VKC Notes · Inorganic solids · Geo-Scientist P-I · IFoS P-I
3.3 Inorganic Solids: Perovskite, Spinel, ReO₃, Corundum and High-Tc Superconductors
★★★ 2021–2025: 11 parts, 87 marks (Geo-Scientist 10 parts / 79 m · IFoS 1 / 8 m). Asked in every Geo-Scientist Paper I since 2021, almost always as question 2: draw the cell, count the ions, explain the site preference or write the synthesis.
Syllabus line. Geo-Scientist: “Synthesis of materials, monoxides of 3d-metals, higher oxides, complex oxides (corundum, ReO₃, spinel, perovskites), framework structures …, nitrides and fluorides, chalcogenides, intercalation chemistry, semiconductors, molecular materials”. IFoS asks spinels through crystal field stabilisation. Close packing, radius ratio and NaCl/ZnS/CsCl are in 3.1 Crystal systems and radius ratio; defects, non-stoichiometry and semiconductors in 3.2 Defects and band theory.
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3.3.1 Structure types built on close packing; polymorphism ★★
- Most ionic oxides and halides are a close-packed array of the larger ion (usually O²⁻) with the cations in some of the holes. Per close-packed ion there is one octahedral (Oh) and two tetrahedral (Td) holes. Name the array, say which holes are filled and what fraction, and the formula and coordination numbers follow.SN
| Type | Examples | Array | Holes filled | CN |
|---|---|---|---|---|
| Rock salt | NaCl, MgO, FeO, NiO | ccp anions | all Oh | 6 : 6 |
| Fluorite | CaF₂, UO₂, cubic ZrO₂ | ccp cations | all Td (by F⁻) | 8 : 4 |
| Antifluorite | Li₂O, Na₂O, K₂O | ccp anions | all Td (by M⁺) | 4 : 8 |
| Rutile | TiO₂, SnO₂, MnO₂ | distorted hcp O | ½ Oh | 6 : 3 |
| Corundum | α-Al₂O₃, Cr₂O₃, Fe₂O₃ | hcp O | ⅔ Oh | 6 : 4 |
| ReO₃ | ReO₃, WO₃ (distorted) | BO₆ sharing all corners | — | 6 : 2 |
| Perovskite ABO₃ | CaTiO₃, BaTiO₃, KMnF₃ | ccp of A + O together | B in ¼ Oh (the all-O ones) | A 12, B 6 |
| Spinel AB₂O₄ | MgAl₂O₄, Fe₃O₄, Co₃O₄ | ccp O | ⅛ Td + ½ Oh | A 4, B 6 |
- Fluorite vs antifluorite Geo 2024 Q2(a)(i) 5m: in CaF₂ the Ca²⁺ ions form the fcc array (4 per cell) and the 8 F⁻ fill all 8 tetrahedral holes: Ca CN 8 (cube of F), F CN 4 (tetrahedron of Ca), AX₂. In antifluorite (Li₂O) the roles swap: O²⁻ fcc, 8 Li⁺ in the Td holes, Li CN 4, O CN 8, A₂X. Z = 4 in both.SN
Draw it in 60 s: a cube; dots on 8 corners and 6 face centres (Ca); an inner dashed cube of 8 open circles at the quarter points (F); write CN 8 : 4 and “antifluorite = swap”.
- Polymorphism Geo 2024 Q2(c) 5m: one compound, more than one crystal structure. CaCO₃ = calcite (trigonal, stable) and aragonite (orthorhombic, denser, the high-pressure form); TiO₂ = rutile, anatase, brookite; SiO₂ = quartz, tridymite, cristobalite; ZnS = zinc blende and wurtzite. Polymorphs differ in density, hardness, optical properties and stability; temperature and pressure decide which one forms. For elements the word is allotropy (diamond, graphite).SN
- A change that goes both ways at a fixed temperature (α ⇌ β quartz) is enantiotropic; one that goes only one way because one form is metastable at all temperatures at that pressure (aragonite → calcite on heating at 1 atm) is monotropic.
3.3.2 Corundum and rhenium trioxide ★★
- Corundum, α-Al₂O₃: hcp O²⁻ with Al³⁺ in two-thirds of the octahedral holes, the filled holes making a honeycomb in each layer. Al CN 6, O CN 4. Ti₂O₃, V₂O₃, Cr₂O₃, Fe₂O₃ (haematite), Rh₂O₃ and Ga₂O₃ take the same structure; ilmenite FeTiO₃ is corundum with Fe and Ti in alternate layers.SN
- Ruby is a solid solution of a little Cr₂O₃ in Al₂O₃. The smaller Al₂O₃ cell squeezes the O²⁻ around Cr³⁺, the ligand field rises, the absorption moves to the blue and the crystal looks red (Cr₂O₃ itself is green).SN
Draw it in 60 s: a row-on-row of circles (O); in the gaps put two dots and one cross, repeating; write “2/3 of Oh filled → M2O3”.
- ReO₃ Geo 2021 Q2(a) 10m: cubic cell, Re at the 8 corners and O at the 12 edge centres, body centre empty. Count: Re 8 × ⅛ = 1, O 12 × ¼ = 3. Each Re has 6 O (along ±x, ±y, ±z): Re CN 6, O CN 2 (O sits midway between two Re, Re–O–Re 180°). The structure is ReO₆ octahedra sharing all six corners.SN
- Put a large cation in the empty body centre and it is surrounded by the 12 edge-centre O: the ABX₃ perovskite structure. ReO₃ is “perovskite with the A site empty”; NaxWO₃ (tungsten bronzes) fill that site partly.SN
- ReO₃ is red, lustrous and conducts like copper: Re(VI) is d¹, and the Re t2g–O 2p π* band holds 6 electrons per Re but has only 1, so it is a partly filled band → metallic. The structure is rare because it needs M(VI) with O.
Draw it in 60 s: cube; small dots on 8 corners (Re), open circles on the 12 edge midpoints (O); a dashed circle at the centre marked “empty, A goes here”; beside it squares on their points sharing corners.
3.3.3 Perovskites ABO₃ ★★★
- Ideal perovskite is cubic: large A (Ca²⁺, Sr²⁺, Ba²⁺, K⁺, La³⁺; CN 12) and small B (Ti⁴⁺, Zr⁴⁺, Nb⁵⁺, Fe³⁺, Mn²⁺; CN 6, in a BO₆ octahedron). The charges need only add to +6: A²⁺B⁴⁺ (CaTiO₃), A⁺B⁵⁺ (KNbO₃), A³⁺B³⁺ (LaFeO₃). Fluorides such as KMnF₃ and NaFeF₃ are A⁺B²⁺F₃.SN
- Each O has 2 B neighbours (linear B–O–B) and 4 A neighbours. A and O together form a ccp array; B sits in the quarter of the Oh holes surrounded only by O.
Draw it in 60 s: (a) cube, big dots on corners (Ca), open circles on the 6 face centres (O), small dot at the centre (Ti); (b) small dots on corners (Ti), open circles on the 12 edge midpoints (O), big dot at the centre (Ca).
Solved PYQ Geo 2022 Q2(a) 10m
Draw the perovskite unit cell with Ti at the centre and with Ca at the centre; find the formula and the coordination number of Ti in each.
- Ti at the body centre: Ca on 8 corners = 8 × ⅛ = 1; O on 6 face centres = 6 × ½ = 3; Ti = 1 → CaTiO₃. Ti touches the 6 face-centre O: CN 6.
- Ca at the body centre (shift the origin by ½, ½, ½): Ti on 8 corners = 1; O on 12 edge centres = 12 × ¼ = 3; Ca = 1 → CaTiO₃. A corner Ti has O at the 6 edge midpoints that meet at that corner (three in this cell, three in neighbours): CN 6.
- Moving the origin does not change the structure: same formula, Ti CN 6 and Ca CN 12 in both drawings.SN
- Goldschmidt tolerance factor: perovskite forms when A is large enough to touch the 12 O while B fits its octahedron.
(3.3.1)
- ZnTiO₃ is not a perovskite (Zn²⁺ too small for the A site); PbTiO₃ is.
- BaTiO₃: local ion displacement and electrical behaviour Geo 2025 Q2(a) 15m. Ba²⁺ is so large that the TiO₆ octahedron is slightly too big for Ti⁴⁺ (t > 1). Above 120 °C (the Curie temperature) the Ti⁴⁺ rattles about the centre and the cell is cubic. Below it the cell becomes tetragonal (c > a) and each Ti⁴⁺ shifts about 0.1 Å towards one apical O: every cell is an electric dipole and neighbouring dipoles line up into domains: spontaneous polarisation.SN
- Consequences: ferroelectric (an external field reverses the polarisation; P against E shows hysteresis); relative permittivity above 1000 (≈ 1000 times the charge of an air capacitor), so BaTiO₃ is the standard capacitor ceramic; piezoelectric (stress produces a voltage and a field changes the shape: transducers, sonar, igniters). Above TC it is an ordinary (paraelectric) insulator. Sr for Ba or Zr for Ti lowers TC.SN
Draw it in 60 s: two octahedra: left with Ti dead centre (cubic); right taller with Ti pushed up towards the top O and a red arrow P beside it.
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