CHEM 3300 / Topic 6e: Solid-State - Complex Lattice Structures

SPINELS

• What is the formula of normal oxide spinels? What cubic unit cell does it take form in? What polyhedra are included here?

• What is the formula of normal oxide spinels? What cubic unit cell does it take form in? What polyhedra are included here?

• How would you determine if your d-block higher oxide is normal or inverse spinel?

• Normally, oxide spinels are formed with a combination of A²⁺B₂³⁺O₄or A⁴⁺B₂²⁺O₄, with it being an arrangement of repeating fcc units of oxide ions. In this arrangement, you have A ions are in 1/8 of the tetrahedral holes while B ions are in 1/2 of the octahedral holes.

  • AO₄ tetrahedra formed by the 1 coefficient of A cations in the tetrahedral holes

  • BO₆ octahedra formed by the 2 coefficients of B cations in octahedral holes.

• Not-so-normally, oxide spinels are formed with the same combination and array but now with:

  • AO₆ octahedra formed by the 1 coefficient of A cations in octahedral holes

  • BO₄ tetrahedra formed by 1 coefficient of B cations in tetrahedral holes.

  • BO₆ octahedra formed by 1 coefficient of B cations in octahedral holes.

• To determine if it is going to be normal or inverse spinel, calculate the LFSE.

METAL OXIDES

• What does metastable mean?

• What ionic structure do most of the 3d metals adopt?

• Metastable means that, at room temperature, it is thermodynamically unstable but will not convert for kinetic reasons.

• The ionic structure that most of the 3d metals adopt are rock-salt.

DEFECTS AND NONSTOICHIOMETRY OF METAL OXIDES

• How do defects arise in metal oxides?

• How does nonstoichiometry arise in metal oxides?

• Iron(II) can easily be oxidized into iron(III). Defects can arise here, as the iron(II) that once held its spot in octahedral sites of rock-salt can pop into the tetrahedral sites of rock-salt when oxidized to iron(III), leaving octahedral sites vacant.

• Because of replacing 3Fe(II) with 2Fe(III), the amounts of Fe in lattice has decreased nonstoichiometrically, forming Fe_1-xO, where 0.04 < x < 0.13.

• What is the general formula for perovskites?

• What is the coordination number of the cation and where is it positioned in a perovskite structure?

• What is the most frequent oxide and fluoride anion in perovskites? What other anions can perovskites use?

• What are the conditions for a perovskite structure when you use heavier and larger X anions?

• What is the formula for an anti-perovskite structure? What structurally makes it different from the normal perovskite structure?

• What is “partial inversion” in perovskites? What is the condition for a perovskite to undergo partial inversion?

• ABX₃.

• The A cation is in the 12-coordinate hole of BX₃.

• X is most frequently oxide anion and fluoride anion. X can also be nitride and hydride.

• X can be heavier and larger halides, as long as the A and B cations are large as well.

• Anti-perovskite with XX’A₃ exists wherein X is a large anion in the 12-coordinate hole, X’ is another anion but smaller, and A is a smaller-than-X cation.

• Some perovskites can have partial inversion wherein the A and B cations can swap spots due to similarity in ionic size.

Explain how the ferroelectric property of perovskites works. Comment on centrosymmetry, polarization, relative permittivity, induced dipoles, and bulk polarization.

(BaTiO₃) A special ability of perovskite is that it can be distorted—at room temperature—in such a way that the unit cell is no longer centrosymmetric. This loss of centrosymmetry leads to an observed ability wherein this portion of the crystal can adopt an overall permanent electric polarization, as a result of the alignment of ions in the lattice. This is ferroelectricity. The relative permittivity, which describes how polar a compound is and how much it can store electricity, is up to 1.5E+4. For comparison, the relative permittivity of liquid water at room temperature is 80. Note that these induced dipoles are weak because they depend on the displacement of ions within the lattice post-loss of centrosymmetry. However, when you apply an external magnetic field, dipoles throughout the entire material can be aligned, resulting in bulk polarization in a particular direction, which can stay after removal of the electric field.

Explain how polarization relates to accumulation of more charge and the application of perovskites, using their ferroelectric properties.

Polarization creates an opposing field that partially cancels the applied electric field within the material. By reducing the net internal electric field, this, via principles of physics, allows for more accumulation of charge in capacitors without increasing the voltage. We have up to 1000 times the charge in our parallel plate capacitors where our parallel plates sandwich a perovskite, compared to the charge in a parallel plate capacitors sandwiching air.

What is the threshold temperature for perovskites’ ferroelectric properties?

There is a threshold temperature for which you can keep the perovskites - the Curie temperature, above which ferroelectric properties are lost.

What can you do to alter perovskites’ ferroelectric properties?

Dopants in perovskites allow the T_C to increase or decrease, affecting the ferroelectric properties.

Explain how the piezoelectric property of perovskites works and how they can be applied.

Another property of centrosymmetry-lacking perovskites is piezoelectricity wherein the material can generate an electric charge in response to applied mechanical stress. When mechanical stress (e.g., compression or bending) is applied, it causes the positions of the positive and negative charges in the material to shift slightly, creating an electric dipole. This results in an electric field across the material. This is useful for sensors and actuators, e.g. the mechanical stress of pressing a button in a gas cooker generates the electric field and thus generates a spark.

What is the related crystal structure of perovskites that are used for high-temperature superconductors? How does this structure assist in high-temperature superconductors?

Perovskites have a related crystal structure called potassium tetrafluoridonickelate(II) or K₂NiF₄. Compounds with this structure type can crystallize with high-temperature superconductors. This crystallization helps because it allows for improved charge transport properties.