Perovskites

Question 1

What is the definition of Goldschmidt’s tolerance factor?

Answer 1

t = r_A + r_X / sqrt2(r_M + r_X)

For AMX3.

Question 2

What is the lowest tolerance factor one can have for a perovskite?

Answer 2

As low as 0.85. The general dividing line dividing perovskites from other structures is at around 0.88.

Question 3

What is an inverse perovskite?

Answer 3

A perovskite with anions on A- and B-site, and cation on X-site.

Also (and now more commonly) known as anti-perovskite.

Example: Au- O2- Rb3+

Question 4

How are Glazer-notation used to describe tilts in perovskites?

Answer 4

Three letters describing the tilt of each axis of an octahedron.

No tilt is a0a0a0.

Letter describes degree of tilt (equal tilt = equal letter), superscript describes phase of tilt (0 = no tilt, - = off-phase, + = in-phase)

Question 5

How many different perovskite structures with zero tilt are there?

Answer 5

1. a0a0a0

Question 6

How many different perovskite structures with one tilt are there?

Answer 6

2. Off-phase (a0a0c-) and in-phase (a0a0c+).

Question 7

How many different perovskite structures with two tilts are there?

Answer 7

6.

Question 8

How many different perovskite structures with three tilts are there?

Answer 8

14.

3 - - -
(4 + + -)
(4 + - - )
(3 + + +)

Question 9

How many perovskite tilt systems have deformed octahedra?

Answer 9

4. (#4-7)

Question 10

What are the most common tilt systems for perovskites?

Answer 10

#10 (a+ b- b-)
#14 (a- a- a-)
#23 (a0 a0 a0)

Question 11

For what values of the Goldschmidt tolerance factor is tilt system #23 (a0 a0 a0) most predominant?

Answer 11

For t ≥ 1.

Question 12

For what values of the Goldschmidt tolerance factor is tilt system #14 (a- a- a-) most predominant?

Answer 12

For t < 1

Question 13

For what values of the Goldschmidt tolerance factor is tilt system #10 (a+ b- b-) most predominant?

Answer 13

For t &laquo_space;1.

Question 14

What are the contributing factors for tilt system #23 (a0 a0 a0) being a common tilt system?

Answer 14

Least repulsion.

Question 15

What are the contributing factors for tilt system #14 (a- a- a-) being a common tilt system?

Answer 15

Best lattice energy (but repulsion increases when t becomes small)

Question 16

What are the contributing factors for tilt system #10 (a+ b- b-) being a common tilt system?

Answer 16

Best lattice energy and off-center shifts of A are allowed.

Question 17

What kind of unit cell transformation do you have to do to get from tilt #23 (a0 a0 a0) to tilt #10 (a+ b- b-)?

Answer 17

Tilt #23 is cubic and tilt #10 is orthorhombic.

Question 18

What kind of unit cell do you have to do to get from tilt #23 (a0 a0 a0) to tilt #14 (a- a- a-)?

Answer 18

Tilt #23 is cubic and til tilt #14 is rhombohedral.

Question 19

What happens if the tolerance factor becomes too large?

Answer 19

The perovskite becomes a hexagonal perovskite.

Question 20

What kind of ordering can you have in a perovskite?

Answer 20

Ordered vacancies or ordered cations (when either A-site is ordered or M-site is ordered).