is SC behaviour. This behaviour with Cu2.15+ to Cu2.2+ in layered cuprates generally gives the optimised Tc. General behaviour but not understood

Question 15

Where do oxidation and reduction occur in La2CuO4?

Answer 15

Oxidation in perovskite block Cu2+ -> Cu3+ + e-.

Reduction in rocksalt block

Question 16

Two methods of oxidation in La2CuO4

Answer 16

Cation substitution with alkali earth ion. The reduction is
La3+ + e- -> Sr2+.
Or intercalation of excess oxygen La2CuO4+δ. Do high pressure synthesis to get excess O2- in rocksalt LaO layers (300kbar at 500C). Forms O2- interstitials in solid
1/2O2(g) + 2e-(from Cu2+) -> O2-(i). Net redox is
2Cu2+ + 1/2O2(g) -> 2Cu3+ + O2-(i) and one excess O produces 2 holes. δ between 0 and 0.12. Tc,max=35K for δ=0.09 so Cu2.18+

Question 17

Simple picture and electronic structure for intergrowth (RP) superconductors

Answer 17

Superconducting perovskite-type planes separated by charge reservoir rocksalt blocks

Question 18

What is the driving force for the redox reactions in La2CuO4?

Answer 18

The CuO2 sheets are under compression and the equatorial Cu-O bonds want to contract. Cu3+ ion is smaller than Cu2+ so the Cu3+ - O bond is shorter. Means e- removed (h+ added) from Cu2+ to make Cu3+. The e- removed go into charge-reservoir layers (rocksalt LaO). For the in-plane/equatorial Cu-O bonds of the octahedra, a bond length between 1.89 and 1.94Å gives rise to SC. Greater will be insulating (not enough Cu3+ underdoped), less will be metallic (too much Cu3+ overdoped).

Question 19

What do apical oxygens do?

Answer 19

These are at the top and bottom of the CuO6 octahedra. The Cu-O bond is about 2.1Å and the apical oxygens act as links between the charge reservoirs and the CuO2 sheets